Related papers: The Memory Function Formalism: A Review

We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients…

Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation…

We present a treatment of non-Markovian character of memory by incorporating different forms of Mittag-Leffler (ML) function, which generally arises in the solution of fractional master equation, as different memory functions in the…

We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG),…

Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…

This paper focuses on a wide class of Collatz-type arithmetic dynamics, and presents a systematic derivation of recursive formulas and functional equations satisfied by the associated generating functions. The main tools belong to complex…

We study a relaxation behavior of an Ornstein-Uhlenbeck (OU) process with a time-dependent and fluctuating diffusivity. In this process, the dynamics of a position vector is modeled by the Langevin equation with a linear restoring force and…

Catastrophic forgetting in continual learning is often measured at the performance or last-layer representation level, overlooking the underlying mechanisms. We introduce a mechanistic framework that offers a geometric interpretation of…

Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value…

Electron transport properties in nanostructures can be modeled, for example, by using the semiclassical Wigner formalism or the quantum mechanical Green's functions formalism. We compare the performance and the results of these methods in…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented…

Multimodal Large Language Models (MLLMs) have gained significant traction for their ability to process diverse input data types and generate coherent, contextually relevant outputs across various applications. While supervised fine-tuning…

We develop a classical density functional theory (DFT) for two site associating fluids in spatially uniform external fields which exhibit orientational inhomogeneities. The Helmholtz free energy functional is obtain using Wertheim's…

Working memory, or the ability to hold and manipulate information in the mind, is a critical component of human intelligence and executive functioning. It is correlated with performance on various cognitive tasks, including measures of…

We propose a systematic approach to the systems of correlated electrons, the so-called $\mathbf{k}$-DE-GWF method, based on reciprocal-space ($\mathbf{k}$-resolved) diagrammatic expansion of the variational Gutzwiller-type wave function for…

Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…

This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein…