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    <title>[2510.01902] Constrained Adaptive Rejection Sampling</title>
    <dc:date>2026-06-10T17:19:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2510.01902</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Language Models (LMs) are increasingly used in applications where generated outputs must satisfy strict semantic or syntactic constraints. Existing approaches to constrained generation fall along a spectrum: greedy constrained decoding methods enforce validity during decoding but distort the LM's distribution, while rejection sampling (RS) preserves fidelity but wastes computation by discarding invalid outputs. Both extremes are problematic in domains such as program fuzzing, where both validity and diversity of samples are essential. We present Constrained Adaptive Rejection Sampling (CARS), an approach that strictly improves the sample-efficiency of RS without distributional distortion. CARS begins with unconstrained LM sampling and adaptively rules out constraint-violating continuations by recording them in a trie and subtracting their probability mass from future draws. This adaptive pruning ensures that prefixes proven invalid are never revisited, acceptance rates improve monotonically, and the resulting samples exactly follow the constrained distribution. In experiments on a variety of domains -- e.g., program fuzzing and molecular generation -- CARS consistently achieves higher efficiency -- measured in the number of LM forward passes per valid sample -- while also producing stronger sample diversity than both GCD and methods that approximate the LM's distribution.
]]></description>
<dc:subject>software-development-is-not-programming LLMs neural-networks probability-theory constraint-satisfaction rather-interesting hey-I-know-this-guy GPTP2026</dc:subject>
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<item rdf:about="https://arxiv.org/abs/2404.05472">
    <title>[2404.05472] The steady-states of splitter networks</title>
    <dc:date>2026-05-24T12:14:16+00:00</dc:date>
    <link>https://arxiv.org/abs/2404.05472</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce splitter networks, which abstract the behavior of conveyor belts found in the video game Factorio. Based on this definition, we show how to compute the steady-state of a splitter network. Then, leveraging insights from the players community, we provide multiple designs of splitter networks capable of load-balancing among several conveyor belts, and prove that any load-balancing network on n belts must have Ω(nlogn) nodes. Incidentally, we establish connections between splitter networks and various concepts including flow algorithms, flows with equality constraints, Markov chains and the Knuth-Yao theorem about sampling over rational distributions using a fair coin.
]]></description>
<dc:subject>systems-dynamics representation games nonlinear-dynamics rather-interesting probability-theory load-balancing engineering-design to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d54d74c2bdbc/</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/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/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>
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<item rdf:about="https://arxiv.org/abs/1910.09707">
    <title>[1910.09707] A Fresh Look at the &quot;Hot Hand&quot; Paradox</title>
    <dc:date>2026-02-20T11:36:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.09707</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We use the backward Kolmogorov equation approach to understand the apparently paradoxical feature that the mean waiting time to encounter distinct fixed-length sequences of heads and tails upon repeated fair coin flips can be different. For sequences of length 2, the mean time until the sequence HH (heads-heads) appears equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. We give complete results for the waiting times of sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). We also derive the moment generating functions, from which any moment of the mean waiting time for specific sequences can be found. Finally, we compute the mean waiting times T2nH for 2n heads in a row and Tn(HT) for n alternating heads and tails. For large n, T2nH∼3Tn(HT). Thus distinct sequences of coin flips of the same length can have very different mean waiting times.


-- I remember arguing so much and so vociferously with Warren Ewens about this, in the context of DNA segments....
]]></description>
<dc:subject>probability-theory old-arguments paradox rather-interesting enumeration</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a5fdb3a520c8/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2503.07811">
    <title>[2503.07811] A primer on optimal transport for causal inference with observational data</title>
    <dc:date>2025-04-05T22:00:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2503.07811</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection of optimal transport and causal inference is only beginning to develop. Yet, many foundational models in causal inference have implicitly relied on optimal transport principles for decades, without recognizing the underlying connection. Therefore, the goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data -- where optimal transport is not just a set of potential tools, but actually builds the foundation of model assumptions. As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics, by pointing out these existing connections, and to explore novel problems and directions for future work in both areas derived from this realization.
]]></description>
<dc:subject>probability-theory optimal-transport causal-inference inference to-understand via:? modeling machine-learning numerical-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:28573aa6a3a3/</dc:identifier>
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</item>
<item rdf:about="https://arxiv.org/abs/2406.14153">
    <title>[2406.14153] On random classical marginal problems with applications to quantum information theory</title>
    <dc:date>2025-04-05T21:58:13+00:00</dc:date>
    <link>https://arxiv.org/abs/2406.14153</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine's theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell-Wigner scenarios providing rations of volumes between the local and non-signaling polytopes.
]]></description>
<dc:subject>quantum-computing probability-theory to-understand graph-theory looking-to-see estimation marginal-problems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d7576cf56f42/</dc:identifier>
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<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/2206.01276">
    <title>[2206.01276] Columnar order in random packings of $2times2$ squares on the square lattice</title>
    <dc:date>2024-10-28T12:54:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.01276</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study random packings of 2×2 squares with centers on the square lattice ℤ2, in which the probability of a packing is proportional to λ to the number of squares. We prove that for large λ, typical packings exhibit columnar order, in which either the centers of most tiles agree on the parity of their x-coordinate or the centers of most tiles agree on the parity of their y-coordinate. This manifests in the existence of four extremal and periodic Gibbs measures in which the rotational symmetry of the lattice is broken while the translational symmetry is only broken along a single axis. We further quantify the decay of correlations in these measures, obtaining a slow rate of exponential decay in the direction of preserved translational symmetry and a fast rate in the direction of broken translational symmetry. Lastly, we prove that every periodic Gibbs measure is a mixture of these four measures.
Additionally, our proof introduces an apparently novel extension of the chessboard estimate, from finite-volume torus measures to all infinite-volume periodic Gibbs measures.
]]></description>
<dc:subject>packing physics probability-theory combinatorics to-understand representation to-simulate consider:looking-to-see consider:animation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2d5e7b086932/</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:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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:animation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.13944">
    <title>[2207.13944] On the Multidimensional Random Subset Sum Problem</title>
    <dc:date>2024-09-21T13:58:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.13944</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In the Random Subset Sum Problem, given n i.i.d. random variables X1,...,Xn, we wish to approximate any point z∈[−1,1] as the sum of a suitable subset Xi1(z),...,Xis(z) of them, up to error ε. Despite its simple statement, this problem is of fundamental interest to both theoretical computer science and statistical mechanics. More recently, it gained renewed attention for its implications in the theory of Artificial Neural Networks. An obvious multidimensional generalisation of the problem is to consider n i.i.d. d-dimensional random vectors, with the objective of approximating every point z∈[−1,1]d. In 1998, G. S. Lueker showed that, in the one-dimensional setting, n=(log1ε) samples guarantee the approximation property with high this http URL this work, we prove that, in d dimensions, n=(d3log1ε⋅(log1ε+logd)) samples suffice for the approximation property to hold with high probability. As an application highlighting the potential interest of this result, we prove that a recently proposed neural network model exhibits universality: with high probability, the model can approximate any neural network within a polynomial overhead in the number of parameters.
]]></description>
<dc:subject>probability-theory number-theory approximation rather-interesting to-simulate consider:lexicase-selection consider:numerical-modeling consider:quasirandom-numbers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5a4d9bfcab6c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<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:consider:lexicase-selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:numerical-modeling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:quasirandom-numbers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.00751">
    <title>[2212.00751] P(Expression|Grammar): Probability of deriving an algebraic expression with a probabilistic context-free grammar</title>
    <dc:date>2024-09-05T00:57:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.00751</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence classes of strings derived by grammar and address the problem of calculating the probability of deriving a given expression with a given grammar. We show that the problem is undecidable in general. We then present specific grammars for generating linear, polynomial, and rational expressions, where algorithms for calculating the probability of a given expression exist. For those grammars, we design algorithms for calculating the exact probability and efficient approximation with arbitrary precision.
