<?xml version="1.0" encoding="UTF-8"?>
 <rdf:RDF xmlns="http://purl.org/rss/1.0/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:taxo="http://purl.org/rss/1.0/modules/taxonomy/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://web.resource.org/cc/" xmlns:syn="http://purl.org/rss/1.0/modules/syndication/" xmlns:admin="http://webns.net/mvcb/">
  <channel rdf:about="http://pinboard.in">
    <title>Pinboard (Vaguery)</title>
    <link>https://pinboard.in/u:Vaguery/public/</link>
    <description>recent bookmarks from Vaguery</description>
    <items>
      <rdf:Seq>	<rdf:li rdf:resource="https://arxiv.org/abs/2111.02607"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2109.03392"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2202.05219"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1610.04080"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2102.02365"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2110.12999"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1804.03979"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1702.02650"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1703.04157"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1906.12272"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2102.00113"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1810.07921"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2010.11406"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1709.08364"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1403.4131"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1605.04416"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1801.04087"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1904.04314"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1904.04412"/>
	<rdf:li rdf:resource="https://www.cs.purdue.edu/homes/gnf/book/hardcrefs.html"/>
	<rdf:li rdf:resource="https://theinnerframe.wordpress.com/2018/04/16/a-double-figure-8/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1706.00399"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1203.3353"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1107.4030"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/nlin/0206025"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1803.02875"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1902.08171"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1807.09196"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1802.09904"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1204.0403"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/math/0111080"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1512.05104"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1506.05276"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1311.4373"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1205.0392"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1105.0095"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1102.1750"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1007.0707"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/0909.5605"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/0810.5750"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/math/0610411"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1806.09644"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1711.03247"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1710.08485"/>
	<rdf:li rdf:resource="https://dl.acm.org/citation.cfm?id=264996"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1708.04597"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1702.04199"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1304.4005"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1901.01624"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1709.09683"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1809.09581"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1806.05739"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1506.02572"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1801.02162"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1605.03502"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1809.07390"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1808.04730"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1710.00217"/>
	<rdf:li rdf:resource="https://www.atlasobscura.com/articles/ansel-adams-mystery-astronomy"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1506.09039"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1710.06647"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1604.02181"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1710.00709"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1710.03370"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1704.07422"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1702.01522"/>
	<rdf:li rdf:resource="https://distill.pub/2017/feature-visualization/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1308.5550"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1709.07208"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1704.08326"/>
      </rdf:Seq>
    </items>
  </channel><item rdf:about="https://arxiv.org/abs/2111.02607">
    <title>[2111.02607] Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation</title>
    <dc:date>2023-09-09T22:43:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.02607</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Then, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of the sequential and iterative calculations of the CEM form-finding algorithm, instead of a numerical approximation. Finally, we encapsulate our research developments into an open-source design tool written in Python that is usable across different CAD platforms and operating systems. After studying four different structures -- a self-stressed planar tensegrity, a tree canopy, a curved bridge, and a spiral staircase -- we demonstrate that our approach enables the solution of constrained form-finding problems on a diverse range of structures more efficiently than in previous work.
]]></description>
<dc:subject>numerical-methods structural-engineering rather-interesting generative-models structure architecture inverse-problems to-understand to-write-about consider:benchmarks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c2c1ce6f5115/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:structural-engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:structure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:architecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:benchmarks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.03392">
    <title>[2109.03392] Joint Search of Optimal Topology and Trajectory for Planar Linkages</title>
    <dc:date>2023-02-05T11:29:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.03392</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex periodic motion, \refined{which is an important component when building low-cost, modular robots, mechanical toys, and foldable structures in our daily lives (chairs, bikes, and shelves). The design of such structures require trial and error even for experienced engineers. Our research provides semi-automatic methods for exploring novel designs given high-level specifications and constraints.} We formulate this problem as a non-smooth numerical optimization with quadratic objective functions and non-convex quadratic constraints involving mixed-integer decision variables (MIQCQP). We propose and compare three approximate algorithms to solve this problem: mixed-integer conic-programming (MICP), mixed-integer nonlinear programming (MINLP), and simulated annealing (SA). We evaluated these algorithms searching for planar linkages involving 10−14 rigid links. Our results show that the best performance can be achieved by combining MICP and MINLP, leading to a hybrid algorithm capable of finding the planar linkages within a couple of hours on a desktop machine, which significantly outperforms the SA baseline in terms of optimality. We highlight the effectiveness of our optimized planar linkages by using them as legs of a walking robot.
]]></description>
<dc:subject>inverse-problems planar-linkages engineering-design rather-interesting operations-research to-write-about to-simulate consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3ded4f6a9aae/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:planar-linkages"/>
	<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:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2202.05219">
    <title>[2202.05219] Solving integral equations in free-space with inverse-designed ultrathin optical metagratings</title>
    <dc:date>2022-10-19T22:22:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2202.05219</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analog optical computing enables processing large amounts of data at a  t energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real-time, in particular for edge detection. By incorporating feedback, it has also been recently shown that metamaterials can be tailored to solve complex mathematical problems in the analog domain, although these efforts have so far been limited to guided-wave systems and bulky setups. Here, we present an ultrathin Si metasurface-based platform for analog computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed Kernel corresponding to the mathematical problem of interest. Next, a semi-transparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analog domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free-space, implying high processing speeds and the possibility of on-chip integration.
]]></description>
<dc:subject>optics indistinguishable-from-magic unconventional-computing engineering-design inverse-problems rather-interesting to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:426cf8000da6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:indistinguishable-from-magic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unconventional-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1610.04080">
    <title>[1610.04080] Cuspidal Robots</title>
    <dc:date>2022-05-12T11:01:00+00:00</dc:date>
    <link>https://arxiv.org/abs/1610.04080</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then been fascinating a lot of researchers. After a brief history of cuspidal robots, the chapter provides the main features of cuspidal robots: explanation of the non-singular change of posture, uniqueness domains, regions of feasible paths, identification and classification of cuspidal robots. The chapter focuses on 3-R orthogonal serial robots. The case of 6-dof robots and parallel robots is discussed in the end of this chapter.
]]></description>
<dc:subject>robotics inverse-problems rather-interesting constraint-satisfaction to-understand kinematics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3316f50a74f2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:robotics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:kinematics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.02365">
    <title>[2102.02365] Wind Field Reconstruction with Adaptive Random Fourier Features</title>
    <dc:date>2022-04-19T10:30:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.02365</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including Kriging and Inverse distance weighting. Random Fourier features is a linear model β(xx)=∑Kk=1βkeiωkxx approximating the velocity field, with frequencies ωk randomly sampled and amplitudes βk trained to minimize a loss function. We include a physically motivated divergence penalty term |∇⋅β(xx)|2, as well as a penalty on the Sobolev norm. We derive a bound on the generalization error and derive a sampling density that minimizes the bound. Following (arXiv:2007.10683 [math.NA]), we devise an adaptive Metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.
]]></description>
<dc:subject>approximation inverse-problems rather-interesting learning-from-data nonlinear-dynamics online-learning to-understand statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3fa7289011de/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning-from-data"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:online-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.12999">
    <title>[2110.12999] Deep learning-based design of broadband GHz complex and random metasurfaces</title>
    <dc:date>2022-01-27T14:17:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.12999</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We are interested to explore the limit in using deep learning (DL) to study the electromagnetic response for complex and random metasurfaces, without any specific applications in mind. For simplicity, we focus on a simple pure reflection problem of a broadband electromagnetic (EM) plane wave incident normally on such complex metasurfaces in the frequency regime of 2 to 12 GHz. In doing so, we create a deep learning (DL) based framework called metasurface design deep convolutional neural network (MSDCNN) for both the forward and inverse design of three different classes of complex metasurfaces: (a) Arbitrary connecting polygons, (b) Basic pattern combination, and (c) Fully random binary patterns. The performance of each metasurface is evaluated and cross-benchmarked. Dependent on the type of complex metasurfaces, sample size, and DL algorithms used, MSDCNN is able to provide good agreements and can be a faster design tool for complex metasurfaces as compared to the traditional full-wave electromagnetic simulation methods. However, no single universal deep convolutional neural network (DCNN) model can work well for all metasurface classes based on detailed statistical analysis (such as mean, variance, kurtosis, mean squared error). Our findings report important information on the advantages and limitation of current DL models in designing these ultimately complex metasurfaces.
]]></description>
<dc:subject>inverse-problems materials-science electromagnetism engineering-design indistinguishable-from-magic to-write-about consider:genetic-programming consider:sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1c41d151f624/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:electromagnetism"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:indistinguishable-from-magic"/>
	<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:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1804.03979">
    <title>[1804.03979] Experimental similarity assessment for a collection of fragmented artifacts</title>
    <dc:date>2022-01-02T21:17:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1804.03979</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In the Visual Heritage domain, search engines are expected to support archaeologists and curators to address cross-correlation and searching across multiple collections. Archaeological excavations return artifacts that often are damaged with parts that are fragmented in more pieces or totally missing. The notion of similarity among fragments cannot simply base on the geometric shape but style, material, color, decorations, etc. are all important factors that concur to this concept. In this work, we discuss to which extent the existing techniques for 3D similarity matching are able to approach fragment similarity, what is missing and what is necessary to be further developed.
]]></description>
<dc:subject>computational-geometry assembly archaeology rather-interesting inverse-problems unbreaking algorithms to-write-about to-simulate consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cd333763fa28/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:assembly"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:archaeology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unbreaking"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1702.02650">
    <title>[1702.02650] Diagonal elements in the Nonnegative Inverse Eigenvalue Problem</title>
    <dc:date>2021-11-09T11:28:52+00:00</dc:date>
    <link>https://arxiv.org/abs/1702.02650</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterising all realisable lists. Although the NIEP remains unsolved, it has been solved in the case where every entry in the list (apart from the Perron eigenvalue) has nonpositive real part. For a given spectrum of this type, we show that a list of nonnegative numbers may arise as the diagonal elements of the realising matrix if and only if these numbers satisfy a remarkably simple inequality. Furthermore, we show that realisation can be achieved by the sum of a companion matrix and a diagonal matrix.
]]></description>
<dc:subject>number-theory inverse-problems matrices analysis to-write-about to-simulate consider:looking-to-see consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f371540bff38/</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:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1703.04157">
    <title>[1703.04157] Using Aggregated Relational Data to feasibly identify network structure without network data</title>
    <dc:date>2021-11-04T12:54:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1703.04157</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Social network data is often prohibitively expensive to collect, limiting empirical network research. Typical economic network mapping requires (1) enumerating a census, (2) eliciting the names of all network links for each individual, (3) matching the list of social connections to the census, and (4) repeating (1)-(3) across many networks. In settings requiring field surveys, steps (2)-(3) can be very expensive. In other network populations such as financial intermediaries or high-risk groups, proprietary data and privacy concerns may render (2)-(3) impossible. Both restrict the accessibility of high-quality networks research to investigators with considerable resources. 
We propose an inexpensive and feasible strategy for network elicitation using Aggregated Relational Data (ARD) -- responses to questions of the form "How many of your social connections have trait k?" Our method uses ARD to recover the parameters of a general network formation model, which in turn, permits the estimation of any arbitrary node- or graph-level statistic. The method works well in simulations and in matching a range of network characteristics in real-world graphs from 75 Indian villages. Moreover, we replicate the results of two field experiments that involved collecting network data. We show that the researchers would have drawn similar conclusions using ARD alone. Finally, using calculations from J-PAL fieldwork, we show that in rural India, for example, ARD surveys are 80% cheaper than full network surveys.
]]></description>
<dc:subject>statistics network-theory social-networks inverse-problems rather-interesting to-write-about to-simulate consider:visualization consider:privacy</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7171afe1aa06/</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:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:social-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:privacy"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.12272">
    <title>[1906.12272] Weighing the Sun with five photographs</title>
    <dc:date>2021-07-16T10:29:17+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.12272</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[With only five photographs of the Sun at different dates we show that the mass of Sun can be calculated by using a telescope, a camera, and the Kepler's third law. With these photographs we are able to calculate the distance between Sun and Earth at different dates in a period of time of about three months. These distances allow us to obtain the correct elliptical orbit of Earth, proving the Kepler's first law. 
The analysis of the data extracted from photographs is performed by using an analytical optimization approach that allow us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using an geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth's orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun's mass by applying the Kepler's third law and Newton's law for gravitation. This method gives a result wich is in excellent agreement with the correct value for the Sun's mass. Thus, in a span of time of about three months, any student is capable to calculate the mass of the sun with only five photographs, a telescope and a camera.
]]></description>
<dc:subject>mathematical-recreations astronomy physics looking-to-see inverse-problems rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ab52c5dbe507/</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:astronomy"/>
	<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:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.00113">
    <title>[2102.00113] A universal solution scheme for fractional and classical PDEs</title>
    <dc:date>2021-06-27T10:10:43+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.00113</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose a unified meshless method to solve classical and fractional PDE problems with (−Δ)α2 for α∈(0,2]. The classical (α=2) and fractional (α<2) Laplacians, one local and the other nonlocal, have distinct properties. Therefore, their numerical methods and computer implementations are usually incompatible. We notice that for any α≥0, the Laplacian (−Δ)α2 of generalized inverse multiquadric (GIMQ) functions can be analytically written by the Gauss hypergeometric function, and thus propose a GIMQ-based method. Our method unifies the discretization of classical and fractional Laplacians and also bypasses numerical approximation to the hypersingular integral of fractional Laplacian. These two merits distinguish our method from other existing methods for the fractional Laplacian. Extensive numerical experiments are carried out to test the performance of our method. Compared to other methods, our method can achieve high accuracy with fewer number of unknowns, which effectively reduces the storage and computational requirements in simulations of fractional PDEs. Moreover, the meshfree nature makes it free of geometric constraints and enables simple implementation for any dimension d≥1. Additionally, two approaches of selecting shape parameters, including condition number-indicated method and random-perturbed method, are studied to avoid the ill-conditioning issues when large number of points.
]]></description>
<dc:subject>numerical-methods diffy-Qs nonlinear-dynamics inverse-problems rather-interesting to-understand simulation representation consider:performance-measures consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d31989508c16/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffy-Qs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.07921">
    <title>[1810.07921] Concentration of the Frobenius norm of generalized matrix inverses</title>
    <dc:date>2021-05-23T21:40:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.07921</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In many applications it is useful to replace the Moore-Penrose pseudoinverse (MPP) by a different generalized inverse with more favorable properties. We may want, for example, to have many zero entries, but without giving up too much of the stability of the MPP. One way to quantify stability is by how much the Frobenius norm of a generalized inverse exceeds that of the MPP. In this paper we derive finite-size concentration bounds for the Frobenius norm of ℓp-minimal general inverses of iid Gaussian matrices, with 1≤p≤2. For p=1 we prove exponential concentration of the Frobenius norm of the sparse pseudoinverse; for p=2, we get a similar concentration bound for the MPP. Our proof is based on the convex Gaussian min-max theorem, but unlike previous applications which give asymptotic results, we derive finite-size bounds.
]]></description>
<dc:subject>matrices generalization rather-interesting inverse-problems performance-measure to-write-about consider:hillclimbing consider:diversity-of-sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b99b9dd7796c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<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:consider:hillclimbing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:diversity-of-sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2010.11406">
    <title>[2010.11406] 1-norm minimization and minimum-rank structured sparsity for symmetric and ah-symmetric generalized inverses: rank one and two</title>
    <dc:date>2020-11-15T11:40:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2010.11406</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Generalized inverses are important in statistics and other areas of applied matrix algebra. A \emph{generalized inverse} of a real matrix A is a matrix H that satisfies the Moore-Penrose (M-P) property AHA=A. If H also satisfies the M-P property HAH=H, then it is called \emph{reflexive}. Reflexivity of a generalized inverse is equivalent to minimum rank, a highly desirable property. We consider aspects of symmetry related to the calculation of various \emph{sparse} reflexive generalized inverses of A. As is common, we use (vector) 1-norm minimization for both inducing sparsity and for keeping the magnitude of entries under control. 
When A is symmetric, a symmetric H is highly desirable, but generally such a restriction on H will not lead to a 1-norm minimizing reflexive generalized inverse. We investigate a block construction method to produce a symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. Letting the rank of A be r, we establish that the 1-norm minimizing generalized inverse of this type is a 1-norm minimizing symmetric generalized inverse when (i) r=1 and when (ii) r=2 and A is nonnegative. 
