Related papers: Representing and Combining Partially Specified CPT…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually…
Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
With the increasing number of texts made available on the Internet, many applications have relied on text mining tools to tackle a diversity of problems. A relevant model to represent texts is the so-called word adjacency (co-occurrence)…
This article (written in Polish) is aimed for a wide mathematical audience. It is intended as an introductory text concerning problems of the asymptotic theory of symmetric groups.
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
Let C be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of C by a direct summand of its relation C-C-bimodule. When C is a tilted algebra, this construction provides an…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is…
The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent ``bias events,''…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…