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In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…

We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…

Recently proposed quasi-classical DBAR-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical DBAR-dressing method to describe dispersive corrections of any…

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is…

Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer…

This paper puts the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, To\"{e}n, Vaqui\'{e} and Vezzosi. We compute the symplectic structures on mapping stacks and show how the AKSZ…

In this paper we construct the category of birational spaces as the category in which Temkin's relative Riemann-Zariski spaces are naturally included. Furthermore we develop an analogue of Raynaud's theory. We prove that the category of…

Cut-and-project sets $\Sigma\subset\mathbb{R}^n$ represent one of the types of uniformly discrete relatively dense sets. They arise by projection of a section of a higher-dimensional lattice to a suitably oriented subspace. Cut-and-project…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…

A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…

We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…

Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some…

Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…

It was demonstrated that the lattice simulation of $B$-meson light-cone distribution amplitude (LCDA) is feasible via the quasi-distribution amplitude (quasi-DA) in large momentum effective theory (LaMET). The structures of logarithmic…

Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…