Related papers: Normal Binary Hierarchical Models
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…
Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
The state space of an operator system of $n$-by-$n$ matrices has, in a sense, many normal cones. Merely this convex geometrical property implies smoothness qualities and a clustering property of exposed faces. The latter holds since each…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
We consider the construction of neural network architectures for data on simplicial complexes. In studying maps on the chain complex of a simplicial complex, we define three desirable properties of a simplicial neural network architecture:…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual \v{C}ech filtration of such a subset can be endowed with a vector…
Let G be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the quotient of a G-stable open subset is a curve. Let X be such a…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions.…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of…
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…
When $I$ is the edge ideal of a graph $G$, we use combinatorial properities, particularly Property $P$ on connectivity of neighbors of an edge, to classify when a binomial sum of vertices is a regular element on $R/I(G)$. Under a mild…