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We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant \emph{global} effect from a \emph{spatial deviation}. An adaptive group penalty selects whether a…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
In this note we draw a connection between noncommutative algebra and geometric group theory. Specifically, we ask whether it is possible to bound the sequence of codimensions for an associative PI-algebra using techniques from geometric…
We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a…
We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…
Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…
We derive non-asymptotic spectral bands that bound the squared InfoNCE gradient norm via alignment, temperature, and batch spectrum, recovering the \(1/\tau^{2}\) law and closely tracking batch-mean gradients on synthetic data and ImageNet.…
Several authors have proposed spatially-coupled (or convolutional-like) variants of product codes (PCs). In this paper, we focus on a parametrized family of generalized PCs that recovers some of these codes (e.g., staircase and block-wise…
Due to the explosion in size and complexity of modern data sets and privacy concerns of data holders, it is increasingly important to be able to solve machine learning problems in distributed manners. The Alternating Direction Method of…
Sum-rank codes have wide applications in multishot network coding, distributed storage and the construction of space-time codes. Asymptotically good sequences of linearized algebraic geometry sum-rank codes, exceeding the…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
In this paper, we consider real-time beamforming design for dynamic wireless environments with varying channels and different numbers of access points (APs) and users in cell-free systems. Specifically, a sum-rate maximization optimization…
A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…
A binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \ge 2$, $L \ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…
In this work, Lie symmetry analysis is performed on a coupled nonlinear cross-diffusion system with varying cross-section geometry. The system describes two interacting quantities whose material properties, namely the capacity functions and…