Another aspect of symmetry that we consider relates to another M-P property: H is \emph{ah-symmetric} if AH is symmetric. The ah-symmetry property is sufficient for a generalized inverse to be used to solve the least-squares problem min{‖Ax−b‖2: x∈ℝn} using H, via x:=Hb. We investigate a column block construction method to produce an ah-symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. We establish that the 1-norm minimizing ah-symmetric generalized inverse of this type is a 1-norm minimizing ah-symmetric generalized inverse when (i) r=1 and when (ii) r=2 and A satisfies a technical condition.
]]></description>
<dc:subject>matrices inverse-problems rather-interesting approximation relaxations-of-rules to-write-about consider:looking-to-see consider:metaheuristics constraint-satisfaction multiobjective-optimization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ae9cc8c70f6c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:relaxations-of-rules"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.08364">
    <title>[1709.08364] Multi-level Chaotic Maps for 3D Textured Model Encryption</title>
    <dc:date>2020-11-14T11:46:19+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.08364</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[With rapid progress of Virtual Reality and Augmented Reality technologies, 3D contents are the next widespread media in many applications. Thus, the protection of 3D models is primarily important. Encryption of 3D models is essential to maintain confidentiality. Previous work on encryption of 3D surface model often consider the point clouds, the meshes and the textures individually. In this work, a multi-level chaotic maps models for 3D textured encryption was presented by observing the different contributions for recognizing cipher 3D models between vertices (point cloud), polygons and textures. For vertices which make main contribution for recognizing, we use high level 3D Lu chaotic map to encrypt them. For polygons and textures which make relatively smaller contributions for recognizing, we use 2D Arnold's cat map and 1D Logistic map to encrypt them, respectively. The experimental results show that our method can get similar performance with the other method use the same high level chaotic map for point cloud, polygons and textures, while we use less time. Besides, our method can resist more method of attacks such as statistic attack, brute-force attack, correlation attack.
]]></description>
<dc:subject>encryption 3d representation rather-interesting algorithms nonlinear-dynamics inverse-problems consider:adversarial-extraction consider:pattern-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7dd4b2ee987e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:encryption"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:3d"/>
	<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:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:adversarial-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:pattern-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1403.4131">
    <title>[1403.4131] Evolving Design Rules for the Inverse Granular Packing Problem</title>
    <dc:date>2020-10-18T13:02:12+00:00</dc:date>
    <link>https://arxiv.org/abs/1403.4131</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a solution to this inverse-packing problem by framing it in the context of artificial evolution. By representing shapes as bonded spheres, we show how shapes may be mutated, simulated, and selected to produce particularly dense or loose packing aggregates, both with and without friction. Moreover, we show how motifs emerge linking these shapes together. The result is a set of design rules that function as an effective solution to the inverse packing problem for given packing procedures and boundary conditions. Finally, we show that these results are verified by experiments on 3D-printed prototypes used to make packings in the real world.
]]></description>
<dc:subject>granular-materials inverse-problems packing rather-interesting to-write-about to-simulate consider:visualization consider:web-interface consider:mixes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4cad691c573/</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:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:packing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:web-interface"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:mixes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1605.04416">
    <title>[1605.04416] On the similarity of AB and BA for normal and other matrices</title>
    <dc:date>2020-07-11T13:12:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1605.04416</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It is well-known that AB and BA are similar when A and B are complex square Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if A is Hermitian and B is normal. Perhaps surprisingly, similarity does hold when A is positive semidefinite and B is normal.
]]></description>
<dc:subject>number-theory analysis matrices rather-interesting inverse-problems consider:looking-to-see consider:feature-discovery to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f3f69c59d076/</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:analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<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/1801.04087">
    <title>[1801.04087] Gene regulatory network inference: an introductory survey</title>
    <dc:date>2020-05-23T13:23:17+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.04087</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Gene regulatory networks are powerful abstractions of biological systems. Since the advent of high-throughput measurement technologies in biology in the late 90s, reconstructing the structure of such networks has been a central computational problem in systems biology. While the problem is certainly not solved in its entirety, considerable progress has been made in the last two decades, with mature tools now available. This chapter aims to provide an introduction to the basic concepts underpinning network inference tools, attempting a categorisation which highlights commonalities and relative strengths. While the chapter is meant to be self-contained, the material presented should provide a useful background to the later, more specialised chapters of this book.
]]></description>
<dc:subject>gene-regulatory-networks inverse-problems bioinformatics systems-biology rather-interesting modeling to-write-about to-simulate consider:data-quality consider:representation consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3c46f24714c8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:gene-regulatory-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bioinformatics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:modeling"/>
	<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:data-quality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<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/1904.04314">
    <title>[1904.04314] Data-driven discovery of partial differential equation models with latent variables</title>
    <dc:date>2020-05-18T21:54:30+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.04314</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially complicates construction of an accurate model for such systems using data-driven approaches. The present paper illustrates how physical constraints can be employed to overcome this limitation using the example of a weakly turbulent quasi-two-dimensional Kolmogorov flow driven by a steady Lorenz force with an unknown spatial profile. Specifically, the terms involving latent variables in the partial differential equations governing the dynamics can be eliminated at the expense of raising the order of that equation. We show that local polynomial interpolation combined with symbolic regression can handle sparse data on grids that are representative of typical experimental measurement techniques such as particle image velocimetry. However, we also find that the reconstructed model is sensitive to measurement noise and trace this sensitivity to the presence of high order spatial and/or temporal derivatives.
]]></description>
<dc:subject>inverse-problems symbolic-regression BUT-NOT-OUR-KIND rather-interesting to-understand numerical-methods to-write-about consider:genetic-programming diff-Qs nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:06eebac4e254/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:BUT-NOT-OUR-KIND"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diff-Qs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.04412">
    <title>[1904.04412] 3D Quantum Cuts for Automatic Segmentation of Porous Media in Tomography Images</title>
    <dc:date>2020-05-18T21:52:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.04412</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Binary segmentation of volumetric images of porous media is a crucial step towards gaining a deeper understanding of the factors governing biogeochemical processes at minute scales. Contemporary work primarily revolves around primitive techniques based on global or local adaptive thresholding that have known common drawbacks in image segmentation. Moreover, absence of a unified benchmark prohibits quantitative evaluation, which further clouds the impact of existing methodologies. In this study, we tackle the issue on both fronts. Firstly, by drawing parallels with natural image segmentation, we propose a novel, and automatic segmentation technique, 3D Quantum Cuts (QCuts-3D) grounded on a state-of-the-art spectral clustering technique. Secondly, we curate and present a publicly available dataset of 68 multiphase volumetric images of porous media with diverse solid geometries, along with voxel-wise ground truth annotations for each constituting phase. We provide comparative evaluations between QCuts-3D and the current state-of-the-art over this dataset across a variety of evaluation metrics. The proposed systematic approach achieves a 26% increase in AUROC while achieving a substantial reduction of the computational complexity of the state-of-the-art competitors. Moreover, statistical analysis reveals that the proposed method exhibits significant robustness against the compositional variations of porous media.
]]></description>
<dc:subject>tomography inverse-problems image-segmentation medical-technology algorithms image-analysis to-simulate to-write-about horse-races performance-measure compare:semantic-classification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:55ba9624fe65/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tomography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-segmentation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:medical-technology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compare:semantic-classification"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cs.purdue.edu/homes/gnf/book/hardcrefs.html">
    <title>hard copy citations - Dissections: Plane &amp; Fancy</title>
    <dc:date>2020-05-10T01:06:08+00:00</dc:date>
    <link>https://www.cs.purdue.edu/homes/gnf/book/hardcrefs.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Hardcopy books and articles with citations to 
Dissections: Plane & Fancy

]]></description>
<dc:subject>mathematical-recreations plane-geometry rather-interesting bibliography review inverse-problems to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5f7f984c6f91/</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:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:bibliography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<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://theinnerframe.wordpress.com/2018/04/16/a-double-figure-8/">
    <title>A Double Figure 8 – The Inner Frame</title>
    <dc:date>2020-05-06T12:39:05+00:00</dc:date>
    <link>https://theinnerframe.wordpress.com/2018/04/16/a-double-figure-8/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Recently, a local artist had an intriguing question. Suppose you have a hook in the ceiling (who hasn’t?), and  two spot lights in front of the hook, slightly to the left and to the right. Suppose also that you have drawn two curves on the back wall. Can you bend a wire and suspend it from the hook so that the two projections match the drawings?

