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  </channel><item rdf:about="https://arxiv.org/abs/1312.6055v3">
    <title>[1312.6055v3] Unit Tests for Stochastic Optimization</title>
    <dc:date>2026-07-04T13:14:28+00:00</dc:date>
    <link>https://arxiv.org/abs/1312.6055v3</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are robust and widely applicable across many different optimization landscapes. In this paper we develop a collection of unit tests for stochastic optimization. Each unit test rapidly evaluates an optimization algorithm on a small-scale, isolated, and well-understood difficulty, rather than in real-world scenarios where many such issues are entangled. Passing these unit tests is not sufficient, but absolutely necessary for any algorithms with claims to generality or robustness. We give initial quantitative and qualitative results on numerous established algorithms. The testing framework is open-source, extensible, and easy to apply to new algorithms.
]]></description>
<dc:subject>benchmarking operations-research unit-testing performance-measure rather-interesting metaheuristics neural-networks machine-learning to-write-about to-use</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ebbe888f0ef2/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unit-testing"/>
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<item rdf:about="https://arxiv.org/abs/2201.12038">
    <title>[2201.12038] A survey on flexible/restricted skyline and their applicability</title>
    <dc:date>2026-06-26T12:54:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2201.12038</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Skyline and Top-k are two of the most important methods to extract information from datasets, but both come with their drawbacks, that's why lately some new technics that try to mix the features of the two have been studied. In this survey three new operators are analysed, F-Skyline, ORU/ORD, and ϵ-Skyline. After giving the main ideas behind those and their properties, they are compered on 3 fundamental features such as personalization, cardinality control, and generalization to guide the user to choose the best one for any task.
]]></description>
<dc:subject>multiobjective-optimization software-development-is-not-programming algorithms performance-measure rather-interesting consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:012c8c11117c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
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<item rdf:about="https://ptgui.com/info/stitching_software_for_macos.html">
    <title>Stitching software for macOS</title>
    <dc:date>2026-06-25T20:01:53+00:00</dc:date>
    <link>https://ptgui.com/info/stitching_software_for_macos.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[PTGui panorama stitching software also runs on macOS. We offer a universal binary for Intel and Apple Silicon processors. PTGui is fully automatic stitching software for Windows and Mac. It will stich any panorama from any lens type. The PTGui free trial version is available for download here.
]]></description>
<dc:subject>image-processing gigapixel software photography to-try</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fe14ba517613/</dc:identifier>
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<item rdf:about="https://spiralator.com/">
    <title>Spiralator | Spirograph Drawing Tool | Free Online Mobile PC SVG Vector Graphics</title>
    <dc:date>2026-06-16T19:08:33+00:00</dc:date>
    <link>https://spiralator.com/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Spiralator

A spirograph drawing tool. Free, online, mobile-friendly. Designed to help explore and express the beautiful geometries of circles rotating in circles. Inspired by the old spirograph toy but not constrained by its practicalities.

Instructions

The vertical sliders set the disc and pen configuration. Draw by dragging the moving disc around the fixed disc. Double-clicking in the main window starts and stops auto-drawing.

Some tips: Press the "Demo" button to watch a random series of shapes being drawn; when you're experimenting, the "Show Preview" button is useful to immediately see the effects of altering the parameters; "View Gallery" in the "Share/Save" menu for inspiration; for a "light mode", the "Set BG" button enables changing the background using the colour sliders.
]]></description>
<dc:subject>interactive visualization web-applications drawing genetic-programming consider:implicit-equations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1ac57c1dab6d/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2406.19562">
    <title>[2406.19562] The Pinnacle Sets of a Graph</title>
    <dc:date>2026-06-12T12:11:33+00:00</dc:date>
    <link>https://arxiv.org/abs/2406.19562</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce and study the pinnacle sets of a simple graph G with n vertices. Given a bijective vertex labeling λ:V(G)→[n], the label λ(v) of vertex v is a pinnacle of (G,λ) if λ(v)>λ(w) for all vertices w in the neighborhood of v. The pinnacle set of (G,λ) contains all the pinnacles of the labeled graph. A subset S⊆[n] is a pinnacle set of G if there exists a labeling λ such that S is the pinnacle set of (G,λ). Of interest to us is the question: Which subsets of [n] are the pinnacle sets of G? Our main results are as follows. We show that when G is connected, G has a size-k pinnacle set if and only if G has an independent set of the same size. Consequently, determining if G has a size-k pinnacle set and determining if G has a particular subset S as a pinnacle set are NP-complete problems. Nonetheless, we completely identify all the pinnacle sets of complete graphs, complete bipartite graphs, cycles and paths. We also present two techniques for deriving new pinnacle sets from old ones that imply a typical graph has many pinnacle sets. Finally, we define a poset on all the size-k pinnacle sets of G and show that it is a join semilattice. If, additionally, the poset has a minimum element, then it is a distributive lattice. We conclude with some open problems for further study.
]]></description>
<dc:subject>combinatorics fitness-landscapes peak-counting enumeration to-write-about to-cite loads-more-refs-needed</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3f066a26b922/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2405.21047">
    <title>[2405.21047] Grammar-Aligned Decoding</title>
    <dc:date>2026-06-10T17:21:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2405.21047</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what tokens an LLM can output at each step to guarantee that the output matches a given constraint. Specifically, in grammar-constrained decoding (GCD), the LLM's output must follow a given grammar. In this paper, we demonstrate that GCD techniques (and in general constrained decoding techniques) can distort the LLM's distribution, leading to outputs that are grammatical but appear with likelihoods that are not proportional to the ones given by the LLM, and so ultimately are low-quality. We call the problem of aligning sampling with a grammar constraint, grammar-aligned decoding (GAD), and propose adaptive sampling with approximate expected futures (ASAp), a decoding algorithm that guarantees the output to be grammatical while provably producing outputs that match the conditional probability of the LLM's distribution conditioned on the given grammar constraint. Our algorithm uses prior sample outputs to soundly overapproximate the future grammaticality of different output prefixes. Our evaluation on code generation and structured NLP tasks shows how ASAp often produces outputs with higher likelihood (according to the LLM's distribution) than existing GCD techniques, while still enforcing the desired grammatical constraints.
]]></description>
<dc:subject>computer-science neural-networks natural-language-processing LLMs grammar constraint-satisfaction hey-I-know-this-guy GPTP2026 consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:bff828266dd3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-science"/>
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<item rdf:about="https://arxiv.org/abs/2510.01902">
    <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>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e71f3985e050/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development-is-not-programming"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2411.12515">
    <title>[2411.12515] Transitions Between Cooperative and Crowding-Dominated Collective Motion in non-Jammed MDCK Monolayers</title>
    <dc:date>2026-06-03T13:32:21+00:00</dc:date>
    <link>https://arxiv.org/abs/2411.12515</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Transitions between solid-like and fluid-like states in living tissues have been found in steps of embryonic development and in stages of disease progression. Our current understanding of these transitions has been guided by experimental and theoretical investigations focused on how motion becomes arrested with increased mechanical coupling between cells, typically as a function of packing density or cell cohesiveness. However, cells actively respond to externally applied forces by contracting after a time delay, so it is possible that at some packing densities or levels of cell cohesiveness, mechanical coupling stimulates cell motion instead of suppressing it. Here we report our findings that at low densities and within multiple ranges of cell cohesiveness, cell migration speeds increase with these measures of mechanical coupling. Our observations run counter to our intuition that cell motion will be suppressed by increasingly packing or sticking cells together and may provide new insight into biological processes involving motion in dense cell populations.
]]></description>
<dc:subject>biophysics cell-biology nonlinear-dynamics rather-interesting developmental-biology models theoretical-biology physiology self-organization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b33a9f06eae1/</dc:identifier>
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<item rdf:about="https://franktisellano.github.io/datatype/">
    <title>Datatype — variable font that turns text into charts</title>
    <dc:date>2026-05-28T11:45:37+00:00</dc:date>
    <link>https://franktisellano.github.io/datatype/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[DATATYPE
A VARIABLE FONT THAT TURNS TEXT INTO CHARTS.
]]></description>
<dc:subject>via:gbilder opentype charts visualization fonts scientific-computing to-try</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ade00a44d963/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:opentype"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:charts"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fonts"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:scientific-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-try"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2507.18467">
    <title>[2507.18467] Contraction, Criticality, and Capacity: A Dynamical-Systems Perspective on Echo-State Networks</title>
    <dc:date>2026-05-26T20:07:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2507.18467</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Echo-State Networks (ESNs) distil a key neurobiological insight: richly recurrent but fixed circuitry combined with adaptive linear read-outs can transform temporal streams with remarkable efficiency. Yet fundamental questions about stability, memory and expressive power remain fragmented across disciplines. We present a unified, dynamical-systems treatment that weaves together functional analysis, random attractor theory and recent neuroscientific findings. First, on compact multivariate input alphabets we prove that the Echo-State Property (wash-out of initial conditions) together with global Lipschitz dynamics necessarily yields the Fading-Memory Property (geometric forgetting of remote inputs). Tight algebraic tests translate activation-specific Lipschitz constants into certified spectral-norm bounds, covering both saturating and rectifying nonlinearities. Second, employing a Stone-Weierstrass strategy we give a streamlined proof that ESNs with polynomial reservoirs and linear read-outs are dense in the Banach space of causal, time-invariant fading-memory filters, extending universality to stochastic inputs. Third, we quantify computational resources via memory-capacity spectrum, show how topology and leak rate redistribute delay-specific capacities, and link these trade-offs to Lyapunov spectra at the \textit{edge of chaos}. Finally, casting ESNs as skew-product random dynamical systems, we establish existence of singleton pullback attractors and derive conditional Lyapunov bounds, providing a rigorous analogue to cortical criticality. The analysis yields concrete design rules-spectral radius, input gain, activation choice-grounded simultaneously in mathematics and neuroscience, and clarifies why modest-sized reservoirs often rival fully trained recurrent networks in practice.
]]></description>
<dc:subject>reservoir-computing neural-networks compressed-sensing compression rather-interesting to-understand nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d5ea99dd617f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reservoir-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compressed-sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compression"/>
	<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:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2502.07192">
    <title>[2502.07192] OscNet: Machine Learning on CMOS Oscillator Networks</title>
    <dc:date>2026-05-26T20:05:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.07192</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Machine learning and AI have achieved remarkable advancements but at the cost of significant computational resources and energy consumption. This has created an urgent need for a novel, energy-efficient computational fabric to replace the current computing pipeline. Recently, a promising approach has emerged by mimicking spiking neurons in the brain and leveraging oscillators on CMOS for direct computation. In this context, we propose a new and energy efficient machine learning framework implemented on CMOS Oscillator Networks (OscNet). We model the developmental processes of the prenatal brain's visual system using OscNet, updating weights based on the biologically inspired Hebbian rule. This same pipeline is then directly applied to standard machine learning tasks. OscNet is a specially designed hardware and is inherently energy-efficient. Its reliance on forward propagation alone for training further enhances its energy efficiency while maintaining biological plausibility. Simulation validates our designs of OscNet architectures. Experimental results demonstrate that Hebbian learning pipeline on OscNet achieves performance comparable to or even surpassing traditional machine learning algorithms, highlighting its potential as a energy efficient and effective computational paradigm.
]]></description>
<dc:subject>coupled-oscillators nonlinear-dynamics machine-learning neural-networks Hebbian-networks to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:77d9725b322e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:coupled-oscillators"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Hebbian-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2504.10703">
    <title>[2504.10703] The Trie Measure, Revisited</title>
    <dc:date>2026-05-26T12:38:49+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.10703</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we study the following problem: given n subsets S1,…,Sn of an integer universe U={0,…,u−1}, having total cardinality N=∑ni=1|Si|, find a prefix-free encoding enc:U→{0,1}+ minimizing the so-called trie measure, i.e., the total number of edges in the n binary tries 1,…,n, where i is the trie packing the encoded integers {enc(x):x∈Si}. We first observe that this problem is equivalent to that of merging u sets with the cheapest sequence of binary unions, a problem which in [Ghosh et al., ICDCS 2015] is shown to be NP-hard. Motivated by the hardness of the general problem, we focus on particular families of prefix-free encodings. We start by studying the fixed-length shifted encoding of [Gupta et al., Theoretical Computer Science 2007]. Given a parameter 0≤a<u, this encoding sends each x∈U to (x+a)modu, interpreted as a bit-string of logu bits. We develop the first efficient algorithms that find the value of a minimizing the trie measure when this encoding is used. Our two algorithms run in O(u+Nlogu) and O(Nlog2u) time, respectively. We proceed by studying ordered encodings (a.k.a. monotone or alphabetic), and describe an algorithm finding the optimal such encoding in O(N+u3) time. Within the same running time, we show how to compute the best shifted ordered encoding, provably no worse than both the optimal shifted and optimal ordered encodings. We provide implementations of our algorithms and discuss how these encodings perform in practice.
]]></description>
<dc:subject>data-structures representation compression rather-interesting information-theory to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8031f0e4ccd5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2507.12720">
    <title>[2507.12720] FLEXITOKENS: Flexible Tokenization for Evolving Language Models</title>
    <dc:date>2026-05-26T12:36:05+00:00</dc:date>
    <link>https://arxiv.org/abs/2507.12720</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Adapting language models to new data distributions by simple finetuning is challenging. This is due to the rigidity of their subword tokenizers, which typically remain unchanged during adaptation. This inflexibility often leads to inefficient tokenization, causing overfragmentation of text in out-of-distribution domains, unseen languages, or scripts. In this work, we develop byte-level LMs with learnable tokenizers to make tokenization adaptive. Our models include a submodule that learns to predict boundaries given the input byte sequence, encoding it into variable-length segments. Most tokenizer-free methods train this boundary predictor using an auxiliary loss that enforces a fixed compression rate across the training corpus, introducing a new kind of rigidity. We propose FLEXITOKENS, a simplified training objective that enables significantly greater flexibility during adaptation. Evaluating across multiple multilingual benchmarks, morphologically diverse tasks, and domains, we demonstrate that FLEXITOKENS consistently reduces token over-fragmentation and achieves up to 10% point improvements on token classification and generative tasks compared to BPE and other gradient-based tokenizer baselines. We validate our findings using models of varying sizes, and our method demonstrates consistent improvements across scales. Code and data for our experiments will be released at this https URL
]]></description>
<dc:subject>neural-networks deep-learning language-models representation define-your-terms rather-interesting consider:data-analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:799b9b8ba111/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:language-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:data-analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.00309">
    <title>[2102.00309] The fair soup division and approximating numbers</title>
    <dc:date>2026-05-25T17:05:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.00309</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a recent The Vee's fair soup division problem, provide its partial solution, and pose a related open problem.
]]></description>
<dc:subject>mathematical-recreations food-division puzzle game-theory optimization to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:af98bc307d6f/</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:food-division"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:puzzle"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2411.12351">
    <title>[2411.12351] Multipacking in Euclidean Metric Space</title>
    <dc:date>2026-05-25T17:03:12+00:00</dc:date>
    <link>https://arxiv.org/abs/2411.12351</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Here we study the multipacking problems for geometric point sets with respect to their Euclidean distances. We consider a set of n points P and define Ns[v] as the subset of P that includes the s nearest points of v∈P and the point v itself. We assume that the \emph{s-th neighbor} of each point is unique, for every s∈{0,1,2,…,n−1}. For a natural number r≤n−1, an r-multipacking is a set M⊆P such that for each point v∈P and for every integer 1≤s≤r, |Ns[v]∩M|≤(s+1)/2. The r-multipacking number of P is the maximum cardinality of an r-multipacking of P and is denoted by $\MP_{r}(P)$. For r=n−1, an r-multipacking is called a multipacking and r-multipacking number is called as multipacking number. For r=1 and 2, we study the problem of computing a maximum r-multipacking of the point sets in ℝ2. We show that a maximum 1-multipacking can be computed in polynomial time but computing a maximum 2-multipacking is \textsc{NP-hard}. Further, we provide approximation and parameterized solutions to the 2-multipacking problem.
]]></description>
<dc:subject>packing computational-geometry operations-research optimization rather-interesting to-write-about to-simulate consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:034d0787c84b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<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-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:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2408.09041">
    <title>[2408.09041] Strain stiffening due to stretching of entangled particles in random packings of granular materials</title>
    <dc:date>2026-05-25T16:57:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.09041</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Stress-strain relations for random packings of entangling chains under triaxial compression can exhibit strain stiffening and sustain stresses several orders-of-magnitude beyond typical granular materials. X-ray tomography reveals the transition to this strong strain stiffening occurs when chains are long enough to entangle an average of about one chain each, which results in system-filling clusters of entangled chains. The number of entanglements is nearly proportional to the area surrounded by entangling particles with an excluded volume effect. A tendency was found for chain links to stretch when the packing was strained. The slope of the stress-strain relation of the packing can be calculated from a mean-field model consisting of the product of the effective extensional modulus of the chain, packing fraction, probability of stretched links, and the ratio of strain of stretched links to packing strain. The stress-strain model requires as input measurements of the ratio between local particle deformation and global average strain, and the probability of stretching for non-rigid particles. This results in a quadratic prediction for the stress-strain curve, with a curvature that agrees with experiments within the model uncertainties. This model explains that the strength of these packings comes from stretching of the links of chains, but only when the system-filling network of entanglements provides constraints that prevents failure by shear banding, so that particles must be deformed to move further under strain. In this model, the increasing slope of the stress-strain curve is mainly due to the fraction of stretched links increasing with strain. This model for the stress-strain relation is shown to be generalizable to different shapes of entangling particles by applying it to staples.
]]></description>
<dc:subject>granular-materials nonlinear-dynamics materials-science metamaterials rather-interesting physics! looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8a6e393828b1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:granular-materials"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metamaterials"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/pii/S0022314X07000595">
    <title>Shrinking the period lengths of continued fractions while still capturing convergents - ScienceDirect</title>
    <dc:date>2026-05-25T14:28:49+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/pii/S0022314X07000595</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Here we prove that every real quadratic irrational α can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α. We close with an application relating the structure of a quadratic α to its conjugate.
]]></description>
<dc:subject>number-theory continued-fractions representation to-understand heavily-cited consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a22f3ff77e98/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heavily-cited"/>
	<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/2112.04275">
    <title>[2112.04275] Alternating $N$-expansions</title>
    <dc:date>2026-05-25T14:25:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2112.04275</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce a family of maps generating continued fractions where the digit 1 in the numerator is replaced cyclically by some given non-negative integers (N1,…,Nm). We prove the convergence of the given algorithm, and study the underlying dynamical system generating such expansions. We prove the existence of a unique absolutely continuous invariant ergodic measure. In special cases, we are able to build the natural extension and give an explicit expression of the invariant measure. For these cases, we formulate a Doeblin-Lenstra type theorem. For other cases we have a more implicit expression that we conjecture gives the invariant density. This conjecture is supported by simulations. For the simulations we use a method that gives us a smooth approximation in every iteration.
]]></description>
<dc:subject>number-theory representation continued-fractions rather-interesting to-understand heuristics 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:75adbfdf72d3/</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:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<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:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.10373">
    <title>[1902.10373] Introducing Minkowski Normality</title>
    <dc:date>2026-05-25T14:23:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.10373</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce the concept of Minkowski normality, a different type of normality for the regular continued fraction expansion. We use the ordering
12,13,23,14,34,25,35,15,⋯
of rationals obtained from the Kepler tree to give a concrete construction of an infinite continued fraction whose digits are distributed according to the Minkowski question mark measure. To do this we define an explicit correspondence between continued fraction expansions and binary codes to show that we can use the dyadic Champernowne number to prove normality of the constructed number. Furthermore, we provide a generalised construction based on the underlying structure of the Kepler tree, which shows that any construction that concatenates the continued fraction expansions of all rationals, ordered so that the sum of the digits of the continued fraction expansion are non-decreasing, results in a number that is Minkowski normal.
]]></description>
<dc:subject>number-theory continued-fractions ergodic-systems heuristics to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:245870b7bb58/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ergodic-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2605.21098">
    <title>[2605.21098] A strange continued fraction associated with the Romik map</title>
    <dc:date>2026-05-25T14:20:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2605.21098</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In 2008, Dan Romik studied in this journal Primitive Pythagorean Triples, or PPTs. In order to do so, he introduced a modified slow (subtractive) Euclidean algorithm, and showed that the underlying dynamical system of this Euclidean algorithm (the ``Romik system''), is ergodic and has a σ-finite, infinite measure, of which is explicitly given.
In this paper, the Romik system is further studied. Various basic properties are determined, such as the expansion of rational numbers and quadratic irrationals. Also (a version of) the planar natural extension of the Romik system is obtained, and the σ-finite, invariant measure is explicitly given, and it is shown that it is ergodic. Furthermore, for Lebesgue almost every x asymptotically half of the regular continued fraction (RCF) convergents of x are among the Romik convergents. We also show that related to the Romik map a ``strange'' continued fraction can be given. ``Strange,'' as the set of possible partial quotients (i.e., digits) for any x∈[0,1] in this expansion is {0,±2}. Various properties of this ``Romik expansion'' are given.
]]></description>
<dc:subject>Pythagorean-triples number-theory continued-fractions rather-interesting edge-cases to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aacb1d7d470e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Pythagorean-triples"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edge-cases"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2504.02350">
    <title>[2504.02350] Inducing contractions of the mother of all continued fractions</title>
    <dc:date>2026-05-25T14:10:49+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.02350</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration techniques -- induced transformations and contraction -- in the setting of Shunji Ito's natural extension of the Farey tent map, which generates `slow' continued fraction expansions. In addition to defining new algorithms, we also realise several existing continued fraction algorithms in our unifying setting. In particular, we find regular continued fractions, the second-named author's S-expansions, and Nakada's parameterised family of α-continued fractions for all 0<α≤1 as examples of contracted Farey expansions. Moreover, we give a new description of a planar natural extension for each of the α-continued fraction transformations as an explicit induced transformation of Ito's natural extension.
]]></description>
<dc:subject>amusing-titles continued-fractions number-theory representation heuristics rather-interesting to-write-about to-simulate consider:normalization consider:open-questions-benchmarks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f8f3fa1c30b2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:amusing-titles"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<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:normalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:open-questions-benchmarks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2504.07092">
    <title>[2504.07092] Are We Done with Object-Centric Learning?</title>
    <dc:date>2026-05-25T12:13:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.07092</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Object-centric learning (OCL) seeks to learn representations that only encode an object, isolated from other objects or background cues in a scene. This approach underpins various aims, including out-of-distribution (OOD) generalization, sample-efficient composition, and modeling of structured environments. Most research has focused on developing unsupervised mechanisms that separate objects into discrete slots in the representation space, evaluated using unsupervised object discovery. However, with recent sample-efficient segmentation models, we can separate objects in the pixel space and encode them independently. This achieves remarkable zero-shot performance on OOD object discovery benchmarks, is scalable to foundation models, and can handle a variable number of slots out-of-the-box. Hence, the goal of OCL methods to obtain object-centric representations has been largely achieved. Despite this progress, a key question remains: How does the ability to separate objects within a scene contribute to broader OCL objectives, such as OOD generalization? We address this by investigating the OOD generalization challenge caused by spurious background cues through the lens of OCL. We propose a novel, training-free probe called Object-Centric Classification with Applied Masks (OCCAM), demonstrating that segmentation-based encoding of individual objects significantly outperforms slot-based OCL methods. However, challenges in real-world applications remain. We provide the toolbox for the OCL community to use scalable object-centric representations, and focus on practical applications and fundamental questions, such as understanding object perception in human cognition. Our code is available here: this https URL.
]]></description>
<dc:subject>image-processing image-segmentation machine-learning rather-interesting algorithms neural-networks image-analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:090aa6203061/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-segmentation"/>
	<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:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2401.17720">
    <title>[2401.17720] Apéry Acceleration of Continued Fractions</title>
    <dc:date>2026-05-25T12:10:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2401.17720</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Apéry in his proof of the irrationality of ζ(3). We show in particular that this can be applied to a large number of continued fractions which can be found in the literature, thus providing a large number of new continued fractions. As examples, we give a new continued fraction for log(2) and for ζ(3), as well as a simple proof of one due to Ramanujan.
]]></description>
<dc:subject>continued-fractions representation rather-interesting heuristics mathematics performance-measure to-write-about to-simulate consider:evolutionary-search consider:accuracy-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aaaab8b3e49a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:evolutionary-search"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:accuracy-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2504.11406">
    <title>[2504.11406] Multi-level Cellular Automata for FLIM networks</title>
    <dc:date>2026-05-25T12:01:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.11406</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The necessity of abundant annotated data and complex network architectures presents a significant challenge in deep-learning Salient Object Detection (deep SOD) and across the broader deep-learning landscape. This challenge is particularly acute in medical applications in developing countries with limited computational resources. Combining modern and classical techniques offers a path to maintaining competitive performance while enabling practical applications. Feature Learning from Image Markers (FLIM) methodology empowers experts to design convolutional encoders through user-drawn markers, with filters learned directly from these annotations. Recent findings demonstrate that coupling a FLIM encoder with an adaptive decoder creates a flyweight network suitable for SOD, requiring significantly fewer parameters than lightweight models and eliminating the need for backpropagation. Cellular Automata (CA) methods have proven successful in data-scarce scenarios but require proper initialization -- typically through user input, priors, or randomness. We propose a practical intersection of these approaches: using FLIM networks to initialize CA states with expert knowledge without requiring user interaction for each image. By decoding features from each level of a FLIM network, we can initialize multiple CAs simultaneously, creating a multi-level framework. Our method leverages the hierarchical knowledge encoded across different network layers, merging multiple saliency maps into a high-quality final output that functions as a CA ensemble. Benchmarks across two challenging medical datasets demonstrate the competitiveness of our multi-level CA approach compared to established models in the deep SOD literature.
]]></description>
<dc:subject>cellular-automata image-processing rather-interesting to-understand to-simulate consider:representation consider:dynamics metaheuristics classification image-segmentation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c02405c5a0f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<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:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-segmentation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2502.07386">
    <title>[2502.07386] Parametric type design in the era of variable and color fonts</title>
    <dc:date>2026-05-25T11:59:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.07386</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Parametric fonts are programatically defined fonts with variable parameters, pioneered by Donald Kunth with his MetaFont technology in the 1980s. While Donald Knuth's ideas in MetaFont and subsequently in MetaPost are often seen as legacy techniques from the pre-graphical user interface (GUI) era of type design, recent trends like variable fonts suggest a resurgence of certain principles. This paper explores a modern type design process built on parametric design principles, specifically using MetaPost. The author created two variable fonts with this method and released them under a free, open-source license. The paper details the methodology, workflow, and insights gained from this process.
