Related papers: Toric Fiber Products in Geometric Modeling
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by…
Let $N\subset \RR^{r}$ be a lattice, and let $\deg\colon N \to \CC$ be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions on $\deg$, the data $(N,\deg)$ determines a…
We study the topology of toric maps. We show that if $f\colon X\to Y$ is a proper toric morphism, with $X$ simplicial, then the cohomology of every fiber of $f$ is pure and of Hodge-Tate type. When the map is a fibration, we give an…
In a toric symplectic manifold, regular fibres of the moment map are Lagrangian tori which are called toric fibres. We discuss the question which two toric fibres are equivalent up to a Hamiltonian diffeomorphism of the ambient space. On…
This is a collection of results on the topology of toric symplectic manifolds. Using an idea of Borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Further, the product of two projective…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and facet enumeration, computation of…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…
A subset K of R^n gives rise to a formal Laurent series with monomials corresponding to lattice points in K. Under suitable hypotheses, this series represents a rational function R(K). Michel Brion has discovered a surprising formula…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns.…
Developed in a series of seminal papers in the early 2010s, the tubal tensor framework provides a clean and effective algebraic setting for tensor computations, supporting matrix-mimetic features such as a tensor Singular Value…
High-resolution range profile (HRRP ) data are in vogue in radar automatic target recognition (RATR). With the interest in classifying models using HRRP, filling gaps in datasets using generative models has recently received promising…
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…
This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are…
We introduce a linear-time algorithm for computing the Frobenius normal form (FNF) of symmetric Toeplitz matrices by utilizing their inherent structural properties through a graph-theoretic approach. Previous results of the authors…
TSF is growing in various domains including manufacturing. Although numerous TSF algorithms have been developed recently, the validation and evaluation of algorithms hold substantial value for researchers and practitioners and are missing.…
A vector species is a functor from the category of finite sets with bijections to vector spaces; informally, one can view this as a sequence of $S_n$-modules. A Hopf monoid (in the category of vector species) consists of a vector species…
In this paper we illustrate an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T. The main step of the construction is a combinatorial…