Related papers: Functional Integration Approach to Hysteresis
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
This thesis presents a formalization of martingales in arbitrary Banach spaces using Isabelle/HOL. We begin by examining formalizations in prominent proof repositories and extend the definition of the conditional expectation operator from…
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…
In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Hysteresis is studied in a disordered Ising model in which diffusion of antiferromagnetic bonds is allowed in addition to spin flips. Saturation behavior changes to a figure-eight loop when diffusion is introduced. The upper and lower…
The gamma process is a natural model for monotonic degradation processes. In practice, it is desirable to extend the single gamma process to incorporate measurement error and to construct models for the degradation of several nominally…
In this research monograph, we deal with a very general asymptotic representation for statistics named GRI expressed in the functional empirical process, both one-dimensional and multidimensional, and another call residual empirical…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
Gaussian processes appear as building blocks in various stochastic models and have been found instrumental to account for imprecisely known, latent functions. It is often the case that such functions may be directly or indirectly evaluated,…
Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics…
We revisit the problem of assigning a score (a quality of fit) to candidate geometric models -- one of the key components of RANSAC for robust geometric fitting. In a non-robust setting, the ``gold standard'' scoring function, known as the…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…