representation   4005

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[1708.09778] Drawing bobbin lace graphs, or, Fundamental cycles for a subclass of periodic graphs
In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to (1,0), that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.
graph-theory  graph-layout  mathematical-recreations  mathematics  rather-interesting  algorithms  representation  to-write-about  consider:performance-measures 
21 hours ago by Vaguery
[1708.05255] Category Theory for Genetics
We introduce a categorical language in which it is possible to talk about DNA sequencing, alignment methods, CRISPR, homologous recombination, haplotypes, and genetic linkage. This language takes the form of a class of limit-sketches whose categories of models can model different concepts of Biology depending on what their categories of values are. We discuss examples of models in the category of sets and in the category of modules over the Boolean semi-ring {0,1}. We identify a subclass of models in sets that models the genetic material of living beings and another subclass of models in modules that models haplotypes. We show how the two classes are related via a universal property.
category-theory  theoretical-biology  genetics  representation  to-read  to-write-about  discrete-mathematics  philosophy-of-science  via:absfac 
22 hours ago by Vaguery
Random sampling of domino and lozenge tilings
A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different strategies to generate random tilings of large grid regions in the plane. This makes it possible to observe the behaviour of large random tilings, in particular the occurrence of boundary phenomena that have been the subject of intensive recent research.
domino-tiling  tiling  probability-theory  representation  random-sampling  algorithms  rather-interesting  to-write-about  am-using 
yesterday by Vaguery
[1704.06456] A Domain Based Approach to Social Relation Recognition
Social relations are the foundation of human daily life. Developing techniques to analyze such relations from visual data bears great potential to build machines that better understand us and are capable of interacting with us at a social level. Previous investigations have remained partial due to the overwhelming diversity and complexity of the topic and consequently have only focused on a handful of social relations. In this paper, we argue that the domain-based theory from social psychology is a great starting point to systematically approach this problem. The theory provides coverage of all aspects of social relations and equally is concrete and predictive about the visual attributes and behaviors defining the relations included in each domain. We provide the first dataset built on this holistic conceptualization of social life that is composed of a hierarchical label space of social domains and social relations. We also contribute the first models to recognize such domains and relations and find superior performance for attribute based features. Beyond the encouraging performance of the attribute based approach, we also find interpretable features that are in accordance with the predictions from social psychology literature. Beyond our findings, we believe that our contributions more tightly interleave visual recognition and social psychology theory that has the potential to complement the theoretical work in the area with empirical and data-driven models of social life.
image-processing  computer-vision  machine-learning  representation  social-psychology  rather-interesting  to-write-about  consider:feature-discovery 
yesterday by Vaguery
[1203.2377] Matrix Stretching for Linear Equations
Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity patterns to render linear equations more easily solved by parallel and sparse techniques. Some stretchings increase matrix condition numbers only moderately, and thus solve linear equations stably. For example, these stretchings solve arrow equations with accuracy and expense preferable to other solution methods.
matrices  algorithms  representation  rather-interesting  out-of-the-box  nudge-targets  consider:rediscovery  consider:performance-measures  linear-algebra 
yesterday by Vaguery
A neural network approach to tiling problems (PDF Download Available)
The family of tiling problems comprises combinatorial optimization problems involving a grid and a number of shapes. Appropriate placements of the shapes on the grid are sought such that specific constraints concerning shape overlap and grid coverage are satisfied. The family of tiling problems has links with graph theory and is, thus, interesting from a theoretical point of view. Being related to VLSI circuit design, tiling problems are also of practical importance. In this piece of research, parallel implementations of representative tiling problems are proposed by employing three distinct harmony theory-based artificial neural networks. Optimal solutions are always produced for appropriately selected values of the network parameters. Problem complexity has been found to affect the computational complexity of the solution. © 2001 John Wiley & Sons, Inc.
tiling  neural-networks  to-understand  to-write-about  machine-learning  representation 
yesterday by Vaguery
Bias, Perception, and Archival Praxis ← dh+lib
Elvia Arroyo-Ramirez is Processing Archivist for Latin American Collections at Princeton University Library. Elvia holds an MLIS with a concentration in Archives, Preservation, and Records Management from the University of Pittsburgh.
archives  power  dh  libraries  politics  representation  neutrality 
6 days ago by jessogden

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