]]></description>
<dc:subject>LaTeX typography parametrization graphic-design rather-interesting to-understand aesthetics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:65ef7b225df3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:LaTeX"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:typography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:parametrization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graphic-design"/>
	<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:aesthetics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2405.17629">
    <title>[2405.17629] Lindenmayer graph languages, first-order theories and expanders</title>
    <dc:date>2026-05-25T11:55:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2405.17629</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Combinatorial generation of expander families and Lindenmayer-style development models are both parallel in nature. Both can be handled within proposed parallel graph grammar formalism. Their first-order properties can then be checked by encompassing the generated graph language into an appropriate automatic structure.
]]></description>
<dc:subject>L-systems rewriting-systems graph-theory grammars automata to-write-about review</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:10b55460d8ee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:L-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:grammars"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2604.17401">
    <title>[2604.17401] Markov fractions and Cohn matrices</title>
    <dc:date>2026-05-24T17:30:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2604.17401</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that the Markov fractions introduced recently by Springborn coincide with the index of the Cohn matrices defined by Aigner. This provides a simple concatenation rule for the corresponding continued fractions on the Conway topograph.
]]></description>
<dc:subject>number-theory continued-fractions topology representation to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6a85ab21a3f4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2604.09723">
    <title>[2604.09723] Order-3 pi-formulas, Apery-like kernels, and Clausen functoriality for Conservative Matrix Fields</title>
    <dc:date>2026-05-24T17:27:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2604.09723</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Raz, Shalyt, Leibtag, Kalisch, Weinbaum, Hadad, and Kaminer recently showed that formulas for π can be organized by canonical polynomial recurrences and partially unified by a rank-2 Conservative Matrix Field (CMF). We prove that each order-3 recurrence explicitly printed in the public Appendix~B.6 of their paper is a shifted summation lift of an explicit order-2 kernel, and identify all three kernels: the two π-kernels are explicit rescalings of the sporadic Apéry-like sequences A036917 and A002895 (Domb numbers, case~(α)), while the Catalan kernel is a hypergeometric twist of the Gauss-square coefficient sequence at (a,b,c)=(12,1,32). We place these kernels in a unified Sym2 framework: the first π-kernel and the Catalan kernel come directly from Gauss-square coefficient sequences, while the Domb kernel is recovered by recasting the classical degree-3 Belyi pullback ϕ(x)=108x2/(1−4x)3 and the associated algebraic twist in CMF language. We write an explicit square-gauge matrix for the Gauss CMF, formulate the standard pullback--twist transport in CMF terms, and show that for rank-2 objects it is compatible with Sym2. We further prove an inverse classification: for a fixed Sym2-type Riemann scheme, the one-parameter family of Fuchsian operators contains a unique Sym2(Gauss) point, cut out by the closed-form condition λ0=2γ1γ2(1−2α) on the accessory parameter. Finally, a Belyi-pullback scan over 5040 configurations produces 11 additional integer sequences of the form [xn]λn2F1(a,b;c;ϕ(x))2; we prove their integrality and place them in the same Sym2-pullback framework.
]]></description>
<dc:subject>number-theory classification continued-fractions approximation can't-wait-to-understand-this rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e52df2334e5f/</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:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:can't-wait-to-understand-this"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2509.18522">
    <title>[2509.18522] Functional Information Decomposition: A First-Principles Approach to Analyzing Functional Relationships</title>
    <dc:date>2026-05-24T17:24:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2509.18522</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate a system's intrinsic functional logic with statistical artifacts of limited data. As a result, distinct systems can yield identical observations, rendering information decomposition fundamentally underdetermined and obscuring true higher-order interactions.
We introduce Functional Information Decomposition (FID), both a computational and theoretical framework, which defines informational components with respect to a system's complete input-output mapping, thereby addressing a core cross-scale inference problem: determining how information carried by individual components combines to shape system-level behavior. When the mapping is fully specified, FID provides a unique decomposition into independent and synergistic contributions. Crucially, given only partial observations, FID characterizes the entire space of consistent decompositions by sampling compatible functions, making inferential limits explicit. A complementary geometric perspective clarifies the structural origin of informational components.
We demonstrate FID's interdisciplinary utility on canonical logical functions, Conway's Game of Life, and gene-expression-based prediction of cancer drug response, and provide an open-source implementation. By separating functional architecture from observational distribution, FID offers a principled foundation for analyzing multivariate dependence in both fully and partially observed complex systems.
]]></description>
<dc:subject>information-theory artificial-life physics randomness hey-I-know-this-guy function philosophy-of-science</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7b913a762d18/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:artificial-life"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:randomness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hey-I-know-this-guy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:function"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://hal.science/tel-05570783v1">
    <title>Combinatorial Contemplations - Archive ouverte HAL</title>
    <dc:date>2026-05-24T17:22:15+00:00</dc:date>
    <link>https://hal.science/tel-05570783v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The monograph contains three Chapters. The first chapter is an introduction, outlining my philosophical views on the nature of counting, combinatorial enumeration, things and their names. It also contains a description of the classical Goulden-Jackson method which is used in the second Chapter. The second Chapter, together with the third, present my contributions as well as some recent findings of the literature. More precisely, the second Chapter is focused on the combinatorics of certain types of patterns in the molecular structure of ribonucleic acids (RNAs, one of the most important elements of biological organisms). It examines the distribution of these patterns in the real-world RNA structures and their theoretical models. The third Chapter essentially addresses two things: a new Motzkin-counted restriction of Dyck paths and a new class of Fibonacci-counted words. Not only does it provide purely scientific results, it also gives some autobiographical context. The third section of the Chapter 3 concludes the monograph by presenting a description of related works and possible directions for further research, as well as several short poems about the mesmerising process of translating thoughts into the language of words and numbers.

]]></description>
<dc:subject>mathematical-recreations combinatorics book rather-interesting RNA-folding philosophy-of-science looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9c46af2bec6a/</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:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:book"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:RNA-folding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://hal.science/hal-05574765v1">
    <title>Structural Study of the Accelerated Collatz Map - Archive ouverte HAL</title>
    <dc:date>2026-05-24T17:17:59+00:00</dc:date>
    <link>https://hal.science/hal-05574765v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we develop a structural analysis of a fully accelerated Collatz map on odd integers, which corresponds to the OEIS sequence A363270, and analyze possible cycles by linking exponential valuation growth, harmonic correction terms, and algebraic encoding. Using an affine logarithmic representation, we derive the recursive identity where the slack variable δ i has an explicit closed form, and is limited by 0 < δ i < 1. Furthermore, we evaluate periodic trajectories under the recursive representation, which yields the identity M N -αK N = ∆ N , expressing exponential imbalance as a cumulative harmonic defect, and show that the same quantity governs the determinant of an associated cyclic linear system. We also analyze convergent and extremal behaviors, congruence restrictions, and collapse configurations for the accelerated map. Combining the affine identity with existing computational bounds, we obtain tight Diophantine constraints that possible periodic orbits must satisfy. While not resolving the longstanding Collatz conjecture, this framework isolates structural mechanisms in the accelerated dynamics.

]]></description>
<dc:subject>dynamical-systems Collatz nonlinear-dynamics statistical-mechanics rather-interesting to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:71e9416a54d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Collatz"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistical-mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.versobooks.com/products/3120-control-science">
    <title>Control Science: How Management Made the Modern World | Verso Books</title>
    <dc:date>2026-05-24T17:12:12+00:00</dc:date>
    <link>https://www.versobooks.com/products/3120-control-science</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[What are the rules that govern our workday? Who made them? And how do these rules dominate the rest of our lives?
Whether on Caribbean plantations in the seven­teenth century or in Amazon warehouses today, the powerful have constantly developed new techniques to control workers—and new justifications for doing so. Ideas of control perfected on the factory floor have expanded to dictate our personal lives, polit­ical rights, national policy, and the global economy.

Seventeenth-century intellectuals such as William Petty and John Locke argued that human beings were selfish machines who had to be controlled for their own good. A century later, Jeremy and Samuel Bentham tried to do exactly that with their infamous Panopticon prison. When nineteenth-century Japa­nese elites imported European factory technologies, they came up with new theories of political control to justify this development. After the Second World War, the General Electric Corporation created an in­ternal propaganda department to fight unions, then pitched that propaganda to the country with the help of an actor, the future President Ronald Reagan. Ex­tending these practices, billionaires today dream of extending the algorithmic control of Amazon ware­houses into every corner of our lives.

Blending intellectual, economic, and labor history, Control Science is a thrilling and lucid work of his­tory. Henry Snow reveals how common sense about work, the economy, and human nature was fabricated and must now be challenged.
]]></description>
<dc:subject>history capitalism economics management seeing-like-a-state rather-interesting to-read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3bde2e7d2731/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:capitalism"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:economics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:management"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:seeing-like-a-state"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2601.21766">
    <title>[2601.21766] CoFrGeNet: Continued Fraction Architectures for Language Generation</title>
    <dc:date>2026-05-24T17:10:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2601.21766</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Transformers are arguably the preferred architecture for language generation. In this paper, inspired by continued fractions, we introduce a new function class for generative modeling. The architecture family implementing this function class is named CoFrGeNets - Continued Fraction Generative Networks. We design novel architectural components based on this function class that can replace Multi-head Attention and Feed-Forward Networks in Transformer blocks while requiring much fewer parameters. We derive custom gradient formulations to optimize the proposed components more accurately and efficiently than using standard PyTorch-based gradients. Our components are a plug-in replacement requiring little change in training or inference procedures that have already been put in place for Transformer-based models thus making our approach easy to incorporate in large industrial workflows. We experiment on two very different transformer architectures GPT2-xl (1.5B) and Llama3 (3.2B), where the former we pre-train on OpenWebText and GneissWeb, while the latter we pre-train on the docling data mix which consists of nine different datasets. Results show that the performance on downstream classification, Q\& A, reasoning and text understanding tasks of our models is competitive and sometimes even superior to the original models with 23 to 12 the parameters and shorter pre-training time. We believe that future implementations customized to hardware will further bring out the true potential of our architectures.
]]></description>
<dc:subject>machine-learning representation continued-fractions rational-arithmetic rather-interesting neural-networks performance-measure</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:89915d1a6a54/</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:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rational-arithmetic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2605.14189">
    <title>[2605.14189] The KnotMosaics Package for SageMath</title>
    <dc:date>2026-05-24T16:28:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2605.14189</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce KnotMosaics, a SageMath package for constructing, visualizing, and analyzing knot mosaic diagrams. The package represents an n-mosaic as a matrix of standard tile labels and implements the local connectivity rules needed to validate mosaics, trace strands and components, compute planar diagram codes, generate random examples, and construct rational tangle mosaics. The planar diagram interface connects the mosaic representation to existing knot and link software, enabling computations such as Jones polynomials and knot Floer homology checks. We describe the package design, its main algorithms, and representative examples that illustrate how KnotMosaics can support computational exploration in knot mosaic theory.
]]></description>
<dc:subject>knot-theory tiling software-development SageMath rather-interesting visualization to-write-about to-try consider:training-cases</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:228a4f6cfa37/</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:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:SageMath"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-try"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:training-cases"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2603.27867">
    <title>[2603.27867] 90+ years of the Scottish Book</title>
    <dc:date>2026-05-24T16:24:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2603.27867</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and results of junior mathematicians and students. Also, we summarize the progress during the decade that has passed since the publication of [55], which contained a review of solved problems from the Scottish Book. We also provide an overview of collections of open problems related in one way or another to the Scottish Book. All formulations of the Scottish Book problems in English are cited here from Mauldin, Richard Daniel (ed.) 2015: The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd updated and enlarged edition. Cham: Birkhäuser/Springer
]]></description>
<dc:subject>history-of-science mathematical-recreations challenge looking-to-see rather-interesting review Stan-Ulam</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b7101d650a17/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:challenge"/>
	<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:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Stan-Ulam"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2603.28468">
    <title>[2603.28468] Farey graphs and geodesic expansions of complex continued fractions</title>
    <dc:date>2026-05-24T16:22:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2603.28468</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We discuss complex Farey graphs for the Euclidean imaginary quadratic number fields ℚ(−d‾‾‾√), d∈{1,2,3,7,11}. We study hyperbolic versions of A. Schmidt's Farey polygons living in 3-dimensional hyperbolic space ℍ3. Using these Farey polygons we recover tessellations of the hyperbolic plane ℍ2 that are defined by the action of the Hecke groups H4 and H6 and have been studied earlier by I. Short and M. Walker. Moreover, hyperbolic Farey polygons allow us to define polyhedra that induce Farey tessellations of ℍ3 by the action of certain Bianchi groups. Using complex Farey graphs we consider geodesic complex continued fraction expansions. Our method provides a different and more general approach as the one from the discussion by M. Hockman.
]]></description>
<dc:subject>number-theory continued-fractions Farey-graphs rational-numbers generalization rather-interesting purdy-pitchers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2cb9c469a84c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Farey-graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rational-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:purdy-pitchers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2604.12392">
    <title>[2604.12392] Enumerations and Bijections for Stanley Polyominoes</title>
    <dc:date>2026-05-24T16:19:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2604.12392</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Stanley polyominoes are a subclass of parallelogram polyominoes in which each row begins strictly to the right of the beginning of the previous row and ends strictly to the right of the end of the previous row. In this paper, we derive generating functions for Stanley polyominoes based on the numbers of columns and rows, area, semiperimeter, and numbers of interior points and edges. We also establish combinatorial connections through bijections with other combinatorial structures such as Dyck paths, skew Ferrer diagrams, and peakless Motzkin paths. As a byproduct, we answer the open question of finding a bijection between parallelogram polyominoes of area n and coin fountains with n coins in the even-numbered rows and n−k coins in the odd-numbered rows.
]]></description>
<dc:subject>combinatorics enumeration polyominoes counting discrete-mathematics Catalan-numbers representation rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e41074f25cbc/</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:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:polyominoes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:counting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrete-mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Catalan-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://hal.science/hal-05580502v1">
    <title>Inversion of the Brillouin Function by Dynamic Geometry and Novel Continued-Fraction and Quadratic Methods - Archive ouverte HAL</title>
    <dc:date>2026-05-24T12:34:55+00:00</dc:date>
    <link>https://hal.science/hal-05580502v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Accurate evaluation and inversion of the Brillouin function are essential for describing magnetisation in paramagnetic systems. This paper introduces three complementary computational approaches: a dynamic geometry method, a powered continued-fraction method, and a quadratic-equation approximation. The Brillouin function is first transformed into a polynomial in the variable e^(x/J), where x denotes the ratio of Zeeman energy to thermal energy and J the total angular-momentum quantum number. The polynomial is represented geometrically through line-segment relations and solved by sliding a construction point to vary the exponential variable until the geometric constraints are satisfied. Accuracy in this method is governed by practical limitations such as line thickness, finite point dimensions, compassbased measurement errors, and the adopted precision of Euler's number. Rewriting the polynomial in terms of e^(-x/J) generates an infinite recursive powered continued fraction. Since the variable remains below unity at each stage, successive powering rapidly contracts its magnitude, rendering higher-order terms negligible after a finite number of iterations. In the quadratic-approximation method, the polynomial is recast as a quadratic in a small correction variable, permitting higher-order terms to be neglected. Solved examples demonstrate that three to four iterations typically achieve precision up to ten decimal places.

]]></description>
<dc:subject>numerical-methods continued-fractions approximation algorithms rather-interesting representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:726d350e5f0b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1208.0482">
    <title>[1208.0482] The concurrent evolution of cooperation and the population structures that support it</title>
    <dc:date>2026-05-24T12:27:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1208.0482</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits that affect their population structure to some degree. These traits, such as a group size preference, affect the relatedness of interacting individuals and hence the opportunity for kin or group selection. We argue that models that do not explicitly consider their evolution cannot provide a satisfactory account of the origin of cooperation, because they cannot explain how the prerequisite population structures arise. Here, we consider the concurrent evolution of genetic traits that affect population structure, with those that affect social behavior. We show that not only does population structure drive social evolution, as in previous models, but that the opportunity for cooperation can in turn drive the creation of population structures that support it. This occurs through the generation of linkage disequilibrium between socio-behavioral and population-structuring traits, such that direct kin selection on social behavior creates indirect selection pressure on population structure. We illustrate our argument with a model of the concurrent evolution of group size preference and social behavior.
]]></description>
<dc:subject>artificial-life machine-learning complexology rather-interesting hey-I-know-this-guy theoretical-biology to-simulate consider:performance-measures coevolution</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b7f06f7b43d1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:artificial-life"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:complexology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hey-I-know-this-guy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:theoretical-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:coevolution"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://inria.hal.science/hal-05593313v1">
    <title>Computing hard-to-round cases of sin, cos, tan in double precision - Inria - Institut national de recherche en sciences et technologies du numérique</title>
    <dc:date>2026-05-24T12:22:36+00:00</dc:date>
    <link>https://inria.hal.science/hal-05593313v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper describes an exhaustive search algorithm to find the hardest-to-round cases of trigonometric functions (sin, cos, tan) in double precision (binary64). This algorithm reuses a clever reduction from the literature, but instead of using a sublinear search, it uses a brute force linear search. This algorithm was implemented using multi-threading and SIMD, and a full set of hard-to-round cases for the binary64 trigonometric functions was computed. As a consequence, the Table Maker's Dilemma is now fully solved for the most common univariate binary64 functions.

