相关论文: Generalised Mersenne Numbers Revisited

We introduce an iterative method named GPMR for solving 2x2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously two rectangular matrices to upper Hessenberg form and that is closely related to the…

We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated…

This paper presents a distinctive prime detection approach. This method use GM-(n+1) sequences to effectively eliminate complex numbers. The sequences, which consist of odd a number of (n+1), exclude all components except for the initial…

The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly not just via their n-tupel distributions. The generalized analysis of many…

A matrix $M$ over the finite field $ \mathbb{F}_q $ is called \emph{maximum distance separable} (MDS) if all of its square submatrices are non-singular. These MDS matrices are very important in cryptography and coding theory because they…

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…

Nowadays, the notion of semi-regular sequences, originally proposed by Fr\"oberg, becomes very important not only in Mathematics, but also in Information Science, in particular Cryptology. For example, it is highly expected that randomly…

This PhD Thesis presents an investigation into the analysis of financial returns using mixture models, focusing on mixtures of generalized normal distributions (MGND) and their extensions. The study addresses several critical issues…

The main advantage of Constraint Programming (CP) approaches for sequential pattern mining (SPM) is their modularity, which includes the ability to add new constraints (regular expressions, length restrictions, etc). The current best CP…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in…

In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity.…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a…

Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of…

General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…

Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing…

ReLU neural networks have been modelled as constraints in mixed integer linear programming (MILP), enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous…