Related papers: Integrable Ito equations with multiple noises
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
The integrability in quadratures of normality equation for spatially homogeneous dynamical systems in two-dimensional space is shown. The classical symmetries of this equation are calculated and the corresponding self-similar solutions are…
The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works…
We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these…
We introduce three biharmonic Steklov problems on differential forms with Neumann boundary conditions and show that they are elliptic. We prove the existence of a discrete spectrum for each of those problems and give associated variational…
This paper is devoted to the study of the defocusing nonlinear Schr\"{o}dinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem. In cases where the source consists of a…
Physical platforms such as trapped ions suffer from coherent noise where errors manifest as rotations about a particular axis and can accumulate over time. We investigate passive mitigation through decoherence free subspaces, requiring the…
Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…
We show theoretically how a correlation of multiple measurements on a qubit undergoing pure dephasing can be expressed as environmental noise filtering. The measurement of such correlations can be used for environmental noise spectroscopy,…
This paper is concerned with the existence of invariant measure for 3D stochastic primitive equations driven by linear multiplicative noise under non-periodic boundary conditions. The common method is to apply Sobolev imbedding theorem to…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
We analyze the influence of noise for qubits implemented using a triple quantum dot spin system. We give a detailed description of the physical realization and develop error models for the dominant external noise sources. We use a Davies…
With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy…
For a composition $I$ whose first part exceeds 1, we can define the multiple $t$-value $t(I)$ as the sum of all the terms in the series for the multiple zeta value $\zeta(I)$ whose denominators are odd. In this paper we show that if $I$ is…
We construct an asymptotic series for a general solution of the Einstein equations near a sudden singularity. The solution is quasi isotropic and contains nine independent arbitrary functions of the space coordinates as required by the…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…
Two classes of algorithms for optimization in the presence of noise are presented, that do not require the evaluation of the objective function. The first generalizes the well-known Adagrad method. Its complexity is then analyzed as a…