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Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
In scientific research, the method is an indispensable means to solve scientific problems and a critical research object. With the advancement of sciences, many scientific methods are being proposed, modified, and used in academic…
Probing classifiers have emerged as one of the prominent methodologies for interpreting and analyzing deep neural network models of natural language processing. The basic idea is simple -- a classifier is trained to predict some linguistic…
This is a set of lecture notes introducing graduate students to the topic of Discontinuous Petrov-Galerkin (DPG) methods.
In this paper we study the existence of solutions to an isotropic differential inclusion.
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
PROBE (Progressive Removal of Blur Residual) is a recursive framework for blind deblurring. Using the elementary modified inverse filter at its core, PROBE's experimental performance meets or exceeds the state of the art, both visually and…
We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
This paper describes some of the ideas used in the development of our work on small gaps between primes.
An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stability of solution is studied in various functional classes.
The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the…
This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum…