Related papers: Algebraic characterisation of one-way patterns
We begin by introducing an algebraic structure with three constants and one ternary operation to which we call mobi algebra. This structure has been designed to capture the most relevant properties of the unit interval that are needed in…
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
We classify all decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that one of the subalgebras contains the identity matrix.
We present a general characterization of k-positivity for a positive map in terms of the estimation of the Ky Fan norm of the matrix constructed from the Kraus operators of the associated completely positive map. Combining this with the…
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.
A real matrix is said to be positive if its every entry is positive, and a real square matrix A is algebraically positive if there exists a real polynomial f such that f(A) is a positive matrix. A sign pattern matrix A is said to require a…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
An important element of the $S$-matrix bootstrap program is the relationship between the modulus of an $S$-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
We present further properties of a previously proposed recursive scheme for parameterisation of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain…