Related papers: An algorithmic approach to Dold-Puppe complexes
We show that, given a finitely generated group $G$ as the coordinate group of a finite system of equations over a torsion-free hyperbolic group $\Gamma$, there is an algorithm which constructs a cover of a canonical solution diagram. The…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations…
We develop a new algorithm to compute a basis for $M_k(\Gamma_0(N))$, the space of weight $k$ holomorphic modular forms on $\Gamma_0(N)$, in the case when the graded algebra of modular forms over $\Gamma_0(N)$ is generated at weight two.…
Let ${\mathfrak g}$ be a simple Lie algebra. For a level $\kappa$ (thought of as a symmetric ${\mathfrak g}$-invariant form of ${\mathfrak g}$), let $\hat{\mathfrak g}_\kappa$ be the corresponding affine Kac-Moody algebra. Let $Gr_G$ be the…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
Let $\Gamma$ be a finitely generated nilpotent group and let G be a complex reductive algebraic group. The representation variety $\mathrm{Hom}(\Gamma,G)$ and the character variety $\mathrm{Hom}(\Gamma,G)//G$ each carry a natural topology,…
Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of…
We present in this article the model Function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from Random Graphs the capability of probabilistic modelling of structural and…
Feature interaction has been recognized as an important problem in machine learning, which is also very essential for click-through rate (CTR) prediction tasks. In recent years, Deep Neural Networks (DNNs) can automatically learn implicit…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
In a recent paper [3], the authors introduced a map $\mathcal{F}$ which associates a Deitmar scheme (which is defined over the field with one element, denoted by $\mathbb{F}_1$) with any given graph $\Gamma$. By base extension, a scheme…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
Factorization machine (FM) is a prevalent approach to modeling pairwise (second-order) feature interactions when dealing with high-dimensional sparse data. However, on the one hand, FM fails to capture higher-order feature interactions…
Click-Through Rate prediction is an important task in recommender systems, which aims to estimate the probability of a user to click on a given item. Recently, many deep models have been proposed to learn low-order and high-order feature…
For a group $G$, the generating graph $\Gamma(G)$ is defined as the graph with the vertex set $G$, and any two distinct vertices of $\Gamma(G)$ are adjacent if they generate $G$. In this paper, we study the generating graph of $D_n,$ where…
A major challenge facing existing sequential Monte-Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results…
We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category…
Over the last decade, Convolutional Neural Network (CNN) models have been highly successful in solving complex vision problems. However, these deep models are perceived as "black box" methods considering the lack of understanding of their…