Related papers: Coroutining Folds with Hyperfunctions
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also…
We study symmetric function analogues of the higher order Bell numbers. Their construction involves iterated plethystic exponential towers mimicking the single variable exponential generating functions for the higher order Bell numbers. We…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…
We introduce an elliptic extension of Clausen-type functions based on a unified recursive framework. Starting from the polylogarithmic master function, we construct a pair of circular functions whose real and imaginary parts correspond to…
Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
We study several bialgebraic structures on boolean functions, that is to say maps defined on the set of subsets of a finite set $X$, taking the value $0$ on $\emptyset$. Examples of boolean functions are given by the indicator function of…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
FOLD-R++ is a new inductive learning algorithm for binary classification tasks. It generates an (explainable) normal logic program for mixed type (numerical and categorical) data. We present a customized FOLD-R++ algorithm with the ranking…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics,…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…
We have been striving to exceed computational complexity, and in the process, we have come to realize the dilemma of classical computing, and in turn we realize that superpositioner may be a way to solve. A superpositioner is a model formed…