Related papers: A New Algorithm for Evaluating Determinants -- The…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
In this paper, we propose a third-order Newton's method which in each iteration solves a semidefinite program as a subproblem. Our approach is based on moving to the local minimum of the third-order Taylor expansion at each iteration,…
Top-N item recommendation has been a widely studied task from implicit feedback. Although much progress has been made with neural methods, there is increasing concern on appropriate evaluation of recommendation algorithms. In this paper, we…
It has previously been shown that response transformations can be very effective in improving dimension reduction outcomes for a continuous response. The choice of transformation used can make a big difference in the visualization of the…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
In this paper we describe a novel method for evidential reasoning [1]. It involves modelling the process of evidential reasoning in three steps, namely, evidence structure construction, evidence accumulation, and decision making. The…
Decision tree is an important method for both induction research and data mining, which is mainly used for model classification and prediction. ID3 algorithm is the most widely used algorithm in the decision tree so far. In this paper, the…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
A certain determinant is evaluated by guessing and computing the LU-decomposition.
Classification is one of the most important tasks of machine learning. Although the most well studied model is the two-class problem, in many scenarios there is the opportunity to label critical items for manual revision, instead of trying…
We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. It is appropriate to call these systems of equations "higher discriminants".
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
A new matrix operation based on inserting columns and rows, similarly to the mediant operation between fractions, gives rise to the Farey determinants matrix or, equivalently, the matrix of the numerators of the differences of Farey…