Search results for "transitive"

A comparison of compatible, finite, and inductive graph properties

1993

Abstract In the theory of hyperedge-replacement grammars and languages, one encounters three types of graph properties that play an important role in proving decidability and structural results. The three types are called compatible, finite, and inductive graph properties. All three of them cover graph properties that are well-behaved with respect to certain operations on hypergraphs. In this paper, we show that the three notions are essentially equivalent. Consequently, three lines of investigation in the theory of hyperedge replacement - so far separated - merge into one.

On finite T-groups

2003

[EN] Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.

2020

Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic allowing to identify key constituents. Several measures based on various aspects of network topology have been proposed in order to quantify these concepts. While numerous studies have investigated whether centrality measures convey redundant information, how centrality and hierarchy measures are related is still an open issue. In this paper, we investigate the association between centrality and hierarchy using several correlation and similarity evaluation mea…

A Neurocomputational Approach to Trained and Transitive Relations in Equivalence Classes

2017

A stimulus class can be composed of perceptually different but functionally equivalent stimuli. The relations between the stimuli that are grouped in a class can be learned or derived from other stimulus relations. If stimulus A is equivalent to B, and B is equivalent to C, then the equivalence between A and C can be derived without explicit training. In this work we propose, with a neurocomputational model, a basic learning mechanism for the formation of equivalence. We also describe how the relatedness between the members of an equivalence class is developed for both trained and derived stimulus relations. Three classic studies on stimulus equivalence are simulated covering typical and at…

Attracteurs de Lorenz de variété instable de dimension arbitraire

1997

Abstract We construct the first examples of flows with robust multidimensional Lorenz-like attractors: the singularity contained in the attractor may have any number of expanding eigenvalues, and the attractor remains transitive in a whole neighbourhood of the initial flow. These attractors support a Sinai-Ruelle-Bowen SRB-measure and, contrary to the usual (low-dimensional) Lorenz models, they have infinite modulus of structural stability.

Imprimitive groups highly transitive on blocks

2004

We classify imprimitive groups acting highly transitively on blocks and satisfying conditions common in geometry. They can be realized as suitable subgroups of twisted wreath products.

On periodic radical groups in which permutability is a transitive relation

2007

Abstract A group G is said to be a PT - group if permutability is a transitive relation in the set of all subgroups of G . Our purpose in this paper is to study PT -groups in the class of periodic radical groups satisfying min- p for all primes p .

On the decision problem for the guarded fragment with transitivity

2002

The guarded fragment with transitive guards, [GF+TG], is an extension of GF in which certain relations are required to be transitive, transitive predicate letters appear only in guards of the quantifiers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. This answers the question posed in (Ganzinger et al., 1999). Moreover, we show that the problem is 2EXPTIME-complete. This result is optimal since the satisfiability problem for GF is 2EXPTIME-complete (Gradel, 1999). We also show that the satisfiability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satisfiability pr…

Highly transitive actions of groups acting on trees

2015

We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex stabilizers and some more general, finite of infinite, edge stabilizers that we call highly core-free. We study the notion of highly core-free subgroups and give some examples. In the case of amalgamated free products over highly core-free subgroups and HNN extensions with highly core-free base groups we obtain a genericity result for faithful and highly transitive actions. In particular, we recover the result of D. Kitroser stating that the fundamental group of …

Unit Operations in Approximation Spaces

2010

Unit operations are some special functions on sets. The concept of the unit operation originates from researches of U. Wybraniec-Skardowska. The paper is concerned with the general properties of such functions. The isomorphism between binary relations and unit operations is proved. Algebraic structures of families of unit operations corresponding to certain classes of binary relations are considered. Unit operations are useful in Pawlak's Rough Set Theory. It is shown that unit operations are upper approximations in approximation space. We prove, that in the approximation space (U, R) generated by a reflexive relation R the corresponding unit operation is the least definable approximation i…