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We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
In this paper we design and analyze algorithms for asynchronously solving linear programs using nonlinear signal processing structures. In particular, we discuss a general procedure for generating these structures such that a fixed-point of…
We present a new algorithm by which the Adomian polynomials can be determined for scalar-valued nonlinear polynomial functional in a Hilbert space. This algorithm calculates the Adomian polynomials without the complicated operations such as…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
Nonequilibrium Green's functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Green's functions formalism to the dynamics…
We investigate the relevance of time ordering in the definition of off-diagonal parton distributions in terms of products of fields. The method we use easily allows determination of their support properties and provides a link to their…
The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of…
Time series forecasting is ubiquitous in the modern world. Applications range from health care to astronomy, and include climate modelling, financial trading and monitoring of critical engineering equipment. To offer value over this range…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
Algorithms of question answering in a computer system oriented on input and logical processing of text information are presented. A knowledge domain under consideration is social behavior of a person. A database of the system includes an…
Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…
A two space dimensional active nonlinear nonlocal cochlear model is formulated in the time domain to capture nonlinear hearing effects such as compression, multi-tone suppression and difference tones. The micromechanics of the basilar…
Deep learning time-series models are often used to make forecasts that inform downstream decisions. Since these decisions can differ from those in the training set, there is an implicit requirement that time-series models will generalize…
Estimating the unknown causal dependencies among graph-connected time series plays an important role in many applications, such as sensor network analysis, signal processing over cyber-physical systems, and finance engineering. Inference of…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori…