Related papers: Functional Integration Approach to Hysteresis
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Judging by its omnipresence in the literature, the hysteresis observed in the transfer characteristics of emerging transistors based on 2D-materials is widely accepted as an important metric related to the device quality. The hysteresis is…
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number $m$ of intervals. We derive an integral representation for it in terms of a…
We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued…
We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or created through saddle-node bifurcations causing the system to…
We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are…
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification of…
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…