Related papers: Parallel dynamics of the fully connected Blume-Eme…
We establish an exact mapping between (i) the equilibrium (imaginary time) dynamics of non-interacting fermions trapped in a harmonic potential at temperature $T=1/\beta$ and (ii) non-intersecting Ornstein-Uhlenbeck (OU) particles…
This paper examines a model involving two dynamic Erd\H{o}s-R\'enyi random graphs that evolve in parallel, with edges in each graph alternating between being present and absent according to specified on- and off-time distributions. A key…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
How the brain performs credit assignment is a fundamental unsolved problem in neuroscience. Many `biologically plausible' algorithms have been proposed, which compute gradients that approximate those computed by backpropagation (BP), and…
In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling…
We analyze the d-dimensional Blume-Emery-Griffiths model in the disordered region of parameters and we show that its free energy can be explicitly written in term of a series which is absolutely convergent at any temperature in an unbounded…
The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion. The transversal correlation function is evaluated in real time…
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with quenched random magnetic interaction. The thermodynamics is worked out in the Full Replica Symmetry…
The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
The reverse process in score-based diffusion models is formally equivalent to overdamped Langevin dynamics in a time-dependent energy landscape. In our prior work we showed that a bilinearly-coupled analog substrate can physically realize…
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
We consider the finite-timestep Brownian dynamics of a single particle confined in one dimension, with a nonuniform temperature profile. In such an open-boundary scenario, one cannot observe any net probability current in the nonequilibrium…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…
A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schemes as well as general…
Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature…
Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author,…
An efficient method of solving the time-dependent Schr\"odinger equation for pure states is described: At each timestep, a restricted subspace of the total Hilbert space is systematically and naturally constructed via the image of repeated…