Related papers: Nonlinear functionals of master equation unravelin…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
Entropy production quantifies the breaking of time-reversal symmetry in non-equilibrium systems. Here, we develop a direct method to obtain closed, tractable expressions for entropy production in a broad class of dynamical density…
Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation which often suffers from grossly corruptions or outliers and the neglect of…
A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…
Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…
This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical…
We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
We study the construction of analytical non-radially solutions for the 1-dimensional compressible adiabatic Euler equations in this article. We could design the perturbational method to construct a new class of analytical solutions. In…
We consider $d$-dimensional configurations, that is, colorings of the $d$-dimensional integer grid $\mathbb{Z}^d$ with finitely many colors. Moreover, we interpret the colors as integers so that configurations are functions $\mathbb{Z}^d…