]]></description>
<dc:subject>mathematical-recreations art inverse-problems rather-interesting to-write-about to-simulate consider:implicit-representation consider:robustness</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:27372c36e5fe/</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:art"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-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:implicit-representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:robustness"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1706.00399">
    <title>[1706.00399] Benchmark problems for phase retrieval</title>
    <dc:date>2020-04-22T23:14:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1706.00399</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is periodic and comprised of atomic distributions arranged homogeneously in the unit cell of the crystal. The crystallographic problem is both the leading application and one of the hardest forms of phase retrieval. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. The data, publicly available online, is provided in an easily interpretable format. We also propose a simple and unambiguous success/failure criterion based on the actual needs in crystallography. Baseline runtimes were obtained with an iterative algorithm that is similar but more transparent than those used in crystallography. Empirically, the runtimes grow exponentially with respect to a new hardness parameter: the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages. This set of benchmark problems, we hope, will encourage the development of new algorithms for the phase retrieval problem in general, and crystallography in particular.
]]></description>
<dc:subject>phase-retrieval inverse-problems signal-processing rather-interesting numerical-methods inference information-theory to-write-about consider:sampling consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ff462c7f56a8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:phase-retrieval"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1203.3353">
    <title>[1203.3353] Solving Structure with Sparse, Randomly-Oriented X-ray Data</title>
    <dc:date>2020-01-19T15:45:09+00:00</dc:date>
    <link>https://arxiv.org/abs/1203.3353</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing of hundreds of thousands (or more) of images that contain very few x-rays. Each low-flux image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of collecting data at these extremes, averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-flux data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal in the high-noise regime.
]]></description>
<dc:subject>diffraction inverse-problems tomography rather-interesting algorithms statistics probability-theory inference to-simulate to-write-about optimization signal-processing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3aebefbb9649/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tomography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1107.4030">
    <title>[1107.4030] Three dimensional structure from intensity correlations</title>
    <dc:date>2020-01-19T14:39:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1107.4030</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.
]]></description>
<dc:subject>signal-processing crystallography inverse-problems rather-interesting diffraction numerical-methods to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:903517046ee1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:crystallography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/nlin/0206025">
    <title>[nlin/0206025] The Mermin fixed point</title>
    <dc:date>2020-01-12T14:40:25+00:00</dc:date>
    <link>https://arxiv.org/abs/nlin/0206025</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The most efficient known method for solving certain computational problems is to construct an iterated map whose fixed points are by design the problem's solution. Although the origins of this idea go back at least to Newton, the clearest expression of its logical basis is an example due to Mermin. A contemporary application in image recovery demonstrates the power of the method.
]]></description>
<dc:subject>inverse-problems rather-interesting algorithms heuristics to-understand to-write-about to-simulate consider:numerical-methods consider:performance-measures consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e57ebe36576c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1803.02875">
    <title>[1803.02875] Machine Learning Inverse Problem for Topological Photonics</title>
    <dc:date>2020-01-12T14:20:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1803.02875</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a novel machine learning approach to the topological inverse problem. We train a neural network system with the band structure of the Aubry-Andre-Harper model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic topological laser design and by resorting to the widely available open-source TensorFlow library. Our results are general and scalable to thousands of topological components. This new inverse design technique based on machine learning potentially extends the applications of topological photonics, for example, to frequency combs, quantum sources, neuromorphic computing and metrology.
]]></description>
<dc:subject>quantum physics simulation inverse-problems neural-networks deep-learning rather-interesting to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a31311ce3822/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quantum"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.08171">
    <title>[1902.08171] A Dictionary Based Generalization of Robust PCA</title>
    <dc:date>2020-01-10T12:41:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.08171</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both undercomplete and overcomplete dictionary cases, and show that the constituent components can be successfully recovered under some relatively mild assumptions up to a certain global sparsity level. Further, we corroborate our theoretical results by presenting empirical evaluations in terms of phase transitions in rank and sparsity for various dictionary sizes.
]]></description>
<dc:subject>dimension-reduction algorithms machine-learning inverse-problems to-write-about to-simulate consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e5af15ca1046/</dc:identifier>
<taxo:topics><rdf:Bag>	<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:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<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:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1807.09196">
    <title>[1807.09196] A Convex Formulation for Binary Tomography</title>
    <dc:date>2020-01-08T13:21:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1807.09196</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are non-convex, many approaches for solving it rely on either relaxing the constraints or heuristics. In this paper we propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares problem. The resulting problem is a generalized LASSO problem which can be solved efficiently. It is a relaxation in the sense that it can only be guaranteed to give a feasible solution; not necessarily the optimal one. In exhaustive experiments on small images (2x2, 3x3, 4x4) we find, however, that if the problem has a unique solution, our dual approach finds it. In case of multiple solutions, our approach finds the commonalities between the solutions. Further experiments on realistic numerical phantoms and an experiment on X-ray dataset show that our method compares favourably to Total Variation and DART.
]]></description>
<dc:subject>tomography inverse-problems rather-interesting benchmarking operations-research optimization to-write-about mathematical-programming consider:genetic-programming to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:018cc48e6971/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tomography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarking"/>
	<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:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1802.09904">
    <title>[1802.09904] Algorithmic Causal Deconvolution of Intertwined Programs and Networks by Generative Mechanism</title>
    <dc:date>2019-11-25T23:47:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.09904</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic probability, that decomposes an observation into its most likely algorithmic generative sources. Our approach uses a causal calculus to infer model representations. We demonstrate its ability to deconvolve interacting mechanisms regardless of whether the resultant objects are strings, space-time evolution diagrams, images or networks. While this is mostly a conceptual contribution and a novel framework, we provide numerical evidence evaluating the ability of our methods to separate data from observations produced by discrete dynamical systems such as cellular automata and complex networks. We think that these separating techniques can contribute to tackling the challenge of causation, thus complementing other statistically oriented approaches.
]]></description>
<dc:subject>machine-learning dynamical-systems inverse-problems rather-interesting system-identification to-simulate to-try to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aa810e1dd392/</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:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:system-identification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-try"/>
	<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/1204.0403">
    <title>[1204.0403] Sets avoiding integral distances</title>
    <dc:date>2019-10-13T12:24:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1204.0403</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study open point sets in Euclidean spaces ℝd without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density zero. We are interested in how large such sets can be in d-dimensional volume. We determine the lower and upper bounds for the volumes of the sets in terms of the number of their connected components and dimension, and also give some exact values. Our problem can be viewed as a kind of inverse to known problems on sets with pairwise rational or integral distances.
]]></description>
<dc:subject>plane-geometry constraint-satisfaction rather-interesting inverse-problems combinatorics Erdös-stuff to-simulate to-sample to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a04f2b30ab85/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Erdös-stuff"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-sample"/>
	<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/math/0111080">
    <title>[math/0111080] Phase retrieval by iterated projections</title>
    <dc:date>2019-09-08T12:44:53+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0111080</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter β. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map for β=1. Other values of β are equally effective in retrieving phases but have no input-output counterparts. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby stagnation is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved.
]]></description>
<dc:subject>inverse-problems mathematical-diffraction rather-interesting to-understand signal-processing algorithms to-write-about to-simulate consider:genetic-programming consider:performance-measures consider:lexicase-for-spectra</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1009b39fea42/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-diffraction"/>
	<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:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase-for-spectra"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1512.05104">
    <title>[1512.05104] What is Aperiodic Order?</title>
    <dc:date>2019-09-08T12:34:23+00:00</dc:date>
    <link>https://arxiv.org/abs/1512.05104</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article provides a brief introductory account of the theory of aperiodic order.
]]></description>
<dc:subject>inverse-problems mathematical-diffraction review spectra to-understand to-simulate to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:66207fdfdd9f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<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:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1506.05276">
    <title>[1506.05276] Aperiodic crystals and beyond</title>
    <dc:date>2019-09-08T12:31:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1506.05276</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order, encompassing both periodic and aperiodic crystals. The current definition of crystals rests on their essentially point-like diffraction. Considering a number of recently investigated toy systems, with particular emphasis on non-crystalline ordered structures, the limits of the current definition are explored.
]]></description>
<dc:subject>inverse-problems mathematical-diffraction spectra review rather-interesting mathematical-physics to-understand to-simulate open-questions to-write-about consider:self-spectra information-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:36cbc9434e9b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-physics"/>
	<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:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:self-spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1311.4373">
    <title>[1311.4373] Recent progress in mathematical diffraction</title>
    <dc:date>2019-09-08T12:26:30+00:00</dc:date>
    <link>https://arxiv.org/abs/1311.4373</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the literature for further details.
]]></description>
<dc:subject>inverse-problems spectra mathematical-diffraction rewriting-systems rather-interesting to-simulate to-write-about review</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:521c5454b92e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<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/1205.0392">
    <title>[1205.0392] A comment on the relation between diffraction and entropy</title>
    <dc:date>2019-09-08T12:21:43+00:00</dc:date>
    <link>https://arxiv.org/abs/1205.0392</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Diffraction methods are used to detect atomic order in solids. While uniquely ergodic systems with pure point diffraction have zero entropy, the relation between diffraction and entropy is not as straightforward in general. In particular, there exist families of homometric systems, which are systems sharing the same diffraction, with varying entropy. We summarise the present state of understanding by several characteristic examples.
]]></description>
<dc:subject>inverse-problems spectra mathematical-physics information-theory to-understand to-write-about dimension-reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4d91dd207f59/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<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:dimension-reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1105.0095">
    <title>[1105.0095] Kinematic Diffraction from a Mathematical Viewpoint</title>
    <dc:date>2019-09-08T12:18:06+00:00</dc:date>
    <link>https://arxiv.org/abs/1105.0095</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Simultaneously, their relevance has grown in practice as well. In this context, the phenomenon of homometry shows various unexpected new facets. This is particularly so for systems with stochastic components. After the introduction to the mathematical tools, we briefly discuss pure point spectra, based on the Poisson summation formula for lattice Dirac combs. This provides an elegant approach to the diffraction formulas of infinite crystals and quasicrystals. We continue by considering classic deterministic examples with singular or absolutely continuous diffraction spectra. In particular, we recall an isospectral family of structures with continuously varying entropy. We close with a summary of more recent results on the diffraction of dynamical systems of algebraic or stochastic origin.
]]></description>
<dc:subject>review idealizations inverse-problems rather-interesting spectra rewriting-systems fractals crystallography to-write-about to-simulate mathematical-physics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c5b45c2f237c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:idealizations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fractals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:crystallography"/>
	<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:mathematical-physics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1102.1750">
    <title>[1102.1750] Some comments on pinwheel tilings and their diffraction</title>
    <dc:date>2019-09-07T22:31:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1102.1750</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so the pinwheel diffraction consists of sharp rings and, possibly, a continuous component with circular symmetry. We consider some combinatorial properties of the tiles and their orientations, and a numerical approach to the diffraction of weighted pinwheel point sets.
]]></description>
<dc:subject>inverse-problems spectra rather-interesting summary-statistics tiling aperiodic-tiling to-understand to-write-about substitution-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:230fe8295711/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:summary-statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t: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:substitution-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1007.0707">
    <title>[1007.0707] Diffraction of limit periodic point sets</title>
    <dc:date>2019-09-07T22:28:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1007.0707</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project sets with p-adic internal spaces. We illustrate this by explicit results for the diffraction measures of two examples with 2-adic internal spaces. The first and well-known example is the period doubling sequence in one dimension, which is based on the period doubling substitution rule. The second example is a weighted planar point set that is derived from the classic chair tiling in the plane. It can be described as a fixed point of a block substitution rule.
]]></description>
<dc:subject>inverse-problems tiling spectra rather-interesting to-understand to-simulate substitution-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:89d694c3fabc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<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:substitution-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/0909.5605">
    <title>[0909.5605] Surprises in aperiodic diffraction</title>
    <dc:date>2019-09-07T22:27:00+00:00</dc:date>
    <link>https://arxiv.org/abs/0909.5605</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Moreover, the phenomenon of homometry shows various unexpected new facets. Here, we report on some of the recent results in an exemplary and informal fashion.
]]></description>
<dc:subject>diffraction spectra inverse-problems rather-interesting tiling quasicrystals to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:de12d36f317f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasicrystals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/0810.5750">
    <title>[0810.5750] Can Kinematic Diffraction Distinguish Order from Disorder?</title>
    <dc:date>2019-09-07T22:25:16+00:00</dc:date>
    <link>https://arxiv.org/abs/0810.5750</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous diffraction intensities, which are generally linked to the presence of disorder. However, based on simple model systems, we demonstrate that it may be impossible to draw conclusions on the degree of order in the system from its diffraction image. In particular, we construct a family of one-dimensional binary systems which cover the entire entropy range but still share the same purely diffuse diffraction spectrum.
]]></description>
<dc:subject>inverse-problems spectra tiling rather-interesting discrete-mathematics combinatorics feature-extraction to-understand to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:93a9ecae96a3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<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:discrete-mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0610411">
    <title>[math/0610411] Homometric model sets and window covariograms</title>
    <dc:date>2019-09-07T22:23:27+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0610411</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set LAMBDA within a given cut and project scheme is a Delone set that is defined through a window W in internal space. The autocorrelation measure of LAMBDA is a pure point measure whose coefficients can be calculated via the so-called covariogram of W. Two windows with the same covariogram thus result in homometric model sets. On the other hand, the inverse problem of determining LAMBDA from its diffraction image ultimately amounts to reconstructing W from its covariogram. This is also known as Matheron's covariogram problem. It is well studied in convex geometry, where certain uniqueness results have been obtained in recent years. However, for non-convex windows, uniqueness fails in a relevant way, so that interesting applications to the homometry problem emerge. We discuss this in a simple setting and show a planar example of distinct homometric model sets.
]]></description>
<dc:subject>inverse-problems plane-geometry tiling rather-interesting to-understand to-write-about spectra consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3fff243d5daf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<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-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<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/1806.09644">
    <title>[1806.09644] How to hear the shape of a billiard table</title>
    <dc:date>2019-07-24T11:31:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1806.09644</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal billiard table both the cyclic ordering of its edge labels and the sizes of its angles. We also show that it is impossible to reconstruct the exact shape of a polygonal billiard table from any finite collection of finite words from its bounce spectrum.
]]></description>
<dc:subject>billiards dynamical-systems spectra rather-interesting inverse-problems to-understand to-write-about to-simulate consider:looking-to-see consider:classification impossibility-proof consider:approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9a50eefee19c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:billiards"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:spectra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:impossibility-proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1711.03247">
    <title>[1711.03247] The nonsmooth landscape of phase retrieval</title>
    <dc:date>2019-07-23T20:30:39+00:00</dc:date>
    <link>https://arxiv.org/abs/1711.03247</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. Seeking to understand the distribution of the stationary points of the problem, we complete the paper by proving that as the number of Gaussian measurements increases, the stationary points converge to a codimension two set, at a controlled rate. Experiments on image recovery problems illustrate the developed algorithm and theory.
]]></description>
<dc:subject>inverse-problems feature-extraction approximation rather-interesting nonlinear-programming to-write-about image-processing signal-processing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:195f98a6d64e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1710.08485">
    <title>[1710.08485] Making Faces: Universal Inverse Design of Surfaces with Thin Nematic Elastomer Sheets</title>
    <dc:date>2019-07-14T12:55:53+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.08485</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem -- programming a sheet to take an arbitrary desired 3D shape -- is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers. We show how blueprints for arbitrary surface geometries as well as local extrinsic curvatures can be generated using approximate numerical methods. Backed by faithfully alignable and rapidly lockable LCE chemistry, we precisely embed our designs in LCE sheets using advanced top-down microfabrication techniques. We thus successfully produce flat sheets that, upon thermal activation, take an arbitrary desired shape, such as a face. The general design principles presented here for creating an arbitrary 3D shape will allow for exploration of unmet needs in flexible electronics, metamaterials, aerospace and medical devices, and more.
