Covering Partial Cubes with Zones

A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio

Linear inequalities among graph invariants: Using GraPHedron to uncover optimal relationships

Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph vertices, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a "small" number of vertices. It greatly helps in conjecturing optimal linear inequalities, which are then hopefully proved for any number of vertices. Two examples are investigated here for the class of connected graphs. First, all the optimal linear inequalities for the stability number and the number of edges are obtained. To this aim, a problem of Ore (1962) related to the Turán Theorem (1941) is solved. Second, several optimal inequalities are established for three invariants: the maximum degree, the irregularity, and the diameter. © 2008 Wiley Periodicals, Inc

Learning valued relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval

EVA: Laparoscopic instrument tracking based on endoscopic video analysis for psychomotor skills assessment

INTRODUCTION: The EVA (Endoscopic Video Analysis) tracking system a new tracking system for extracting motions of laparoscopic instruments based on non-obtrusive video tracking was developed. The feasibility of using EVA in laparoscopic settings has been tested in a box trainer setup. METHODS: EVA makes use of an algorithm that employs information of the laparoscopic instrument's shaft edges in the image, the instrument's insertion point, and the camera's optical centre to track the 3D position of the instrument tip. A validation study of EVA comprised a comparison of the measurements achieved with EVA and the TrEndo tracking system. To this end, 42 participants (16 novices, 22 residents, and 4 experts) were asked to perform a peg transfer task in a box trainer. Ten motion-based metrics were used to assess their performance. RESULTS: Construct validation of the EVA has been obtained for seven motion-based metrics. Concurrent validation revealed that there is a strong correlation between the results obtained by EVA and the TrEndo for metrics such as path length (p=0,97), average speed (p=0,94) or economy of volume (p=0,85), proving the viability of EVA. CONCLUSIONS: EVA has been successfully used in the training setup showing potential of endoscopic video analysis to assess laparoscopic psychomotor skills. The results encourage further implementation of video tracking in training setups and in image guided surgery

Introduction to the mathematical theory of knowledge conceptualization: Conceptual systems and structures

The paper departs from the general problem of knowledge integration and the basic strategies that can be adopted to confront this challenge. With the purpose of providing a sound meta-theoretical framework to facilitate knowledge conceptualization and integration, as well as assessment criteria to evaluate achievements regarding knowledge integration, the paper first reviews the previous work in the field of conceptual spaces. It subsequently gives an overview of structural tools and mechanisms for knowledge representation, recapped in the modal stratified bond model of global knowledge. On these groundings, a novel formalized representation of conceptual systems, structures, spaces and algebras is developed through a set of definitions which goes beyond the exploration of mental knowledge representation and the semantics of natural languages. These two components provide a sound framework for the development of the glossaLAB international project with respect to its two basic objectives, namely (i) facilitating knowledge integration in general and particularly in the context of the general study of information and systems; (ii) facilitating the assessment of the achievements as regards knowledge integration in interdisciplinary settings. An additional article tackles the solutions adopted to integrate these results in the elucidation of the conceptual network of the general study of information and systems.2019-2

InfoSyll: A Syllabary Providing Statistical Information on Phonological and Orthographic Syllables

here is now a growing body of evidence in various languages supporting the claim that syllables are functional units of visual word processing. In the perspective of modeling the processing of polysyllabic words and the activation of syllables, current studies investigate syllabic effects with subtle manipulations. We present here a syllabary of the French language aiming at answering new constraints when designing experiments on the syllable issue. The InfoSyll syllabary provides exhaustive characteristics and statistical information for each phonological syllable (e.g. /fi/) and for its corresponding orthographic syllables (e.g. fi, phi, phy, fee, fix, fis). Variables such as the type and token positional frequencies, the number and frequencies of the correspondences between orthographic and phonological syllables are provided. As discussed, such computations should allow precise controls, manipulations and quantitative descriptions of syllabic variables in the field of psycholinguistic research.SCOPUS: ar.jinfo:eu-repo/semantics/publishe