Related papers: Finite Confluences and Closed Pattern Mining
Mining dense quasi-cliques is a well-known clustering task with applications ranging from social networks over collaboration graphs to document analysis. Recent work has extended this task to multiple graphs; i.e. the goal is to find groups…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
The modeling and control of networks over finite lattices are studied via the algebraic state space approach. Using the semi-tensor product of matrices, we obtain the algebraic state space representation of the dynamics of (control)…
This paper provides some evidence for conjectural relations between extensions of (right) weak order on Coxeter groups, closure operators on root systems, and Bruhat order. The conjecture focused upon here refines an earlier question as to…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this…
The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
The scalar and vector Laplacians are basic operators in physics and engineering. In applications, they show up frequently perturbed by lower-order terms. The effect of such perturbations on mixed finite element methods in the scalar case is…
This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…
We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice…
We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic…
We review the notion of (finitary) filter pair as a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with…
A closure operator on a set $X$ is a function $\operatorname{cl}: \wp(X) \to \wp(X)$ satisfying, for all $A, B \subseteq X$, the following properties: extensivity, $A \subseteq \operatorname{cl}(A)$; monotonicity, which states that if $A…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…