]]></description>
<dc:subject>materials-science indistinguishable-from-magic inverse-problems origami self-assembly engineering-design to-write-about rather-interesting consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4004dc5a9364/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:indistinguishable-from-magic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:origami"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:self-assembly"/>
	<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:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/citation.cfm?id=264996">
    <title>A survey of Boolean matching techniques for library binding</title>
    <dc:date>2019-06-27T10:52:03+00:00</dc:date>
    <link>https://dl.acm.org/citation.cfm?id=264996</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[When binding a logic network to a set of cells, a fundamental problem is recognizing whether a cell can implement a portion of the network. Boolean matching means solving this task using a formalism based on Boolean algebra. In its simplest form, Boolean matching can be posed as a tautology check. We review several approaches to Boolean matching as well as to its generalization to cases involving don't care conditions and its restriction to specific libraries such as those typical of anti-fuse based FPGAs. We then present a general formulation of Boolean matching supporting multiple-output logic cells.
]]></description>
<dc:subject>Boolean-functions inverse-problems rather-odd machine-learning information-theory engineering-design representation nudge-targets to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:67c631359897/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Boolean-functions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-odd"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1708.04597">
    <title>[1708.04597] An Efficient NPN Boolean Matching Algorithm Based on Structural Signature and Shannon Expansion</title>
    <dc:date>2019-06-27T10:38:18+00:00</dc:date>
    <link>https://arxiv.org/abs/1708.04597</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[An efficient pairwise Boolean matching algorithm to solve the problem of matching single-output specified Boolean functions under input negation and/or input permutation and/or output negation (NPN) is proposed in this paper. We present the Structural Signature (SS) vector, which is composed of a 1st signature value, two symmetry marks, and a group mark. As a necessary condition for NPN Boolean matching, the structural signature is more effective than is the traditional signature. Two Boolean functions, f and g, may be equivalent when they have the same SS vector. The symmetry mark can distinguish symmetric variables and asymmetric variables and search multiple variable mappings in a single variable-mapping search operation, which reduces the search space significantly. Updating the SS vector using Shannon decomposition provides benefits in distinguishing unidentified variables, and the group mark and the phase collision check discover incorrect variable mappings quickly, which also speeds up the NPN Boolean matching process. Using the algorithm proposed in this paper, we tested both equivalent and non-equivalent matching peeds on the MCNC benchmark circuit sets and the random circuit sets. In the experiment, our algorithm is two times faster than competitors when testing equivalent circuits and averages at least one hundred times faster when testing non-equivalent circuits. The experimental results show that our approach is highly effective in solving the NPN Boolean matching problem.
]]></description>
<dc:subject>jargon-overlap-warning Boolean-functions inverse-problems rather-interesting machine-learning algorithms to-understand no-really-why-are-they-using-these-terms-it-hurts</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:bd0ecf0338ce/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:jargon-overlap-warning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Boolean-functions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:no-really-why-are-they-using-these-terms-it-hurts"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1702.04199">
    <title>[1702.04199] The problem of camouflaging via mirror reflections</title>
    <dc:date>2019-05-06T11:46:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1702.04199</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We introduce a {\it visibility index} of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate to this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.
]]></description>
<dc:subject>billiards optics optimization geometry inverse-problems rather-interesting approximation to-write-about nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e0c3966edb17/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:billiards"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1304.4005">
    <title>[1304.4005] Bodies with mirror surface invisible from two points</title>
    <dc:date>2019-05-06T11:44:34+00:00</dc:date>
    <link>https://arxiv.org/abs/1304.4005</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Here we are concerned with a special issue of billiard invisibility, where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is identified with the dynamics of light rays outside the body in the framework of geometric optics. We show that in this setting it is possible to construct a body invisible from two points.
]]></description>
<dc:subject>billiards dynamical-systems rather-interesting inverse-problems invisibility nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:882fbd019eac/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:billiards"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:invisibility"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.01624">
    <title>[1901.01624] Composite optimization for robust blind deconvolution</title>
    <dc:date>2019-05-03T23:31:00+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.01624</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The blind deconvolution problem seeks to recover a pair of vectors from a set of rank one bilinear measurements. We consider a natural nonsmooth formulation of the problem and show that under standard statistical assumptions, its moduli of weak convexity, sharpness, and Lipschitz continuity are all dimension independent. This phenomenon persists even when up to half of the measurements are corrupted by noise. Consequently, standard algorithms, such as the subgradient and prox-linear methods, converge at a rapid dimension-independent rate when initialized within constant relative error of the solution. We then complete the paper with a new initialization strategy, complementing the local search algorithms. The initialization procedure is both provably efficient and robust to outlying measurements. Numerical experiments, on both simulated and real data, illustrate the developed theory and methods.
]]></description>
<dc:subject>approximation inverse-problems statistics inference algorithms numerical-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a32e17810786/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.09683">
    <title>[1709.09683] Exact Camera Location Recovery by Least Unsquared Deviations</title>
    <dc:date>2019-04-27T11:57:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.09683</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski, but with typically less corruption.
]]></description>
<dc:subject>inverse-problems image-processing rather-interesting benchmarking nudge-targets consider:feature-discovery consider:rediscovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1ea9d5a60ac9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarking"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.09581">
    <title>[1809.09581] Dispersion relations of periodic quantum graphs associated with Archimedean tiling (I)</title>
    <dc:date>2019-04-24T14:14:38+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.09581</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[There are totally 11 kinds of Archimedean tiling for the plane. Applying the Floquet-Bloch theory, we derive the dispersion relations of the periodic quantum graphs associated with a number of Archimedean tiling, namely the triangular tiling {(36)}, the elongated triangular tiling {(33,42)}, the trihexagonal tiling {(3,6,3,6)} and the truncated square tiling {(4,82)}. The derivation makes use of characteristic functions, with the help of the symbolic software Mathematica. 
The resulting dispersion relations are surprisingly simple and symmetric. They show that in each case the spectrum is composed of point spectrum and an absolutely continuous spectrum. We further analyzed on the structure of the absolutely continuous spectra. Our work is motivated by the studies on the periodic quantum graphs associated with hexagonal tiling in \cite{KP} and \cite{KL}.
]]></description>
<dc:subject>combinatorics physics! quantums inverse-problems rather-interesting rather-odd to-understand enumeration</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4197e8c090f4/</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:physics!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quantums"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-odd"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1806.05739">
    <title>[1806.05739] Properties of reciprocity formulas for the Rogers-Ramanujan continued fractions</title>
    <dc:date>2019-03-09T13:29:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1806.05739</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Ramanujan recorded four reciprocity formulas for the Roger-Ramanujan continued fraction. Two reciprocity formulas each are also associated with the Ramanujan--Göllnitz--Gordon continued fraction and a level-13 analog of the Roger-Ramanujan continued fraction. We show that all eight reciprocity formulas are related to a pair of quadratic equations. The solution to the first equation generalizes the golden ratio and is used to set the value of a coefficient in the second equation; and the solution to the second equation gives a pair of values for a continued fraction. We relate the coefficients of the quadratic equations to important formulas obtained by Ramanujan, examine the pattern of the relation between a continued fraction and its parameters, and use the reciprocity formulas to obtain close approximations for all values of the continued fraction. We highlight patterns in the expressions for certain explicit values of the Rogers-Ramanujan continued fraction by expressing them in terms of the golden ratio. We extend the results to reciprocity formulas for Ramanujan's cubic continued fraction and the Ramanujan-Selberg continued fraction.
]]></description>
<dc:subject>number-theory integer-partitions combinatorics rather-interesting inverse-problems algebra strange-formulas nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c16e97d1aaf0/</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:integer-partitions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strange-formulas"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1506.02572">
    <title>[1506.02572] Probing Convex Polygons with a Wedge</title>
    <dc:date>2019-03-04T13:31:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1506.02572</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Minimizing the number of probes is one of the main challenges in reconstructing geometric objects with probing devices. In this paper, we investigate the problem of using an ω-wedge probing tool to determine the exact shape and orientation of a convex polygon. An ω-wedge consists of two rays emanating from a point called the apex of the wedge and the two rays forming an angle ω. To probe with an ω-wedge, we set the direction that the apex of the probe has to follow, the line L→, and the initial orientation of the two rays. A valid ω-probe of a convex polygon O contains O within the ω-wedge and its outcome consists of the coordinates of the apex, the orientation of both rays and the coordinates of the closest (to the apex) points of contact between O and each of the rays. 
We present algorithms minimizing the number of probes and prove their optimality. In particular, we show how to reconstruct a convex n-gon (with all internal angles of size larger than ω) using 2n−2 ω-probes; if ω=π/2, the reconstruction uses 2n−3 ω-probes. We show that both results are optimal. Let NB be the number of vertices of O whose internal angle is at most ω, (we show that 0≤NB≤3). We determine the shape and orientation of a general convex n-gon with NB=1 (respectively NB=2, NB=3) using 2n−1 (respectively 2n+3, 2n+5) ω-probes. We prove optimality for the first case. Assuming the algorithm knows the value of NB in advance, the reconstruction of O with NB=2 or NB=3 can be achieved with 2n+2 probes,- which is optimal.]]></description>
<dc:subject>computational-geometry inverse-problems rather-interesting inference to-write-about plane-geometry algorithms</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:df0bc460b95a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1801.02162">
    <title>[1801.02162] Reconstructing a convex polygon from its $omega$-cloud</title>
    <dc:date>2019-03-04T13:23:09+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.02162</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[An ω-wedge is the (closed) set of all points contained between two rays that are emanating from a single point (the apex), and are separated by an angle ω<π. Given a convex polygon P, we place the ω-wedge such that P is inside the wedge and both rays are tangent to P. The ω-cloud of P is the curve traced by the apex of the ω-wedge as it rotates around P while maintaining tangency in both rays. 
We investigate reconstructing a polygon P from its ω-cloud. Previous work on reconstructing P from probes with the ω-wedge required knowledge of the points of tangency between P the two rays of the ω-wedge. 
Here we show that if ω is known, the ω-cloud alone uniquely determines P, and we give a linear-time reconstruction algorithm. Furthermore, even if we only know that ω<π/2, we can still reconstruct P, albeit in cubic time in the number of vertices. This reduces to quadratic time if in addition we are given the location of one of the vertices of P.]]></description>
<dc:subject>computational-geometry inverse-problems rather-interesting nudge-targets consider:looking-to-see consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0873e4103af7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1605.03502">
    <title>[1605.03502] A solution to the reversible embedding problem for finite Markov chains</title>
    <dc:date>2018-12-30T18:34:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1605.03502</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which has a deep physical and biochemical background and provide a complete solution to this new problem. We prove that the reversible embedding of a stochastic matrix, if it exists, must be unique. Moreover, we obtain the sufficient and necessary conditions for the existence of the reversible embedding and provide an effective method to compute the reversible embedding. Some examples are also given to illustrate the main results of this paper.]]></description>
<dc:subject>inverse-problems Markov-chains probability-theory algorithms nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0dc1e19c0d6f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Markov-chains"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.07390">
    <title>[1809.07390] A general framework for secondary constructions of bent and plateaued functions</title>
    <dc:date>2018-12-16T13:53:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.07390</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this work, we employ the concept of {\em composite representation} of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying new secondary constructions of bent/plateaued functions. This representation gives a better understanding of the existing secondary constructions and it also allows us to provide a general construction framework of these objects. This framework essentially gives rise to an {\em infinite number} of possibilities to specify such secondary construction methods (with some induced sufficient conditions imposed on initial functions) and in particular we solve several open problems in this context. We provide several explicit methods for specifying new classes of bent/plateaued functions and demonstrate through examples that the imposed initial conditions can be easily satisfied. Our approach is especially efficient when defining new bent/plateaued functions on larger variable spaces than initial functions. For instance, it is shown that the indirect sum methods and Rothaus' construction are just special cases of this general framework and some explicit extensions of these methods are given. In particular, similarly to the basic indirect sum method of Carlet, we show that it is possible to derive (many) secondary constructions of bent functions without any additional condition on initial functions apart from the requirement that these are bent functions. In another direction, a few construction methods that generalize the secondary constructions which do not extend the variable space of the employed initial functions are also proposed.
]]></description>
<dc:subject>representation boolean-functions decomposition construction inverse-problems rather-interesting Walsh-polynomials to-write-about consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b9b17c6f2161/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:boolean-functions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:decomposition"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Walsh-polynomials"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<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/1808.04730">
    <title>[1808.04730] Analyzing Inverse Problems with Invertible Neural Networks</title>
    <dc:date>2018-08-20T11:31:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.04730</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. In this setting, the posterior parameter distribution, conditioned on an input measurement, has to be determined. We argue that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs). Although INNs are not new, they have, so far, received little attention in literature. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.
]]></description>
<dc:subject>machine-learning neural-networks inverse-problems rather-interesting representation to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:118ccd4051a0/</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:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<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/1710.00217">
    <title>[1710.00217] A Framework for Inferring Combination Lock Codes using Smartwatches</title>
    <dc:date>2018-07-04T11:34:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.00217</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Wrist-wearables such as smartwatches and fitness bands are equipped with a variety of high-precision sensors that enable collection of rich contextual information related to the wearer and his/her surroundings and support a variety of novel context- and activity-based applications. The presence of such a diverse set of on-board sensors, however, also expose an additional attack surface which, if not adequately protected, could be potentially exploited to leak private user information. In this paper, we comprehensively investigate the feasibility of a new vulnerability that attempts to take advantage of a wrist-wearable's seemingly innocuous and poorly regulated motion sensors to infer a user's input on mechanical devices typically used to secure physical access, for example, combination locks. In this direction, we outline two motion-based inference frameworks: i) a deterministic attack framework that attempts to infer a lock's unlock combination from the wrist motion (specifically, angular displacement) data obtained from a wrist-wearable's gyroscope sensor, and ii) a probabilistic attack framework that extends the output of the deterministic framework to produce a ranked list of likely unlock combinations. Further, we conduct a thorough empirical evaluation of the proposed frameworks by employing unlocking-related motion data collected from human subject participants in a variety of controlled and realistic settings. Evaluation results from these experiments demonstrate that motion data from wrist-wearables can be effectively employed as an information side-channel to significantly reduce the unlock combination search-space of commonly-found combination locks, thus compromising the physical security provided by these locks.]]></description>
<dc:subject>security inference to-write-about inverse-problems rather-interesting nudge-targets feature-extraction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c3336bd6a2a9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:security"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.atlasobscura.com/articles/ansel-adams-mystery-astronomy">
    <title>Solved: A Decades-Old Ansel Adams Mystery - Atlas Obscura</title>
    <dc:date>2018-04-30T11:20:56+00:00</dc:date>
    <link>https://www.atlasobscura.com/articles/ansel-adams-mystery-astronomy</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[WHEN YOU LOOK AT THE image above, what do you think of? Most will probably take in the beauty of its subjects, the mountain Denali and nearby Wonder Lake. A photographer might admire the skill of its creator, Ansel Adams. Adventurers may feel the urge to climb.

Donald Olson sees all that and something else: a mystery. He wants to know the moment it was taken. An astrophysicist and forensic astronomer, Olson uses quantitative methods to answer questions raised by artwork, literature, and historical accounts—not the heady ones, but the basic, surprisingly slippery who, what, when, and where.

]]></description>
<dc:subject>photography art-history rather-interesting inverse-problems astronomy via:kottke.org</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c942e5b71130/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:photography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:art-history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:astronomy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:kottke.org"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1506.09039">
    <title>[1506.09039] Scalable Discrete Sampling as a Multi-Armed Bandit Problem</title>
    <dc:date>2018-02-24T14:38:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1506.09039</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We study the problem of sampling a discrete random variable with a high degree of dependency that is typical in large-scale Bayesian inference and graphical models, and propose an efficient approximate solution with a subsampling approach. We make a novel connection between the discrete sampling and Multi-Armed Bandits problems with a finite reward population and provide three algorithms with theoretical guarantees. Empirical evaluations show the robustness and efficiency of the approximate algorithms in both synthetic and real-world large-scale problems.
]]></description>
<dc:subject>sampling inverse-problems rather-interesting probability-theory simulation engineering-design nudge-targets consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a5d2f38629b4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<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/1710.06647">
    <title>[1710.06647] Image Restoration by Iterative Denoising and Backward Projections</title>
    <dc:date>2018-02-24T12:11:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.06647</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Inverse problems appear in many applications such as image deblurring and inpainting. The common approach to address them is to design a specific algorithm for each problem. The Plug-and-Play (P&P) framework, which has been recently introduced, allows solving general inverse problems by leveraging the impressive capabilities of existing denoising algorithms. While this fresh strategy has found many applications, a burdensome parameter tuning is often required in order to obtain high-quality results. In this work, we propose an alternative method for solving inverse problems using denoising algorithms, which requires less parameter tuning. We provide a theoretical analysis of the method, and empirically demonstrate that it is competitive with task-specific techniques and the P&P approach for image inpainting and deblurring.
]]></description>
<dc:subject>inverse-problems image-processing superresolution algorithms performance-measure to-write-about nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b1b97064eb8d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:superresolution"/>
	<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:nudge-targets"/>
	<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/1604.02181">
    <title>[1604.02181] A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem</title>
    <dc:date>2018-02-03T16:07:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1604.02181</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.
]]></description>
<dc:subject>matrices inverse-problems algorithms rather-interesting nudge-targets performance-measure to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d453244854f0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<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/1710.00709">
    <title>[1710.00709] Synthesising Evolutionarily Stable Normative Systems</title>
    <dc:date>2018-02-02T16:52:46+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.00709</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Within the area of multi-agent systems, normative systems are a widely used framework for the coordination of interdependent activities. A crucial problem associated with normative systems is that of synthesising norms that effectively accomplish a coordination task and whose compliance forms a rational choice for the agents within the system. In this work, we introduce a framework for the synthesis of normative systems that effectively coordinate a multi-agent system and whose norms are likely to be adopted by rational agents. Our approach roots in evolutionary game theory. Our framework considers multi-agent systems in which evolutionary forces lead successful norms to prosper and spread within the agent population, while unsuccessful norms are discarded. The outputs of this evolutionary norm synthesis process are normative systems whose compliance forms a rational choice for the agents. We empirically show the effectiveness of our approach through empirical evaluation in a simulated traffic domain.
]]></description>
<dc:subject>evolutionary-dynamics game-theory rather-interesting meta-simulation performance-measure inverse-problems to-write-about consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2065954a2e31/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:evolutionary-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:meta-simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<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/1710.03370">
    <title>[1710.03370] iVQA: Inverse Visual Question Answering</title>
    <dc:date>2017-11-27T12:25:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.03370</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In recent years, visual question answering (VQA) has become topical as a long-term goal to drive computer vision and multi-disciplinary AI research. The premise of VQA's significance, is that both the image and textual question need to be well understood and mutually grounded in order to infer the correct answer. However, current VQA models perhaps `understand' less than initially hoped, and instead master the easier task of exploiting cues given away in the question and biases in the answer distribution. 
In this paper we propose the inverse problem of VQA (iVQA), and explore its suitability as a benchmark for visuo-linguistic understanding. The iVQA task is to generate a question that corresponds to a given image and answer pair. Since the answers are less informative than the questions, and the questions have less learnable bias, an iVQA model needs to better understand the image to be successful. We pose question generation as a multi-modal dynamic inference process and propose an iVQA model that can gradually adjust its focus of attention guided by both a partially generated question and the answer. For evaluation, apart from existing linguistic metrics, we propose a new ranking metric. This metric compares the ground truth question's rank among a list of distractors, which allows the drawbacks of different algorithms and sources of error to be studied. Experimental results show that our model can generate diverse, grammatically correct and content correlated questions that match the given answer.]]></description>
<dc:subject>artificial-intelligence image-analysis rather-interesting jeopardy-questions inverse-problems natural-language-processing to-write-about nudge-targets benchmarks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a3248633e3a5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:artificial-intelligence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:jeopardy-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:natural-language-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1704.07422">
    <title>[1704.07422] Iterative Methods for Photoacoustic Tomography in Attenuating Acoustic Media</title>
    <dc:date>2017-11-17T13:30:12+00:00</dc:date>
    <link>https://arxiv.org/abs/1704.07422</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation accounting for frequency dependent attenuation according to a wide class of attenuation laws that may include memory. We formulate the inverse problem of photoacoustic tomography in attenuating medium as an ill-posed operator equation in a Hilbert space framework that is tackled by iterative regularization methods. Our approach comes with a clear convergence analysis. For that purpose we derive explicit expressions for the adjoint problem that can efficiently be implemented. In contrast to time reversal, the employed adjoint wave equation is again damping and, thus has a stable solution. This stability property can be clearly seen in our numerical results. Moreover, the presented numerical results clearly demonstrate the Efficiency and accuracy of the derived iterative reconstruction algorithms in various situations including the limited view case.]]></description>
<dc:subject>tomography numerical-methods inverse-problems rather-interesting signal-processing algorithms nudge-targets consider:benchmarking consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d44587545833/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tomography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:benchmarking"/>
	<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/1702.01522">
    <title>[1702.01522] Inverse statistical problems: from the inverse Ising problem to data science</title>
    <dc:date>2017-11-17T13:25:26+00:00</dc:date>
    <link>https://arxiv.org/abs/1702.01522</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetisations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.]]></description>
<dc:subject>data-science statistics inverse-problems complexology rather-interesting inference to-write-about review to-simulate philosophy-of-science</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:18875f985d44/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<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:inference"/>
	<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:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://distill.pub/2017/feature-visualization/">
    <title>Feature Visualization</title>
    <dc:date>2017-11-09T23:20:14+00:00</dc:date>
    <link>https://distill.pub/2017/feature-visualization/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article focusses on feature visualization. While feature visualization is a powerful tool, actually getting it to work involves a number of details. In this article, we examine the major issues and explore common approaches to solving them. We ﬁnd that remarkably simple methods can produce high-quality visualizations. Along the way we introduce a few tricks for exploring variation in what neurons react to, how they interact, and how to improve the optimization process.

]]></description>
<dc:subject>neural-networks inverse-problems generative-art to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fca13690b659/</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:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-art"/>
	<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/1308.5550">
    <title>[1308.5550] Fitting Voronoi Diagrams to Planar Tesselations</title>
    <dc:date>2017-11-06T12:40:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1308.5550</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given a tesselation of the plane, defined by a planar straight-line graph G, we want to find a minimal set S of points in the plane, such that the Voronoi diagram associated with S "fits" \ G. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of G, assuming that the smallest angle in G is constant.]]></description>
<dc:subject>inverse-problems computational-geometry rather-interesting nudge-targets consider:looking-to-see to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8643fc9cbc28/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.07208">
    <title>[1709.07208] The size of $3$-uniform hypergraphs with given matching number and codegree</title>
    <dc:date>2017-11-03T11:52:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.07208</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Determine the size of r-graphs with given graph parameters is an interesting problem. Chv\'atal and Hanson (JCTB, 1976) gave a tight upper bound of the size of 2-graphs with restricted maximum degree and matching number; Khare (DM, 2014) studied the same problem for linear 3-graphs with restricted matching number and maximum degree. In this paper, we give a tight upper bound of the size of 3-graphs with bounded codegree and matching number.]]></description>
<dc:subject>hypergraphs inverse-problems rather-interesting combinatorics nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:946e90598607/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1704.08326">
    <title>[1704.08326] Multidimensional Rational Covariance Extension with Approximate Covariance Matching</title>
    <dc:date>2017-09-26T11:04:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1704.08326</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important applications in image processing, and spectral estimation in radar, sonar, and medical imaging. This is an inverse problem where a power spectrum with a rational absolutely continuous part is reconstructed from a finite set of moments. However, in most applications these moments are determined from observed data and are therefore only approximate, and RCEP may not have a solution. In this paper we extend the results to handle approximate covariance matching. We consider two problems, one with a soft constraint and the other one with a hard constraint, and show that they are connected via a homeomorphism. We also demonstrate that the problems are well-posed and illustrate the theory by examples in spectral estimation and texture generation.
]]></description>
<dc:subject>image-processing inverse-problems optimization compressed-sensing signal-processing nudge-targets consider:looking-to-see representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f77bbd017520/</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:inverse-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compressed-sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:signal-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>