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We present some results, both rigorously mathematical and computational, showing unexpected relations between different identities expressing nilpotence in nonassociative algebras, and formulate a number of conjectural generalizations and…

We propose and study the properties of a new potential demanded by the self-consistency of the duality scheme in electromagnetic-like field theories of totally anti-symmetric tensors in diverse dimensions. Physical implications of this new…

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to each other by first-order (self-)duality equations that follow from…

Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using…

We study non-linear phenomena in quantum dots. Non linearities are reflected in the I-V characteristic curve as bistabilities, instabilities and time dependent oscillations of the currents. The nature of the non-linear behavior depends upon…

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…

The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can in principle be revealed by measurements.…

We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the…

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and…

In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier transform such as the orthogonality relation, the…

In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…

Bilinear magnetoresistance is a nonlinear transport phenomenon that scales linearly with the electric and magnetic fields, and appears in nonmagnetic systems with strong spin-orbit coupling, such as topological insulators (TIs). Using the…

This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…

We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the…

In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the…

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as…

This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on the non-asymptotic setting and derive the estimation error bounds depending on the number of samples n and the dimension…

We develop a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions, based on connecting the Ehrhard-Regnier derivative from linear logic with the role of geometry in Watanabe's…

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…

As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product…