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There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…

Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…

With the growing complexity and capability of large language models, a need to understand model reasoning has emerged, often motivated by an underlying goal of controlling and aligning models. While numerous interpretability and steering…

Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices…

Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…

Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…

Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…

The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…

It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory…

We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…

Spiking neural networks (SNNs) are powerful mathematical models that integrate the biological details of neural systems, but their complexity often makes them computationally expensive and analytically untractable. The firing rate of an SNN…

Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation…

As deep learning (DL) efficacy grows, concerns for poor model explainability grow also. Attribution methods address the issue of explainability by quantifying the importance of an input feature for a model prediction. Among various methods,…

Time series modeling and forecasting has fundamental importance to various practical domains. Thus a lot of active research works is going on in this subject during several years. Many important models have been proposed in literature for…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…