]]></description>
<dc:subject>formal-languages symbolic-regression symbolic-expressions grammar probability-theory enumeration rather-interesting to-write-about to-simulate consider:genetic-programming consider:semantics consider:pragmatics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0506929faddf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-expressions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:grammar"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<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:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:semantics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:pragmatics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2405.17919">
    <title>[2405.17919] Fisher's Legacy of Directional Statistics, and Beyond to Statistics on Manifolds</title>
    <dc:date>2024-07-01T14:19:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2405.17919</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It will not be an exaggeration to say that R A Fisher is the Albert Einstein of Statistics. He pioneered almost all the main branches of statistics, but it is not as well known that he opened the area of Directional Statistics with his 1953 paper introducing a distribution on the sphere which is now known as the Fisher distribution. He stressed that for spherical data one should take into account that the data is on a manifold. We will describe this Fisher distribution and reanalyse his geological data. We also comment on the two goals he set himself in that paper, and how he reinvented the von Mises distribution on the circle. Since then, many extensions of this distribution have appeared bearing Fisher's name such as the von Mises Fisher distribution and the matrix Fisher distribution. In fact, the subject of Directional Statistics has grown tremendously in the last two decades with new applications emerging in Life Sciences, Image Analysis, Machine Learning and so on. We give a recent new method of constructing the Fisher type distribution which has been motivated by some problems in Machine Learning. The subject related to his distribution has evolved since then more broadly as Statistics on Manifolds which also includes the new field of Shape Analysis. We end with a historical note pointing out some correspondence between D'Arcy Thompson and R A Fisher related to Shape Analysis.
]]></description>
<dc:subject>statistics history-of-science directional-statistics probability-theory models-and-modes biography</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:76b988d8705b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:directional-statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:biography"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2210.14707">
    <title>[2210.14707] Is Out-of-Distribution Detection Learnable?</title>
    <dc:date>2023-10-10T10:29:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.14707</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD) detection, where test data may come from classes that are unknown during training (i.e., OOD data). Due to the unavailability and diversity of OOD data, good generalization ability is crucial for effective OOD detection algorithms. To study the generalization of OOD detection, in this paper, we investigate the probably approximately correct (PAC) learning theory of OOD detection, which is proposed by researchers as an open problem. First, we find a necessary condition for the learnability of OOD detection. Then, using this condition, we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating, we find that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation, we next give several necessary and sufficient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly, we also offer theoretical supports for several representative OOD detection works based on our OOD theory.
]]></description>
<dc:subject>machine-learning rather-interesting probability-theory to-write-about to-understand consider:online-learning consider:triggers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a98225133e02/</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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:online-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:triggers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.14440">
    <title>[2209.14440] GeONet: a neural operator for learning the Wasserstein geodesic</title>
    <dc:date>2023-09-30T12:46:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.14440</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Optimal transport (OT) offers a versatile framework to compare complex data distributions in a geometrically meaningful way. Traditional methods for computing the Wasserstein distance and geodesic between probability measures require mesh-dependent domain discretization and suffer from the curse-of-dimensionality. We present GeONet, a mesh-invariant deep neural operator network that learns the non-linear mapping from the input pair of initial and terminal distributions to the Wasserstein geodesic connecting the two endpoint distributions. In the offline training stage, GeONet learns the saddle point optimality conditions for the dynamic formulation of the OT problem in the primal and dual spaces that are characterized by a coupled PDE system. The subsequent inference stage is instantaneous and can be deployed for real-time predictions in the online learning setting. We demonstrate that GeONet achieves comparable testing accuracy to the standard OT solvers on simulation examples and the MNIST dataset with considerably reduced inference-stage computational cost by orders of magnitude.
]]></description>
<dc:subject>machine-learning probability-theory rather-interesting metrics distance numerical-methods approximation neural-networks consider:looking-to-see consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2550a216a21d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.youtube.com/watch?v=5q32heFz1bs">
    <title>Go First Dice - Numberphile - YouTube</title>
    <dc:date>2023-05-22T20:35:00+00:00</dc:date>
    <link>https://www.youtube.com/watch?v=5q32heFz1bs</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[James Grime reveals a breakthrough in the dice world.]]></description>
<dc:subject>mathematical-recreations probability-theory optimization constraint-satisfaction rather-interesting to-write-about consider:metaheuristics consider:approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b2ccaf12da90/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.03002">
    <title>[1901.03002] On the least common multiple of several random integers</title>
    <dc:date>2022-03-13T17:49:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.03002</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Let Ln(k) denote the least common multiple of k independent random integers uniformly chosen in {1,2,…,n}. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as n→∞ of f(Ln(k))nrk for a wide class of multiplicative arithmetic functions~f with polynomial growth r>−1. Furthermore, we identify the limit as an infinite product of independent random variables indexed by prime numbers. Along the way, we compute the generating function of a trimmed sum of independent geometric laws, occurring in the above infinite product. This generating function is rational; we relate it to the generating function of a certain max-type Diophantine equation, of which we solve a generalized version. Our results extend theorems by Erdős and Wintner (1939), Fernández and Fernández (2013) and Hilberdink and Tóth (2016).
]]></description>
<dc:subject>number-theory primes rather-interesting probability-theory sampling random-variables to-write-about consider:visualization consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2c7b79b563d5/</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:primes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-variables"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<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/1803.00250">
    <title>[1803.00250] Distance Measure Machines</title>
    <dc:date>2022-02-12T13:26:09+00:00</dc:date>
    <link>https://arxiv.org/abs/1803.00250</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of Balcan et al. (2008) to the population distribution case and we show that, for some learning problems, some dissimilarity on distribution achieves low-error linear decision functions with high probability. Our key result is to prove that the theory also holds for empirical distributions. Algorithmically, the proposed approach consists in computing a mapping based on pairwise dissimilarity where learning a linear decision function is amenable. Our experimental results show that the Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions.
]]></description>
<dc:subject>machine-learning representation rather-interesting probability-theory to-understand approximation consider:EDAs consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:89b7794363b0/</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:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<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:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:EDAs"/>
	<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/2107.10318">
    <title>[2107.10318] MacMahon Partition Analysis: a discrete approach to broken stick problems</title>
    <dc:date>2022-01-29T12:31:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.10318</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose a discrete approach to solve problems on forming polygons from broken sticks, which is akin to counting polygons with sides of integer length subject to certain Diophantine inequalities. Namely, we use MacMahon's Partition Analysis to obtain a generating function for the size of the set of segments of a broken stick subject to these inequalities. In particular, we use this approach to show that for n≥k≥3, the probability that a k-gon cannot be formed from a stick broken into n parts is given by n! over a product of linear combinations of partial sums of generalized Fibonacci numbers, a problem which proved to be very hard to generalize in the past.
]]></description>
<dc:subject>combinatorics probability-theory rather-interesting plane-geometry constraint-satisfaction number-theory all-kinds-of-stuff-really to-write-about to-understand OEIS</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9999dc880227/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:all-kinds-of-stuff-really"/>
	<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:OEIS"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1701.07719">
    <title>[1701.07719] The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices</title>
    <dc:date>2022-01-26T13:34:22+00:00</dc:date>
    <link>https://arxiv.org/abs/1701.07719</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The asymptotic volume of the polytope of symmetric stochastic matrices can be determined by asymptotic enumeration techniques as in the case of the Birkhoff polytope. These methods can be extended to polytopes of symmetric stochastic matrices with given diagonal, if this diagonal varies not too wildly. To this end, the asymptotic number of symmetric matrices with natural entries, zero diagonal and varying row sums is determined and a third order correction factor to this is examined.
]]></description>
<dc:subject>probability-theory linear-algebra looking-to-see rather-interesting to-write-about to-visualize consider:sampling consider:varying-radius</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a902a505da03/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:linear-algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<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:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:varying-radius"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1801.01288">
    <title>[1801.01288] There are 174 Subdivisions of the Hexahedron into Tetrahedra</title>
    <dc:date>2022-01-24T12:31:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.01288</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra. However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions. Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. 
The enumeration of these 174 subdivisions of the hexahedron into tetrahedra is our combinatorial result. Each of the 174 subdivisions has between 5 and 15 tetrahedra and is actually a class of 2 to 48 equivalent instances which are identical up to vertex relabeling. We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid. We exhibit the tetrahedral meshes for these configurations and show in particular subdivisions of hexahedra with 15 tetrahedra that have a strictly positive Jacobian.
]]></description>
<dc:subject>enumeration combinatorics probability-theory rather-interesting to-write-about to-simulate consider:visualization consider:sampling-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e443746bbcee/</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:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t: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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:sampling-methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1703.04862">
    <title>[1703.04862] Exploring the Combination Rules of D Numbers From a Perspective of Conflict Redistribution</title>
    <dc:date>2021-11-09T11:32:15+00:00</dc:date>
    <link>https://arxiv.org/abs/1703.04862</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Dempster-Shafer theory of evidence is widely applied to uncertainty modelling and knowledge reasoning because of its advantages in dealing with uncertain information. But some conditions or requirements, such as exclusiveness hypothesis and completeness constraint, limit the development and application of that theory to a large extend. To overcome the shortcomings and enhance its capability of representing the uncertainty, a novel model, called D numbers, has been proposed recently. However, many key issues, for example how to implement the combination of D numbers, remain unsolved. In the paper, we have explored the combination of D Numbers from a perspective of conflict redistribution, and proposed two combination rules being suitable for different situations for the fusion of two D numbers. The proposed combination rules can reduce to the classical Dempster's rule in Dempster-Shafer theory under a certain conditions. Numerical examples and discussion about the proposed rules are also given in the paper.
]]></description>
<dc:subject>representation belief-networks formalization rather-interesting constraint-satisfaction to-understand probability-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d3ff61921ca2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:belief-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1808.05934">
    <title>[1808.05934] Periodic points in random substitution subshifts</title>
    <dc:date>2021-07-21T21:26:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.05934</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible random substitutions-random substitutions for which a well-defined abelianisation exists. We find some simple necessary criteria for primitive, compatible random substitutions to admit periodic points in their subshifts. In the case that the random substitution further has disjoint images and is of constant length, we provide a stronger criterion. A method is outlined for enumerating periodic points of any specified length in a random substitution subshift.
]]></description>
<dc:subject>rewriting-systems rather-interesting formal-languages probability-theory dynamical-systems to-write-about to-simulate consider:looking-to-see consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:583f2d50b1ff/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<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:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2009.06080">
    <title>[2009.06080] The Penney's Game with Group Action</title>
    <dc:date>2021-07-14T11:10:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2009.06080</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Consider equipping an alphabet  with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the Penney's game on patterns and show non-transitivity for the game on patterns as the length of the pattern tends to infinity. We also analyze bounds on the pattern-based Conway leading number and expected wait time, and further explore the game under the cyclic and symmetric group actions.
]]></description>
<dc:subject>mathematical-recreations strings LOL-at-grad-school-when-I-tried-to-convince-Ewens-about-this probability-theory combinatorics formal-languages to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:62d7868af328/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:LOL-at-grad-school-when-I-tried-to-convince-Ewens-about-this"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<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/1407.4711">
    <title>[1407.4711] On Levine's notorious hat puzzle</title>
    <dc:date>2021-06-07T10:37:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1407.4711</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Levine hat game requires n players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. 
They are allowed a strategy session before the game, but no further communication. The players collectively win if and only if all their guesses are correct. In addition to giving an overview, we discuss the case n=2 in considerable detail (giving a conjecture for an optimal strategy) and prove that Vn, the optimal value of the joint success probability in the n-player game, is a strictly decreasing function of n.
]]></description>
<dc:subject>combinatorics probability-theory mathematical-recreations information-theory communication-theory to-write-about to-simulate consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c7acfb945d85/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:communication-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1911.09377">
    <title>[1911.09377] The asymptotics of the clustering transition for random constraint satisfaction problems</title>
    <dc:date>2021-05-26T10:54:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1911.09377</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Random Constraint Satisfaction Problems exhibit several phase transitions when their density of constraints is varied. One of these threshold phenomena, known as the clustering or dynamic transition, corresponds to a transition for an information theoretic problem called tree reconstruction. In this article we study this threshold for two CSPs, namely the bicoloring of k-uniform hypergraphs with a density α of constraints, and the q-coloring of random graphs with average degree c. We show that in the large k,q limit the clustering transition occurs for α=2k−1k(lnk+lnlnk+γd+o(1)), c=q(lnq+lnlnq+γd+o(1)), where γd is the same constant for both models. We characterize γd via a functional equation, solve the latter numerically to estimate γd≈0.871, and obtain an analytic lowerbound γd≥1+ln(2(2‾√−1))≈0.812. Our analysis unveils a subtle interplay of the clustering transition with the rigidity (naive reconstruction) threshold that occurs on the same asymptotic scale at γr=1.
]]></description>
<dc:subject>constraint-satisfaction rather-interesting looking-to-see random-structures probability-theory to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b7779b69990a/</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: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:random-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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://www.ncbi.nlm.nih.gov/pmc/articles/PMC3250568/">
    <title>Probability Machines: Consistent Probability Estimation Using Nonparametric Learning Machines</title>
    <dc:date>2021-05-22T11:27:00+00:00</dc:date>
    <link>https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3250568/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem.

]]></description>
<dc:subject>via:GPTP machine-learning statistics modeling representation probability-theory to-write-about to-visualize classification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e98d77ff6c6e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:GPTP"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:modeling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:classification"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://math-frolic.blogspot.com/2020/04/another-classic-puzzle.html">
    <title>Math-Frolic!: Another Classic Puzzle</title>
    <dc:date>2021-03-25T21:09:20+00:00</dc:date>
    <link>https://math-frolic.blogspot.com/2020/04/another-classic-puzzle.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA["You are seated at a table in a dark room. On the table there are twelve pennies, five of which are heads up and seven of which are  tails up. (You know where the coins are, so you can move or flip any coin, but because it is dark you will not know if the coin you are touching was originally heads up or tails up.) You are to separate the coins into two piles (possibly flipping some of them) so that when the lights are turned on there will be an equal number of heads in each pile."
]]></description>
<dc:subject>mathematical-recreations oh-wow probability-theory rather-interesting to-simulate to-write-about consider:visualization consider:generalizations puzzles</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:32026c53926e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:oh-wow"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t: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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:generalizations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:puzzles"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2004.13440">
    <title>[2004.13440] Asymptotics of product of nonnegative 2-by-2 matrices with applications to random walks with asymptotically zero drifts</title>
    <dc:date>2021-03-12T14:41:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2004.13440</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Let AkAk−1⋯A1 be product of some nonnegative 2-by-2 matrices. In general, its elements are hard to evaluate. Under some conditions, we show that ∀i,j∈{1,2}, (AkAk−1⋯A1)i,j∼cϱ(Ak)ϱ(Ak−1)⋯ϱ(A1) as k→∞, where ϱ(An) is the spectral radius of the matrix An and c∈(0,∞) is some constant, so that the elements of AkAk−1⋯A1 can be estimated. As applications, consider the maxima of certain excursions of (2,1) and (1,2) random walks with asymptotically zero drifts. 
We get some delicate limit theories which are quite different from the ones of simple random walks. Limit theories of both the tail and critical tail sequences of continued fractions play important roles in our studies.
