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    <description>recent bookmarks from Vaguery</description>
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  </channel><item rdf:about="https://hal.science/hal-05580502v1">
    <title>Inversion of the Brillouin Function by Dynamic Geometry and Novel Continued-Fraction and Quadratic Methods - Archive ouverte HAL</title>
    <dc:date>2026-05-24T12:34:55+00:00</dc:date>
    <link>https://hal.science/hal-05580502v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Accurate evaluation and inversion of the Brillouin function are essential for describing magnetisation in paramagnetic systems. This paper introduces three complementary computational approaches: a dynamic geometry method, a powered continued-fraction method, and a quadratic-equation approximation. The Brillouin function is first transformed into a polynomial in the variable e^(x/J), where x denotes the ratio of Zeeman energy to thermal energy and J the total angular-momentum quantum number. The polynomial is represented geometrically through line-segment relations and solved by sliding a construction point to vary the exponential variable until the geometric constraints are satisfied. Accuracy in this method is governed by practical limitations such as line thickness, finite point dimensions, compassbased measurement errors, and the adopted precision of Euler's number. Rewriting the polynomial in terms of e^(-x/J) generates an infinite recursive powered continued fraction. Since the variable remains below unity at each stage, successive powering rapidly contracts its magnitude, rendering higher-order terms negligible after a finite number of iterations. In the quadratic-approximation method, the polynomial is recast as a quadratic in a small correction variable, permitting higher-order terms to be neglected. Solved examples demonstrate that three to four iterations typically achieve precision up to ten decimal places.

]]></description>
<dc:subject>numerical-methods continued-fractions approximation algorithms rather-interesting representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:726d350e5f0b/</dc:identifier>
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<item rdf:about="https://inria.hal.science/hal-05593313v1">
    <title>Computing hard-to-round cases of sin, cos, tan in double precision - Inria - Institut national de recherche en sciences et technologies du numérique</title>
    <dc:date>2026-05-24T12:22:36+00:00</dc:date>
    <link>https://inria.hal.science/hal-05593313v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper describes an exhaustive search algorithm to find the hardest-to-round cases of trigonometric functions (sin, cos, tan) in double precision (binary64). This algorithm reuses a clever reduction from the literature, but instead of using a sublinear search, it uses a brute force linear search. This algorithm was implemented using multi-threading and SIMD, and a full set of hard-to-round cases for the binary64 trigonometric functions was computed. As a consequence, the Table Maker's Dilemma is now fully solved for the most common univariate binary64 functions.

]]></description>
<dc:subject>numerical-methods computational-complexity algorithms rather-interesting special-cases to-write-about to-simulate approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6249741238f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
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<item rdf:about="https://arxiv.org/abs/2407.03357">
    <title>[2407.03357] Elementary Formulas for Greatest Common Divisors and Semiprime Factors</title>
    <dc:date>2026-05-24T11:08:57+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.03357</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We conjecture new elementary formulas for computing the greatest common divisor (GCD) of two integers, alongside an elementary formula for extracting the prime factors of semiprimes. These formulas are of fixed-length and require only the basic arithmetic operations of: addition, subtraction, multiplication, division with remainder, and exponentiation. Our GCD formulas result from simplifying a formula of Mazzanti and are derived using Kronecker substitution techniques from our earlier research. By applying these GCD formulas together with our recent discovery of an arithmetic expression for n‾√, we are able to derive explicit elementary formulas for the prime factors of a semiprime n=pq.
]]></description>
<dc:subject>algorithms numerical-methods computational-complexity rather-interesting performance-measure consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:99ab92c256bf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
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<item rdf:about="https://arxiv.org/abs/2512.06522v2">
    <title>[2512.06522v2] Hierarchical Clustering With Confidence</title>
    <dc:date>2026-05-23T12:01:40+00:00</dc:date>
    <link>https://arxiv.org/abs/2512.06522v2</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often producing different clustering results and making it difficult to separate genuine structure from spurious patterns. In this paper, we show how randomizing hierarchical clustering can be useful not just for measuring stability but also for designing valid hypothesis testing procedures based on the clustering results.
We propose a simple randomization scheme together with a method for constructing a valid p-value at each node of the hierarchical clustering dendrogram that quantifies evidence against performing the greedy merge. Our test controls the Type I error rate, works with any hierarchical linkage without case-specific derivations, and simulations show it is substantially more powerful than existing selective inference approaches. To demonstrate the practical utility of our p-values, we develop an adaptive α-spending procedure that estimates the number of clusters, with a probabilistic guarantee on overestimation. Experiments on simulated and real data show that this estimate yields powerful clustering and can be used, for example, to assess clustering stability across multiple runs of the randomized algorithm.
]]></description>
<dc:subject>clustering statistics numerical-methods probability-theory unsupervised-learning algorithms rather-interesting to-write-about to-cite consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a39717e23952/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:clustering"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
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<item rdf:about="https://arxiv.org/abs/2310.12160">
    <title>[2310.12160] On geometric interpretation of Euler's substitutions</title>
    <dc:date>2026-04-20T11:46:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2310.12160</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler's substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.
]]></description>
<dc:subject>rewriting-systems Euler numerical-methods constraint-satisfaction rather-interesting visualization calculus heuristics consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:61f7d0665756/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Euler"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
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<item rdf:about="https://arxiv.org/abs/2504.11440">
    <title>[2504.11440] Greedy Restart Schedules: A Baseline for Dynamic Algorithm Selection on Numerical Black-box Optimization Problems</title>
    <dc:date>2026-02-20T14:04:43+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.11440</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In many optimization domains, there are multiple different solvers that contribute to the overall state-of-the-art, each performing better on some, and worse on other types of problem instances. Meta-algorithmic approaches, such as instance-based algorithm selection, configuration and scheduling, aim to close this gap by extracting the most performance possible from a set of (configurable) optimizers. In this context, the best performing individual algorithms are often hand-crafted hybrid heuristics which perform many restarts of fast local optimization approaches. However, data-driven techniques to create optimized restart schedules have not yet been extensively studied.
Here, we present a simple scheduling approach that iteratively selects the algorithm performing best on the distribution of unsolved training problems at time of selection, resulting in a problem-independent solver schedule. We demonstrate our approach using well-known optimizers from numerical black-box optimization on the BBOB testbed, bridging much of the gap between single and virtual best solver from the original portfolio across various evaluation protocols. Our greedy restart schedule presents a powerful baseline for more complex dynamic algorithm selection models.
]]></description>
<dc:subject>numerical-methods optimization meta-optimization rather-interesting to-understand consider:stochastc-ones consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7d0cd9df7f70/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:meta-optimization"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2601.10667">
    <title>[2601.10667] Stable evaluation of derivatives for barycentric and continued fraction representations of rational functions</title>
    <dc:date>2026-01-21T12:46:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2601.10667</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Fast algorithms for approximation by rational functions exist for both barycentric and Thiele continued fraction (TCF) representations. We present the first numerically stable methods for derivative evaluation in the barycentric representation, including an O(n) algorithm for all derivatives. We also extend an earlier O(n) algorithm for evaluation of the TCF first derivative to higher orders. Numerical experiments confirm the robustness and efficiency of the proposed methods.
]]></description>
<dc:subject>numerical-methods approximation rather-interesting algorithms continued-fractions representation to-write-about to-simulate consider:constructive-generalizations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f185ff1f75fd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:constructive-generalizations"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2509.01105">
    <title>[2509.01105] Distance between cubics and rationals</title>
    <dc:date>2025-11-01T20:35:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2509.01105</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We investigate the following problem: what is the smallest possible distance between a cubic irrational ξ and a rational number p/q in terms of the height H(ξ) and q? More precisely, we consider the set D3,1 of all pairs (u,v) of positive real numbers such that |ξ−p/q|>cH−u(ξ)q−v for all cubic irrationals ξ and rationals p/q. First, we transform this problem into one about the root separation of cubic polynomials. Second, we establish a conditional result: under the Hall conjecture (a special case of the famous abc-conjecture), every pair (u,v)=(3+2ϵ,5/2+ϵ) belongs to D3,1. Third, we show that every pair (u,v)∈D3,1 must satisfy u≥10−3v. Finally, we discuss an analogue of the set D3,1 in function fields where we are able to give a complete description.
]]></description>
<dc:subject>number-theory approximation numerical-methods rather-interesting continued-fractions to-write-about to-visualize consider:polynomial-approximations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f1bcb2412e97/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:polynomial-approximations"/>
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<item rdf:about="https://arxiv.org/abs/2504.11124">
    <title>[2504.11124] A Unified Hardware Accelerator for Fast Fourier Transform and Number Theoretic Transform</title>
    <dc:date>2025-08-21T17:11:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.11124</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most widely used algorithm in digital signal processing. In this work, we demonstrate a unified hardware accelerator supporting both 512-point complex FFT as well as 256-point NTT for the recently standardized NIST post-quantum key encapsulation and digital signature algorithms ML-KEM and ML-DSA respectively. Our proposed architecture effectively utilizes the arithmetic circuitry required for complex FFT, and the only additional circuits required are for modular reduction along with modifications in the control logic. Our implementation achieves performance comparable to state-of-the-art ML-KEM / ML-DSA NTT accelerators on FPGA, thus demonstrating how an FFT accelerator can be augmented to support NTT and the unified hardware can be used for both digital signal processing and post-quantum lattice-based cryptography applications.
]]></description>
<dc:subject>numerical-methods engineering-design circuits to-write-about consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3667b43c765e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:circuits"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://biomath.math.bas.bg/biomath/index.php/biomath/article/view/j.biomath.2025.08.055">
    <title>A biological growth model using continued fraction of straight lines. Methodological aspects | BIOMATH</title>
    <dc:date>2025-08-12T13:12:27+00:00</dc:date>
    <link>https://biomath.math.bas.bg/biomath/index.php/biomath/article/view/j.biomath.2025.08.055</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[S-shaped curves are ubiquitous in biology especially when it comes to growth of a population or even an individual. Growth models such as the classical Verhulst-Pearl logistic growth equation and its extensions effectively model such S-shaped growth curves. Most of these models are parametrized by three or more parameters. In this work, continued fraction of straight lines has been applied to model S-shaped curves of biological growth through the use of only two parameters a and m. Here, m is the maximum growth rate and a is the parameter restricting the growth rate. The parameters a and m help to better interpret the data when compared to the logistic growth model since m represents factors promoting growth while a represents restricting factors of growth. This model is effective for modeling both population as well as individual growth, especially around the phase of rapid growth.
]]></description>
<dc:subject>models-and-modes curve-fitting rather-interesting continued-fractions numerical-methods to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:83f520489747/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:curve-fitting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/doi/abs/10.1145/3715739">
    <title>QSF: Multi-objective Optimization Based Efficient Solving for Floating-Point Constraints | Proceedings of the ACM on Software Engineering</title>
    <dc:date>2025-06-24T14:55:59+00:00</dc:date>
    <link>https://dl.acm.org/doi/abs/10.1145/3715739</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Floating-point constraint solving is challenging due to the complex representation and non-linear computations. Search-based constraint solving provides an effective method for solving floating-point constraints. In this paper, we propose QSF to improve the efficiency of search-based solving for floating-point constraints. The key idea of QSF is to model the floating-point constraint solving problem as a multi-objective optimization problem. Specifically, QSF considers both the number of unsatisfied constraints and the sum of the violation degrees of unsatisfied constraints as the objectives for search-based optimization. Besides, we propose a new evolutionary algorithm in which the mutation operators are specially designed for floating-point numbers, aiming to solve the multi-objective problem more efficiently. We have implemented QSF and conducted extensive experiments on both the SMT-COMP benchmark and the benchmark from real-world floating-point programs. The results demonstrate that compared to SOTA floating-point solvers, QSF achieved an average speedup of 15.72X under a 60-second timeout and an impressive 87.48X under a 600-second timeout on the first benchmark. Similarly, on the second benchmark, QSF delivered an average speedup of 22.44X and 29.23X, respectively, under the two timeout configurations. Furthermore, QSF has also enhanced the performance of symbolic execution for floating-point programs.]]></description>
<dc:subject>numerical-methods multiobjective-optimization constraint-satisfaction computational-complexity rather-interesting operations-research to-write-about to-simulate consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:52946ee4b76f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2410.08304">
    <title>[2410.08304] Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers</title>
    <dc:date>2025-04-06T19:26:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2410.08304</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.
]]></description>
<dc:subject>nonlinear-dynamics machine-learning reinventing-the-wheel symbolic-regression but-not-quite numerical-methods rather-interesting to-replicate consider:representation consider:performance-measures neural-networks transformer-models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b39ac4a5b24e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reinventing-the-wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:but-not-quite"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-replicate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:transformer-models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2503.07811">
    <title>[2503.07811] A primer on optimal transport for causal inference with observational data</title>
    <dc:date>2025-04-05T22:00:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2503.07811</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection of optimal transport and causal inference is only beginning to develop. Yet, many foundational models in causal inference have implicitly relied on optimal transport principles for decades, without recognizing the underlying connection. Therefore, the goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data -- where optimal transport is not just a set of potential tools, but actually builds the foundation of model assumptions. As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics, by pointing out these existing connections, and to explore novel problems and directions for future work in both areas derived from this realization.
]]></description>
<dc:subject>probability-theory optimal-transport causal-inference inference to-understand via:? modeling machine-learning numerical-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:28573aa6a3a3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimal-transport"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:causal-inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:modeling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.11533">
    <title>[2407.11533] Transforming the Challenge of Constructing Low-Discrepancy Point Sets into a Permutation Selection Problem</title>
    <dc:date>2024-12-21T17:43:43+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.11533</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear how low the discrepancy of point sets can go; in other words, how regularly distributed can points be in a given space. Recent insights using optimization and machine learning techniques have led to substantial improvements in the construction of low-discrepancy point sets, resulting in configurations of much lower discrepancy values than previously known. Building on the optimal constructions, we present a simple way to obtain L∞-optimized placement of points that follow the same relative order as an (arbitrary) input set. Applying this approach to point sets in dimensions 2 and 3 for up to 400 and 50 points, respectively, we obtain point sets whose L∞ star discrepancies are up to 25% smaller than those of the current-best sets, and around 50% better than classical constructions such as the Fibonacci set.
]]></description>
<dc:subject>low-discrepancy-samples algorithms numerical-methods approximation rather-interesting to-write-about to-simulate combinatorics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1f07890f97e1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-samples"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2408.06475">
    <title>[2408.06475] Quasi-Monte Carlo Beyond Hardy-Krause</title>
    <dc:date>2024-12-21T17:39:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.06475</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The classical approaches to numerically integrating a function f are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate f and have error O(σ(f)/n‾√), where σ(f) is the standard deviation of f. QMC methods are based on evaluating f at explicit point sets with low discrepancy, and as given by the classical Koksma-Hlawka inequality, they have error O˜(σ𝖧𝖪(f)/n), where σ𝖧𝖪(f) is the variation of f in the sense of Hardy and Krause. These two methods have distinctive advantages and shortcomings, and a fundamental question is to find a method that combines the advantages of both.
In this work, we give a simple randomized algorithm that produces QMC point sets with the following desirable features: (1) It achieves substantially better error than given by the classical Koksma-Hlawka inequality. In particular, it has error O˜(σ𝖲𝖮(f)/n), where σ𝖲𝖮(f) is a new measure of variation that we introduce, which is substantially smaller than the Hardy-Krause variation. (2) The algorithm only requires random samples from the underlying distribution, which makes it as flexible as MC. (3) It automatically achieves the best of both MC and QMC (and the above improvement over Hardy-Krause variation) in an optimal way. (4) The algorithm is extremely efficient, with an amortized O˜(1) runtime per sample.
Our method is based on the classical transference principle in geometric discrepancy, combined with recent algorithmic innovations in combinatorial discrepancy that besides producing low-discrepancy colorings, also guarantee certain subgaussian properties. This allows us to bypass several limitations of previous works in bridging the gap between MC and QMC methods and go beyond the Hardy-Krause variation.
]]></description>
<dc:subject>low-discrepancy-numbers numerical-methods integration algorithms rather-interesting number-theory probability-theory to-understand to-simulate approximation sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f356a8ba7caa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:integration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2306.16998">
    <title>[2306.16998] Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms</title>
    <dc:date>2024-10-20T16:10:17+00:00</dc:date>
    <link>https://arxiv.org/abs/2306.16998</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The L∞ star discrepancy is a measure for the regularity of a finite set of points taken from [0,1)d. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other applications. Unfortunately, computing the L∞ star discrepancy of a given point set is known to be a hard problem, with the best exact algorithms falling short for even moderate dimensions around 8. However, despite the difficulty of finding the global maximum that defines the L∞ star discrepancy of the set, local evaluations at selected points are inexpensive. This makes the problem tractable by black-box optimization approaches.
In this work we compare 8 popular numerical black-box optimization algorithms on the L∞ star discrepancy computation problem, using a wide set of instances in dimensions 2 to 15. We show that all used optimizers perform very badly on a large majority of the instances and that in many cases random search outperforms even the more sophisticated solvers. We suspect that state-of-the-art numerical black-box optimization techniques fail to capture the global structure of the problem, an important shortcoming that may guide their future development.
We also provide a parallel implementation of the best-known algorithm to compute the discrepancy.
