Related papers: Almost-lossless compression of a low-rank random t…
We represent the number of mxn non-negative integer matrices (contingency tables) with prescribed row sums and column sums as the expected value of the permanent of a non-negative random matrix with exponentially distributed entries. We…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank,…
Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. This gives a…
This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…
We systematically compute improved asymptotic rank bounds for tensors. Using numerical implicitization, we implement the geometric framework of Kaski and Micha{\l}ek across all computationally feasible cases. By detecting the absence of…
This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimization), a new hierarchy of semidefinite programming…
We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these…
An alternative approach to two-part 'critical compression' is presented. Whereas previous results were based on summing a lossless code at reduced precision with a lossy-compressed error or noise term, the present approach uses a similar…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [MP19] established…
This paper studies the fundamental limits of the minimum average length of lossless and lossy variable-length compression, allowing a nonzero error probability $\epsilon$, for lossless compression. We give non-asymptotic bounds on the…
For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavior of these twisted Alexander polynomials evaluated at unit…
This paper presents a multigrid algorithm for the computation of the rank-R canonical decomposition of a tensor for low rank R. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level…
We show that the typical coordinate-wise encoding of multivariate ergodic source into prescribed alphabets has the entropy profile close to the convolution of the entropy profile of the source and the modular polymatroid that is determined…
It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the…