相关论文: New Results on Scrambling Using the Mesh Array
We reconsider a recently published algorithm (Dalkilic et al.) for merging lists by way of the perfect shuffle. The original publication gave only experimental results which, although consistent with linear execution time on the samples…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
This article develops a Bayesian approach for estimating panel quantile regression with binary outcomes in the presence of correlated random effects. We construct a working likelihood using an asymmetric Laplace (AL) error distribution and…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a…
Complex motion patterns of natural systems, such as fish schools, bird flocks, and cell groups, have attracted great attention from scientists for years. Trajectory measurement of individuals is vital for quantitative and high-throughput…
Hierarchical Agglomerative Clustering (HAC) is one of the oldest but still most widely used clustering methods. However, HAC is notoriously hard to scale to large data sets as the underlying complexity is at least quadratic in the number of…
In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we…
We introduce a new matrix operation on a pair of matrices, $\text{swirl}(A,X),$ and discuss its implications on the limiting spectral distribution. In a special case, the resultant ensemble converges almost surely to the Rayleigh…
The block Kaczmarz method and its variants are designed for solving the over-determined linear system. They involve iteratively projecting the current point onto the solution space of a subset of constraints. In this work, by alternately…
We continue the study of the assignment problem for a random cost matrix. We analyse the number of $k$-cycles for the solution and their dependence on the symmetry of the random matrix. We observe that for a symmetric matrix one and…
The development of an algorithm with related mathematical concepts and supporting hypothesis for detecting changes in system dynamics from time series along with empirical analysis and theoretical justification is presented. For the method,…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…
This paper reports the results of an experiment on the use of Kak's B-Matrix approach to spreading activity in a Hebbian neural network. Specifically, it concentrates on the memory retrieval from single neurons and compares the performance…
Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…
Optimized multiple precision basic linear computation, especially matrix multiplication, is crucial for solving ill-conditioned problems. The recently proposed Ozaki scheme, which implements accurate matrix multiplication using existing…