Related papers: Linear Response Theory: A Modern Analytic-Algebrai…
Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…
We systematically present a new approach for studying the coupled linear transport of holographic systems. In this approach, the set of equations for the linear perturbations can be reduced to a first-order nonlinear ordinary differential…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not…
Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results…
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\tilde{g}}_{ab} = g_{ab} -…
Nonlinear tunneling current through a quantum dot (an Anderson impurity system) subject to both constant and alternating electric fields is studied in the Kondo regime. A systematic diagram technique is developed for perturbation study of…
Real-world control applications in complex and uncertain environments require adaptability to handle model uncertainties and robustness against disturbances. This paper presents an online, output-feedback, critic-only, model-based…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
In this paper we present a novel approach combining linear response theory (Kubo) for the conductance and the Density Matrix Renormalization Group (DMRG). The system considered is one-dimensional and consists of non-interacting tight…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
We consider the problem of strategic classification, where the act of deploying a classifier leads to strategic behaviour that induces a distribution shift on subsequent observations. Current approaches to learning classifiers in strategic…