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We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from…
We propose an extension to time series with several simultaneously measured variables of the nonlinearity test, which combines the redundancy -- linear redundancy approach with the surrogate data technique. For several variables various…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Most of neural approaches to relation classification have focused on finding short patterns that represent the semantic relation using Convolutional Neural Networks (CNNs) and those approaches have generally achieved better performances…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. We show for the first time…
This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…
This paper proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit and the other is a correlation between units in the same cluster. This model…
We adapt the improved duality estimates for bounded coefficients derived by Canizo et al. to the framework of cross diffusion. Since the estimates can not be directly applied we need to derive a time discrete version of their results and…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…
No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…
Identifying causal relationships in climate systems remains challenging due to nonlinear, coupled dynamics that limit the effectiveness of linear and stochastic causal discovery approaches. This study benchmarks Convergence Cross Mapping…
In a novel approach to quantum dynamics, we apply the tools of recurrence network analysis to the dynamics of the quantum mechanical expectation values of observables. We construct and analyse $\epsilon$-recurrence networks from the…
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important…