Related papers: Comment on "Indispensable Finite Time Correlations…
We develop a general technique to prove uniqueness of solutions for Fokker--Planck equations on infinite dimensional spaces. We illustrate this method by implementing it for Fokker--Planck equations in Hilbert spaces with Kolmogorov…
The paper introduces a one dimensional analogy of Poincare's "section" method. Its application to numerical study of sequences of fractional parts is considered. As a result, the possibility of Cantorian structure of time flow is deduced. A…
Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…
In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…
We study the pointwise (in the space and time variables) behavior of the Fokker-Planck Equation with flat confinement. The solution has very clear description in the $xt-$plane, including large time behavior, initial layer and asymptotic…
Basic issues of the time-dependent density-functional theory are discussed, especially on the real-time calculation of the linear response functions. Some remarks on the derivation of the time-dependent Kohn-Sham equations and on the…
We consider the linear Fokker-Planck equation in a confining potential in space dimension $d \geq 3$. Using spectral methods, we prove bounds on the derivatives of the solution for short and long time, and give some applications.
Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]
Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]
Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]
Controlling complex dynamical systems has been a topic of considerable interest in academic circles in recent decades. While existing works have primarily focused on closed-loop control schemes with infinite-time durations, this paper…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…
In this brief paper we justify observations made in El Naschie's paper "On the Unification of the Fundamental Forces...", on the Planck scale, fractal space time and the unification of interactions, from different standpoints.
We respond to comments on our paper, titled "Instrumental variable estimation of the causal hazard ratio."
Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation…
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficient,…
We consider the Fokker-Planck equation on the abstract Wiener space associated to the Ornstein-Uhlenbeck operator. Using the Weitzenb\"ock formula, we prove an explicit estimate on the time derivative of the entropy of the solution to the…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
The Comment by Holas et al. [A. Holas, M. Cinal, and N. H. March, Phys. Rev. A 78, 016501 (2008)] on our recent paper [J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. is an appropriate and valuable contribution. As a small…
We show that recent results on the interaction of causality-respecting particles with particles on closed timelike curves derived in [Phys. Rev. A 82, 062330 (2010)] depend on ambiguous assumption about the form of the state which is…