Related papers: A computer algebra package for bivariate asymptoti…
Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional…
In this paper we propose a novel data-level algorithm for handling data imbalance in the classification task, Synthetic Majority Undersampling Technique (SMUTE). SMUTE leverages the concept of interpolation of nearby instances, previously…
We study statistical properties of the random variables $X_{\sigma}(\pi)$, the number of occurrences of the pattern $\sigma$ in the permutation $\pi$. We present two contrasting approaches to this problem: traditional probability theory and…
We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, $\sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ...…
We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen's theorem for correlated probability,…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
We describe here the package {\tt subdivision\\_solver} for the mathematical software {\tt SageMath}. It provides a solver on real numbers for square systems of large dense polynomials. By large polynomials we mean multivariate polynomials…
Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $\sigma(G)$ denotes…
We investigate saddlepoint approximations applied to the score test statistic in genome-wide association studies with binary phenotypes. The inaccuracy in the normal approximation of the score test statistic increases with increasing sample…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
We present Ca$\Sigma$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Inspired by the recent pioneering work, dubbed "The Ramanujan Machine" by Raayoni et al. (arXiv:1907.00205), we (automatically) [rigorously] prove some of their conjectures regarding the exact values of some specific infinite continued…
In a 1916 paper, Ramanujan studied the additive convolution $S_{a, b}(n)$ of sum-of-divisors functions $\sigma_a(n)$ and $\sigma_b(n)$, and proved an asymptotic formula for it when $a$ and $b$ are positive odd integers. He also conjectured…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…