]]></description>
<dc:subject>discrepancy approximation numerical-methods randomness quasirandom-numbers monte-carlo-methods sampling visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ee82b8852476/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrepancy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:randomness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasirandom-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:monte-carlo-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.06804">
    <title>[1811.06804] Evolutionary Diversity Optimization Using Multi-Objective Indicators</title>
    <dc:date>2024-10-07T12:39:06+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.06804</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Evolutionary diversity optimization aims to compute a diverse set of solutions where all solutions meet a given quality criterion. With this paper, we bridge the areas of evolutionary diversity optimization and evolutionary multi-objective optimization. We show how popular indicators frequently used in the area of multi-objective optimization can be used for evolutionary diversity optimization. Our experimental investigations for evolving diverse sets of TSP instances and images according to various features show that two of the most prominent multi-objective indicators, namely the hypervolume indicator and the inverted generational distance, provide excellent results in terms of visualization and various diversity indicators.
]]></description>
<dc:subject>evolutionary-algorithms low-discrepancy-series monte-carlo-methods numerical-methods to-write-about to-cite consider:combinatorics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6523d8d429ae/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:evolutionary-algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:monte-carlo-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-cite"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:combinatorics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.18014">
    <title>[2402.18014] Set-valued Star-Shaped Risk Measures</title>
    <dc:date>2024-09-23T13:18:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.18014</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems in the set-valued framework. It is demonstrated that set-valued risk measures can be represented as the union of a family of set-valued convex risk measures, and set-valued normalized star-shaped risk measures can be represented as the union of a family of set-valued normalized convex risk measures. The link between set-valued risk measures and set-valued star-shaped risk measures is also established.
]]></description>
<dc:subject>approximation numerical-methods statistics risk rather-interesting portfolio-theory to-understand geometry error</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2b593313b435/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:risk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:portfolio-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:error"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.06298">
    <title>[2109.06298] Uniformly distributed sequences generated by a greedy minimization of the $L_2$ discrepancy</title>
    <dc:date>2024-09-17T20:46:18+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.06298</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The aim of this paper is to develop greedy algorithms which generate uniformly distributed sequences in the d-dimensional unit cube [0,1]d. The figures of merit are three different variants of L2 discrepancy. Theoretical results along with numerical experiments suggest that the resulting sequences have excellent distribution properties. The approach we follow here is motivated by recent work of Steinerberger and Pausinger who consider similar greedy algorithms, where they minimize functionals that can be related to the star discrepancy or energy of point sets. In contrast to many greedy algorithms where the resulting elements of the sequence can only be given numerically, we will find that in the one-dimensional case our algorithms yield rational numbers which we can describe precisely. In particular, we will observe that any initial segment of a sequence in [0,1) can be naturally extended to a uniformly distributed sequence where all subsequent elements are of the form xN=2n−12N for some n∈{1,…,N}. We will also investigate the dependence of the L2 discrepancy of the resulting sequences on the dimension d.
]]></description>
<dc:subject>discrepancy numerical-methods rather-interesting algorithms low-discrepancy-sequences simulation nudge-targets consider:looking-to-see consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:de2649ccabc1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrepancy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-sequences"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2409.02086">
    <title>[2409.02086] Taming Randomness in Agent-Based Models using Common Random Numbers</title>
    <dc:date>2024-09-04T22:48:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2409.02086</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Random numbers are at the heart of every agent-based model (ABM) of health and disease. By representing each individual in a synthetic population, agent-based models enable detailed analysis of intervention impact and parameter sensitivity. Yet agent-based modeling has a fundamental signal-to-noise problem, in which small differences between simulations cannot be reliably differentiated from stochastic noise resulting from misaligned random number realizations. We introduce a novel methodology that eliminates noise due to misaligned random numbers, a first for agent-based modeling. Our approach enables meaningful individual-level analysis between ABM scenarios because all differences are driven by mechanistic effects rather than random number noise. A key result is that many fewer simulations are needed for some applications. We demonstrate the benefits of our approach on three disparate examples and discuss limitations.
]]></description>
<dc:subject>agent-based stochastic-systems nonlinear-dynamics simulation numerical-methods software-development-is-not-programming rather-interesting to-write-about to-pass-along reproducibility</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d69b0e73e586/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:agent-based"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:stochastic-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development-is-not-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-pass-along"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reproducibility"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.11713">
    <title>[2407.11713] AutoFreeFem: Automatic code generation with FreeFEM++ and LaTex output for shape and topology optimization of non-linear multi-physics problems</title>
    <dc:date>2024-08-08T13:42:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.11713</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For an educational purpose we develop the Python package AutoFreeFem which generates all ingredients for shape optimization with non-linear multi-physics in FreeFEM++ and also outputs the expressions for use in LaTex. As an input, the objective function and the weak form of the problem have to be specified only once. This ensures consistency between the simulation code and its documentation. In particular, AutoFreeFem provides the linearization of the state equation, the adjoint problem, the shape derivative, as well as a basic implementation of the level-set based mesh evolution method for shape optimization. For the computation of shape derivatives we utilize the mathematical Lagrangian approach for differentiating PDE-constrained shape functions. Differentiation is done symbolically using Sympy. In numerical experiments we verify the accuracy of the computed derivatives. Finally, we showcase the capabilities of AutoFreeFem by considering shape optimization of a non-linear diffusion problem, linear and non-linear elasticity problems, a thermo-elasticity problem and a fluid-structure interaction problem.
]]></description>
<dc:subject>engineering-design finite-elements-analysis Python numerical-methods scientific-computing simulation rather-interesting library to-understand to-write-about consider:optimization consider:benchmarking</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3ed33361e396/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:finite-elements-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Python"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scientific-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:benchmarking"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2304.10521">
    <title>[2304.10521] A class of mesh-free algorithms for some problems arising in finance and machine learning</title>
    <dc:date>2024-08-06T14:25:33+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.10521</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce a numerical methodology, referred to as the transport-based mesh-free method, which allows us to deal with continuous, discrete, or statistical models in the same unified framework, and leads us to a broad class of numerical algorithms recently implemented in a Python library (namely, CodPy). Specifically, we propose a mesh-free discretization technique based on the theory of reproducing kernels and the theory of transport mappings, in a way that is reminiscent of Lagrangian methods in computational fluid dynamics. We introduce kernel-based discretizations of a variety of differential and discrete operators (gradient, divergence, Laplacian, Leray projection, extrapolation, interpolation, polar factorization). The proposed algorithms are nonlinear in nature and enjoy quantitative error estimates based on the notion of discrepancy error, which allows one to evaluate the relevance and accuracy of, both, the given data and the numerical solutions. Our strategy is relevant when a large number of degrees of freedom are present as is the case in mathematical finance and machine learning. We consider the Fokker-Planck-Kolmogorov system (relevant for problems arising in finance and material dynamics) and a class of neural networks based on support vector machines.
]]></description>
<dc:subject>numerical-methods python library kernel-methods calculus machine-learning to-understand to-learn consider:constant-fitting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0c3ef89e8233/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:python"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:kernel-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:calculus"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-learn"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:constant-fitting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.15099">
    <title>[2206.15099] Automatic generation of interpretable hyperelastic material models by symbolic regression</title>
    <dc:date>2024-07-03T11:01:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.15099</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney-Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied for the multi-axial loading data set of vulcanized rubber. Finally, a data set for a temperature-dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.
]]></description>
<dc:subject>symbolic-regression materials-science numerical-methods models models-and-modes to-write-about explainable-modeling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4c415c4559a1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explainable-modeling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.14775">
    <title>[2209.14775] On Constructing Spanners from Random Gaussian Projections</title>
    <dc:date>2023-10-12T11:11:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.14775</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA'12) that has since found numerous applications in streaming, distributed computing, and massively parallel algorithms, among others. Graph sketching has proven to be quite successful for various problems such as connectivity, minimum spanning trees, edge or vertex connectivity, and cut or spectral sparsifiers. Yet, the problem of approximating shortest path metric of a graph, and specifically computing a spanner, is notably missing from the list of successes. This has turned the status of this fundamental problem into one of the most longstanding open questions in this area.
We present a partial explanation of this lack of success by proving a strong lower bound for a large family of graph sketching algorithms that encompasses prior work on spanners and many (but importantly not also all) related cut-based problems mentioned above. Our lower bound matches the algorithmic bounds of the recent result of Filtser, Kapralov, and Nouri (SODA'21), up to lower order terms, for constructing spanners via the same graph sketching family. This establishes near-optimality of these bounds, at least restricted to this family of graph sketching techniques, and makes progress on a conjecture posed in this latter work.
]]></description>
<dc:subject>graph-theory numerical-methods matrices rather-interesting linear-projection transformations heuristics to-understand to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:82ddc5bf2751/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:linear-projection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:transformations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.14440">
    <title>[2209.14440] GeONet: a neural operator for learning the Wasserstein geodesic</title>
    <dc:date>2023-09-30T12:46:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.14440</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Optimal transport (OT) offers a versatile framework to compare complex data distributions in a geometrically meaningful way. Traditional methods for computing the Wasserstein distance and geodesic between probability measures require mesh-dependent domain discretization and suffer from the curse-of-dimensionality. We present GeONet, a mesh-invariant deep neural operator network that learns the non-linear mapping from the input pair of initial and terminal distributions to the Wasserstein geodesic connecting the two endpoint distributions. In the offline training stage, GeONet learns the saddle point optimality conditions for the dynamic formulation of the OT problem in the primal and dual spaces that are characterized by a coupled PDE system. The subsequent inference stage is instantaneous and can be deployed for real-time predictions in the online learning setting. We demonstrate that GeONet achieves comparable testing accuracy to the standard OT solvers on simulation examples and the MNIST dataset with considerably reduced inference-stage computational cost by orders of magnitude.
]]></description>
<dc:subject>machine-learning probability-theory rather-interesting metrics distance numerical-methods approximation neural-networks consider:looking-to-see consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2550a216a21d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.09663">
    <title>[2205.09663] Collision Detection Accelerated: An Optimization Perspective</title>
    <dc:date>2023-09-30T12:37:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.09663</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Collision detection between two convex shapes is an essential feature of any physics engine or robot motion planner. It has often been tackled as a computational geometry problem, with the Gilbert, Johnson and Keerthi (GJK) algorithm being the most common approach today. In this work we leverage the fact that collision detection is fundamentally a convex optimization problem. In particular, we establish that the GJK algorithm is a specific sub-case of the well-established Frank-Wolfe (FW) algorithm in convex optimization. We introduce a new collision detection algorithm by adapting recent works linking Nesterov acceleration and Frank-Wolfe methods. We benchmark the proposed accelerated collision detection method on two datasets composed of strictly convex and non-strictly convex shapes. Our results show that our approach significantly reduces the number of iterations to solve collision detection problems compared to the state-of-the-art GJK algorithm, leading to up to two times faster computation times.
]]></description>
<dc:subject>numerical-methods computational-complexity computational-geometry algorithms rather-interesting nudge-targets consider:looking-to-see to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:28b76b883a7e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2111.02607">
    <title>[2111.02607] Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation</title>
    <dc:date>2023-09-09T22:43:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.02607</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Then, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of the sequential and iterative calculations of the CEM form-finding algorithm, instead of a numerical approximation. Finally, we encapsulate our research developments into an open-source design tool written in Python that is usable across different CAD platforms and operating systems. After studying four different structures -- a self-stressed planar tensegrity, a tree canopy, a curved bridge, and a spiral staircase -- we demonstrate that our approach enables the solution of constrained form-finding problems on a diverse range of structures more efficiently than in previous work.
]]></description>
<dc:subject>numerical-methods structural-engineering rather-interesting generative-models structure architecture inverse-problems to-understand to-write-about consider:benchmarks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c2c1ce6f5115/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:structural-engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:structure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:architecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:benchmarks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.10529">
    <title>[2109.10529] Numerical Continued Fraction Interpolation</title>
    <dc:date>2023-09-09T22:36:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.10529</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that highly accurate approximations can often be obtained from constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained results are comparable with the outcome from state-of-the-art rational interpolation techniques based on the barycentric form.
]]></description>
<dc:subject>continued-fractions approximation numerical-methods rather-interesting to-understand representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3a16dc1b8540/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.07838">
    <title>[2109.07838] Computing the exact sign of sums of products with floating point arithmetic</title>
    <dc:date>2023-09-09T22:35:16+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.07838</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed for the exact solution of linear programming problems and systems of linear inequalities. Computing these signs exactly with inexact floating point arithmetic is challenging, and we present yet another algorithm for this task. Our algorithm is efficient and uses only of floating point arithmetic, which is much faster than exact arithmetic. We prove that the algorithm is correct and provide efficient and tested \texttt{C++} code for it.
]]></description>
<dc:subject>numerical-methods floating-point approximation error rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e1c6d71a6a09/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:floating-point"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:error"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.13802">
    <title>[2207.13802] Digital Nets and Sequences for Quasi-Monte Carlo Methods</title>
    <dc:date>2023-09-09T13:45:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.13802</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results pertaining to digital nets and sequences: implementing randomized digital nets, finding the distribution of the discrepancy of scrambled digital nets, and obtaining better quality of digital nets through evolutionary computation. Finally, applications of scrambled and non-scrambled digital nets are provided.
]]></description>
<dc:subject>low-discrepancy-seqwuences numerical-methods rather-interesting algorithms to-write-about to-cite consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:566f729013b0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-seqwuences"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-cite"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2308.04825">
    <title>[2308.04825] Repelled point processes with application to numerical integration</title>
    <dc:date>2023-09-09T13:01:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2308.04825</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Linear statistics of point processes yield Monte Carlo estimators of integrals. While the simplest approach relies on a homogeneous Poisson point process, more regularly spread point processes, such as scrambled low-discrepancy sequences or determinantal point processes, can yield Monte Carlo estimators with fast-decaying mean square error. Following the intuition that more regular configurations result in lower integration error, we introduce the repulsion operator, which reduces clustering by slightly pushing the points of a configuration away from each other. Our main theoretical result is that applying the repulsion operator to a homogeneous Poisson point process yields an unbiased Monte Carlo estimator with lower variance than under the original point process. On the computational side, the evaluation of our estimator is only quadratic in the number of integrand evaluations and can be easily parallelized without any communication across tasks. We illustrate our variance reduction result with numerical experiments and compare it to popular Monte Carlo methods. Finally, we numerically investigate a few open questions on the repulsion operator. In particular, the experiments suggest that the variance reduction also holds when the operator is applied to other motion-invariant point processes.
]]></description>
<dc:subject>low-discrepancy-sequence numerical-methods sampling algorithms horse-races rather-interesting approximation performance-measure nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1d714b506f44/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-sequence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2307.15584">
    <title>[2307.15584] Quasi-Monte Carlo Algorithms (not only) for Graphics Software</title>
    <dc:date>2023-09-09T12:58:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2307.15584</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We then take a look at massively parallel quasi-Monte Carlo integro-approximation for image synthesis by light transport simulation. Beyond superior uniformity, low discrepancy points may be optimized with respect to additional criteria, such as noise characteristics at low sampling rates or the quality of low-dimensional projections.
]]></description>
<dc:subject>low-discrepancy-numbers algorithms numerical-methods computer-graphics sampling rather-interesting performance-measure to-write-about to-cite</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3865da3252e2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-graphics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-cite"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2302.05116">
    <title>[2302.05116] Example-Based Sampling with Diffusion Models</title>
    <dc:date>2023-09-09T12:49:21+00:00</dc:date>
    <link>https://arxiv.org/abs/2302.05116</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Much effort has been put into developing samplers with specific properties, such as producing blue noise, low-discrepancy, lattice or Poisson disk samples. These samplers can be slow if they rely on optimization processes, may rely on a wide range of numerical methods, are not always differentiable. The success of recent diffusion models for image generation suggests that these models could be appropriate for learning how to generate point sets from examples. However, their convolutional nature makes these methods impractical for dealing with scattered data such as point sets. We propose a generic way to produce 2-d point sets imitating existing samplers from observed point sets using a diffusion model. We address the problem of convolutional layers by leveraging neighborhood information from an optimal transport matching to a uniform grid, that allows us to benefit from fast convolutions on grids, and to support the example-based learning of non-uniform sampling patterns. We demonstrate how the differentiability of our approach can be used to optimize point sets to enforce properties.
]]></description>
<dc:subject>numerical-methods low-discrepancy-numbers quasirandom-numbers algorithms rather-interesting sampling performance-measure to-understand to-cite</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e86eac84f2cb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasirandom-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-cite"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.07881">
    <title>[2101.07881] Star Discrepancy Subset Selection: Problem Formulation and Efficient Approaches for Low Dimensions</title>
    <dc:date>2023-08-19T21:40:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.07881</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Motivated by applications in instance selection, we introduce the star discrepancy subset selection problem, which consists of finding a subset of m out of n points that minimizes the star discrepancy. First, we show that this problem is NP-hard. Then, we introduce a mixed integer linear formulation (MILP) and a combinatorial branch-and-bound (BB) algorithm for the star discrepancy subset selection problem and we evaluate both approaches against random subset selection and a greedy construction on different use-cases in dimension two and three. Our results show that the MILP and BB are efficient in dimension two for large and small m/n ratio, respectively, and for not too large n. However, the performance of both approaches decays strongly for larger dimensions and set sizes. 
As a side effect of our empirical comparisons we obtain point sets of discrepancy values that are much smaller than those of common low-discrepancy sequences, random point sets, and of Latin Hypercube Sampling. This suggests that subset selection could be an interesting approach for generating point sets of small discrepancy value.
]]></description>
<dc:subject>low-discrepancy-numbers numerical-methods looking-to-see algorithms rather-interesting quasi-monte-carlo</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:399c26067cf4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasi-monte-carlo"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.07833">
    <title>[2102.07833] Quasi-Monte Carlo Software</title>
    <dc:date>2023-08-19T21:39:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.07833</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC) software available. We highlight the key software components required by QMC to approximate multivariate integrals or expectations of functions of vector random variables. We have combined these components in QMCPy, a Python open-source library, which we hope will draw the support of the QMC community. Here we introduce QMCPy.
]]></description>
<dc:subject>numerical-methods low-discrepancy-numbers algorithms tutorial approximation rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a246e9d597c9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tutorial"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2210.16548">
    <title>[2210.16548] The importance of being scrambled: supercharged Quasi Monte Carlo</title>
    <dc:date>2023-08-19T14:16:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.16548</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized QMC (RQMC) method combines the best of two methods. Application of scrambled LDS allow to compute confidence intervals around the estimated value, providing a practical error bound. Randomization of Sobol' LDS by two methods: Owen's scrambling and digital shift are compared considering computation of Asian options and Greeks using hyperbolic local volatility model. RQMC demonstrated the superior performance over standard QMC showing increased convergence rates and providing practical error bounds.
]]></description>
<dc:subject>approximation numerical-methods low-discrepancy quasirandom-numbers rather-interesting heuristics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ded4a361ce8c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasirandom-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/doi/10.1145/234535.234536">
    <title>Computing the discrepancy with applications to supersampling patterns | ACM Transactions on Graphics</title>
    <dc:date>2023-08-08T11:27:53+00:00</dc:date>
    <link>https://dl.acm.org/doi/10.1145/234535.234536</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy—how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.
]]></description>
<dc:subject>computational-geometry algorithms computational-complexity discrepancy numerical-methods monte-carlo to-write-about to-implement to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:607e399d731c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrepancy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:monte-carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-implement"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10589-005-4615-1">
    <title>Application of Deterministic Low-Discrepancy Sequences in Global Optimization | SpringerLink</title>
    <dc:date>2023-08-07T21:53:29+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10589-005-4615-1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It has been recognized through theory and practice that uniformly distributed deterministic sequences provide more accurate results than purely random sequences. A quasi Monte Carlo (QMC) variant of a multi level single linkage (MLSL) algorithm for global optimization is compared with an original stochastic MLSL algorithm for a number of test problems of various complexities. An emphasis is made on high dimensional problems. Two different low-discrepancy sequences (LDS) are used and their efficiency is analysed. It is shown that application of LDS can significantly increase the efficiency of MLSL. The dependence of the sample size required for locating global minima on the number of variables is examined. It is found that higher confidence in the obtained solution and possibly a reduction in the computational time can be achieved by the increase of the total sample size N. N should also be increased as the dimensionality of problems grows. For high dimensional problems clustering methods become inefficient. For such problems a multistart method can be more computationally expedient.

]]></description>
<dc:subject>numerical-methods optimization quasi-random numbers to-write-about to-visualize consider:evolutionary-algorithms nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f151a67c6fb0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasi-random"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:evolutionary-algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.09618">
    <title>[2207.09618] Dynamical system-based computational models for solving combinatorial optimization on hypergraphs</title>
    <dc:date>2023-07-30T16:19:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.09618</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping such dynamics to combinatorial optimization problems whose objective functions have quadratic degree (e.g., MaxCut); such problems can be represented and analyzed using graphs. However, the work on developing such models for problems that need objective functions with degree greater than two, and subsequently, entail the use of hypergraph data structures, is relatively sparse. In this work, we develop dynamical system-inspired computational models for several such problems. Specifically, we define the 'energy function' for hypergraph-based combinatorial problems ranging from Boolean SAT and its variants to integer factorization, and subsequently, define the resulting system dynamics. We also show that the design approach is applicable to optimization problems with quadratic degree, and use it develop a new dynamical system formulation for minimizing the Ising Hamiltonian. Our work not only expands on the scope of problems that can be directly mapped to, and solved using physics-inspired models, but also creates new opportunities to design high-performance accelerators for solving combinatorial optimization.
]]></description>
<dc:subject>optimization computational-complexity metaheuristics rather-interesting numerical-methods hypergraphs representation distributed-processing to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f9687f995259/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.10847">
    <title>[2107.10847] Accelerating Quadratic Optimization with Reinforcement Learning</title>
    <dc:date>2023-06-30T13:12:17+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.10847</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges: manual hyperparameter tuning and convergence time to high-accuracy solutions. To address these, we explore how Reinforcement Learning (RL) can learn a policy to tune parameters to accelerate convergence. In experiments with well-known QP benchmarks we find that our RL policy, RLQP, significantly outperforms state-of-the-art QP solvers by up to 3x. RLQP generalizes surprisingly well to previously unseen problems with varying dimension and structure from different applications, including the QPLIB, Netlib LP and Maros-Meszaros problems. Code for RLQP is available at this https URL.
]]></description>
<dc:subject>mathematical-programming heuristics neural-networks rather-interesting stylized-optimization numerical-methods guessing-is-always-a-start to-write-about to-do</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8d76c4ff7f67/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:stylized-optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:guessing-is-always-a-start"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-do"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://blog.acolyer.org/2020/09/28/fpspy/">
    <title>Spying on the floating point behavior of existing, unmodified scientific applications | the morning paper</title>
    <dc:date>2022-10-30T12:13:14+00:00</dc:date>
    <link>https://blog.acolyer.org/2020/09/28/fpspy/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It’s common knowledge that the IEEE standard floating point number representations used in modern computers have their quirks, for example not being able to accurately represent numbers such as 1/3, or 0.1. The wikipedia page on floating point numbers describes a number of related accuracy problems including the difficulty of testing for equality. In day-to-day usage, beyond judicious use of ‘within’ for equality testing, I suspect most of us ignore the potential difficulties of floating point arithmetic even if we shouldn’t. You’d like to think that scientific computing applications which heavily depend on floating point operations would do better than that, but the results in today’s paper choice give us reason to doubt.

]]></description>
<dc:subject>scientific-computing accuracy validation verification numerical-methods floats software-development-is-not-programming rather-interesting to-write-about consider:genetic-programming consider:fixes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4f6ae25c730d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scientific-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:accuracy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:validation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:verification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:floats"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development-is-not-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:fixes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.00528">
    <title>[2203.00528] On genetic programming representations and fitness functions for interpretable dimensionality reduction</title>
    <dc:date>2022-10-04T10:52:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.00528</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its lower-dimensional representation (e.g., MDS, t-SNE, isomap), or produce mappings that cannot be easily interpreted (e.g., kernel PCA, neural-based autoencoder). Recently, genetic programming (GP) has been used to evolve interpretable DR mappings in the form of symbolic expressions. There exists a number of ways in which GP can be used to this end and no study exists that performs a comparison. In this paper, we fill this gap by comparing existing GP methods as well as devising new ones. We evaluate our methods on several benchmark datasets based on predictive accuracy and on how well the original features can be reconstructed using the lower-dimensional representation only. Finally, we qualitatively assess the resulting expressions and their complexity. We find that various GP methods can be competitive with state-of-the-art DR algorithms and that they have the potential to produce interpretable DR mappings.
]]></description>
<dc:subject>symbolic-regression genetic-programming dimension-reduction numerical-methods no-mention-of-Kotanchek le-sigh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:054bc1003978/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dimension-reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:no-mention-of-Kotanchek"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:le-sigh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1712.07897">
    <title>[1712.07897] Non-convex Optimization for Machine Learning</title>
    <dc:date>2022-09-05T12:11:15+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.07897</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or that train non-linear models such as tensor models and deep networks. 
The freedom to express the learning problem as a non-convex optimization problem gives immense modeling power to the algorithm designer, but often such problems are NP-hard to solve. A popular workaround to this has been to relax non-convex problems to convex ones and use traditional methods to solve the (convex) relaxed optimization problems. However this approach may be lossy and nevertheless presents significant challenges for large scale optimization. 
On the other hand, direct approaches to non-convex optimization have met with resounding success in several domains and remain the methods of choice for the practitioner, as they frequently outperform relaxation-based techniques - popular heuristics include projected gradient descent and alternating minimization. However, these are often poorly understood in terms of their convergence and other properties. 
This monograph presents a selection of recent advances that bridge a long-standing gap in our understanding of these heuristics. The monograph will lead the reader through several widely used non-convex optimization techniques, as well as applications thereof. The goal of this monograph is to both, introduce the rich literature in this area, as well as equip the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems.
]]></description>
<dc:subject>via:cshalizi operations-research machine-learning optimization algorithms nonconvex-problems review numerical-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0d6682608a03/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:cshalizi"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonconvex-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2001.04109">
    <title>[2001.04109] On fast multiplication of a matrix by its transpose</title>
    <dc:date>2022-02-28T13:59:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2001.04109</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions.Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite this http URL conclude, we show how to use our result in LDLT factorization.
]]></description>
<dc:subject>matrices algorithms numerical-methods computational-complexity rather-interesting to-write-about to-visualize consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:14bb5e1045e9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.08150">
    <title>[1901.08150] Hypergraph Convolution and Hypergraph Attention</title>
    <dc:date>2022-02-10T11:18:17+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.08150</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise formulation. To efficiently learn deep embeddings on the high-order graph-structured data, we introduce two end-to-end trainable operators to the family of graph neural networks, i.e., hypergraph convolution and hypergraph attention. Whilst hypergraph convolution defines the basic formulation of performing convolution on a hypergraph, hypergraph attention further enhances the capacity of representation learning by leveraging an attention module. With the two operators, a graph neural network is readily extended to a more flexible model and applied to diverse applications where non-pairwise relationships are observed. Extensive experimental results with semi-supervised node classification demonstrate the effectiveness of hypergraph convolution and hypergraph attention.
]]></description>
<dc:subject>hypergraphs representation rather-interesting define-your-terms algorithms numerical-methods to-read to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:34a92ee77974/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.14274">
    <title>[2106.14274] Learning Mesh Representations via Binary Space Partitioning Tree Networks</title>
    <dc:date>2022-02-05T13:36:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.14274</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at this https URL.
]]></description>
<dc:subject>computational-geometry numerical-methods neural-networks machine-learning mesh-generation 3d optimization rather-interesting approximation to-write-about consider:performance-measures consider:edge-cases</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7f9a89ab9655/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mesh-generation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:3d"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:edge-cases"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.15069">
    <title>[2109.15069] $K$-selective percolation: A simple model leading to a rich repertoire of phase transitions</title>
    <dc:date>2022-01-26T13:40:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.15069</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose the K-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree K is deactivated one by one until no more nodes with degree K remain. The non-monotonic response of the giant component size on various synthetic and real-world networks implies a conclusion that a network can be more robust against such selective attack by removing further edges. In the theoretical perspective, the K-selective percolation process exhibits a rich repertoire of phase transitions, including double transitions of hybrid and continuous, as well as reentrant transitions. Notably, we observe a tricritical-like point on Erdős-Rényi networks. We also examine a discontinuous transition with unusual order parameter fluctuation and distribution on simple cubic lattices, which does not appear in other percolation models with cascade processes. Finally, we perform finite-size scaling analysis to obtain critical exponents on various transition points, including those exotic ones.
]]></description>
<dc:subject>network-theory graph-theory feature-construction rather-interesting robustness algorithms numerical-methods to-write-about to-simulate consider:inverse-problem consider:weird-maxima percolation phase-transitions</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4c1fae0a3809/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:inverse-problem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:weird-maxima"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:percolation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:phase-transitions"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1704.06467">
    <title>[1704.06467] Visibility graphs and symbolic dynamics</title>
    <dc:date>2022-01-26T13:37:04+00:00</dc:date>
    <link>https://arxiv.org/abs/1704.06467</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the system. Via Pesin identity, this in turn suggests that these block entropies are converging to the Kolmogorov- Sinai entropy of the map, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x), x \in[0,1] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs.
]]></description>
<dc:subject>nonlinear-dynamics feature-construction rather-interesting representation discretization graph-theory time-series to-understand to-write-about consider:a-little-library numerical-methods chaos</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f7b7ad957779/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discretization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:time-series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:a-little-library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:chaos"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1804.02795">
    <title>[1804.02795] Weak Rigidity Theory and its Application to Multi-agent Formation Stabilization</title>
    <dc:date>2022-01-24T12:29:52+00:00</dc:date>
    <link>https://arxiv.org/abs/1804.02795</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to determine a geometric shape in an arbitrarily dimensional space. A necessary and sufficient graphical condition for infinitesimal weak rigidity of planar frameworks is derived. As an application of the proposed weak rigidity theory, a gradient based control law and a non-gradient based control law are designed for a group of single-integrator modeled agents to stabilize a desired formation shape, respectively. Using the gradient control law, we prove that an infinitesimally weakly rigid formation is locally exponentially stable. In particular, if the number of agents is one greater than the dimension of the space, a minimally infinitesimally weakly rigid formation is almost globally asymptotically stable. In the literature of rigid formation, the sensing graph is always required to be rigid. Using the non-gradient control law based on weak rigidity theory, the sensing graph is unnecessary to be rigid for local exponential stability of the formation. A numerical simulation is performed for illustrating effectiveness of our main results.
]]></description>
<dc:subject>agent-based simulation numerical-methods mechanics rather-interesting to-write-about to-understand consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cb4d2381c591/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:agent-based"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.14151">
    <title>[2110.14151] Voxelization based packing analysis for discrete element simulations of non-spherical particles</title>
    <dc:date>2022-01-22T13:10:00+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.14151</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric features of the granular assembly in various spatial sub-domains (2D surface or 3D region) and investigate the localized packing behaviour. Analyzing the local packing behaviour enables determining con-fined influences such as the wall-effect, stacking behaviour, local expansion/contraction and localized loading. The efficacy of the proposed technique to analyze practical granular assemblies is demonstrated through the packing analysis of different assemblies of superquadric cubes, superquadric ellipsoidals, and multi-spherical coffee beans.
]]></description>
<dc:subject>algorithms approximation numerical-methods 3d rather-interesting optimization to-write-about to-understand consider:visualization granular-materials</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:20ffc45d5548/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:3d"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:granular-materials"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.11826">
    <title>[1910.11826] Weighted Quasi Interpolant Spline Approximations: Properties and Applications</title>
    <dc:date>2022-01-02T21:20:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.11826</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we propose the Weighted Quasi Interpolant Spline Approximation method (wQISA). We provide global and local bounds of the method and discuss how it still preserves the shape properties of the classical quasi-interpolation scheme. This approach is particularly useful when the data noise can be represented as a probabilistic distribution: from the point of view of nonparametric regression, the wQISA estimator is robust to random perturbations, such as noise and outliers. Finally, we show the effectiveness of the method with several numerical simulations on real data, including curve fitting on images, surface approximation and simulation of rainfall precipitations.
]]></description>
<dc:subject>numerical-methods optimization rather-interesting approximation algorithms to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9eb87d8d8377/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2003.07798">
    <title>[2003.07798] Pressio: Enabling projection-based model reduction for large-scale nonlinear dynamical systems</title>
    <dc:date>2021-10-23T06:50:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2003.07798</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This work introduces Pressio, an open-source project aimed at enabling leading-edge projection-based reduced order models (ROMs) for large-scale nonlinear dynamical systems in science and engineering. Pressio provides model-reduction methods that can reduce both the number of spatial and temporal degrees of freedom for any dynamical system expressible as a system of parameterized ordinary differential equations (ODEs). We leverage this simple, expressive mathematical framework as a pivotal design choice to enable a minimal application programming interface (API) that is natural to dynamical systems. The core component of Pressio is a C++11 header-only library that leverages generic programming to support applications with arbitrary data types and arbitrarily complex programming models. This is complemented with Python bindings to expose these C++ functionalities to Python users with negligible overhead and no user-required binding code. We discuss the distinguishing characteristics of Pressio relative to existing model-reduction libraries, outline its key design features, describe how the user interacts with it, and present two test cases -- including one with over 20 million degrees of freedom -- that highlight the performance results of Pressio and illustrate the breath of problems that can be addressed with it.
]]></description>
<dc:subject>nonlinear-dynamics approximation numerical-methods rather-interesting dynamical-systems to-understand system-identification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:69ce0d534dcf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:system-identification"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.09715">
    <title>[2012.09715] Approximating inverse cumulative distribution functions to produce approximate random variables</title>
    <dc:date>2021-06-27T10:12:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.09715</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are designed to be computationally inexpensive, and much cheaper than exact library functions, and thus highly suitable for use in Monte Carlo simulations. Two approximations are presented for the Gaussian distribution: a piecewise constant on equally spaced intervals, and a piecewise linear using geometrically decaying intervals. The error of the approximations are bounded and the convergence demonstrated, and the computational savings measured for C and C++ implementations. Implementations tailored for Intel and Arm hardwares are inspected, alongside hardware agnostic implementations built using OpenMP. The savings are incorporated into a nested multilevel Monte Carlo framework with the Euler-Maruyama scheme to exploit the speed ups without losing accuracy, offering speed ups by a factor of 5--7. These ideas are empirically extended to the Milstein scheme, and the Cox-Ingersoll-Ross process' non central chi-squared distribution, which offer speed ups by a factor of 250 or more.
]]></description>
<dc:subject>numerical-methods approximation rather-interesting simulation sampling performance-measure computational-complexity nudge-targets consider:representation consider:performance-measures consider:lexicase consider:extreme-values</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8ed61cde1044/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:extreme-values"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.00113">
    <title>[2102.00113] A universal solution scheme for fractional and classical PDEs</title>
    <dc:date>2021-06-27T10:10:43+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.00113</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose a unified meshless method to solve classical and fractional PDE problems with (−Δ)α2 for α∈(0,2]. The classical (α=2) and fractional (α<2) Laplacians, one local and the other nonlocal, have distinct properties. Therefore, their numerical methods and computer implementations are usually incompatible. We notice that for any α≥0, the Laplacian (−Δ)α2 of generalized inverse multiquadric (GIMQ) functions can be analytically written by the Gauss hypergeometric function, and thus propose a GIMQ-based method. Our method unifies the discretization of classical and fractional Laplacians and also bypasses numerical approximation to the hypersingular integral of fractional Laplacian. These two merits distinguish our method from other existing methods for the fractional Laplacian. Extensive numerical experiments are carried out to test the performance of our method. Compared to other methods, our method can achieve high accuracy with fewer number of unknowns, which effectively reduces the storage and computational requirements in simulations of fractional PDEs. Moreover, the meshfree nature makes it free of geometric constraints and enables simple implementation for any dimension d≥1. Additionally, two approaches of selecting shape parameters, including condition number-indicated method and random-perturbed method, are studied to avoid the ill-conditioning issues when large number of points.
]]></description>
<dc:subject>numerical-methods diffy-Qs nonlinear-dynamics inverse-problems rather-interesting to-understand simulation representation consider:performance-measures consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d31989508c16/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffy-Qs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2103.01614">
    <title>[2103.01614] VEM and the Mesh</title>
    <dc:date>2021-03-28T12:20:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.01614</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail, after reviewing the state of the art, we present a) an experimental analysis of the convergence of the VEM under condition violating the standard shape regularity assumptions, b) an analysis of the correlation between some mesh quality metrics and a set of different performance indexes, and c) a suitably designed mesh quality indicator, aimed at predicting the quality of the performance of the VEM on a given mesh.
]]></description>
<dc:subject>numerical-methods rather-interesting finite-elements-analysis algorithms computational-geometry approximation to-understand consider:performance-measures consider:visualization how-hard-to-show-in-browser?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4e5f1293d09d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:finite-elements-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:how-hard-to-show-in-browser?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.07672">
    <title>[1902.07672] Non-asymptotic Analysis of Stochastic Methods for Non-Smooth Non-Convex Regularized Problems</title>
    <dc:date>2020-07-22T11:21:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.07672</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics. However, to the best of our knowledge no non-asymptotic convergence analysis of SPG exists for non-convex optimization with a non-smooth and non-convex regularizer. All existing non-asymptotic analysis of SPG for solving non-smooth non-convex problems require the non-smooth regularizer to be a convex function, and hence are not applicable to a non-smooth non-convex regularized problem. This work initiates the analysis to bridge this gap and opens the door to non-asymptotic convergence analysis of non-smooth non-convex regularized problems. We analyze several variants of mini-batch SPG methods for minimizing a non-convex objective that consists of a smooth non-convex loss and a non-smooth non-convex regularizer. Our contributions are two-fold: (i) we show that they enjoy the same complexities as their counterparts for solving convex regularized non-convex problems in terms of finding an approximate stationary point; (ii) we develop more practical variants using dynamic mini-batch size instead of a fixed mini-batch size without requiring the target accuracy level of solution. The significance of our results is that they improve upon the-state-of-art results for solving non-smooth non-convex regularized problems. We also empirically demonstrate the effectiveness of the considered SPG methods in comparison with other peer stochastic methods.
]]></description>
<dc:subject>performance-measure guessing rather-interesting statistics numerical-methods algorithms machine-learning horse-races to-understand to-simulate consider:lexicase consider:comparisons-in-GP</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f5aabb982183/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:guessing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:comparisons-in-GP"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2004.12497">
    <title>[2004.12497] Forty New Invariants of N-Periodics in the Elliptic Billiard</title>
    <dc:date>2020-06-14T11:04:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2004.12497</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present some 40 newfound invariants displayed by N-periodics in the Elliptic Billiard, obtained through experimental exploration. These involve distances, areas, angles and centers of mass of N-periodics and associated polygons (inner, outer, pedal, antipedal). Some depend on the parity of N, others on other positional constraints. A few invariants have already been proven with elegant tools of Analytic and Algebraic Geometry. We welcome reader input to add to the list of proofs.
]]></description>
<dc:subject>billiards dynamical-systems rather-interesting numerical-methods invariants feature-construction looking-to-see to-write-about to-simulate consider:genec</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6936f8f957f7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:billiards"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:invariants"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genec"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1710.03634">
    <title>[1710.03634] LinXGBoost: Extension of XGBoost to Generalized Local Linear Models</title>
    <dc:date>2020-06-13T21:25:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.03634</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[XGBoost is often presented as the algorithm that wins every ML competition. Surprisingly, this is true even though predictions are piecewise constant. This might be justified in high dimensional input spaces, but when the number of features is low, a piecewise linear model is likely to perform better. XGBoost was extended into LinXGBoost that stores at each leaf a linear model. This extension, equivalent to piecewise regularized least-squares, is particularly attractive for regression of functions that exhibits jumps or discontinuities. Those functions are notoriously hard to regress. Our extension is compared to the vanilla XGBoost and Random Forest in experiments on both synthetic and real-world data sets.
]]></description>
<dc:subject>machine-learning numerical-methods curve-fitting statistics to-understand to-write-about consider:genetic-programming consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:74ae28f026fc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:curve-fitting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.09015">
    <title>[1906.09015] Trefftz Finite Elements on Curvilinear Polygons</title>
    <dc:date>2020-06-10T00:33:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.09015</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in the formation of local stiffness matrices. To define our local finite element spaces in the presence of curved edges, we must also properly define what it means for a function defined on a curved edge to be "polynomial" of a given degree on that edge. We consider two natural choices, before settling on the one that yields the inclusion of complete polynomial spaces in our local finite element spaces, and discuss how to work with these edge polynomial spaces in practice. An interpolation operator is introduced for the resulting finite elements, and we prove that it provides optimal order convergence for interpolation error under reasonable assumptions. We provide a description of the integral equation approach used for the examples in this paper, which was recently developed precisely with these applications in mind. A few numerical examples illustrate this optimal order convergence of the finite element solution on some families of meshes in which every element has at least one curved edge. We also demonstrate that it is possible to exploit the approximation power of locally singular functions that may exist in our finite element spaces in order to achieve optimal order convergence without the typical adaptive refinement toward singular points.
]]></description>
<dc:subject>numerical-methods representation rather-interesting computational-geometry to-write-about to-simulate consider:variations consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:847f160d01a0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:variations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.04314">
    <title>[1904.04314] Data-driven discovery of partial differential equation models with latent variables</title>
    <dc:date>2020-05-18T21:54:30+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.04314</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially complicates construction of an accurate model for such systems using data-driven approaches. The present paper illustrates how physical constraints can be employed to overcome this limitation using the example of a weakly turbulent quasi-two-dimensional Kolmogorov flow driven by a steady Lorenz force with an unknown spatial profile. Specifically, the terms involving latent variables in the partial differential equations governing the dynamics can be eliminated at the expense of raising the order of that equation. We show that local polynomial interpolation combined with symbolic regression can handle sparse data on grids that are representative of typical experimental measurement techniques such as particle image velocimetry. However, we also find that the reconstructed model is sensitive to measurement noise and trace this sensitivity to the presence of high order spatial and/or temporal derivatives.
]]></description>
<dc:subject>inverse-problems symbolic-regression BUT-NOT-OUR-KIND rather-interesting to-understand numerical-methods to-write-about consider:genetic-programming diff-Qs nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:06eebac4e254/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:BUT-NOT-OUR-KIND"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diff-Qs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://en.wikipedia.org/wiki/RANDU">
    <title>RANDU - Wikipedia</title>
    <dc:date>2020-05-02T12:31:54+00:00</dc:date>
    <link>https://en.wikipedia.org/wiki/RANDU</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In general, when an LCG with modulus 231 is used to produce points (xk, xk+1, xk+2) in 3-dimensional space, the points fall into no more than 2,344 parallel planes[5], a result which indicates an LCG is unsuitable for Monte Carlo simulation. Choice of multiplier determines the number of planes. To show the problem with the values of multiplier 65539 and modulus 231 chosen for RANDU, consider the following calculation where every term should be taken mod 231. Start by writing the recursive relation as:
]]></description>
<dc:subject>randomness algorithms pseudorandom-number-generator numerical-methods performance-measure bad-design to-write-about to-simulate consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5c61b299eaf5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:randomness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pseudorandom-number-generator"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bad-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1706.00399">
    <title>[1706.00399] Benchmark problems for phase retrieval</title>
    <dc:date>2020-04-22T23:14:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1706.00399</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is periodic and comprised of atomic distributions arranged homogeneously in the unit cell of the crystal. The crystallographic problem is both the leading application and one of the hardest forms of phase retrieval. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. The data, publicly available online, is provided in an easily interpretable format. We also propose a simple and unambiguous success/failure criterion based on the actual needs in crystallography. Baseline runtimes were obtained with an iterative algorithm that is similar but more transparent than those used in crystallography. Empirically, the runtimes grow exponentially with respect to a new hardness parameter: the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages. This set of benchmark problems, we hope, will encourage the development of new algorithms for the phase retrieval problem in general, and crystallography in particular.
]]></description>
<dc:subject>phase-retrieval inverse-problems signal-processing rather-interesting numerical-methods inference information-theory to-write-about consider:sampling consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ff462c7f56a8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:phase-retrieval"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.biorxiv.org/content/10.1101/393835v1">
    <title>Regularization Improves the Robustness of Learned Sequence-to-Expression Models | bioRxiv</title>
    <dc:date>2020-02-18T22:52:54+00:00</dc:date>
    <link>https://www.biorxiv.org/content/10.1101/393835v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Understanding of the gene regulatory activity of enhancers is a major problem in regulatory biology. The nascent field of sequence-to-expression modelling seeks to create quantitative models of gene expression based on regulatory DNA (cis) and cellular environmental (trans) contexts. All quantitative models are defined partially by numerical parameters, and it is common to fit these parameters to data provided by existing experimental results. However, the relative paucity of experimental data appropriate for this task, and lacunae in our knowledge of all components of the systems, results in problems often being under-specified, which in turn may lead to a situation where wildly different model parameterizations perform similarly well on training data. It may also lead to models being fit to the idiosyncrasies of the training data, without representing the more general process (overfitting).

In other contexts where parameter-fitting is performed, it is common to apply regularization to reduce overfitting. We systematically evaluated the efficacy of three types of regularization in improving the generalizability of trained sequence-to-expression models. The evaluation was performed in two types of cross-validation experiments: one training on D. melanogaster data and predicting on orthologous enhancers from related species, and the other cross-validating between four D. melanogaster neurogenic ectoderm enhancers, which are thought to be under control of the same transcription factors. We show that training with a combination of noise-injection, L1, and L2 regularization can drastically reduce overfitting and improve the generalizability of learned sequence-to-expression models. These results suggest that it may be possible to mitigate the tendency of sequence-to-expression models to overfit available data, thus improving predictive power and potentially resulting in models that provide better insight into underlying biological processes.

]]></description>
<dc:subject>bioinformatics systems-biology nonlinear-dynamics machine-learning regularization statistics numerical-methods heuristics to-write-about to-simulate consider:symbolic-regression consider:robustness</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f08dfb1849d5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bioinformatics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:regularization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:robustness"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1712.04922">
    <title>[1712.04922] Closing the gap for pseudo-polynomial strip packing</title>
    <dc:date>2020-01-26T13:55:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.04922</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of rectangular axis parallel items and a strip with bounded width and infinite height the objective is to find a packing of the items into the strip which minimizes the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. 
It is known that there is no pseudo-polynomial algorithm for Strip Packing with a ratio better than 5/4 unless P=NP. The best algorithm so far has a ratio of (4/3+ε). In this paper, we close this gap between inapproximability result and best known algorithm by presenting an algorithm with approximation ratio (5/4+ε) and thus categorize the problem accurately. The algorithm uses a structural result which states that each optimal solution can be transformed such that it has one of a polynomial number of different forms. The strength of this structural result is that it applies to other problem settings as well for example to Strip Packing with rotations (90 degrees) and Contiguous Moldable Task Scheduling. This fact enabled us to present algorithms with approximation ratio (5/4+ε) for these problems as well.
]]></description>
<dc:subject>operations-research optimization strip-packing packing numerical-methods mathematical-programming algorithms computational-complexity horse-races to-write-about to-simulate consider:genetic-programming consider:performance-measures consider:heuristics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7db3e06cfac1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strip-packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:heuristics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1107.4030">
    <title>[1107.4030] Three dimensional structure from intensity correlations</title>
    <dc:date>2020-01-19T14:39:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1107.4030</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.
]]></description>
<dc:subject>signal-processing crystallography inverse-problems rather-interesting diffraction numerical-methods to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:903517046ee1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:crystallography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0202236">
    <title>[math/0202236] On comparing the writhe of a smooth curve to the writhe of an inscribed polygon</title>
    <dc:date>2020-01-19T13:56:46+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0202236</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We find bounds on the difference between the writhing number of a smooth curve, and the writhing number of a polygon inscribed within. The proof is based on an extension of Fuller's difference of writhe formula to the case of polygonal curves. The results establish error bounds useful in the computation of writhe.
]]></description>
<dc:subject>algorithms approximation computational-complexity computational-geometry numerical-methods rather-interesting to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:222f7e579671/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1212.1617">
    <title>[1212.1617] Similarity of Polygonal Curves in the Presence of Outliers</title>
    <dc:date>2020-01-13T00:31:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1212.1617</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Fréchet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently occurring phenomenon in practice, a robust variant of Fréchet distance is required which absorbs outliers. We study such a variant here. In this modified variant, our objective is to minimize the length of subcurves of two polygonal curves that need to be ignored (MinEx problem), or alternately, maximize the length of subcurves that are preserved (MaxIn problem), to achieve a given Fréchet distance. An exact solution to one problem would imply an exact solution to the other problem. However, we show that these problems are not solvable by radicals over ℚ and that the degree of the polynomial equations involved is unbounded in general. This motivates the search for approximate solutions. We present an algorithm, which approximates, for a given input parameter δ, optimal solutions for the \MinEx\ and \MaxIn\ problems up to an additive approximation error δ times the length of the input curves. The resulting running time is upper bounded by (n3δlog(nδ)), where n is the complexity of the input polygonal curves.
]]></description>
<dc:subject>computational-geometry robustness algorithms numerical-methods to-write-about to-simulate consider:robustness consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:91231f87099d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1812.01502">
    <title>[1812.01502] Parallelising Particle Filters with Butterfly Interactions</title>
    <dc:date>2020-01-12T14:47:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1812.01502</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Bootstrap particle filter (BPF) is the corner stone of many popular algorithms used for solving inference problems involving time series that are observed through noisy measurements in a non-linear and non-Gaussian context. The long term stability of BPF arises from particle interactions which in the context of modern parallel computing systems typically means that particle information needs to be communicated between processing elements, which makes parallel implementation of BPF nontrivial. 
In this paper we show that it is possible to constrain the interactions in a way which, under some assumptions, enables the reduction of the cost of communicating the particle information while still preserving the consistency and the long term stability of the BPF. Numerical experiments demonstrate that although the imposed constraints introduce additional error, the proposed method shows potential to be the method of choice in certain settings.
]]></description>
<dc:subject>parallel-processing distributed-processing algorithms collective-behavior simulation numerical-methods heuristics to-understand to-write-about optimization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0b8938e31ee0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:parallel-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:collective-behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1812.02987">
    <title>[1812.02987] Time Series Featurization via Topological Data Analysis</title>
    <dc:date>2019-11-25T23:25:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1812.02987</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series. The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the stability properties of the proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach. We expect our method to provide new insights on feature extraction from granular, noisy time series data.
]]></description>
<dc:subject>time-series feature-construction feature-extraction topology statistics heuristics numerical-methods to-understand to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:911c6fb3332d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:time-series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.05031">
    <title>[1811.05031] A Review of automatic differentiation and its efficient implementation</title>
    <dc:date>2019-11-25T23:13:36+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.05031</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the calculation of derivatives and is preferable to more traditional methods, especially when differentiating complex algorithms and mathematical functions. The implementation of automatic differentiation however requires some care to insure efficiency. Modern differentiation packages deploy a broad range of computational techniques to improve applicability, run time, and memory management. Among these techniques are operation overloading, region based memory, and expression templates. There also exist several mathematical techniques which can yield high performance gains when applied to complex algorithms. For example, semi-analytical derivatives can reduce by orders of magnitude the runtime required to numerically solve and differentiate an algebraic equation. Open problems include the extension of current packages to provide more specialized routines, and efficient methods to perform higher-order differentiation.
]]></description>
<dc:subject>algorithms numerical-methods machine-learning automatic-differentiation gradient-methods to-understand review</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4331b17a10fe/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:automatic-differentiation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:gradient-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>