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A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
Meta-analysis, because of both logistical convenience and statistical efficiency, is widely popular for synthesizing information on common parameters of interest across multiple studies. We propose developing a generalized meta-analysis…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…
In this paper we present closed-form solutions for efficiently updating the principal components of a set of $n$ points, when $m$ points are added or deleted from the point set. For both operations performed on a discrete point set in…
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
In this paper, we generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of regular index filtration for every Morse decomposition.
This is the second part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general…
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…
We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss…
Assessing fit in common factor models solely through the lens of mean and covariance structures, as is commonly done with conventional goodness-of-fit (GOF) assessments, may overlook critical aspects of misfit, potentially leading to…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
We propose a procedure to determine the dimension of the common factor space in a large, possibly non-stationary, dataset. Our procedure is designed to determine whether there are (and how many) common factors (i) with linear trends, (ii)…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
Due to domain shift, deep neural networks (DNNs) usually fail to generalize well on unknown test data in practice. Domain generalization (DG) aims to overcome this issue by capturing domain-invariant representations from source domains.…
We study a generalization of deduplication, which enables lossless deduplication of highly similar data and show that standard deduplication with fixed chunk length is a special case. We provide bounds on the expected length of coded…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM), that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces.…