Related papers: Memristive Networks: from Graph Theory to Statisti…
Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph…
We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…
We study the phase diagram of memristive circuit models in the replica-symmetric case using a novel Lyapunov function for the dynamics of these devices. Effectively, the model we propose is an Ising model with interacting quenched disorder,…
The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our…
Self-organizing memristive networks are physical circuits that dynamically reconfigure their circuitry in response to external input signals. Their adaptive behavior arises from intrinsic neuro-synaptic dynamics combined with a…
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific…
In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…
Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Differentiable physical networks provide a simple setting in which learning can be studied through the interaction between trainable parameters and physical equilibrium constraints. We investigate sequential learning in differentiable…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…
Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions.…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…