Related papers: The MIXMAX random number generator

Understanding how crossover works is still one of the big challenges in evolutionary computation research, and making our understanding precise and proven by mathematical means might be an even bigger one. As one of few examples where…

A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and…

Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash},…

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the…

We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…

The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…

Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group…

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…

Let $n$ be a positive integer and $G$ be a transitive permutation subgroup of $S_n$. Given a number field $K$ with $[K:\mathbb{Q}]=n$, we let $\widetilde{K}$ be its Galois closure over $\mathbb{Q}$ and refer to…

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the ``ordered'' and ``chaotic'' distribution of such pairs by solving the eigenvalue…

Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic. In parallel, the interest in sparse generator matrices of Reed-Solomon and…

Let $G =<S>$ be a solvable permutation group of the symmetric group $S_n$ given as input by the generating set $S$. We give a deterministic polynomial-time algorithm that computes an \emph{expanding generating set} of size $\tilde{O}(n^2)$…

In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high…

Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…

There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…

We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…

We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that…

We present MuMax, a general-purpose micromagnetic simulation tool running on Graphical Processing Units (GPUs). MuMax is designed for high performance computations and specifically targets large simulations. In that case speedups of over a…

The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating $k$-independent random values over a…

Shift registers/Primitive polynomials find applications in various branches of Mathematics, Coding Theory and Cryptography. Matrix analogues of primitive polynomials do exist. In this paper, an algorithmic approach to generating all such…