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A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
In this paper we compare two methods for finding extremal eigenvalues and eigenvectors: the restarted Lanczos method and momentum accelerated power iterations. The convergence of both methods is based on ratios of Chebyshev polynomials…
In the shallow water approximation, the cross-sectional profiles of laboratory rivers satisfy a differential equation here shown to be formally the Friedmann equation of cosmology ruling the evolution of Anti-de Sitter universe. The ensuing…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
Hypothesis tests based on linear models are widely accepted by organizations that regulate clinical trials. These tests are derived using strong assumptions about the data-generating process so that the resulting inference can be based on…
In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical…
We characterize all pairs $(\beta,n),(\beta^\prime,m)$ such that the alternate $(\beta,n)$ and $(\beta^\prime,m)$-transformations $K_{(\beta,n)}$ and $K_{(\beta^\prime,m)}$ have the same absolutely continuous invariant measure, where…
It is known that the Littlewood-Richardson coefficients can be calculated using a certain class of measures, and these measures have a rigidity property when the coefficient is equal to 1. Rigid measures decompose uniquely into sums of…
In this paper, we consider the Strichartz inequality for a fourth-order Schr\"odinger equation on $\mathbb{R}^{2+1}$. We show that extremizers exist using a linear profile decomposition which follows from the endpoint version decomposition…
Transformers are widely used in natural language processing, where they consistently achieve state-of-the-art performance. This is mainly due to their attention-based architecture, which allows them to model rich linguistic relations…
Although implicit-explicit (IMEX) methods for approximating solutions to semilinear parabolic equations are relatively standard, most recent works examine the case of a fully discretized model. We show that by discretizing time only, one…
The block maxima method is a standard approach for analyzing the extremal behavior of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved…
Consider the problem {ll} \Delta^2 u= \lambda e^{u} &\text{in} B u=\frac{\partial u}{\partial n}=0 &\text{on}\partial B, where $B$ is the unit ball in $\R^N$ and $\lambda$ is a parameter. Unlike the Gelfand problem the natural candidate…
Counterfactual explanations can be used to interpret and debug text classifiers by producing minimally altered text inputs that change a classifier's output. In this work, we evaluate five methods for generating counterfactual explanations…
The change point is a moment of an abrupt alteration in the data distribution. Current methods for change point detection are based on recurrent neural methods suitable for sequential data. However, recent works show that transformers based…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are…
Practical anomaly detection requires applying numerous approaches due to the inherent difficulty of unsupervised learning. Direct comparison between complex or opaque anomaly detection algorithms is intractable; we instead propose a…
We show that the difference of the extension dimensions of two derived equivalent algebras is bounded above by the minimal length of a tilting complex associated with a derived equivalence, and that the extension dimension is an invariant…