]]></description>
<dc:subject>branching-processes probability-theory random-walks matrices to-write-about to-simulate consider:looking-to-see consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e1fc64c0ef53/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:branching-processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<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:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.02229">
    <title>[1909.02229] Optimal UCB Adjustments for Large Arm Sizes</title>
    <dc:date>2020-07-12T12:01:04+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.02229</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The regret lower bound of Lai and Robbins (1985), the gold standard for checking optimality of bandit algorithms, considers arm size fixed as sample size goes to infinity. We show that when arm size increases polynomially with sample size, a surprisingly smaller lower bound is achievable. This is because the larger experimentation costs when there are more arms permit regret savings by exploiting the best performer more often. In particular we are able to construct a UCB-Large algorithm that adaptively exploits more when there are more arms. It achieves the smaller lower bound and is thus optimal. Numerical experiments show that UCB-Large performs better than classical UCB that does not correct for arm size, and better than Thompson sampling.
]]></description>
<dc:subject>bandit-problems probability-theory planning operations-research game-theory online-learning to-write-about to-simulate consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:292474063e44/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bandit-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:online-learning"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/cond-mat/0406593">
    <title>[cond-mat/0406593] Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk</title>
    <dc:date>2020-07-10T22:55:41+00:00</dc:date>
    <link>https://arxiv.org/abs/cond-mat/0406593</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p. At a critical value p(1)c=1/2 where memory effects vanish there is a transition from a weakly localized regime (where the walker returns to its starting point) to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant k=(2p−1)/t. The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.
]]></description>
<dc:subject>random-walks probability-theory background-reading to-simulate to-write-about consider:visualization consider:interactivity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:195491b3073b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:background-reading"/>
	<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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:interactivity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.07345">
    <title>[1709.07345] On the multi-dimensional elephant random walk</title>
    <dc:date>2020-07-10T22:51:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.07345</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional elephant random walk (MERW). It is a non-Markovian random walk which has a complete memory of its entire history. A wide range of literature is available on the one-dimensional ERW. Surprisingly, no references are available on the MERW. The goal of this paper is to fill the gap by extending the results on the one-dimensional ERW to the MERW. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the MERW. The asymptotic normality of the MERW, properly normalized, is also provided. In the superdiffusive regime, we prove the almost sure convergence as well as the mean square convergence of the MERW. All our analysis relies on asymptotic results for multi-dimensional martingales.
]]></description>
<dc:subject>random-walks probability-theory to-simulate to-write-about consider:visualization consider:comparison</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a85ccd7dfc42/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:comparison"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2003.02725">
    <title>[2003.02725] Central limit theorems for additive functionals and fringe trees in tries</title>
    <dc:date>2020-05-23T11:48:16+00:00</dc:date>
    <link>https://arxiv.org/abs/2003.02725</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We give general theorems on asymptotic normality for additive functionals of random tries generated by a sequence of independent strings. These theorems are applied to show asymptotic normality of the distribution of random fringe trees in a random trie. Formulas for asymptotic mean and variance are given. In particular, the proportion of fringe trees of size k (defined as number of keys) is asymptotically, ignoring oscillations, c/(k(k−1)) for k≥2, where c=1/(1+H) with H the entropy of the digits. Another application gives asymptotic normality of the number of k-protected nodes in a random trie. For symmetric tries, it is shown that the asymptotic proportion of k-protected nodes (ignoring oscillations) decreases geometrically as k→∞.
]]></description>
<dc:subject>probability-theory data-structures rather-interesting needs-pictures to-write-about to-simulate consider:visualization consider:plots!</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d342ff737d8a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:needs-pictures"/>
	<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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:plots!"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.02063">
    <title>[1904.02063] Generalized Variational Inference: Three arguments for deriving new Posteriors</title>
    <dc:date>2020-05-22T21:16:22+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.02063</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We advocate an optimization-centric view on and introduce a novel generalization of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional optimization problem (Csiszar, 1975; Donsker and Varadhan; 1975, Zellner; 1988). First, we use it to prove an optimality result of standard Variational Inference (VI): Under the proposed view, the standard Evidence Lower Bound (ELBO) maximizing VI posterior is preferable to alternative approximations of the Bayesian posterior. Next, we argue for generalizing standard Bayesian inference. The need for this arises in situations of severe misalignment between reality and three assumptions underlying standard Bayesian inference: (1) Well-specified priors, (2) well-specified likelihoods, (3) the availability of infinite computing power. Our generalization addresses these shortcomings with three arguments and is called the Rule of Three (RoT). We derive it axiomatically and recover existing posteriors as special cases, including the Bayesian posterior and its approximation by standard VI. In contrast, approximations based on alternative ELBO-like objectives violate the axioms. Finally, we study a special case of the RoT that we call Generalized Variational Inference (GVI). GVI posteriors are a large and tractable family of belief distributions specified by three arguments: A loss, a divergence and a variational family. GVI posteriors have appealing properties, including consistency and an interpretation as approximate ELBO. The last part of the paper explores some attractive applications of GVI in popular machine learning models, including robustness and more appropriate marginals. After deriving black box inference schemes for GVI posteriors, their predictive performance is investigated on Bayesian Neural Networks and Deep Gaussian Processes, where GVI can comprehensively improve upon existing methods.
]]></description>
<dc:subject>models-and-modes to-understand probability-theory machine-learning define-your-terms performance-measure</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ae6c80a8d812/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.06781">
    <title>[1810.06781] On the local pairing behavior of critical points and roots of random polynomials</title>
    <dc:date>2020-05-18T21:34:06+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.06781</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the pairing between zeros and critical points of the polynomial pn(z)=∏nj=1(z−Xj), whose roots X1,…,Xn are complex-valued random variables. Under a regularity assumption, we show that if the roots are independent and identically distributed, the Wasserstein distance between the empirical distributions of roots and critical points of pn is on the order of 1/n, up to logarithmic corrections. The proof relies on a careful construction of disjoint random Jordan curves in the complex plane, which allow us to naturally pair roots and nearby critical points. In addition, we establish asymptotic expansions to order 1/n2 for the locations of the nearest critical points to several fixed roots. This allows us to describe the joint limiting fluctuations of the critical points as n tends to infinity, extending a recent result of Kabluchko and Seidel. Finally, we present a local law that describes the behavior of the critical points when the roots are neither independent nor identically distributed.
]]></description>
<dc:subject>algebra probability-theory polynomials number-theory rather-interesting to-write-about consider:simulation consider:extreme-values</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:196fefc01786/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:polynomials"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:extreme-values"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1711.07420">
    <title>[1711.07420] Outliers in the spectrum for products of independent random matrices</title>
    <dc:date>2020-05-18T21:32:42+00:00</dc:date>
    <link>https://arxiv.org/abs/1711.07420</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical distribution of the eigenvalues is described by the m-th power of the circular law. Moreover, this same limiting distribution continues to hold if each iid random matrix is additively perturbed by a bounded rank deterministic error. However, the bounded rank perturbations may create one or more outlier eigenvalues. We describe the asymptotic location of the outlier eigenvalues, which extends a result of Terence Tao for the case of a single iid matrix. Our methods also allow us to consider several other types of perturbations, including multiplicative perturbations.
