Related papers: Transient dynamics for sequence processing neural …
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
We describe a simple and systematic method for obtaining approximate sensitivity information from a chaotic dynamical system using a hierarchy of cumulant equations. The resulting forward and adjoint systems yield information about…
Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…
Microscopic theory of counting statistics of electrical noise is reviewed. We discuss a model of passive charge detector based on current fluctuations coupled to a spin, and its relation with the theory of photon counting in quantum optics.…
Cross-modal retrieval maps data under different modality via semantic relevance. Existing approaches implicitly assume that data pairs are well-aligned and ignore the widely existing annotation noise, i.e., noisy correspondence (NC).…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. A particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
We investigate the transient evolution of finite-frequency current noise after abrupt switching on of the tunneling coupling in two paradigmatic, exactly solvable models of mesoscopic physics: the resonant level model and the Majorana…
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
Relying on an exact time evolution scheme, we identify a novel transient energy transfer phe- nomenon in an exactly-solvable quantum microscopic model consisting of a three-level system coupled to two non-Markovian zero-temperature bosonic…
We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path integral…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
We consider the statics and dynamics of a single particle trapped in a one-dimensional harmonic potential, and subjected to a driving noise with memory, that is represented by a resetting stochastic process. The finite memory of this…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…