Related papers: Simple constructions of linear-depth t-designs and…

Conventional clustering methods based on pairwise affinity usually suffer from the concentration effect while processing huge dimensional features yet low sample sizes data, resulting in inaccuracy to encode the sample proximity and…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval…

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…

Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be…

An attempt is made to describe random matrix ensembles with unitary invariance of measure (UE) in a unified way, using a combination of Tracy-Widom (TW) and Adler-Shiota-Van Moerbeke (ASvM) approaches to derivation of partial differential…

It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from…

The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…

A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate…

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…

We present a structure-adaptive topology optimization framework for engineering photonic band gaps with TM-polarized sources based on computation of the photonic density of states with a uniform source substituting for the standard Dirac…

Prevalent lossy image compression schemes can be divided into: 1) explicit image compression (EIC), including traditional standards and neural end-to-end algorithms; 2) implicit image compression (IIC) based on implicit neural…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

Unsupervised Domain Adaptation (UDA) transfers predictive models from a fully-labeled source domain to an unlabeled target domain. In some applications, however, it is expensive even to collect labels in the source domain, making most…

We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…

An M-sequence generated by a primitive polynomial has many interesting and desirable properties. A pseudo-random array is the two-dimensional generalization of an M-sequence. There are non-primitive polynomials all of whose non-zero…

Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the…

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…

Topological interface states (TISs) in phononic crystals (PnCs) are robust acoustic modes against external perturbations, which are of great significance in scientific and engineering communities. However, designing a pair of PnCs with…

Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…