]]></description>
<dc:subject>random-matrices matrices sampling probability-theory rather-interesting to-write-about consider:extreme-values</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1f57f7bf96f0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:extreme-values"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1803.04221">
    <title>[1803.04221] Extremal dependence of random scale constructions</title>
    <dc:date>2020-05-18T21:18:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1803.04221</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of vectors with a random scale construction (X1,X2)=R(W1,W2), with non-degenerate R>0 independent of (W1,W2). Focusing on the presence and strength of asymptotic tail dependence, as expressed through commonly-used summary parameters, broad factors that affect the results are: the heaviness of the tails of R and (W1,W2), the shape of the support of (W1,W2), and dependence between (W1,W2). When R is distinctly lighter tailed than (W1,W2), the extremal dependence of (X1,X2) is typically the same as that of (W1,W2), whereas similar or heavier tails for R compared to (W1,W2) typically result in increased extremal dependence. Similar tail heavinesses represent the most interesting and technical cases, and we find both asymptotic independence and dependence of (X1,X2) possible in such cases when (W1,W2) exhibit asymptotic independence. The bivariate case often directly extends to higher-dimensional vectors and spatial processes, where the dependence is mainly analyzed in terms of summaries of bivariate sub-vectors. The results unify and extend many existing examples, and we use them to propose new models that encompass both dependence classes.
]]></description>
<dc:subject>probability-theory representation bivariate-distributions correlation simulation approximation rather-interesting to-understand to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:98f5d851db63/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bivariate-distributions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:correlation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<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-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math-ph/0311005">
    <title>[math-ph/0311005] Dimers and Amoebae</title>
    <dc:date>2020-05-16T12:06:05+00:00</dc:date>
    <link>https://arxiv.org/abs/math-ph/0311005</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on an weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension and local Gibbs measure probabilities of these models. The answers involve a certain plane algebraic curve, which is the spectral curve of the Kasteleyn operator of the graph. For example, the surface tension is the Legendre dual of the Ronkin function of the spectral curve. The amoeba of the spectral curve represents the phase diagram of the dimer model. Further, we prove that the spectral curve of a dimer model is always a real curve of special type, namely it is a Harnack curve. This implies many qualitative and quantitative statement about the behavior of the dimer model, such as existence of smooth phases, decay rate of correlations, growth rate of height function fluctuations, etc.
]]></description>
<dc:subject>domino-tiling probability-theory rather-interesting to-understand statistical-mechanics to-simulate consider:looking-to-see consider:sampling algebra idealization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:77f2c1e0a3bd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:domino-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistical-mechanics"/>
	<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:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:idealization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0406503">
    <title>[math/0406503] Topological mixing for substitutions on two letters</title>
    <dc:date>2020-05-16T11:57:27+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0406503</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We investigate topological mixing for Z and R actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue θ2 of the substitution matrix satisfies |θ2|≠1. If |θ2|<1, then (as is well-known) the substitution system is not topologically weak mixing, so it is not topologically mixing. We prove that if |θ2|>1, then topological mixing is equivalent to topological weak mixing, which has an explicit arithmetic characterization. The case |θ2|=1 is more delicate, and we only obtain some partial results.
]]></description>
<dc:subject>rewriting-systems automata probability-theory rather-interesting algebra topology to-simulate to-write-about consider:transitions proof</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:859b7be367a8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<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:transitions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1506.02340">
    <title>[1506.02340] Permutations with fixed pattern densities</title>
    <dc:date>2020-05-16T11:43:23+00:00</dc:date>
    <link>https://arxiv.org/abs/1506.02340</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In particular, we compute (exactly or numerically) the limit shapes with fixed \hbox{12} density, with fixed \hbox{12} and \hbox{123} densities, with fixed \hbox{12} density and the sum of \hbox{123} and \hbox{213} densities, and with fixed \hbox{123} and \hbox{321} densities. In the last case we explore a particular phase transition. To obtain our results, we also provide a description of permutons using a dynamic construction.
]]></description>
<dc:subject>combinatorics permutations rather-interesting enumeration statistical-mechanics probability-theory to-simulate to-write-about consider:heuristics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e041fc25be6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:permutations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistical-mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:heuristics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1610.06248">
    <title>[1610.06248] Pairing between zeros and critical points of random polynomials with independent roots</title>
    <dc:date>2020-05-13T23:41:33+00:00</dc:date>
    <link>https://arxiv.org/abs/1610.06248</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Let pn be a random, degree n polynomial whose roots are chosen independently according to the probability measure μ on the complex plane. For a deterministic point ξ lying outside the support of μ, we show that almost surely the polynomial qn(z):=pn(z)(z−ξ) has a critical point at distance O(1/n) from ξ. In other words, conditioning the random polynomials pn to have a root at ξ, almost surely forces a critical point near ξ. More generally, we prove an analogous result for the critical points of qn(z):=pn(z)(z−ξ1)⋯(z−ξk), where ξ1,…,ξk are deterministic. In addition, when k=o(n), we show that the empirical distribution constructed from the critical points of qn converges to μ in probability as the degree tends to infinity, extending a recent result of Kabluchko.
]]></description>
<dc:subject>number-theory algebra to-understand counterintuitive rather-interesting to-simulate to-write-about consider:minimizing-similarity probability-theory sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6829f44f888a/</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:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:counterintuitive"/>
	<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:minimizing-similarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1411.6247">
    <title>[1411.6247] Degree-degree distribution in a power law random intersection graph with clustering</title>
    <dc:date>2020-05-09T12:13:01+00:00</dc:date>
    <link>https://arxiv.org/abs/1411.6247</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree distribution of a sparse inhomogeneous random intersection graph and discuss its relation to the clustering and power law properties of the graph.
]]></description>
<dc:subject>graph-theory generative-models sampling probability-theory scaling to-simulate to-write-about consider:robustness</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:02f9f162a795/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scaling"/>
	<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:robustness"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.10428">
    <title>[1809.10428] Scheduling on (Un-)Related Machines with Setup Times</title>
    <dc:date>2020-05-04T11:56:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.10428</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a natural generalization of scheduling n jobs on m parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches from processing jobs of one class to jobs of a different class. During such a setup, a machine cannot process jobs and the duration of a setup may depend on the machine as well as the class of the job to be processed next. 
For this problem, we study approximation algorithms for non-identical machines. We develop a polynomial-time approximation scheme for uniformly related machines. For unrelated machines we obtain an O(logn+logm)-approximation, which we show to be optimal (up to constant factors) unless NP⊂RP. We also identify two special cases that admit constant factor approximations.
]]></description>
<dc:subject>operations-research scheduling planning queueing-theory probability-theory to-write-about to-simulate consider:variability consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:41affee1d179/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scheduling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:planning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:queueing-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:variability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1707.00083">
    <title>[1707.00083] Notes on Growing a Tree in a Graph</title>
    <dc:date>2020-05-04T11:54:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1707.00083</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the height of a spanning tree T of a graph G obtained by starting with a single vertex of G and repeatedly selecting, uniformly at random, an edge of G with exactly one endpoint in T and adding this edge to T.]]></description>
<dc:subject>graph-theory network-theory probability-theory rather-interesting looking-to-see simulation feature-construction to-write-about to-simulate consider:variation consider:inverse-problem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:dc0a1c70540d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<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:variation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:inverse-problem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1112.3304">
    <title>[1112.3304] Avoidance Coupling</title>
    <dc:date>2020-04-22T23:18:11+00:00</dc:date>
    <link>https://arxiv.org/abs/1112.3304</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We examine the question of whether a collection of random walks on a graph can be coupled so that they never collide. In particular, we show that on the complete graph on n vertices, with or without loops, there is a Markovian coupling keeping apart Omega(n/log n) random walks, taking turns to move in discrete time.
]]></description>
<dc:subject>random-walks algorithms distributed-processing constraint-satisfaction rather-interesting probability-theory existence-proof to-write-about to-simulate consider:algorithms consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:dc9ae3d8035b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:existence-proof"/>
	<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:algorithms"/>
	<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/1707.02867">
    <title>[1707.02867] Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent</title>
    <dc:date>2020-04-19T12:38:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1707.02867</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that the average size of self-avoiding polygons (SAP) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an "enhancement" of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the equilibrium length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the equilibrium length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.
