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  </channel><item rdf:about="https://arxiv.org/abs/2201.12038">
    <title>[2201.12038] A survey on flexible/restricted skyline and their applicability</title>
    <dc:date>2026-06-26T12:54:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2201.12038</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Skyline and Top-k are two of the most important methods to extract information from datasets, but both come with their drawbacks, that's why lately some new technics that try to mix the features of the two have been studied. In this survey three new operators are analysed, F-Skyline, ORU/ORD, and ϵ-Skyline. After giving the main ideas behind those and their properties, they are compered on 3 fundamental features such as personalization, cardinality control, and generalization to guide the user to choose the best one for any task.
]]></description>
<dc:subject>multiobjective-optimization software-development-is-not-programming algorithms performance-measure rather-interesting consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:012c8c11117c/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2504.07092">
    <title>[2504.07092] Are We Done with Object-Centric Learning?</title>
    <dc:date>2026-05-25T12:13:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.07092</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Object-centric learning (OCL) seeks to learn representations that only encode an object, isolated from other objects or background cues in a scene. This approach underpins various aims, including out-of-distribution (OOD) generalization, sample-efficient composition, and modeling of structured environments. Most research has focused on developing unsupervised mechanisms that separate objects into discrete slots in the representation space, evaluated using unsupervised object discovery. However, with recent sample-efficient segmentation models, we can separate objects in the pixel space and encode them independently. This achieves remarkable zero-shot performance on OOD object discovery benchmarks, is scalable to foundation models, and can handle a variable number of slots out-of-the-box. Hence, the goal of OCL methods to obtain object-centric representations has been largely achieved. Despite this progress, a key question remains: How does the ability to separate objects within a scene contribute to broader OCL objectives, such as OOD generalization? We address this by investigating the OOD generalization challenge caused by spurious background cues through the lens of OCL. We propose a novel, training-free probe called Object-Centric Classification with Applied Masks (OCCAM), demonstrating that segmentation-based encoding of individual objects significantly outperforms slot-based OCL methods. However, challenges in real-world applications remain. We provide the toolbox for the OCL community to use scalable object-centric representations, and focus on practical applications and fundamental questions, such as understanding object perception in human cognition. Our code is available here: this https URL.
]]></description>
<dc:subject>image-processing image-segmentation machine-learning rather-interesting algorithms neural-networks image-analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:090aa6203061/</dc:identifier>
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<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"/>
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<item rdf:about="https://arxiv.org/abs/2206.07391">
    <title>[2206.07391] &quot;Why Here and Not There?&quot; -- Diverse Contrasting Explanations of Dimensionality Reduction</title>
    <dc:date>2026-05-24T12:09:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.07391</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based systems like classifiers and recommender systems. However, transparency of dimensionality reduction and other data mining tools have not been considered in much depth yet, still it is crucial to understand their behavior -- in particular practitioners might want to understand why a specific sample got mapped to a specific location.
In order to (locally) understand the behavior of a given dimensionality reduction method, we introduce the abstract concept of contrasting explanations for dimensionality reduction, and apply a realization of this concept to the specific application of explaining two dimensional data visualization.
]]></description>
<dc:subject>explanation rather-interesting machine-learning dimension-reduction algorithms performance-measure to-write-about to-do</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:50665668209e/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2302.06457">
    <title>[2302.06457] A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithms</title>
    <dc:date>2026-05-24T12:06:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2302.06457</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The transistor celebrated its 75th birthday in 2022. The continued scaling of the transistor defined by Moore's Law continues, albeit at a slower pace. Meanwhile, computing demands and energy consumption required by modern artificial intelligence (AI) algorithms have skyrocketed. As an alternative to scaling transistors for general-purpose computing, the integration of transistors with unconventional technologies has emerged as a promising path for domain-specific computing. In this article, we provide a full-stack review of probabilistic computing with p-bits as a representative example of the energy-efficient and domain-specific computing movement. We argue that p-bits could be used to build energy-efficient probabilistic systems, tailored for probabilistic algorithms and applications. From hardware, architecture, and algorithmic perspectives, we outline the main applications of probabilistic computers ranging from probabilistic machine learning and AI to combinatorial optimization and quantum simulation. Combining emerging nanodevices with the existing CMOS ecosystem will lead to probabilistic computers with orders of magnitude improvements in energy efficiency and probabilistic sampling, potentially unlocking previously unexplored regimes for powerful probabilistic algorithms.
]]></description>
<dc:subject>probability-theory probabilistic-computing algorithms rather-interesting machine-learning engineering-design approximation to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:77469b3f11a6/</dc:identifier>
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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>
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<item rdf:about="https://arxiv.org/abs/2203.01628">
    <title>[2203.01628] Early Time-Series Classification Algorithms: An Empirical Comparison</title>
    <dc:date>2026-02-20T15:25:10+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.01628</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Early Time-Series Classification (ETSC) is the task of predicting the class of incoming time-series by observing as few measurements as possible. Such methods can be employed to obtain classification forecasts in many time-critical applications. However, available techniques are not equally suitable for every problem, since differentiations in the data characteristics can impact algorithm performance in terms of earliness, accuracy, F1-score, and training time. We evaluate six existing ETSC algorithms on publicly available data, as well as on two newly introduced datasets originating from the life sciences and maritime domains. Our goal is to provide a framework for the evaluation and comparison of ETSC algorithms and to obtain intuition on how such approaches perform on real-life applications. The presented framework may also serve as a benchmark for new related techniques.
]]></description>
<dc:subject>time-series classification machine-learning algorithms rather-interesting to-understand benchmarking</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f60942d80779/</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:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<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:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarking"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2405.08532">
    <title>[2405.08532] A dynamical view of Tijdeman's solution of the chairman assignment problem</title>
    <dc:date>2026-02-20T13:53:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2405.08532</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In 1980, R. Tijdeman provided an on-line algorithm that generates sequences over a finite alphabet with minimal discrepancy, that is, such that the occurrence of each letter optimally tracks its frequency. In this article, we define discrete dynamical systems generating these sequences. The dynamical systems are defined as exchanges of polytopal pieces, yielding cut and project schemes, and they code tilings of the line whose sets of vertices form model sets. We prove that these sequences of low discrepancy are natural codings of toral translations with respect to polytopal atoms, and that they generate a minimal and uniquely ergodic subshift with purely discrete spectrum. Finally, we show that the factor complexity of these sequences is of polynomial growth order nd−1, where d is the cardinality of the alphabet.
]]></description>
<dc:subject>discrepancy permutations combinatorics symbolic-dynamics to-understand to-simulate consider:higher-order-substrings algorithms probability-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:37b92b01207d/</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:permutations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-dynamics"/>
	<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:higher-order-substrings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
</rdf:Bag></taxo:topics>
</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"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2512.23146">
    <title>[2512.23146] A Network of Biologically Inspired Rectified Spectral Units (ReSUs) Learns Hierarchical Features Without Error Backpropagation</title>
    <dc:date>2026-01-18T21:15:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2512.23146</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce a biologically inspired, multilayer neural architecture composed of Rectified Spectral Units (ReSUs). Each ReSU projects a recent window of its input history onto a canonical direction obtained via canonical correlation analysis (CCA) of previously observed past-future input pairs, and then rectifies either its positive or negative component. By encoding canonical directions in synaptic weights and temporal filters, ReSUs implement a local, self-supervised algorithm for progressively constructing increasingly complex features.
To evaluate both computational power and biological fidelity, we trained a two-layer ReSU network in a self-supervised regime on translating natural scenes. First-layer units, each driven by a single pixel, developed temporal filters resembling those of Drosophila post-photoreceptor neurons (L1/L2 and L3), including their empirically observed adaptation to signal-to-noise ratio (SNR). Second-layer units, which pooled spatially over the first layer, became direction-selective -- analogous to T4 motion-detecting cells -- with learned synaptic weight patterns approximating those derived from connectomic reconstructions.
Together, these results suggest that ReSUs offer (i) a principled framework for modeling sensory circuits and (ii) a biologically grounded, backpropagation-free paradigm for constructing deep self-supervised neural networks.
]]></description>
<dc:subject>machine-learning algorithms neural-networks representation rather-interesting nonlinear-dynamics collective-behavior to-understand consider:parameter-fitting consider:structure-learning biologically-inspired</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:85f0f61be13d/</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:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<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:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:collective-behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:parameter-fitting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:structure-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:biologically-inspired"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1109.5635">
    <title>[1109.5635] Approximating Edit Distance in Near-Linear Time</title>
    <dc:date>2025-12-31T18:17:15+00:00</dc:date>
    <link>https://arxiv.org/abs/1109.5635</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show how to compute the edit distance between two strings of length n up to a factor of 2^{Õ(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n^(1/3+o(1)) approximation. Previously, approximation of 2^{Õ(sqrt(log n))} was known only for embedding edit distance into l_1, and it is not known if that embedding can be computed in less than quadratic time.
]]></description>
<dc:subject>strings edit-distance algorithms computational-complexity rather-interesting to-understand follow-cites</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7479f24f2b7a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:follow-cites"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.07678">
    <title>[2005.07678] Edit Distance in Near-Linear Time: it's a Constant Factor</title>
    <dc:date>2025-12-31T17:56:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.07678</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present an algorithm for approximating the edit distance between two strings of length n in time n1+ε up to a constant factor, for any ε>0. Our result completes a research direction set forth in the recent breakthrough paper [Chakraborty-Das-Goldenberg-Koucky-Saks, FOCS'18], which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time. The recent results of [Koucky-Saks, STOC'20] and [Brakensiek-Rubinstein, STOC'20] have shown near-linear time algorithms that obtain an additive approximation, near-linear in n (equivalently, constant-factor approximation when the edit distance value is close to n). In contrast, our algorithm obtains a constant-factor approximation in near-linear time for any input strings.
In contrast to prior algorithms, which are mostly recursing over smaller substrings, our algorithm gradually smoothes out the local contribution to the edit distance over progressively larger substrings. To accomplish this, we iteratively construct a distance oracle data structure for the metric of edit distance on all substrings of input strings, of length niε for i=0,1,…,1/ε. The distance oracle approximates the edit distance over these substrings in a certain average sense, just enough to estimate the overall edit distance.
]]></description>
<dc:subject>strings computational-complexity algorithms rather-interesting approximation to-write-about to-implement consider:Push-code</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:71df08420968/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<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:approximation"/>
	<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:consider:Push-code"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2508.15078">
    <title>[2508.15078] Integer continued fractions for complex numbers</title>
    <dc:date>2025-11-01T20:45:33+00:00</dc:date>
    <link>https://arxiv.org/abs/2508.15078</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation.
]]></description>
<dc:subject>number-theory continued-fractions representation algorithms to-understand to-write-about consider:computational-complexity consider:translations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:958abf10d5f0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<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:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:translations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.10300">
    <title>[2402.10300] Early Warning Signals for Bifurcations Embedded in High Dimensions</title>
    <dc:date>2025-10-29T22:00:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.10300</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can play out on a manifold embedded in a much higher dimensional state space. In many cases of practical relevance, the form of this embedding is poorly understood or entirely unknown. This paper explores how measurement of the critical phenomena that generically precede such bifurcations can be used to make inferences about the properties of their embeddings, and, conversely, how prior knowledge about the mechanism of bifurcation can robustify predictions of an oncoming tipping event. These modes of analysis are first demonstrated on a simple fluid flow system undergoing a Hopf bifurcation. The same approach is then applied to data associated with the West African monsoon shift, with results corroborated by existing models of the same system. This example highlights the effectiveness of the methodology even when applied to complex climate data, and demonstrates how a well-resolved spatial structure associated with the onset of atmospheric instability can be inferred purely from time series measurements.
]]></description>
<dc:subject>nonlinear-dynamics anomaly-detection time-series rather-interesting dimension-reduction to-understand to-simulate algorithms feature-extraction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fe04d093d18b/</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:anomaly-detection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:time-series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dimension-reduction"/>
	<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:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2501.10003">
    <title>[2501.10003] Triangular and dice quasicrystals modulated by generic 1D aperiodic sequences</title>
    <dc:date>2025-08-21T17:20:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2501.10003</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a method for generating hexagonal aperiodic tilings that are topologically equivalent to the triangular and dice lattices. This approach incorporates aperiodic sequences into the spacing between three sets of grids for the triangular lattice, resulting in "modulated triangular lattices". Subsequently, by replacing the triangles with rhombuses, parallelograms, or hexagons, modulated dice or honeycomb lattices are constructed. Using generalized Fibonacci, Thue-Morse, and tribonacci sequences, we demonstrate several examples of hexagonal aperiodic tilings. Structural analysis confirms that their diffraction patterns reflect the properties of the one-dimensional aperiodic sequences, namely pure point (Bragg peaks) or singular continuous. Our method establishes a general framework for constructing a broad range of hexagonal aperiodic systems, advancing aperiodic-crystal research into higher dimensions that were previously focused on one-dimensional aperiodic sequences.
]]></description>
<dc:subject>tiling aperiodic-tiling purdy-pitchers plane-geometry algorithms rewriting-systems rather-interesting to-write-about to-simulate consider:other-symbolic-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4d68065a72b6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:purdy-pitchers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<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:consider:other-symbolic-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2408.14405">
    <title>[2408.14405] Topographs for binary quadratic forms and class numbers</title>
    <dc:date>2025-08-17T12:31:21+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.14405</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this work we study, in greater detail than before, J.H. Conway's topographs for integral binary quadratic forms. These are trees in the plane with regions labeled by integers following a simple pattern. Each topograph can display the values of a single form, or represent an equivalence class of forms. We give a new treatment of reduction of forms to canonical equivalence class representatives by employing topographs and a novel continued fraction for complex numbers. This allows uniform reduction for any positive, negative, square or non-square discriminant. Topograph geometry also provides new class number formulas, and short proofs of results of Gauss relating to sums of three squares. Generalizations of the series of Hurwitz for class numbers give evaluations of certain infinite series, summed over the regions or edges of a topograph.
]]></description>
<dc:subject>number-theory John-Conway algorithms representation to-write-about to-understand visualization Diophantine-equations rather-interesting news-to-me</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:16008a1ed811/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:John-Conway"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Diophantine-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:news-to-me"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.aimspress.com/article/doi/10.3934/math.2025696">
    <title>New approach of factoring the RSA cryptosystem</title>
    <dc:date>2025-07-14T15:37:07+00:00</dc:date>
    <link>https://www.aimspress.com/article/doi/10.3934/math.2025696</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The invention of the Rivest–Shamir–Adleman (RSA) cryptosystem was a groundbreaking advancement in cryptography. While the RSA remains relevant in securing global communications and digital transactions, with widespread use in public parameter infrastructure (PKI) and secure online exchanges, its vulnerability to algebraic attacks must be addressed. In this paper, we propose an equation, thereby revealing its potential application in the factorization of the modulus . By introducing this equation, we demonstrate a method in the first attack named the continued fraction for recovering the primes  and  without necessitating the original  used in the RSA encryption. The results were extended to the case where a condition exists such that multiple sets of public parameters were used against a constant private parameter. We retrieved the primes  and  of the moduli  via the lattice reduction technique. This breakthrough could potentially expose the prime factors while circumventing standard cryptographic barriers. Our findings open new possibilities for cryptographic analysis and challenge the presumed security of widely used RSA systems.
]]></description>
<dc:subject>cryptography number-theory continued-fractions hey-is-this-bad-it-seems-bad algorithms rather-interesting to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:37981ef60706/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cryptography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hey-is-this-bad-it-seems-bad"/>
	<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:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://vadim.sdsu.edu/cf21.pdf">
    <title>Continued Fractions in the 21st Century [PDF]</title>
    <dc:date>2025-07-14T15:33:00+00:00</dc:date>
    <link>https://vadim.sdsu.edu/cf21.pdf</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Abstract. We present useful (though largely not original) continued fraction tools, that deserve
to be more widely known to a broad mathematical audience]]></description>
<dc:subject>mathematics continued-fractions number-theory algorithms rather-interesting review representation to-write-about to-simulate consider:general-CFs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b45d19fc41b4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<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:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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:general-CFs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/doi/10.1073/pnas.0710743106">
    <title>Efficient computation of optimal actions | PNAS</title>
    <dc:date>2025-05-27T22:44:00+00:00</dc:date>
    <link>https://www.pnas.org/doi/10.1073/pnas.0710743106</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress—as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.]]></description>
<dc:subject>machine-learning approximation algorithms rather-interesting computational-complexity to-understand mathematical-programming metaheuristics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d4e94025ab87/</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:approximation"/>
	<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:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2210.02580">
    <title>[2210.02580] Functional Labeled Optimal Partitioning</title>
    <dc:date>2025-04-17T14:14:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.02580</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Peak detection is a problem in sequential data analysis that involves differentiating regions with higher counts (peaks) from regions with lower counts (background noise).
It is crucial to correctly predict areas that deviate from the background noise, in both the train and test sets of labels.
Dynamic programming changepoint algorithms have been proposed to solve the peak detection problem by constraining the mean to alternatively increase and then decrease.
The current constrained changepoint algorithms only create predictions on the test set, while completely ignoring the train set.
Changepoint algorithms that are both accurate when fitting the train set, and make predictions on the test set, have been proposed but not in the context of peak detection models.
We propose to resolve these issues by creating a new dynamic programming algorithm, FLOPART, that has zero train label errors, and is able to provide highly accurate predictions on the test set.
We provide an empirical analysis that shows FLOPART has a similar time complexity while being more accurate than the existing algorithms in terms of train and test label errors.
]]></description>
<dc:subject>machine-learning time-series algorithms rather-interesting data-analysis to-understand to-write-about consider:data-labeling consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:96c4dc95518d/</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:time-series"/>
	<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:data-analysis"/>
	<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:data-labeling"/>
	<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/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/2411.12304">
    <title>[2411.12304] Emergence of Implicit World Models from Mortal Agents</title>
    <dc:date>2024-12-21T16:31:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2411.12304</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We discuss the possibility of world models and active exploration as emergent properties of open-ended behavior optimization in autonomous agents. In discussing the source of the open-endedness of living things, we start from the perspective of biological systems as understood by the mechanistic approach of theoretical biology and artificial life. From this perspective, we discuss the potential of homeostasis in particular as an open-ended objective for autonomous agents and as a general, integrative extrinsic motivation. We then discuss the possibility of implicitly acquiring a world model and active exploration through the internal dynamics of a network, and a hypothetical architecture for this, by combining meta-reinforcement learning, which assumes domain adaptation as a system that achieves robust homeostasis.
]]></description>
<dc:subject>autopoiesis open-ended-evolution artificial-life machine-learning algorithms to-read to-understand philosophy-of-engineering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:24353b147828/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:autopoiesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-ended-evolution"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:artificial-life"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<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:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.04320">
    <title>[2212.04320] A 65nm 8b-Activation 8b-Weight SRAM-Based Charge-Domain Computing-in-Memory Macro Using A Fully-Parallel Analog Adder Network and A Single-ADC Interface</title>
    <dc:date>2024-11-01T19:14:15+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.04320</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Performing data-intensive tasks in the von Neumann architecture is challenging to achieve both high performance and power efficiency due to the memory wall bottleneck. Computing-in-memory (CiM) is a promising mitigation approach by enabling parallel in-situ multiply-accumulate (MAC) operations within the memory with support from the peripheral interface and datapath. SRAM-based charge-domain CiM (CD-CiM) has shown its potential of enhanced power efficiency and computing accuracy. However, existing SRAM-based CD-CiM faces scaling challenges to meet the throughput requirement of high-performance multi-bit-quantization applications. This paper presents an SRAM-based high-throughput ReLU-optimized CD-CiM macro. It is capable of completing MAC and ReLU of two signed 8b vectors in one CiM cycle with only one A/D conversion. Along with non-linearity compensation for the analog computing and A/D conversion interfaces, this work achieves 51.2GOPS throughput and 10.3TOPS/W energy efficiency, while showing 88.6% accuracy in the CIFAR-10 dataset.
]]></description>
<dc:subject>algorithms computer-science architecture to-understand unconventional-computing acceleration computational-complexity consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c7c2b27eeb14/</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:computer-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:architecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unconventional-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:acceleration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<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/2102.05747">
    <title>[2102.05747] A better lower bound for Lower-Left Anchored Rectangle Packing</title>
    <dc:date>2024-10-28T12:43:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.05747</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given any set of points S in the unit square that contains the origin, does a set of axis aligned rectangles, one for each point in S, exist, such that each of them has a point in S as its lower-left corner, they are pairwise interior disjoint, and the total area that they cover is at least 1/2? This question is also known as Freedman's conjecture (conjecturing that such a set of rectangles does exist) and has been open since Allen Freedman posed it in 1969. In this paper, we improve the best known lower bound on the total area that can be covered from 0.09121 to 0.1039. Although this step is small, we introduce new insights that push the limits of this analysis.
Our lower bound uses a greedy algorithm with a particular order of the points in S. Therefore, it also implies that this greedy algorithm achieves an approximation ratio of 0.1039. We complement the result with an upper bound of 3/4 on the approximation ratio for a natural class of greedy algorithms that includes the one that achieves the lower bound.
]]></description>
<dc:subject>packing optimization game-theory computational-geometry rather-interesting algorithms to-write-about to-simulate consider:representation consider:ontology</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b2baa5a97f98/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<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-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:ontology"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.01537">
    <title>[2102.01537] Efficient algorithms for the dense packing of congruent circles inside a square</title>
    <dc:date>2024-10-27T23:35:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.01537</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the square container. The search for these configurations is carried out with the help of two algorithms that we have devised: a first algorithm is in charge of obtaining sufficiently dense configurations starting from a random guess, while a second algorithm improves the configurations obtained in the first stage. The algorithms can be used sequentially or independently. The performance of these algorithms is assessed by carrying out numerical tests for configurations with a large number of circles.
]]></description>
<dc:subject>packing computational-geometry algorithms optimization rather-interesting horse-races heuristics to-write-about to-simulate consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:26eb87824a61/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<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:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<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:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.14614">
    <title>[2203.14614] Sublinear-Time Probabilistic Cellular Automata</title>
    <dc:date>2024-10-13T22:09:17+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.14614</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose and investigate a probabilistic model of sublinear-time one-dimensional cellular automata. In particular, we modify the model of ACA (which are cellular automata that accept if and only if all cells simultaneously accept) so that every cell changes its state not only dependent on the states it sees in its neighborhood but also on an unbiased coin toss of its own. The resulting model is dubbed probabilistic ACA (PACA). We consider one- and two-sided error versions of the model (in the same spirit as the classes 𝖱𝖯 and 𝖡𝖯𝖯) and establish a separation between the classes of languages they can recognize all the way up to o(n‾√) time. As a consequence, we have a Ω(n‾√) lower bound for derandomizing constant-time two-sided error PACAs (using deterministic ACAs). We also prove that derandomization of T(n)-time PACAs (to polynomial-time deterministic cellular automata) for various regimes of T(n)=ω(logn) implies non-trivial derandomization results for the class 𝖱𝖯 (e.g., 𝖯=𝖱𝖯). The main contribution is an almost full characterization of the constant-time PACA classes: For one-sided error, the class equals that of the deterministic model; that is, constant-time one-sided error PACAs can be fully derandomized with only a constant multiplicative overhead in time complexity. As for two-sided error, we identify a natural class we call the linearly testable languages (𝖫𝖫𝖳) and prove that the languages decidable by constant-time two-sided error PACAs are "sandwiched" in-between the closure of 𝖫𝖫𝖳 under union and intersection and the class of locally threshold testable languages (𝖫𝖳𝖳).
]]></description>
<dc:subject>distributed-processing asynchronous-behavior collective-behavior cellular-automata algorithms rather-interesting approximation to-write-about to-simulate consider:ACA-as-a-language</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3966cfb54e9d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:asynchronous-behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:collective-behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<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:approximation"/>
	<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:ACA-as-a-language"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2408.12657">
    <title>[2408.12657] Ten Problems in Geobotics</title>
    <dc:date>2024-10-08T19:27:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.12657</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Robots sense, move and act in the physical world. It is therefore natural that algorithmic problems in robotics and automation have a geometric component, often central to the problem. Below we review ten challenging problems at the intersection of robotics and computational geometry -- let's call this intersection Geobotics. What is common to most of these problems is that the prevalent algorithmic techniques used in robotics do not seem suitable for solving them, or at least do not suggest quality guarantees for the solution. Solving some of them, even partially, can shed light on less well-understood aspects of computation in robotics.
]]></description>
<dc:subject>computational-geometry open-problems rather-interesting benchmarks to-write-about nudge-targets consider:performance-measures algorithms</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fd935a12b16b/</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:open-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2210.14132">
    <title>[2210.14132] p-adic Cellular Neural Networks: Applications to Image Processing</title>
    <dc:date>2024-09-28T15:43:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.14132</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The p-adic cellular neural networks (CNNs) are mathematical generalizations of the neural networks introduced by Chua and Yang in the 80s. In this work we present two new types of CNNs that can perform computations with real data, and whose dynamics can be understood almost completely. The first type of networks are edge detectors for grayscale images. The stationary states of these networks are organized hierarchically in a lattice structure. The dynamics of any of these networks consists of transitions toward some minimal state in the lattice. The second type is a new class of reaction-diffusion networks. We investigate the stability of these networks and show that they can be used as filters to reduce noise, preserving the edges, in grayscale images polluted with additive Gaussian noise. The networks introduced here were found experimentally. They are abstract evolution equations on spaces of real-valued functions defined in the p-adic unit ball for some prime number p. In practical applications the prime p is determined by the size of image, and thus, only small primes are used. We provide several numerical simulations showing how these networks work.
]]></description>
<dc:subject>rather-interesting p-adic-numbers cellular-automata to-understand image-processing approximation algorithms representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:32e459800586/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:p-adic-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<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:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://magicsquare6.net/doku.php?id=magicsquare6">
    <title>magicsquare6 [The number of magic squares of order 6]</title>
    <dc:date>2024-09-21T13:50:22+00:00</dc:date>
    <link>https://magicsquare6.net/doku.php?id=magicsquare6</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The number of magic squares of order six counted up to rotations and reflections

]]></description>
<dc:subject>enumeration cloud-computing looking-to-see algorithms rather-interesting hardware-faults GPU to-write-about consider:classification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:20653753d39c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cloud-computing"/>
	<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:hardware-faults"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:GPU"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:classification"/>
</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://en.wikipedia.org/wiki/FRACTRAN">
    <title>FRACTRAN - Wikipedia</title>
    <dc:date>2024-09-09T15:34:11+00:00</dc:date>
    <link>https://en.wikipedia.org/wiki/FRACTRAN</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input n. The program is run by updating the integer n as follows:

for the first fraction f in the list for which nf is an integer, replace n by nf
repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt.
]]></description>
<dc:subject>number-theory esoteric-languages programming-language nonlinear-dynamics rather-interesting algorithms to-write-about to-simulate consider:looking-to-see consider:other-tasks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:97cb676fb388/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:esoteric-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<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-simulate"/>
	<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:other-tasks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2304.02354">
    <title>[2304.02354] Neural Cellular Automata for Solidification Microstructure Modelling</title>
    <dc:date>2024-08-08T14:04:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.02354</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred growth direction and competitive grain growth, and are up to six orders of magnitude faster than the conventional Cellular Automata (CA). Notably, NCA delivers reliable predictions also outside their training range, which indicates that they learn the physics of the solidification process. While in this study we employ data produced by CA for training, NCA can be trained based on any microstructural simulation data, e.g. from phase-field models.
]]></description>
<dc:subject>materials-science simulation cellular-automata neural-networks to-understand metallurgy rather-interesting collective-behavior algorithms to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:73312bb556c6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metallurgy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:collective-behavior"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.01069">
    <title>[2110.01069] Hinged Truchet tiling fractals</title>
    <dc:date>2024-08-08T13:34:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.01069</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article describes a new method of producing space filling fractal dragon curves based on a hinged tiling procedure. The fractals produced can be generated by a simple L-system. The construction as a hinged tiling has the advantage of automatically implying that the fractiles produced tessellate, and that the Heighway fractal dragon curve, and the other curves constructed by this method, do not cross themselves. This also gives a new limiting procedure to apply to certain Truchet tilings. I include the computation of the fractal dimension of the boundary of one of the curves, and describe an algorithm for computing the sim value of the fractal boundary of these curves. The curves produced are well known. The hinged tiling approach is new, as is the algorithm for computing the sim value.
]]></description>
<dc:subject>tiling fractals rather-interesting mathematical-recreations algorithms symmetry to-simulate to-write-about consider:planning consider:classification rewriting-systems nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4fb85354d7b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fractals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:planning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.02705">
    <title>[2402.02705] Representation Surgery for Multi-Task Model Merging</title>
    <dc:date>2024-08-02T11:26:47+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.02705</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Multi-task learning (MTL) compresses the information from multiple tasks into a unified backbone to improve computational efficiency and generalization. Recent work directly merges multiple independently trained models to perform MTL instead of collecting their raw data for joint training, greatly expanding the application scenarios of MTL. However, by visualizing the representation distribution of existing model merging schemes, we find that the merged model often suffers from the dilemma of representation bias. That is, there is a significant discrepancy in the representation distribution between the merged and individual models, resulting in poor performance of merged MTL. In this paper, we propose a representation surgery solution called "Surgery" to reduce representation bias in the merged model. Specifically, Surgery is a lightweight task-specific module that takes the representation of the merged model as input and attempts to output the biases contained in the representation from the merged model. We then designed an unsupervised optimization objective that updates the Surgery module by minimizing the distance between the merged model's representation and the individual model's representation. Extensive experiments demonstrate significant MTL performance improvements when our Surgery module is applied to state-of-the-art (SOTA) model merging schemes.
]]></description>
<dc:subject>multitask-learning machine-learning rather-interesting generalization algorithms representation to-understand to-simulate consider:functional-models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a37943ea4923/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multitask-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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:functional-models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.05482">
    <title>[2203.05482] Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time</title>
    <dc:date>2024-07-21T15:46:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.05482</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The conventional recipe for maximizing model accuracy is to (1) train multiple models with various hyperparameters and (2) pick the individual model which performs best on a held-out validation set, discarding the remainder. In this paper, we revisit the second step of this procedure in the context of fine-tuning large pre-trained models, where fine-tuned models often appear to lie in a single low error basin. We show that averaging the weights of multiple models fine-tuned with different hyperparameter configurations often improves accuracy and robustness. Unlike a conventional ensemble, we may average many models without incurring any additional inference or memory costs -- we call the results "model soups." When fine-tuning large pre-trained models such as CLIP, ALIGN, and a ViT-G pre-trained on JFT, our soup recipe provides significant improvements over the best model in a hyperparameter sweep on ImageNet. The resulting ViT-G model, which attains 90.94% top-1 accuracy on ImageNet, achieved a new state of the art. Furthermore, we show that the model soup approach extends to multiple image classification and natural language processing tasks, improves out-of-distribution performance, and improves zero-shot performance on new downstream tasks. Finally, we analytically relate the performance similarity of weight-averaging and logit-ensembling to flatness of the loss and confidence of the predictions, and validate this relation empirically. Code is available at this https URL.
]]></description>
<dc:subject>machine-learning collective-behavior rather-interesting algorithms to-understand to-write-about constant-fitting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0e9d3e705931/</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:collective-behavior"/>
	<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-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constant-fitting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2302.01235">
    <title>[2302.01235] Printing Protocol: Physical ZKPs for Decomposition Puzzles</title>
    <dc:date>2024-05-08T14:40:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2302.01235</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Decomposition puzzles are pencil-and-paper logic puzzles that involve partitioning a rectangular grid into several regions to satisfy certain rules. In this paper, we construct a generic card-based protocol called printing protocol, which can be used to physically verify solutions of decompositon puzzles. We apply the printing protocol to develop card-based zero-knowledge proof protocols for two such puzzles: Five Cells and Meadows. These protocols allow a prover to physically show that he/she knows solutions of the puzzles without revealing them.
]]></description>
<dc:subject>algorithms mathematical-recreations proof rather-interesting to-understand formal-languages verification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:dc5bedd9e597/</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:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<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:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:verification"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2312.13988">
    <title>[2312.13988] A unifying theory for metrical results on regular continued fraction convergents and mediants</title>
    <dc:date>2024-04-01T11:50:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2312.13988</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We revisit Ito's \cite{I1989} natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a slight shift in perspective on the order in which these convergents and mediants arise, this natural extension is shown to provide an elegant and powerful tool in the metric theory of continued fractions. A wealth of old and new results -- including limiting distributions of approximation coefficients, analogues of a theorem of Legendre and their refinements, and a generalisation of Lévy's Theorem to subsequences of convergents and mediants -- are presented as corollaries within this unifying theory.
]]></description>
<dc:subject>continued-fractions representation number-theory algorithms rather-interesting to-understand consider:other-criteria consider:evenness consider:randomize-and-recover</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d116664660ef/</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:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<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:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:other-criteria"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:evenness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:randomize-and-recover"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2308.08868">
    <title>[2308.08868] Computing complexity measures of degenerate graphs</title>
    <dc:date>2024-04-01T11:33:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2308.08868</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that the VC-dimension of a graph can be computed in time nlogd+1dO(d), where d is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that see a specific subset of vertices inside of a (small) query set. The construction of this data structure takes time O(d2dn), afterwards queries can be computed efficiently using fast Möbius inversion.
This data structure turns out to be useful for a range of tasks, especially for finding bipartite patterns in degenerate graphs, and we outline an efficient algorithms for counting the number of times specific patterns occur in a graph. The largest factor in the running time of this algorithm is O(nc), where c is a parameter of the pattern we call its left covering number.
Concrete applications of this algorithm include counting the number of (non-induced) bicliques in linear time, the number of co-matchings in quadratic time, as well as a constant-factor approximation of the ladder index in linear time.
Finally, we supplement our theoretical results with several implementations and run experiments on more than 200 real-world datasets -- the largest of which has 8 million edges -- where we obtain interesting insights into the VC-dimension of real-world networks.
]]></description>
<dc:subject>computational-complexity graph-theory algorithms horse-races rather-interesting looking-to-see to-write-about consider:evolved consider:stress-testing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:368bb27f15be/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<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: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:consider:evolved"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:stress-testing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.09982">
    <title>[2104.09982] Explaining the Entombed Algorithm</title>
    <dc:date>2024-03-31T19:21:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.09982</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In \cite{entombed}, John Aycock and Tara Copplestone pose an open question, namely the explanation of the mysterious lookup table used in the Entombed Game's Algorithm for two dimensional maze generation. The question attracted media attention (BBC etc) and was open until today. This paper answers this question, explains the algorithm and even extends it to three dimensions.
]]></description>
<dc:subject>reverse-engineering mysteries-of-code rather-interesting algorithms to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:15b9815e21da/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reverse-engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mysteries-of-code"/>
	<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-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.05551">
    <title>[2203.05551] Cellular automata can classify data by inducing trajectory phase coexistence</title>
    <dc:date>2024-03-31T00:23:34+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.05551</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the number of state changes that occur in a trajectory initiated from the image. When the number of timesteps of the automaton is a trainable parameter, the search scheme identifies automata that generate a population of dynamical trajectories displaying high or low activity, depending on initial conditions. Automata of this nature behave as nonlinear activation functions with an output that is effectively binary, resembling an emergent version of a spiking neuron.
]]></description>
<dc:subject>cellular-automata nonstandard-computation rather-interesting classification algorithms self-organization to-write-about consider:ReQ reservoir-computing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0816afa27d56/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonstandard-computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:self-organization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:ReQ"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reservoir-computing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.07524">
    <title>[2209.07524] $tilde{O}(n+mathrm{poly}(k))$-time Algorithm for Bounded Tree Edit Distance</title>
    <dc:date>2023-10-10T10:10:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.07524</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of dissimilarity between two (unweighted) rooted trees with node labels. Perhaps the most notable recent application of tree edit distance is in NoSQL big databases, such as MongoDB, where each row of the database is a JSON document represented as a labeled rooted tree, and finding dissimilarity between two rows is a basic operation. Until recently, the fastest algorithm for tree edit distance ran in cubic time (Demaine, Mozes, Rossman, Weimann; TALG'10); however, Mao (FOCS'21) broke the cubic barrier for the tree edit distance problem using fast matrix multiplication.
Given a parameter k as an upper bound on the distance, an O(n+k2)-time algorithm for edit distance has been known since the 1980s due to the works of Myers (Algorithmica'86) and Landau and Vishkin (JCSS'88). The existence of an Õ(n+poly(k))-time algorithm for tree edit distance has been posed as an open question, e.g., by Akmal and Jin (ICALP'21), who gave a state-of-the-art Õ(nk2)-time algorithm. In this paper, we answer this question positively.
]]></description>
<dc:subject>distance metrics edit-distance rather-interesting algorithms computational-complexity to-understand to-write-about consider:genetic-programming consider:structure-function</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:266589466b64/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<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:computational-complexity"/>
	<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:structure-function"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.01147">
    <title>[2209.01147] Algorithms for Discrepancy, Matchings, and Approximations: Fast, Simple, and Practical</title>
    <dc:date>2023-10-10T10:04:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.01147</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study one of the key tools in data approximation and optimization: low-discrepancy colorings. Formally, given a finite set system (X,), the \emph{discrepancy} of a two-coloring χ:X→{−1,1} is defined as maxS∈|χ(S)|, where χ(S)=∑x∈Sχ(x).
We propose a randomized algorithm which, for any d>0 and (X,) with dual shatter function π∗(k)=O(kd), returns a coloring with expected discrepancy O(|X|1−1/dlog||‾‾‾‾‾‾‾‾‾‾‾‾‾‾√) (this bound is tight) in time Õ(||⋅|X|1/d+|X|2+1/d), improving upon the previous-best time of O(||⋅|X|3) by at least a factor of |X|2−1/d when ||≥|X|. This setup includes many geometric classes, families of bounded dual VC-dimension, and others. As an immediate consequence, we obtain an improved algorithm to construct ε-approximations of sub-quadratic size.
Our method uses primal-dual reweighing with an improved analysis of randomly updated weights and exploits the structural properties of the set system via matchings with low crossing number -- a fundamental structure in computational geometry. In particular, we get the same |X|2−1/d factor speed-up on the construction time of matchings with crossing number O(|X|1−1/d), which is the first improvement since the 1980s.
The proposed algorithms are very simple, which makes it possible, for the first time, to compute colorings with near-optimal discrepancies and near-optimal sized approximations for abstract and geometric set systems in dimensions higher than 2.
]]></description>
<dc:subject>low-discrepancy-samples sampling approximation algorithms rather-interesting to-understand to-visualize to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2c854195ad31/</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:sampling"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<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/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/2110.14968">
    <title>[2110.14968] DocScanner: Robust Document Image Rectification with Progressive Learning</title>
    <dc:date>2023-09-17T18:35:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.14968</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Compared with flatbed scanners, portable smartphones provide more convenience for physical document digitization. However, such digitized documents are often distorted due to uncontrolled physical deformations, camera positions, and illumination variations. To this end, we present DocScanner, a novel framework for document image rectification. Different from existing solutions, DocScanner addresses this issue by introducing a progressive learning mechanism. Specifically, DocScanner maintains a single estimate of the rectified image, which is progressively corrected with a recurrent architecture. The iterative refinements make DocScanner converge to a robust and superior rectification performance, while the lightweight recurrent architecture ensures the running efficiency. To further improve the rectification quality, based on the geometric priori between the distorted and the rectified images, a geometric regularization is introduced during training to further improve the performance. Extensive experiments are conducted on the Doc3D dataset and the DocUNet Benchmark dataset, and the quantitative and qualitative evaluation results verify the effectiveness of DocScanner, which outperforms previous methods on OCR accuracy, image similarity, and our proposed distortion metric by a considerable margin. Furthermore, our DocScanner shows superior efficiency in runtime latency and model size.
]]></description>
<dc:subject>OCR image-processing algorithms self-organization rather-interesting digitization digital-humanities to-understand to-write-about consider:stitching</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:50e950233055/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:OCR"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:self-organization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:digitization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:digital-humanities"/>
	<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:stitching"/>
</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/2210.02292">
    <title>[2210.02292] Double-Ended Palindromic Trees: A Linear-Time Data Structure and Its Applications</title>
    <dc:date>2023-09-09T13:40:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.02292</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The palindromic tree (a.k.a. eertree) is a linear-size data structure that provides access to all palindromic substrings of a string. In this paper, we propose a generalized version of eertree, called double-ended eertree, which supports linear-time online double-ended queue operations on the stored string. At the heart of our construction, is a class of substrings, called surfaces, of independent interest. Namely, surfaces are neither prefixes nor suffixes of any other palindromic substrings and characterize the link structure of all palindromic substrings in the eertree. 
As an application, we develop a framework for range queries involving palindromes on strings, including counting distinct palindromic substrings, and finding the longest palindromic substring, shortest unique palindromic substring and shortest absent palindrome of any substring. In particular, offline queries only use linear space. Apart from range queries, we enumerate palindromic rich strings with a given word in linear time on the length of the given word.
]]></description>
<dc:subject>strings palindromes algorithms computational-complexity data-structures rather-interesting to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fa87703719d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:palindromes"/>
	<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:data-structures"/>
	<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: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/2302.13943">
    <title>[2302.13943] Generator Matrices by Solving Integer Linear Programs</title>
    <dc:date>2023-09-09T12:55:18+00:00</dc:date>
    <link>https://arxiv.org/abs/2302.13943</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In particular, it is challenging to take advantage of the intrinsic structure of a given numerical problem to design samplers of low discrepancy in certain subsets of dimensions. To address this issue, we devise a greedy algorithm allowing us to translate desired net properties into linear constraints on the generator matrix entries. Solving the resulting integer linear program yields generator matrices that satisfy the desired net properties. We demonstrate that our method finds generator matrices in challenging settings, offering low discrepancy sequences beyond the limitations of classic constructions.
]]></description>
<dc:subject>optimization mathematical-programming low-discrepancy-sequences quasirandom-numbers algorithms to-understand to-write-about consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0a8b845747b4/</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:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:low-discrepancy-sequences"/>
	<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: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:performance-measures"/>
</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://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://arxiv.org/abs/2304.14395">
    <title>[2304.14395] string2string: A Modern Python Library for String-to-String Algorithms</title>
    <dc:date>2023-05-16T11:01:30+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.14395</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce string2string, an open-source library that offers a comprehensive suite of efficient algorithms for a broad range of string-to-string problems. It includes traditional algorithmic solutions as well as recent advanced neural approaches to tackle various problems in string alignment, distance measurement, lexical and semantic search, and similarity analysis -- along with several helpful visualization tools and metrics to facilitate the interpretation and analysis of these methods. Notable algorithms featured in the library include the Smith-Waterman algorithm for pairwise local alignment, the Hirschberg algorithm for global alignment, the Wagner-Fisher algorithm for edit distance, BARTScore and BERTScore for similarity analysis, the Knuth-Morris-Pratt algorithm for lexical search, and Faiss for semantic search. Besides, it wraps existing efficient and widely-used implementations of certain frameworks and metrics, such as sacreBLEU and ROUGE, whenever it is appropriate and suitable. Overall, the library aims to provide extensive coverage and increased flexibility in comparison to existing libraries for strings. It can be used for many downstream applications, tasks, and problems in natural-language processing, bioinformatics, and computational social sciences. It is implemented in Python, easily installable via pip, and accessible through a simple API. Source code, documentation, and tutorials are all available on our GitHub page: this https URL.
]]></description>
<dc:subject>strings algorithms library rather-interesting python to-try consider:trees</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:92f9faee842c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:python"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-try"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:trees"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.13202">
    <title>[2205.13202] More Recent Advances in (Hyper)Graph Partitioning</title>
    <dc:date>2023-04-12T13:06:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.13202</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic. In particular, the survey extends the previous survey by also covering hypergraph partitioning and streaming algorithms, and has an additional focus on parallel algorithms.
]]></description>
<dc:subject>hypergraphs graph-theory algorithms computational-complexity rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aa408bec37d3/</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:graph-theory"/>
	<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:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.01794">
    <title>[2203.01794] Efficient Fréchet distance queries for segments</title>
    <dc:date>2023-01-01T13:09:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.01794</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the problem of constructing a data structure that can store a two-dimensional polygonal curve P, such that for any query segment ab⎯⎯⎯⎯⎯⎯ one can efficiently compute the Fréchet distance between P and ab⎯⎯⎯⎯⎯⎯. First we present a data structure of size O(nlogn) that can compute the Fréchet distance between P and a horizontal query segment ab⎯⎯⎯⎯⎯⎯ in O(logn) time, where n is the number of vertices of P. In comparison to prior work, this significantly reduces the required space. We extend the type of queries allowed, as we allow a query to be a horizontal segment ab⎯⎯⎯⎯⎯⎯ together with two points s,t∈P (not necessarily vertices), and ask for the Fréchet distance between ab⎯⎯⎯⎯⎯⎯ and the curve of P in between s and t. Using O(nlog2n) storage, such queries take O(log3n) time, simplifying and significantly improving previous results. We then generalize our results to query segments of arbitrary orientation. We present an O(nk3+ε+n2) size data structure, where k∈[1..n] is a parameter the user can choose, and ε>0 is an arbitrarily small constant, such that given any segment ab⎯⎯⎯⎯⎯⎯ and two points s,t∈P we can compute the Fréchet distance between ab⎯⎯⎯⎯⎯⎯ and the curve of P in between s and t in O((n/k)log2n+log4n) time. This is the first result that allows efficient exact Fréchet distance queries for arbitrarily oriented segments. 
We also present two applications of our data structure: we show that we can compute a local δ-simplification (with respect to the Fréchet distance) of a polygonal curve in O(n5/2+ε) time, and that we can efficiently find a translation of an arbitrary query segment ab⎯⎯⎯⎯⎯⎯ that minimizes the Fréchet distance with respect to a subcurve of P.
]]></description>
<dc:subject>computational-geometry computational-complexity algorithms distance preprocessing approximation rather-interesting to-simulate to-write-about consider:oracles</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5471ba660ae6/</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:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:preprocessing"/>
	<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-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:oracles"/>
</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/2005.01988">
    <title>[2005.01988] One-step regression and classification with crosspoint resistive memory arrays</title>
    <dc:date>2022-05-14T10:35:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.01988</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Machine learning has been getting a large attention in the recent years, as a tool to process big data generated by ubiquitous sensors in our daily life. High speed, low energy computing machines are in demand to enable real-time artificial intelligence at the edge, i.e., without the support of a remote frame server in the cloud. Such requirements challenge the complementary metal-oxide-semiconductor (CMOS) technology, which is limited by the Moore's law approaching its end and the communication bottleneck in conventional computing architecture. Novel computing concepts, architectures and devices are thus strongly needed to accelerate data-intensive applications. Here we show a crosspoint resistive memory circuit with feedback configuration can execute linear regression and logistic regression in just one step by computing the pseudoinverse matrix of the data within the memory. The most elementary learning operation, that is the regression of a sequence of data and the classification of a set of data, can thus be executed in one single computational step by the novel technology. One-step learning is further supported by simulations of the prediction of the cost of a house in Boston and the training of a 2-layer neural network for MNIST digit recognition. The results are all obtained in one computational step, thanks to the physical, parallel, and analog computing within the crosspoint array.
]]></description>
<dc:subject>analog-computing rather-interesting to-understand algorithms engineering-design hardware nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:21f1656dd658/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:analog-computing"/>
	<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:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hardware"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.00110">
    <title>[2107.00110] Classical Planning in Deep Latent Space</title>
    <dc:date>2022-04-19T10:24:46+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.00110</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose Latplan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), Latplan learns a complete propositional PDDL action model of the environment. Later, when a pair of images representing the initial and the goal states (planning inputs) is given, Latplan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. We evaluate Latplan using image-based versions of 6 planning domains: 8-puzzle, 15-Puzzle, Blocksworld, Sokoban and Two variations of LightsOut.
]]></description>
<dc:subject>machine-learning artificial-intelligence planning operations-research rather-interesting algorithms looking-to-see benchmarking</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:bcc7415665a8/</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:artificial-intelligence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:planning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<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:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarking"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.07411">
    <title>[2203.07411] On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel</title>
    <dc:date>2022-03-16T13:58:10+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.07411</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Deep Gaussian Process as a Bayesian learning model is promising because it is expressive and capable of uncertainty estimation. With Bochner's theorem, we can view the deep Gaussian process with squared exponential kernels as a deep trigonometric network consisting of the random feature layers, sine and cosine activation units, and random weight layers. Focusing on this particular class of models allows us to obtain analytical results. We shall show that the weight space view yields the same effective covariance functions which were obtained previously in function space. The heavy statistical tails can be studied with multivariate characteristic function. In addition, the trig networks are flexible and expressive as one can freely adopt different prior distributions over the parameters in weight and feature layers. Lastly, the deep trigonometric network representation of deep Gaussian process allows the derivation of its neural tangent kernel, which can reveal the mean of predictive distribution from the intractable inference.
