Related papers: Computing the Asymptotic Spectrum for Networks Rep…
The asymptotic spectrum of graphs, introduced by Zuiddam (arXiv:1807.00169, 2018), is the space of graph parameters that are additive under disjoint union, multiplicative under the strong product, normalized and monotone under homomorphisms…
Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central fusion…
We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Gas-fired generators, with their ability to quickly ramp up and down their electricity production, play an important role in managing renewable energy variability. However, these changes in electricity production translate into variability…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
One of the simplest models for the slow relaxation and aging of glasses is the trap model by Bouchaud and others, which represents a system as a point in configuration-space hopping between local energy minima. The time evolution depends on…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
A stochastic EDQNM approach is used to investigate self-similar decaying isotropic turbulence at high Reynolds number ($400 \leq Re_\lambda \leq 10^4$). The realistic energy spectrum functional form recently proposed by Meyers & Meneveau is…
The singular limit $\eps\ra 0$ of the $S$-matrix associated with the equation $i\eps d\psi(t)/dt=H(t)\psi(t)$ is considered, where the analytic generator $H(t)\in M_n(\C)$ is such that its spectrum is real and non-degenerate for all…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…
Distributed energy resources are better for the environment but may cause transformer overload in distribution grids, calling for recovering meter-transformer mapping to provide situational awareness, i.e., the transformer loading. The…
We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are…
We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We explore various tree architectures, ranging from the simple…
We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and…
The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the…
An asymptotic technique is presented to characterize the bits/symbol achievable on a representative wireless link in a spatially distributed network with active interferers at correlated positions, N receive diversity branches, and linear…
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to…
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing…
Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…