]]></description>
<dc:subject>knot-theory probability-theory rather-interesting scaling looking-to-see to-simulate to-write-about consider:detectors consider:feature-discovery consider:some-drawings</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:421fa7064f24/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scaling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<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:detectors"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:some-drawings"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1801.06924">
    <title>[1801.06924] Hyperuniform States of Matter</title>
    <dc:date>2020-03-17T11:24:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.06924</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties.
]]></description>
<dc:subject>statistical-mechanics materials-science models rather-interesting probability-theory emergent-design to-write-about to-simulate consider:heuristics consider:boundary-conditions consider:optimization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a2dea0f2aa19/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistical-mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:emergent-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:boundary-conditions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:optimization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1608.02638">
    <title>[1608.02638] Asymptotic laws for random knot diagrams</title>
    <dc:date>2020-03-08T21:24:19+00:00</dc:date>
    <link>https://arxiv.org/abs/1608.02638</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices n, as first established in recent work with Cantarella and Mastin. The knot diagram model is an exciting new model which captures both the random geometry of space curve models of knotting as well as the ease of computing invariants from diagrams. 
We prove that unknot diagrams are asymptotically exponentially rare, an analogue of Sumners and Whittington's landmark result for self-avoiding walks. Our proof uses the same key idea: We first show that knot diagrams obey a pattern theorem, which describes their fractal structure. We examine how quickly this behavior occurs in practice. As a consequence, almost all diagrams are asymmetric, simplifying sampling from this model. We conclude with experimental data on knotting in this model. This model of random knotting is similar to those studied by Diao et al., and Dunfield et al.
]]></description>
<dc:subject>knot-theory probability-theory rather-interesting generative-models representation to-write-about to-simulate consider:sampling consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cf2e993a9781/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<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:sampling"/>
	<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/1801.01570">
    <title>[1801.01570] How Many Rounds Should You Expect in Urn Solitaire?</title>
    <dc:date>2020-03-08T21:10:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.01570</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[As I've mentioned...

"Peter Winkler’s book is full of challenging problems that (smart) humans can do all by themselves, but take any of these problems, and tweak it ever-so-slightly, and then humans are hopeless, but luckily they can ask computer-kind to do their work."]]></description>
<dc:subject>probability-theory open-questions rather-interesting to-simulate to-write-about consider:symbolic-regression winkler-project</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:152bc089218a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<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:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:winkler-project"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2001.11709">
    <title>[2001.11709] Gaussian Random Embeddings of Multigraphs</title>
    <dc:date>2020-02-05T12:22:13+00:00</dc:date>
    <link>https://arxiv.org/abs/2001.11709</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper generalizes the Gaussian random walk and Gaussian random polygon models for linear and ring polymers to polymer topologies specified by an arbitrary multigraph $G$. Probability distributions of monomer positions and edge displacements are given explicitly and the spectrum of the graph Laplacian of $G$ is shown to predict the geometry of the configurations. This provides a new perspective on the James-Guth-Flory theory of phantom elastic networks. The model is based on linear algebra motivated by ideas from homology and cohomology theory. It provides a robust theoretical foundation for more detailed models of topological polymers.
]]></description>
<dc:subject>structural-biology probability-theory random-walks rather-interesting to-simulate constraint-satisfaction polymers to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8473fce4e2d9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:structural-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<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:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:polymers"/>
	<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/1809.10737">
    <title>[1809.10737] Plane and Planarity Thresholds for Random Geometric Graphs</title>
    <dc:date>2020-01-31T14:52:19+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.10737</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A random geometric graph, G(n,r), is formed by choosing n points independently and uniformly at random in a unit square; two points are connected by a straight-line edge if they are at Euclidean distance at most r. For a given constant k, we show that n−k2k−2 is a distance threshold function for G(n,r) to have a connected subgraph on k points. Based on this, we show that n−2/3 is a distance threshold for G(n,r) to be plane, and n−5/8 is a distance threshold to be planar. We also investigate distance thresholds for G(n,r) to have a non-crossing edge, a clique of a given size, and an independent set of a given size.]]></description>
<dc:subject>graph-theory graph-layout sampling probability-theory looking-to-see to-write-about to-simulate consider:planarity random-graphs geometric-graphs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9524471ee261/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-layout"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:planarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometric-graphs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/doi/abs/10.1145/1414558.1414592">
    <title>Constructing random polygons | Proceedings of the 9th ACM SIGITE conference on Information technology education</title>
    <dc:date>2020-01-30T17:27:58+00:00</dc:date>
    <link>https://dl.acm.org/doi/abs/10.1145/1414558.1414592</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The construction of random polygons has been used in psychological research and for the testing of algorithms. With the increased popularity of client-side vector based graphics in the web browser such as seen in Flash and SVG, as well as the newly introduced <canvas> tag in HTML5.0, the use of random shapes for creation of scenes for animation and interactive art requires the construction of random polygons. A natural question, then, is how to generate random polygons in a way which is computationally efficient (particularly in a resource limited environment such as the web browser). This paper presents a random polygon algorithm (RPA) that generates polygons that are random and representative of the class of all n-gons in O(n2logn) time. Our algorithm differs from other approaches in that the vertices are generated randomly, the algorithm is inclusive (i.e. each polygon has a non-zero probability to be constructed), and it runs efficiently in polynomial time.
]]></description>
<dc:subject>probability-theory sampling computational-geometry algorithms rather-interesting to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:75b4bf92f3b4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<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:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.5609">
    <title>CiteSeerX — RPG - Heuristics for the Generation of Random Polygons</title>
    <dc:date>2020-01-30T16:52:43+00:00</dc:date>
    <link>http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.5609</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider the problem of randomly generating simple and star-shaped polygons on a given set of points. This problem is of considerable importance in the practical evaluation of algorithms that operate on polygons, where it is necessary to check the correctness and to determine the actual CPU-consumption of an algorithm experimentally. Since no polynomial-time solution for the uniformly random generation of polygons is known, we present and analyze several heuristics. All heuristics described in this paper have been implemented and are part of our RandomPolygonGenerator, RPG. We have tested all heuristics, and report experimental results on their CPU-consumption, their quality, and their characteristics. RPG is publically available via http://www.cosy.sbg.ac.at/~held/projects/rpg/rpg.html. 1 Introduction In this paper 1 we deal with the random generation of simple polygons on a given set of points: Ideally, given a set S = fs 1 ; : : : ; s n g of n points, we would like to generat...
]]></description>
<dc:subject>probability-theory computational-geometry sampling rather-interesting performance-measure to-simulate to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3adbf07e0b0c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<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-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://blog.tanyakhovanova.com/2019/11/my-new-favorite-probability-puzzle/">
    <title>Tanya Khovanova's Math Blog » Blog Archive » My New Favorite Probability Puzzle</title>
    <dc:date>2020-01-23T12:03:51+00:00</dc:date>
    <link>https://blog.tanyakhovanova.com/2019/11/my-new-favorite-probability-puzzle/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is my favorite puzzle in the last issue of the Emissary, proposed by Peter Winkler.

]]></description>
<dc:subject>probability-theory puzzles to-simulate to-write-about rather-interesting consider:generalizations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6707d11b367d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:puzzles"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:generalizations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1203.3353">
    <title>[1203.3353] Solving Structure with Sparse, Randomly-Oriented X-ray Data</title>
    <dc:date>2020-01-19T15:45:09+00:00</dc:date>
    <link>https://arxiv.org/abs/1203.3353</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing of hundreds of thousands (or more) of images that contain very few x-rays. Each low-flux image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of collecting data at these extremes, averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-flux data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal in the high-noise regime.
