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On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of…
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…
Consensus strategies find a variety of applications in distributed coordination and decision making in multi-agent systems. In particular, average consensus plays a key role in a number of applications and is closely associated with two…
Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…
We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
The problem of developing models and algorithms for multilevel association mining pose for new challenges for mathematics and computer science. These problems become more challenging, when some form of uncertainty like fuzziness is present…
Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
Like bisimulations, simulations and directed simulations are used for analyzing graph-based structures such as automata, labeled transition systems, linked data networks, Kripke models and interpretations in description logic. Simulations…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
Graphs are by nature unifying abstractions that can leverage interconnectedness to represent, explore, predict, and explain real- and digital-world phenomena. Although real users and consumers of graph instances and graph workloads…
We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
The need to measure bias encoded in tabular data that are used to solve pattern recognition problems is widely recognized by academia, legislators and enterprises alike. In previous work, we proposed a bias quantification measure, called…
The $\pi$-calculus is a process algebra where agents interact by sending communication links to each other via noiseless communication channels. Taking into account the reality of noisy channels, an extension of the $\pi$-calculus, called…
We define and construct a new data structure, the tables, this structure generalizes the (finite) $k$-sets sets of Eilenberg \cite{Ei}, it is versatile (one can vary the letters, the words and the coefficients). We derive from this…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
With web and mobile platforms becoming more prominent devices utilized in data analysis, there are currently few systems which are not without flaw. In order to increase the performance of these systems and decrease errors of data…