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We introduce an extension to the Discrete Multiplier Method (DMM), called Minimal $\ell_2$ Norm Discrete Multiplier Method (MN-DMM), where conservative finite difference schemes for dynamical systems with multiple conserved quantities are…

The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…

Multi-camera tracking plays a pivotal role in various real-world applications. While end-to-end methods have gained significant interest in single-camera tracking, multi-camera tracking remains predominantly reliant on heuristic techniques.…

Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…

Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these…

We study the singularity probability of random integer matrices. Concretely, the probability that a random $n \times n$ matrix, with integer entries chosen uniformly from $\{-m,\ldots,m\}$, is singular. This problem has been well studied in…

Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…

An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…

Motivated by the wide presence of multilayer networks in both natural and human-made systems, within a random matrix theory (RMT) approach, in this study we compute eigenfunction and spectral properties of multilayer directed random…

The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and matdot codes are generalized by making use of algebraic…

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…

Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…

Recognition of Off-line Chinese characters is still a challenging problem, especially in historical documents, not only in the number of classes extremely large in comparison to contemporary image retrieval methods, but also new unseen…

In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…

We propose a restricted collapsed draw (RCD) sampler, a general Markov chain Monte Carlo sampler of simultaneous draws from a hierarchical Chinese restaurant process (HCRP) with restriction. Models that require simultaneous draws from a…

We present a novel multimodal deep learning framework for cardiac resynchronisation therapy (CRT) response prediction from 2D echocardiography and cardiac magnetic resonance (CMR) data. The proposed method first uses the `nnU-Net'…

In this work, a MIMO detection problem is considered. At first, we derive the Generalized Likelihood Ratio Test (GLRT) for arbitrary transmitted signals and arbitrary time-correlation of the disturbance. Then, we investigate design criteria…

Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…

We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…