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In a recent paper, De Baets et al. have characterized the fuzzy tolerance and fuzzy equivalence relations that a given strict order relation is compatible with. In this paper, we generalize this characterization by considering an ...
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In a recent paper, De Baets et al. have characterized the fuzzy tolerance and fuzzy equivalence relations that a given strict order relation is compatible with. In this paper, we generalize this characterization by considering an arbitrary (crisp) relation instead of a strict order relation, while paying attention to the particular cases of a reflexive or irreflexive relation. The reasoning largely draws upon the notion of the clone relation of a (crisp) relation, introduced recently by Bouremel et al., and the partition of this clone relation in terms of three different types of pairs of clones. More specifically, reflexive related clones and irreflexive unrelated clones turn out to play a key role in the characterization of the fuzzy tolerance and fuzzy equivalence relations that a given (crisp) relation is compatible with.
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Extracting semantic relations from text is a preliminary step towards understanding the meaning of text. The more semantic relations are extracted from a sentence, the better the representation of the knowledge encoded into that s...
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Extracting semantic relations from text is a preliminary step towards understanding the meaning of text. The more semantic relations are extracted from a sentence, the better the representation of the knowledge encoded into that sentence. This article introduces a framework for the Composition of Semantic Relations (CSR). CSR aims to reveal more text semantics than existing semantic parsers by composing new relations out of previously extracted relations. Semantic relations are defined using vectors of semantic primitives, and an algebra is suggested to manipulate these vectors according to a CSR algorithm. Inference axioms that combine two relations and yield another relation are generated automatically. CSR is a language-agnostic, inventory-independent method to extract semantic relations. The formalism has been applied to a set of 26 well-known relations and results are reported.
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In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introdu...
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In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.
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In this paper we study presentations of finite simple groups G from a quantitative point of view. Our main result provides unexpected answers to the following questions: how many relations are needed to define G, and how short can...
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In this paper we study presentations of finite simple groups G from a quantitative point of view. Our main result provides unexpected answers to the following questions: how many relations are needed to define G, and how short can these relations be?
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In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one...
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In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterization of the L-fuzzy tolerance relations and the L-fuzzy equivalence relations that a strict order relation is compatible with. In this paper, we extend the notion of clone relation to any binary relation. Although the definition of such extension is trivial, the corresponding properties significantly differ from those of the clone relation of a strict order relation. We analyse the most important ones among these properties, paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones. (C) 2016 Elsevier Inc. All rights reserved.
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We propose a mathematical apparatus based on binary relations that expands the possibility of traditional analysis applied to problems in mathematical and theoretical physics. We illustrate the general constructions with examples ...
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We propose a mathematical apparatus based on binary relations that expands the possibility of traditional analysis applied to problems in mathematical and theoretical physics. We illustrate the general constructions with examples with an algebraic description of Backlund transformations of nonlinear systems of partial differential equations and the dynamics of wave packet propagation.
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We define relations and their composition in a category with (#epsilon#, M)-factorization structure, with M consisting of monomorphisms, but #epsilon# not restricted to epimorphisms. We obtain an associativity criterion for compos...
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We define relations and their composition in a category with (#epsilon#, M)-factorization structure, with M consisting of monomorphisms, but #epsilon# not restricted to epimorphisms. We obtain an associativity criterion for composition of relations, and we study functional and induced relations. We show that under our assumptions, the categories of relations on functional and induced relations are isomorphic to the category of relations for the given category.
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In this paper we investigate reachability relations on the vertices of digraphs. IfW is a walk in a digraph D, then the height of W is equal to the number of edgestraversed in the direction coinciding with their orientation, minus...
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In this paper we investigate reachability relations on the vertices of digraphs. IfW is a walk in a digraph D, then the height of W is equal to the number of edgestraversed in the direction coinciding with their orientation, minus the number ofedges traversed opposite to their orientation. Two vertices u, v E V(D) are Ra,b-related if there exists a walk of height 0 between u and v such that the height ofevery subwalk of W, starting at u, is contained in the interval [a, b], where a is anon-positive integer or a = and b is a non-negative integer or b = no. Of coursethe relations Ra,b are equivalence relations on V (D). Factorising digraphs by Ra,and R,b, respectively, we can only obtain a few different digraphs. Dependingupon these factor graphs with respect to R,b and Ra, it is possible to definefive different "basic relation-properties for R,b and Ra,, respectively. Besides proving general properties of the relations Ra,b, we investigate the ques-tion which of the "basic relation-properties" with respect to R,b and Ra, canoccur simultaneously in locally finite connected transitive digraphs. Furthermorewe investigate these properties for some particular subclasses of locally finite con-nected transitive digraphs such as Cayley digraphs, digraphs with one, with two orwith infinitely many ends, digraphs containing or not containing certain directedsubtrees, and highly arc transitive digraphs.
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To relate the complex macroscopic flow of soft colloids to details of its microscopic equilibrium and non-equilibrium structure is still one big challenge in soft matter science. We investigated several well-defined colloidal mode...
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To relate the complex macroscopic flow of soft colloids to details of its microscopic equilibrium and non-equilibrium structure is still one big challenge in soft matter science. We investigated several well-defined colloidal model systems like star polymers or diblock copolymer micelles by linear/non-linear rheology, static/dynamic light scattering (SLS/DLS) and small angle neutron scattering (SANS). In addition, in-situ SANS experiments during shear (Rheo-SANS) revealed directly shear induced structural changes on a microscopic level. Varying the molecular architecture of the individual colloidal particle as well as particle-particle interactions and covering at the same time a broad concentration range from the very dilute to highly concentrated, glassy regime, we could separate contributions from intra- and inter-particle softness. Both can be precisely "tuned" by varying systematically the functionality, 6 ≤ f≤ 64, for star polymers or aggregation number, 30 ≤ N _(agg)≤ 1000 for diblock copolymer micelles, as well as the degree of polymerization of the individual polymer arm 100 ≤ D _p ≤ 3000. In dilute solutions, the characteristic shear rate at which deformation of the soft colloid is observed can be related to the Zimm time of the polymeric corona. In concentrated solutions, we validated a generalized Stokes-Einstein approach to describe the increase in macroscopic viscosity and mesoscopic self diffusion coefficient on approaching the glassy regime. Both can be explained in terms of an ultra-soft interaction potential. Moreover, non-equilibrium structure factors are obtained by Rheo-SANS. All experimental results are in excellent quantitative agreement with recent theoretical predictions.
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