Related papers: The ideas behind the Self Consistent Expansion
The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration…
We propose a systematic expansion method which is applied to freely evolving granular fluids contained in sufficiently small systems. Restricting ourselves to small systems, we show that there exists a small parameter which characterizes a…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
I analyze the Nonlocal Conserved Kardar-Parisi-Zhang (NCKPZ) equation with spatially correlated noise. This equation is also known as the Nonlocal Molecular Beam Epitaxy (NMBE) equation andv was originally suggested to study the effect of…
Continual learning (CL) aims to continually accumulate knowledge from a non-stationary data stream without catastrophic forgetting of learned knowledge, requiring a balance between stability and adaptability. Relying on the generalizable…
From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…
We study the phenomenon of system size stochastic resonance within the nonequilibrium potential's framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing…
The design of small scale non-equilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for non-equilibrium systems is…
With the advances in deep learning, speech enhancement systems benefited from large neural network architectures and achieved state-of-the-art quality. However, speaker-agnostic methods are not always desirable, both in terms of quality and…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
With a large number of baseline covariates, we propose a new semi-parametric modeling strategy for heterogeneous treatment effect estimation and individualized treatment selection, which are two major goals in personalized medicine. We…
An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In…
Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for…
A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore,…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
In Phys. Rev. Lett. 114 (2015) 6, 061601, we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and $N$-component self-interacting scalar field theories. Using…