]]></description>
<dc:subject>numerical-methods computational-complexity algorithms rather-interesting special-cases to-write-about to-simulate approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6249741238f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<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:special-cases"/>
	<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:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<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>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:systems-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:games"/>
	<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:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:load-balancing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-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:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.07391">
    <title>[2206.07391] &quot;Why Here and Not There?&quot; -- Diverse Contrasting Explanations of Dimensionality Reduction</title>
    <dc:date>2026-05-24T12:09:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.07391</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based systems like classifiers and recommender systems. However, transparency of dimensionality reduction and other data mining tools have not been considered in much depth yet, still it is crucial to understand their behavior -- in particular practitioners might want to understand why a specific sample got mapped to a specific location.
In order to (locally) understand the behavior of a given dimensionality reduction method, we introduce the abstract concept of contrasting explanations for dimensionality reduction, and apply a realization of this concept to the specific application of explaining two dimensional data visualization.
]]></description>
<dc:subject>explanation rather-interesting machine-learning dimension-reduction algorithms performance-measure to-write-about to-do</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:50665668209e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dimension-reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-do"/>
</rdf:Bag></taxo:topics>
</item>
<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>
<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:probabilistic-computing"/>
	<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:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.12942">
    <title>[2207.12942] Fractal Images as Number Sequences I An Introduction</title>
    <dc:date>2026-05-24T12:00:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.12942</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This numbering system converts a curve on that grid into a sequence of integers, corresponding with the curve's edges. The corresponding sequence contains the same fractal structure, i.e., an approximant of the curve corresponds to that of the sequence. We introduced a normalized sequence which is unique for a curve. The morphisms of the grid generators were translated into signed permutations on the alphabet of all the numbers used. By ordering the fractal sequences, we obtained an encyclopedia of fractals. A variety of examples and images enriched the text.
]]></description>
<dc:subject>fractals representation number-theory mathematical-recreations rather-interesting tiling consider:aperiodic-tiling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4986c524f4e4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fractals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:aperiodic-tiling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.03892">
    <title>[2012.03892] Three characterizations of a self-similar aperiodic 2-dimensional subshift</title>
    <dc:date>2026-05-24T11:57:00+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.03892</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The goal of this chapter is to illustrate a generalization of the Fibonacci word to the case of 2-dimensional configurations on ℤ2. More precisely, we consider a particular subshift of ℤ2 on the alphabet ={0,…,15} for which we give three characterizations: as the subshift Φ generated by a 2-dimensional morphism Φ defined on ; as the Wang shift Ω defined by a set  of 16 Wang tiles; as the symbolic dynamical system ,R representing the orbits under some ℤ2-action R defined by rotations on 𝕋2 and coded by some topological partition  of 𝕋2 into 16 polygonal atoms. We prove their equality Ω=Φ=,R by showing that they are self-similar with respect to the substitution Φ.
This chapter provides a transversal reading of results divided into four different articles obtained through the study of the Jeandel-Rao Wang shift. It gathers in one place the methods introduced to desubstitute Wang shifts and to desubstitute codings of ℤ2-actions by focussing on a simple 2-dimensional self-similar subshift. SageMath code to find marker tiles and compute the Rauzy induction of ℤ2-rotations is provided allowing to reproduce the computations. The chapter contains many exercises whose solutions are provided at the end.
]]></description>
<dc:subject>nonlinear-dynamics rewriting-systems dynamical-systems permutations research-maneuvers rather-interesting to-write-about to-simulate consider:L-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fdc10ba71d50/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:permutations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:research-maneuvers"/>
	<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:L-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathenchant.wordpress.com/2025/07/17/when-999-isnt-1/">
    <title>When .999… Isn’t 1 |</title>
    <dc:date>2026-05-24T11:51:05+00:00</dc:date>
    <link>https://mathenchant.wordpress.com/2025/07/17/when-999-isnt-1/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In ordinary math, the infinite decimal .999… is defined to be the limit of the terminating decimals .9, .99, .999, …; that is, it’s defined to be the real number that the fractions 9/10, 99/100, 999/1000, … approach in the ordinary sense. And that limit is most definitely 1, not some real number that’s a tiny bit less than 1. This is not an approximate truth; it’s a 100% accurate, rigorously established mathematical fact. It’s a part of how the real number system works, and it’s a feature, not a bug.

]]></description>
<dc:subject>q-adic-numbers number-theory mathematical-recreations explanation rather-interesting continued-fractions to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f1586b49ab62/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:q-adic-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2204.11111">
    <title>[2204.11111] Planar Substitutions to Lebesgue type Space-Filling Curves and Relatively Dense Fractal-like Sets in the Plane</title>
    <dc:date>2026-05-24T11:22:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2204.11111</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild condition. The generated space-filling curves for some known substitutions are elucidated. Some of those substitutions further induce relatively dense fractal-like sets in the plane, whenever some additional assumptions are met.
]]></description>
<dc:subject>aperiodic-tiling fractals mathematical-recreations tiling rather-interesting to-write-about to-simulate consider:ghost</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:66de3652a835/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fractals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<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:ghost"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.04298">
    <title>[2107.04298] An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition</title>
    <dc:date>2026-05-24T11:15:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.04298</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[An algorithm for reversible logic synthesis is proposed. The task is, for a given n-bit substitution map Pn:{0,1}n→{0,1}n, to find a sequence of reversible logic gates that implements the map. The gate library adopted in this work consists of multiple-controlled Toffoli gates denoted by CmX, where m is the number of control bits that ranges from 0 to n−1. Controlled gates with large m(>2) are then further decomposed into C0X, C1X, and C2X gates. A primary concern in designing the algorithm is to reduce the use of C2X gate (also known as Toffoli gate) which is known to be universal.
The main idea is to view an n-bit substitution map as a rank-2n tensor and to transform it such that the resulting map can be written as a tensor product of a rank-(2n−2) tensor and the 2×2 identity matrix. Let n be a set of all n-bit substitution maps. What we try to find is a size reduction map red:n→{Pn:Pn=Pn−1⊗I2}. %, where Im is the m×m identity matrix. One can see that the output Pn−1⊗I2 acts nontrivially on n−1 bits only, meaning that the map to be synthesized becomes Pn−1. The size reduction process is iteratively applied until it reaches tensor product of only 2×2 matrices.
]]></description>
<dc:subject>circuit-synthesis quantum-computing engineering-design rather-interesting cellular-automata metaheuristics to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a1381ee122ec/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:circuit-synthesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quantum-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<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/2407.03357">
    <title>[2407.03357] Elementary Formulas for Greatest Common Divisors and Semiprime Factors</title>
    <dc:date>2026-05-24T11:08:57+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.03357</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We conjecture new elementary formulas for computing the greatest common divisor (GCD) of two integers, alongside an elementary formula for extracting the prime factors of semiprimes. These formulas are of fixed-length and require only the basic arithmetic operations of: addition, subtraction, multiplication, division with remainder, and exponentiation. Our GCD formulas result from simplifying a formula of Mazzanti and are derived using Kronecker substitution techniques from our earlier research. By applying these GCD formulas together with our recent discovery of an arithmetic expression for n‾√, we are able to derive explicit elementary formulas for the prime factors of a semiprime n=pq.
]]></description>
<dc:subject>algorithms numerical-methods computational-complexity rather-interesting performance-measure consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:99ab92c256bf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.03510">
    <title>[2407.03510] Evolutionary Approach to S-box Generation: Optimizing Nonlinear Substitutions in Symmetric Ciphers</title>
    <dc:date>2026-05-24T11:07:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.03510</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This study explores the application of genetic algorithms in generating highly nonlinear substitution boxes (S-boxes) for symmetric key cryptography. We present a novel implementation that combines a genetic algorithm with the Walsh-Hadamard Spectrum (WHS) cost function to produce 8x8 S-boxes with a nonlinearity of 104. Our approach achieves performance parity with the best-known methods, requiring an average of 49,399 iterations with a 100% success rate. The study demonstrates significant improvements over earlier genetic algorithm implementations in this field, reducing iteration counts by orders of magnitude. By achieving equivalent performance through a different algorithmic approach, our work expands the toolkit available to cryptographers and highlights the potential of genetic methods in cryptographic primitive generation. The adaptability and parallelization potential of genetic algorithms suggest promising avenues for future research in S-box generation, potentially leading to more robust, efficient, and innovative cryptographic systems. Our findings contribute to the ongoing evolution of symmetric key cryptography, offering new perspectives on optimizing critical components of secure communication systems.
]]></description>
<dc:subject>metaheuristics evolutionary-algorithms cryptography rather-interesting to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:64007245b44e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:evolutionary-algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cryptography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2501.10090">
    <title>[2501.10090] Variations on a theme of Apéry</title>
    <dc:date>2026-05-24T11:05:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2501.10090</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Apéry's remarkable discovery of rapidly converging continued fractions with small coefficients for ζ(2) and ζ(3) has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to show that modifications of Apéry's continued fractions can give interesting results including new rapidly convergent continued fractions for certain interesting constants.
