Related papers: Factorization of network reliability with perfect …
We establish a factorisation theorem for invertible, cross-symmetric, totally nonnegative matrices, and illustrate the theory by verifying that certain cases of Holte's Amazing Matrix are totally nonnegative.
Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically…
In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum…
In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We study matroidal networks introduced by Dougherty et al. We prove the converse of the following theorem: If a network is scalar-linearly solvable over some finite field, then the network is a matroidal network associated with a…
In this paper, we propose a model for building natural language explanations for Bayesian Network Reasoning in terms of factor arguments, which are argumentation graphs of flowing evidence, relating the observed evidence to a target…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after successive steps where the driving potential is suitably…
We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different…
We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices,…
We describe a remarkable relation between the notion of valid formula of predicate logic and the specification of network protocols. We give several examples such as the acknowledgement of one packet or of a sequence of packets. We show how…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes…
We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…
Here the definitions of nearest neighbor, robustness, concordance, and correlation, all of which feature in (Temple 2023) (henceforth abbreviated (T23)), are adjusted to make them completely mathematical while preserving their significance.…
We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…