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In a common experimental setting, the behaviour of a noisy dynamical system is monitored in response to manipulations of one or more control parameters. Here, we introduce a structured model to describe parametric changes in qualitative…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
Cascades and speculative decoding are two common approaches to improving language models' inference efficiency. Both approaches involve interleaving models of different sizes, but via fundamentally distinct mechanisms: cascades employ a…
Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow)…
In this paper, we utilize a variant of the scaled relative graph (SRG), referred to as the $\theta$-symmetric SRG, to develop a graphical stability criterion for the feedback interconnection of a cascade of systems. A crucial…
A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the…
In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…
By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, asymptotic behavior of running coupling constants is derived in an algebraic manner. A benefit of this method is presented…
We discuss two important techniques, series expansion and Monte Carlo simulation, for random sequential adsorption study. Random sequential adsorption is an idealization for surface deposition where the time scale of particle relaxation is…
Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…
We obtain long series (28 terms or more) for the coverage (occupation fraction) $\theta$, in powers of time $t$ for two models of random sequential adsorption with diffusional relaxation using an efficient algorithm developed by the…
Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of…
This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
We introduce an approach to training a given compact network. To this end, we leverage over-parameterization, which typically improves both neural network optimization and generalization. Specifically, we propose to expand each linear layer…
Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant.…
Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…
In this paper, we discuss the application of the author's $\tilde{d}^{(m)}$ transformation to accelerate the convergence of infinite series $\sum^\infty_{n=1}a_n$ when the terms $a_n$ have asymptotic expansions that can be expressed in the…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…