]]></description>
<dc:subject>continued-fractions approximation number-theory elegant-mathematics rather-interesting to-write-about representation consider:symbolic-regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f73b97ad1bf4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:elegant-mathematics"/>
	<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:representation"/>
	<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/2410.04480">
    <title>[2410.04480] Learning to Solve Abstract Reasoning Problems with Neurosymbolic Program Synthesis and Task Generation</title>
    <dc:date>2026-05-24T10:59:46+00:00</dc:date>
    <link>https://arxiv.org/abs/2410.04480</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The ability to think abstractly and reason by analogy is a prerequisite to rapidly adapt to new conditions, tackle newly encountered problems by decomposing them, and synthesize knowledge to solve problems comprehensively. We present TransCoder, a method for solving abstract problems based on neural program synthesis, and conduct a comprehensive analysis of decisions made by the generative module of the proposed architecture. At the core of TransCoder is a typed domain-specific language, designed to facilitate feature engineering and abstract reasoning. In training, we use the programs that failed to solve tasks to generate new tasks and gather them in a synthetic dataset. As each synthetic task created in this way has a known associated program (solution), the model is trained on them in supervised mode. Solutions are represented in a transparent programmatic form, which can be inspected and verified. We demonstrate TransCoder's performance using the Abstract Reasoning Corpus dataset, for which our framework generates tens of thousands of synthetic problems with corresponding solutions and facilitates systematic progress in learning.
]]></description>
<dc:subject>ARC machine-learning genetic-programming neural-networks program-synthesis learning-from-data artificial-intelligence rather-interesting hey-I-know-this-guy</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5ba29e7a72c7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ARC"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:program-synthesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning-from-data"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:artificial-intelligence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hey-I-know-this-guy"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2408.06691">
    <title>[2408.06691] Complete ergodicity in one-dimensional reversible cellular automata</title>
    <dc:date>2026-05-24T10:53:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.06691</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure.
]]></description>
<dc:subject>nonlinear-dynamics cellular-automata ergodic-systems combinatorics complexology rather-interesting classification to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:163a69784c1b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ergodic-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:complexology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t: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/2408.05395">
    <title>[2408.05395] The evolution of systems biology and systems medicine: From mechanistic models to uncertainty quantification</title>
    <dc:date>2026-05-24T10:49:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.05395</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing biochemical regulatory mechanisms. Building on experiments, mechanistic models are widely used to describe small-scale intracellular networks and uncover biochemical mechanisms in healthy and diseased states. The rapid development of high-throughput sequencing techniques and computational tools has recently enabled models that span multiple scales, often integrating signaling, gene regulatory, and metabolic networks. These multiscale models enable comprehensive investigations of cellular networks and thus reveal previously unknown disease mechanisms and pharmacological interventions. Here, we review systems biology models from classical mechanistic models to larger, multiscale models that integrate multiple layers of cellular networks. We introduce several examples of models of hypertrophic cardiomyopathy, exercise, and cancer cell proliferation. Additionally, we discuss methods that increase the certainty and accuracy of model predictions. Integrating multiscale models has become a powerful tool for understanding disease and inspiring drug discoveries by incorporating omics data within the cell and across tissues and organisms.
]]></description>
<dc:subject>systems-biology molecular-machinery medicine medical-technology network-theory pharmaceutical machine-learning rather-interesting models-and-modes reaction-networks systems-thinking</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d028f0a81a52/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:molecular-machinery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:medicine"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:medical-technology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pharmaceutical"/>
	<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:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:reaction-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:systems-thinking"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.11632">
    <title>[2407.11632] Wigglyhedra</title>
    <dc:date>2026-05-24T10:47:17+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.11632</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Motivated by categorical representation theory, we define the wiggly complex, whose vertices are arcs wiggling around n+2 points on a line, and whose faces are sets of wiggly arcs which are pairwise pointed and non-crossing. The wiggly complex is a (2n−1)-dimensional pseudomanifold, whose facets are wiggly pseudotriangulations. We show that wiggly pseudotriangulations are in bijection with wiggly permutations, which are permutations of [2n] avoiding the patterns (2j−1)⋯i⋯(2j) for i<2j−1 and (2j)⋯k⋯(2j−1) for k>2j. These permutations define the wiggly lattice, an induced sublattice of the weak order. We then prove that the wiggly complex is isomorphic to the boundary complex of the polar of the wigglyhedron, for which we give explicit and simple vertex and facet descriptions. Interestingly, we observe that any Cambrian associahedron is normally equivalent to a well-chosen face of the wigglyhedron. Finally, we recall the correspondence of wiggly arcs with objects in a category, and we develop categorical criteria for a subset of wiggly arcs to form a face of the wiggly complex.
]]></description>
<dc:subject>category-theory combinatorics enumeration mathematical-recreations rather-interesting to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c6f72fa24635/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="https://talk.objc.io/">
    <title>Swift Talk - objc.io</title>
    <dc:date>2026-05-23T12:10:37+00:00</dc:date>
    <link>https://talk.objc.io/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Swift Talk
A weekly video series on Swift programming]]></description>
<dc:subject>swift programming-language software-development video to-watch training</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1e2b9337fc8c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:swift"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:video"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-watch"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:training"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2512.06522v2">
    <title>[2512.06522v2] Hierarchical Clustering With Confidence</title>
    <dc:date>2026-05-23T12:01:40+00:00</dc:date>
    <link>https://arxiv.org/abs/2512.06522v2</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often producing different clustering results and making it difficult to separate genuine structure from spurious patterns. In this paper, we show how randomizing hierarchical clustering can be useful not just for measuring stability but also for designing valid hypothesis testing procedures based on the clustering results.
We propose a simple randomization scheme together with a method for constructing a valid p-value at each node of the hierarchical clustering dendrogram that quantifies evidence against performing the greedy merge. Our test controls the Type I error rate, works with any hierarchical linkage without case-specific derivations, and simulations show it is substantially more powerful than existing selective inference approaches. To demonstrate the practical utility of our p-values, we develop an adaptive α-spending procedure that estimates the number of clusters, with a probabilistic guarantee on overestimation. Experiments on simulated and real data show that this estimate yields powerful clustering and can be used, for example, to assess clustering stability across multiple runs of the randomized algorithm.
]]></description>
<dc:subject>clustering statistics numerical-methods probability-theory unsupervised-learning algorithms rather-interesting to-write-about to-cite consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a39717e23952/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unsupervised-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-cite"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.objc.io/blog/2019/12/16/drawing-trees/">
    <title>Drawing Trees in SwiftUI · objc.io</title>
    <dc:date>2026-05-23T11:56:43+00:00</dc:date>
    <link>https://www.objc.io/blog/2019/12/16/drawing-trees/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For a new project, we need to draw tree diagrams in SwiftUI. In this post, we'll walk you through our attempts, and show how we use SwiftUI’s preference system to draw clean and interactive diagrams with minimal code.
]]></description>
<dc:subject>swift visualization programming-language rather-interesting SwiftUI</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a3bde1c0e2df/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:swift"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:SwiftUI"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2502.12717">
    <title>[2502.12717] Learning the symmetric group: large from small</title>
    <dc:date>2026-05-22T11:20:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.12717</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not suffer from noise, but a challenge is the amount of data required to train these models and that this data can be computationally expensive to generate. Key challenges further comprise difficulty in a posteriori interpretation of statistical models and the implementation of deep and abstract mathematical problems.
We propose a method for scalable tasks, by which models trained on simpler versions of a task can then generalize to the full task. Specifically, we demonstrate that a transformer neural-network trained on predicting permutations from words formed by general transpositions in the symmetric group S10 can generalize to the symmetric group S25 with near 100\% accuracy. We also show that S10 generalizes to S16 with similar performance if we only use adjacent transpositions. We employ identity augmentation as a key tool to manage variable word lengths, and partitioned windows for training on adjacent transpositions. Finally we compare variations of the method used and discuss potential challenges with extending the method to other tasks.
]]></description>
<dc:subject>machine-learning mathematical-programming combinatorics neural-networks formal-languages to-understand to-write-about group-theory rather-interesting feature-construction approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:062e950d111d/</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:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2603.10941">
    <title>[2603.10941] Covariate-adjusted statistical dependence representation through partial copulas: bounds and new insights</title>
    <dc:date>2026-05-22T11:17:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2603.10941</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a covariate. Building upon results previously presented in the literature, we show that partial copulas can be seen as a nonlinear analogue of partial correlation. Then, we prove several results showing how dependence properties of the conditional copulas constrain the form of the partial copula. Finally, a simulation study is conducted to illustrate the results and to show the potential of partial copula as a way to describe covariate-adjusted statistical dependence. This highlights the potential of the method to be used in causal inference problems and recover the true sign of a causal effect.
]]></description>
<dc:subject>statistics correlation models models-and-modes to-understand representation causality via:?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:36c7daa074e0/</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:correlation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:causality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://msp.org/cnt/2026/15-2/p02.xhtml">
    <title>Combinatorics and Number Theory Vol. 15, No. 2, 2026</title>
    <dc:date>2026-05-22T10:51:00+00:00</dc:date>
    <link>https://msp.org/cnt/2026/15-2/p02.xhtml</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We explore a new form of periodic behavior among continued fractions having telescoping periods. Informally speaking, a quasiperiodic continued fraction...
