Related papers: A Simple Method Which Generates Infinitely Many Co…
It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations…
A monolithic process is a single recursive equation with data parameters, which only uses non-determinism, action prefixing, and recursion. We present a technique that decomposes such a monolithic process into multiple processes where each…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…
The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we…
A pancyclic graph is a simple graph containing a cycle of length $k$ for all $3\leq k\leq n$. Let $m(n)$ be the minimum number of edges of all pancyclic graphs on $n$ vertices. Exact values are given for $m(n)$ for $n\leq 37$, combining…
We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…
A fake octagon is a genus two translation surface with only one singular point and the same periods as the octagon. Existence of infinitely many fakes was first established by McMullen in 2007, and more generally follows from dynamical…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
In multicentric representation of piecewise holomorphic functions one combines Lagrange interpolation at roots of a polynomial $p$ with convergent power series of $p$ as the "coefficients" multiplying the Lagrange basis polynomials. When…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…