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We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
Neural ordinary differential equations (neural ODEs) have emerged as a natural tool for supervised learning from a control perspective, yet a complete understanding of their optimal architecture remains elusive. In this work, we examine the…
We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using…
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a…
We study a two-dimensional Bose-Hubbard model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the…
We consider systems of linear differential and difference equations \begin{eqnarray*} \partial Y(x) =A(x)Y(x), \sigma Y(x) =B(x)Y(x) \end{eqnarray*} with $\partial = \frac{d}{dx}$, $\sigma$ a shift operator $\sigma(x) = x+a$, $q$-dilation…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Two of the main factors shaping an individual's opinion are social coordination and personal preferences, or personal biases. To understand the role of those and that of the topology of the network of interactions, we study an extension of…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…
For over half a century, statistical mechanics of spin glasses played as a paradigm to model and interpret disparate phenomena, ranging from quantitative biology to computer science. However, despite the extensive body of research in this…
We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a…
Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here…
Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which…
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium…