Related papers: Rigged Configurations and Cylindric Loop Schur Fun…
A Schur-class function in $d$ variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler class if it is contractive when evaluated on any commutative…
We construct a maximal function associated with a family of skewed cylinders. These cylinders, which are defined as tubular neighborhoods of trajectories of a mollified flow, appear in the study of fluid equations such as the Navier-Stokes…
In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation…
In previous work with Mikhail Khovanov and Aaron Lauda we introduced two odd analogues of the Schur functions: one via the combinatorics of Young tableaux (odd Kostka numbers) and one via the odd symmetrization operator. In this paper we…
The theory of polar forms of polynomials is used to provide for sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic stability radius), to be…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations…
We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function…
The purpose of this work is twofold: to present mathematical expressions for the kinematics of an articulated mechanism and to perform numerical experiments with the implemented code. The system of rigid parts is made of two slender bars…
Schur-type methods in \cite{Chu2} and \cite{GCQX} solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure of robustness. They work well generally when all poles to…
Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to…
Lam and Pylyavskyy introduced loop symmetric functions as a generalization of symmetric functions. They defined loop Schur functions as generating functions over semistandard tableaux with respect to a `colored weight,' and they proved a…
In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…