]]></description>
<dc:subject>hey-I-know-this-guy machine-learning algorithms representation to-understand Bayesian-learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2abb0ed13763/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hey-I-know-this-guy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Bayesian-learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.02990">
    <title>[1709.02990] Large monochromatic components and long monochromatic cycles in random hypergraphs</title>
    <dc:date>2022-03-15T15:51:26+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.02990</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We extend results of Gyárfás and Füredi on the largest monochromatic component in r-colored complete k-uniform hypergraphs to the setting of random hypergraphs. We also study long monochromatic loose cycles in r-colored random hypergraphs. In particular, we obtain a random analog of a result of Gyárfás, Sárközy, and Szemerédi on the longest monochromatic loose cycle in 2-colored complete k-uniform hypergraphs.
]]></description>
<dc:subject>hypergraphs graph-theory algorithms graph-coloring computational-complexity to-understand to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c45ed0ef1df5/</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:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-coloring"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<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:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2201.04888">
    <title>[2201.04888] Generating graphs randomly</title>
    <dc:date>2022-03-12T13:08:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2201.04888</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which are similar in some way. One way to do this is to take a sample of several random graphs from the family, to gather information about what is "typical". Hence there is a need for algorithms which can generate graphs uniformly (or approximately uniformly) at random from the given family. Since a large sample may be required, the algorithm should also be computationally efficient. 
Rigorous analysis of such algorithms is often challenging, involving both combinatorial and probabilistic arguments. We will focus mainly on the set of all simple graphs with a particular degree sequence, and describe several different algorithms for sampling graphs from this family uniformly, or almost uniformly.
]]></description>
<dc:subject>review graph-theory random-graphs rather-interesting algorithms combinatorics sampling to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:10e6ca326168/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-graphs"/>
	<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:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<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"/>
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</item>
<item rdf:about="https://arxiv.org/abs/1904.04513">
    <title>[1904.04513] Towards a complete perspective on labeled tree indexing: new size bounds, efficient constructions, and beyond</title>
    <dc:date>2022-03-04T11:27:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.04513</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A labeled tree (or a trie) is a natural generalization of a string, which can also be seen as a compact representation of a set of strings. This paper considers the labeled tree indexing problem, and provides a number of new results on space bound analysis, and on algorithms for efficient construction and pattern matching queries. Kosaraju [FOCS 1989] was the first to consider the labeled tree indexing problem, and he proposed the suffix tree for a backward trie, where the strings in the trie are read in the leaf-to-root direction. In contrast to a backward trie, we call a usual trie as a forward trie. Despite a few follow-up works after Kosaraju's paper, indexing forward/backward tries is not well understood yet. In this paper, we show a full perspective on the sizes of indexing structures such as suffix trees, DAWGs, CDAWGs, suffix arrays, affix trees, affix arrays for forward and backward tries. Some of them take O(n) space in the size n of the input trie, while the others can occupy O(n2) space in the worst case. In particular, we show that the size of the DAWG for a forward trie with n nodes is Ω(σn), where σ is the number of distinct characters in the trie. This becomes Ω(n2) for an alphabet of size σ=Θ(n). Still, we show that there is a compact O(n)-space implicit representation of the DAWG for a forward trie, whose space requirement is independent of the alphabet size. This compact representation allows for simulating each DAWG edge traversal in O(logσ) time, and can be constructed in O(n) time and space over any integer alphabet of size O(n). In addition, this readily extends to the first indexing structure that permits bidirectional pattern searches over a trie within linear space in the input trie size.
]]></description>
<dc:subject>strings data-structures optimization algorithms rather-interesting performance-measure information-theory engineering-design to-write-about to-simulate consider:error</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7cd802a335d2/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:error"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2009.00363">
    <title>[2009.00363] A Benchmark for Multi-UAV Task Assignment of an Extended Team Orienteering Problem</title>
    <dc:date>2022-03-02T11:33:43+00:00</dc:date>
    <link>https://arxiv.org/abs/2009.00363</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A benchmark for multi-UAV task assignment is presented in order to evaluate different algorithms. An extended Team Orienteering Problem is modeled for a kind of multi-UAV task assignment problem. Three intelligent algorithms, i.e., Genetic Algorithm, Ant Colony Optimization and Particle Swarm Optimization are implemented to solve the problem. A series of experiments with different settings are conducted to evaluate three algorithms. The modeled problem and the evaluation results constitute a benchmark, which can be used to evaluate other algorithms used for multi-UAV task assignment problems.
]]></description>
<dc:subject>metaheuristics horse-races algorithms rather-interesting operations-research to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4b5f407f9d68/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<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: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: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/2104.15040">
    <title>[2104.15040] Using Small MUSes to Explain How to Solve Pen and Paper Puzzles</title>
    <dc:date>2022-02-22T12:55:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.15040</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Pen and paper puzzles like Sudoku, Futoshiki and Skyscrapers are hugely popular. Solving such puzzles can be a trivial task for modern AI systems. However, most AI systems solve problems using a form of backtracking, while people try to avoid backtracking as much as possible. This means that existing AI systems do not output explanations about their reasoning that are meaningful to people. We present Demystify, a tool which allows puzzles to be expressed in a high-level constraint programming language and uses MUSes to allow us to produce descriptions of steps in the puzzle solving. We give several improvements to the existing techniques for solving puzzles with MUSes, which allow us to solve a range of significantly more complex puzzles and give higher quality explanations. We demonstrate the effectiveness and generality of Demystify by comparing its results to documented strategies for solving a range of pen and paper puzzles by hand, showing that our technique can find many of the same explanations.
]]></description>
<dc:subject>constraint-satisfaction explainability interpretability algorithms heuristics to-understand to-write-about consider:GP</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5c50bfb48e5c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explainability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:interpretability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<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:consider:GP"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2009.09983">
    <title>[2009.09983] Physical Zero-Knowledge Proof for Ripple Effect</title>
    <dc:date>2022-02-17T11:36:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2009.09983</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Ripple Effect is a logic puzzle where the player has to fill numbers into empty cells in a rectangular grid. The grid is divided into rooms, and each room must contain consecutive integers starting from 1 to its size. Also, if two cells in the same row or column contain the same number x, there must be a space of at least x cells separating the two cells. In this paper, we develop a physical zero-knowledge proof for the Ripple Effect puzzle using a deck of cards, which allows a prover to convince a verifier that he/she knows a solution without revealing it. In particular, given a secret number x and a list of numbers, our protocol can physically verify that x does not appear among the first x numbers in the list without revealing x or any number in the list.
]]></description>
<dc:subject>mathematical-recreations strategy heuristics rather-interesting algorithms constraint-satisfaction to-write-about to-simulate consider:information-spread</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:99b19d1e1d67/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:information-spread"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>