]]></description>
<dc:subject>diffraction inverse-problems tomography rather-interesting algorithms statistics probability-theory inference to-simulate to-write-about optimization signal-processing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3aebefbb9649/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tomography"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<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:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1805.06512">
    <title>[1805.06512] The Broken Stick Project</title>
    <dc:date>2020-01-19T15:37:00+00:00</dc:date>
    <link>https://arxiv.org/abs/1805.06512</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The broken stick problem is the following classical question. 
You have a segment [0,1]. You choose two points on this segment at random. They divide the segment into three smaller segments. Show that the probability that the three segments form a triangle is 1/4. 
The MIT PRIMES program, together with Art of Problem Solving, organized a high school research project where participants worked on several variations of this problem. Participants were generally high school students who posted ideas and progress to the Art of Problem Solving forums over the course of an entire year, under the supervision of PRIMES mentors. This report summarizes the findings of this CrowdMath project.
]]></description>
<dc:subject>crowdsourcing see-author open-questions geometry probability-theory rather-interesting to-write-about to-simulate consider:genetic-programming consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d7f139a0c81c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:crowdsourcing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:see-author"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1310.5924">
    <title>[1310.5924] The symplectic geometry of closed equilateral random walks in 3-space</title>
    <dc:date>2020-01-19T14:29:28+00:00</dc:date>
    <link>https://arxiv.org/abs/1310.5924</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. The sample space of such walks with n edges is the (2n−3)-dimensional Riemannian manifold of equilateral closed polygons in ℝ3. We study closed random walks using the symplectic geometry of the (2n−6)-dimensional quotient of the manifold of polygons by the action of the rotation group SO(3). The basic objects of study are the moment maps on equilateral random polygon space given by the lengths of any (n−3)-tuple of nonintersecting diagonals. The Atiyah-Guillemin-Sternberg theorem shows that the image of such a moment map is a convex polytope in (n−3)-dimensional space, while the Duistermaat-Heckman theorem shows that the pushforward measure on this polytope is Lebesgue measure on ℝn−3. Together, these theorems allow us to define a measure-preserving set of "action-angle" coordinates on the space of closed equilateral polygons. The new coordinate system allows us to make explicit computations of exact expectations for total curvature and for some chord lengths of closed (and confined) equilateral random walks, to give statistical criteria for sampling algorithms on the space of polygons and to prove that the probability that a randomly chosen equilateral hexagon is unknotted is at least 12. We then use our methods to construct a new Markov chain sampling algorithm for equilateral closed polygons, with a simple modification to sample (rooted) confined equilateral closed polygons. We prove rigorously that our algorithm converges geometrically to the standard measure on the space of closed random walks, give a theory of error estimators for Markov chain Monte Carlo integration using our method and analyze the performance of our method. Our methods also apply to open random walks in certain types of confinement, and in general to walks with arbitrary (fixed) edgelengths as well as equilateral walks.
]]></description>
<dc:subject>probability-theory combinatorics random-walks sampling rather-interesting computational-geometry looking-to-see to-simulate to-write-about consider:rendering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5997ce869ad0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-walks"/>
	<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:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<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:rendering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.07715">
    <title>[1709.07715] Core-biased random walks in complex networks</title>
    <dc:date>2019-11-23T17:23:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.07715</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A simple strategy to explore a network is to use a random-walk where the walker jumps from one node to an adjacent node at random. It is known that biasing the random jump, the walker can explore every walk of the same length with equal probability, this is known as a Maximal Entropy Random Walk (MERW). To construct a MERW requires the knowledge of the largest eigenvalue and corresponding eigenvector of the adjacency matrix, this requires global knowledge of the network. When this global information is not available, it is possible to construct a biased random walk which approximates the MERW using only the degree of the nodes, a local property. Here we show that it is also possible to construct a good approximation to a MERW by biasing the random walk via the properties of the network's core, which is a mesoscale property of the network. We present some examples showing that the core-biased random walk outperforms the degree-biased random walks.
]]></description>
<dc:subject>network-theory probability-theory algorithms rather-interesting approximation consider:feature-discovery consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:96eb09726083/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-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:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<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/1711.10470">
    <title>[1711.10470] Models of Random Knots</title>
    <dc:date>2019-11-23T13:28:39+00:00</dc:date>
    <link>https://arxiv.org/abs/1711.10470</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of random curves arises also in applications to the natural sciences, such as in the context of the structure of polymers. We present here several known and new randomized models of knots and links. We review the main known results on the knot distribution in each model. We discuss the nature of these models and the properties of the knots they produce. Of particular interest to us are finite type invariants of random knots, and the recently studied Petaluma model. We report on rigorous results and numerical experiments concerning the asymptotic distribution of such knot invariants. Our approach raises questions of universality and classification of the various random knot models.
]]></description>
<dc:subject>knot-theory probability-theory rather-interesting representation random-sampling consider:truchet-tiling to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:af3fd84dbba5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:random-sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:truchet-tiling"/>
	<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/1909.10140">
    <title>[1909.10140] A new coefficient of correlation</title>
    <dc:date>2019-11-23T12:50:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.10140</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the degree of dependence between the variables, which is 0 if and only if the variables are independent and 1 if and only if one is a measurable function of the other, and (c) has a simple asymptotic theory under the hypothesis of independence, like the classical coefficients? This article answers this question in the affirmative, by producing such a coefficient. No assumptions are needed on the distributions of the variables. There are several coefficients in the literature that converge to 0 if and only if the variables are independent, but none that satisfy any of the other properties mentioned above.
]]></description>
<dc:subject>statistics probability-theory performance-measure rather-interesting nudge-targets to-write-about to-replicate consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9623577ab990/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<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:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-replicate"/>
	<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/1802.00296">
    <title>[1802.00296] $S$-Leaping: An adaptive, accelerated stochastic simulation algorithm, bridging $τ$-leaping and $R$-leaping</title>
    <dc:date>2019-11-03T11:48:18+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.00296</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ-leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the τ-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ-leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the τ-leaping and R-leaping on a number of benchmark systems involving biological reaction networks.
]]></description>
<dc:subject>simulation numerical-methods Markov-models Monte-Carlo-models probability-theory algorithms horse-races rather-interesting to-write-about performance-measure approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4efe05241f4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Markov-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Monte-Carlo-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-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:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1712.04166">
    <title>[1712.04166] Weighted p-bits for FPGA implementation of probabilistic circuits</title>
    <dc:date>2019-11-02T12:46:19+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.04166</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Probabilistic spin logic (PSL) is a recently proposed computing paradigm based on unstable stochastic units called probabilistic bits (p-bits) that can be correlated to form probabilistic circuits (p-circuits). These p-circuits can be used to solve problems of optimization, inference and also to implement precise Boolean functions in an "inverted" mode, where a given Boolean circuit can operate in reverse to find the input combinations that are consistent with a given output. In this paper we present a scalable FPGA implementation of such invertible p-circuits. We implement a "weighted" p-bit that combines stochastic units with localized memory structures. We also present a generalized tile of weighted p-bits to which a large class of problems beyond invertible Boolean logic can be mapped, and how invertibility can be applied to interesting problems such as the NP-complete Subset Sum Problem by solving a small instance of this problem in hardware.
]]></description>
<dc:subject>representation probability-theory probabilistic-languages reaction-networks concurrency rather-interesting boolean-networks to-simulate to-write-about consider:operations consider:constants</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:272be299ee78/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probabilistic-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reaction-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:concurrency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:boolean-networks"/>
	<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:operations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:constants"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.00196">
    <title>[1909.00196] Peculiarities of kinetics in the presence of Lévy noises</title>
    <dc:date>2019-10-26T13:04:06+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.00196</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Stochastic evolution of various reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation. When implemented for systems close to equilibrium, the approach correctly explains emergence of Boltzmann distribution for the ensemble of trajectories generated by Langevin equation and relates intensity of the noise strength to the mobility. 