We then take a closer look into negative unary continued fractions (NUCFs), and present a theorem showing that by deviating from the least integer algorithm, every irrational number has uncountably many NUCF representations.

]]></description>
<dc:subject>continued-fractions number-theory representation rather-interesting to-understand paywall</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:103f201e9b72/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<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:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:paywall"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2603.21852v2">
    <title>[2603.21852v2] All elementary functions from a single binary operator</title>
    <dc:date>2026-05-22T10:46:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2603.21852v2</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions. For example, exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as S -> 1 | eml(S,S). This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.
]]></description>
<dc:subject>mathematics representation rather-interesting amusing-also to-write-about consider:genetic-programming consider:alternatives</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0c232cea7a85/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:amusing-also"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:alternatives"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://medium.com/@jaberi.mohamedhabib/swift-enums-unleashed-a-deep-dive-into-power-and-versatility-5ab9d45da560">
    <title>Swift Enums Unleashed: A Deep Dive into Power and Versatility | by JABERI Mohamed Habib | Medium</title>
    <dc:date>2026-05-22T10:41:13+00:00</dc:date>
    <link>https://medium.com/@jaberi.mohamedhabib/swift-enums-unleashed-a-deep-dive-into-power-and-versatility-5ab9d45da560</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In the dynamic landscape of Swift programming, enums stand as a powerful and versatile feature, bringing a structured approach to defining enumerations. This article delves into the world of Swift enums, exploring their syntax, capabilities, and the myriad ways they enhance code organisation and readability.
]]></description>
<dc:subject>swift programming-language explanation bullshit invalid-syntax incorrect-advice slop?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:884fa7ccd741/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:swift"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bullshit"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:invalid-syntax"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:incorrect-advice"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:slop?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2605.22129">
    <title>[2605.22129] On Isotopies and hyperbolicity of weaves</title>
    <dc:date>2026-05-22T10:22:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2605.22129</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A weave is a type of textile that consists of vertical and horizontal threads, and typically it has a periodic structure. In this paper, we regard a weave as a link in the thickened torus with a diagram consisting of closed geodesics. As main results, we characterize isotopies and hyperbolicity of weaves to determine them from diagrams. Moreover, we show that there does not exist an essential Conway sphere for a weave. We use normal positions of essential surfaces of weave complements to describe them.
]]></description>
<dc:subject>topology combinatorics mathematical-recreations mathematics knot-theory to-understand enumeration consider:structural-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:67c9f5ce3c4c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:structural-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.science.org/doi/10.1126/science.adv7924">
    <title>DefensePredictor: A machine learning model to discover prokaryotic immune systems | Science</title>
    <dc:date>2026-04-26T12:32:02+00:00</dc:date>
    <link>https://www.science.org/doi/10.1126/science.adv7924</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Bacteria have diverse immune systems that protect them from viral infection, yet the full extent of this diversity remains unknown. Two groups of researchers have now independently developed machine learning and deep learning models that leverage protein sequences and genomic context to predict antiphage defense systems at scale. DeWeirdt et al. developed a model called DefensePredictor and applied it to Escherichia coli, experimentally validating dozens of previously uncharacterized defense systems. Mordret et al. developed several different models and applied them to over 120 million proteins from bacterial genomes, identifying hundreds of thousands of candidate antiphage families, many lacking any prior annotation. Together, these studies reveal that bacterial immunity is far more extensive than previously thought and highlight how such discoveries can inspire powerful biotechnologies. —Di Jiang
]]></description>
<dc:subject>structural-biology machine-learning bioinformatics indistinguishable-from-magic learning-from-data to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d94701a9a214/</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:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bioinformatics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:indistinguishable-from-magic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning-from-data"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2604.09726">
    <title>[2604.09726] Error terms for continued fractions of $e^{1/s}$ and $sqrt{frac{v}{u}}tanh!Bigl(frac{1}{sqrt{uv}}Bigr)$</title>
    <dc:date>2026-04-26T12:30:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2604.09726</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Many classical identities arise from nothing more mysterious than looking at the same object in two different ways. A number, a function, or a combinatorial object may admit several natural decompositions, and by disassembling it in one way and reassembling it in another, we often obtain unexpected corollaries. Telescoping sums provide a particularly vivid incarnation of this principle: by arranging terms so that successive contributions cancel, one performs a conceptual ``cut-and-paste'' that often admits a clean geometric interpretation. Generating functions offer a complementary perspective. Encoding a problem into a formal power series and then evaluating that series at a prescribed point naturally expresses the same quantity as an infinite (or finite) expansion, and equating these representations yields a wealth of identities.
For example, for a real number \(\alpha\) given by its continued fraction expansion α=[a0,a1,a2,…], with convergents \(p_n/q_n\) and error terms En:=pn−αqn, one can obtain ``additive'' decompositions of the form ∑n≥−1an+1|En|=α+1, ∑n≥−1an+1E2n=α. Thus α and α+1 themselves appear as weighted sums of the local approximation errors of their convergents. In this note we explore what such decompositions yield in two explicit cases: the continued fraction
e1/s=[1;(2k−1)s−1,1,1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯]∞k=1
and the continued fraction
sutanh(1s)=[0;(4k−3)u,(4k−1)s2u⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯]∞k=1
]]></description>
<dc:subject>continued-fractions representation looking-to-see rather-interesting consider:pattern-discovery consider:symbolic-regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b4120f24c2b2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t: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:consider:pattern-discovery"/>
	<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/2502.08396">
    <title>[2502.08396] Periodic double tilings of the plane</title>
    <dc:date>2026-04-20T15:57:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.08396</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both in the case of a fixed lattice or for an arbitrary periodic lattice. We find three different configurations depending on the ratio between the assigned areas of the two tiles and compute the isoperimetric profile. The three different configurations are composed of tiles with a different number of circular edges, moreover, different configurations exhibit a different optimal lattice. Finally, we raise some open problems related to our investigation.
]]></description>
<dc:subject>tiling geometry plane-geometry rather-interesting constraint-satisfaction optimization to-understand consider:visualization consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:bb01f0f94f1a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<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:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2502.08188">
    <title>[2502.08188] Breakdown of Magic Numbers in Spherical Confinement</title>
    <dc:date>2026-04-20T15:54:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.08188</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Magic numbers in finite particle systems correspond to specific system sizes that allow configurations with low free energy, often exhibiting closed surface shells to maximize the number of nearest neighbors. Since their discovery in atomic nuclei, magic numbers have been essential for understanding the number-structure-property relationship in finite clusters across different scales. However, as system size increases, the significance of magic numbers diminishes, and the precise system size at which magic number phenomena disappear remains uncertain. In this study, we investigate colloidal clusters formed through confined self-assembly. Small magic number clusters display icosahedral symmetry with closed surface shells, corresponding to pronounced free energy minima. Our findings reveal that beyond a critical system size, closed surface shells disappear, and free energy minima become less pronounced. Instead, we observe a distinct type of colloidal cluster, termed football cluster, which retains icosahedral symmetry but features lower-coordinated facets disconnected by terraces. A sphere packing model demonstrates that forming closed surface shells becomes impossible beyond a critical system size, explaining the breakdown of magic numbers in large confined systems.
]]></description>
<dc:subject>self-organization self-assembly packing molecular-design looking-to-see physics! rather-interesting colloids combinatorics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2386898a5462/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:self-organization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:self-assembly"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:molecular-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:colloids"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2502.06926">
    <title>[2502.06926] Quasilattices of the Spectre monotile</title>
    <dc:date>2026-04-20T15:50:49+00:00</dc:date>
    <link>https://arxiv.org/abs/2502.06926</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Spectre is a family of recently discovered aperiodic monotiles that tile the plane only in non-periodic ways, and novel physical phenomena have been predicted for planar systems made of aperiodic monotiles. It is shown that point decorations of Tile(1,1), the base tile for all Spectres, supports the generation of a large variety of non-periodic quasilattices, in contrast to Bravais-lattices in which all point decorations would be periodic. A lattice generating function is introduced as a mapping from point decorations to quasilattice space, and investigated systematically. It is found that some lattices result from the properties of nearest-neighbor distances of point decorations, and that other lattices show near-periodicity in projections along one of the symmetry axes of the tiling. It is concluded that the lattice generating function can serve as a template for the design of physical potential landscapes that can be controlled by the point decoration as a parameter.
]]></description>
<dc:subject>tiling monotiles! quasicrystals nonlinear-dynamics rather-interesting spectra aperiodic-tiling to-simulate consider:animation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:84b51209adc8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:monotiles!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasicrystals"/>
	<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:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:animation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2310.12160">
    <title>[2310.12160] On geometric interpretation of Euler's substitutions</title>
    <dc:date>2026-04-20T11:46:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2310.12160</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler's substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.
]]></description>
<dc:subject>rewriting-systems Euler numerical-methods constraint-satisfaction rather-interesting visualization calculus heuristics consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:61f7d0665756/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Euler"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<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:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:calculus"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>