This scenario can be further generalized to include effects of non-thermal, external burst-like forcing modeled by Lévy noise. In the paper forward and reverse kinetics of Langevin equations with Lévy noise are analyzed for simple model of potential wells pointing to the most probable escape which is executed via a single long jump. 
Heavy tails of Lévy noise distributions not only facilitate escape kinetics, but more importantly, change the escape protocol by altering final stationary state to a non-Boltzmann, non-equilibrium form. As a result, contrary to the kinetics induced by a Gaussian white noise, escape rates in environments with Lévy noise are determined not by the barrier height, but instead, by the barrier width. 
We discuss consequences of simultaneous action of thermal and Lévy noises on statistics of passage times and population of reactants in double-well potentials.
]]></description>
<dc:subject>reaction-networks nonlinear-dynamics rather-interesting thermodynamics simulation to-write-about to-simulate probability-theory heavy-tailed-distributions</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ffc77affc313/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reaction-networks"/>
	<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:thermodynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<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:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heavy-tailed-distributions"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.02016">
    <title>[1810.02016] The Four Point Permutation Test for Latent Block Structure in Incidence Matrices</title>
    <dc:date>2019-10-26T12:42:46+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.02016</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Transactional data may be represented as a bipartite graph G:=(L∪R,E), where L denotes agents, R denotes objects visible to many agents, and an edge in E denotes an interaction between an agent and an object. Unsupervised learning seeks to detect block structures in the adjacency matrix Z between L and R, thus grouping together sets of agents with similar object interactions. New results on quasirandom permutations suggest a non-parametric \textbf{four point test} to measure the amount of block structure in G, with respect to vertex orderings on L and R. Take disjoint 4-edge random samples, order these four edges by left endpoint, and count the relative frequencies of the 4! possible orderings of the right endpoint. When these orderings are equiprobable, the edge set E corresponds to a quasirandom permutation π of |E| symbols. Total variation distance of the relative frequency vector away from the uniform distribution on 24 permutations measures the amount of block structure. Such a test statistic, based on ⌊|E|/4⌋ samples, is computable in O(|E|/p) time on p processors. Possibly block structure may be enhanced by precomputing \textbf{natural orders} on L and R, related to the second eigenvector of graph Laplacians. In practice this takes O(d|E|) time, where d is the graph diameter. Five open problems are described.
]]></description>
<dc:subject>combinatorics counting rather-interesting probability-theory data-analysis data-mining graph-theory network-theory hypergraphs to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5d0e64d5a30a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:counting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<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/1808.05740">
    <title>[1808.05740] Extremality, Stationarity and Generalized Separation of Collections of Sets</title>
    <dc:date>2019-09-25T10:31:11+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.05740</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining 'extremal' statements. For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements. Some new characterizations of extremality properties are obtained.
]]></description>
<dc:subject>statistics clustering extreme-values to-understand discrimination algorithms rather-odd rather-general-sounding optimization probability-theory consider:weird-GP-stuff</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d7f86b2621f8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:extreme-values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrimination"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-odd"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-general-sounding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:weird-GP-stuff"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1401.3668">
    <title>[1401.3668] The existence and abundance of ghost ancestors in biparental populations</title>
    <dc:date>2019-09-11T11:55:21+00:00</dc:date>
    <link>https://arxiv.org/abs/1401.3668</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In a randomly-mating biparental population of size N there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately log2(N) generations into the past. We use this result of J. Chang to prove a curious corollary under standard models of recombination: there exist, with high probability, individuals within a constant multiple of log2(N) generations into the past who are simultaneously (i) genealogical ancestors of {\em each} of the individuals at the present, and (ii) genetic ancestors to {\em none} of the individuals at the present. Such ancestral individuals - ancestors of everyone today that left no genetic trace -- represent `ghost' ancestors in a strong sense. In this short note, we use simple analytical argument and simulations to estimate how many such individuals exist in finite Wright-Fisher populations.
]]></description>
<dc:subject>theoretical-biology genetics rather-interesting probability-theory to-write-about to-simulate consider:genetic-programming consider:lee's-lab</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a81189982824/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:theoretical-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:genetics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lee's-lab"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math-ph/9809010">
    <title>[math-ph/9809010] The Entropy of Square-Free Words</title>
    <dc:date>2019-09-07T14:33:58+00:00</dc:date>
    <link>https://arxiv.org/abs/math-ph/9809010</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters.
]]></description>
<dc:subject>probability-theory information-theory formal-languages combinatorics optimization rather-interesting constraint-satisfaction Thue-Morse permutations to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:917172c25214/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<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:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Thue-Morse"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:permutations"/>
	<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/1210.6537">
    <title>[1210.6537] The Expected Total Curvature of Random Polygons</title>
    <dc:date>2019-09-07T11:18:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1210.6537</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution. 
We then consider the symmetric measure on closed polygons of fixed total length constructed by Cantarella, Deguchi, and Shonkwiler. For this measure, we are able to prove that the expected value of total curvature for a closed n-gon is exactly \pi/2 n + (\pi/4) 2n/(2n-3). As a consequence, we show that at least 1/3 of fixed-length hexagons and 1/11 of fixed-length heptagons in 3-space are unknotted.
]]></description>
<dc:subject>combinatorics looking-to-see rather-interesting plane-geometry probability-theory to-simulate to-write-about consider:symbolic-regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cdf49d02cc11/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<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:symbolic-regression"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1609.04106">
    <title>[1609.04106] The Inverse Gamma Distribution and Benford's Law</title>
    <dc:date>2019-08-06T22:20:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1609.04106</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[According to Benford's Law, many data sets have a bias towards lower leading digits (about 30% are 1's). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive sports. There are many common distributions that exhibit such bias, i.e. they are almost Benford. These include the exponential and the Weibull distributions. Motivated by these examples and the fact that the underlying distribution of factors in protein structure follows an inverse gamma distribution, we determine the closeness of this distribution to a Benford distribution as its parameters change.
]]></description>
<dc:subject>probability-theory Benford's-law counterintuitive-stuff algorithms rather-interesting to-write-about to-simulate consider:rediscovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:924b167d6140/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Benford's-law"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:counterintuitive-stuff"/>
	<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:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1608.02895">
    <title>[1608.02895] The power of online thinning in reducing discrepancy</title>
    <dc:date>2019-08-03T11:23:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1608.02895</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Consider an infinite sequence of independent, uniformly chosen points from [0,1]d. After looking at each point in the sequence, an overseer is allowed to either keep it or reject it, and this choice may depend on the locations of all previously kept points. However, the overseer must keep at least one of every two consecutive points. We call a sequence generated in this fashion a \emph{two-thinning} sequence. Here, the purpose of the overseer is to control the discrepancy of the empirical distribution of points, that is, after selecting n points, to reduce the maximal deviation of the number of points inside any axis-parallel hyper-rectangle of volume A from nA. Our main result is an explicit low complexity two-thinning strategy which guarantees discrepancy of O(log2d+1n) for all n with high probability (compare with Θ(nloglogn‾‾‾‾‾‾‾‾‾‾√) without thinning). The case d=1 of this result answers a question of Benjamini. 
We also extend the construction to achieve the same asymptotic bound for (1+β)-thinning, a set-up in which rejecting is only allowed with probability β independently for each point. In addition, we suggest an improved and simplified strategy which we conjecture to guarantee discrepancy of O(logd+1n) (compare with θ(logdn), the best known construction of a low discrepancy sequence). Finally, we provide theoretical and empirical evidence for our conjecture, and provide simulations supporting the viability of our construction for applications.
]]></description>
<dc:subject>online-algorithms decision-making probability-theory online-learning optimization rather-interesting to-understand consider:selection consider:performance-measures consider:data-balancing to-write-about consider:approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8687afabfc60/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:online-algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:decision-making"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:online-learning"/>
	<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:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:data-balancing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:approximation"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>