Related papers: Negative mobility, sliding and delocalization for …
The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…
Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible experimental studies of the physics of off-diagonal…
The energy transition towards an increased supply of renewable energy raises concerns that existing electricity grids, built to connect few centralized large power plants with consumers, may become more difficult to control and stabilized…
A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…
We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in coarse grained sense acts as an excellent order…
In probability theory and statistics notions of correlation among random variables, decay of correlation, and bias-variance trade-off are fundamental. In this work we introduce analogous notions in optimization, and we show their usefulness…
Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture - the number…
We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for a class of negatively dependent linear random fields on ${\mathbb{Z}}^2$ with moving-average coefficients $a(t,s)$ decaying as…
We consider the problem of sliding motion of a charge-density-wave subject to static disorder within an elastic medium model. Starting with a field-theoretical formulation, which allows exact disorder averaging, we propose a self-consistent…
Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…
A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states…
Negative conductance elements are key to shape the input-output behavior at the terminals of a network through localized positive feedback amplification. The balance of positive and negative differential conductances creates singularities…
We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the…
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here,…
We study the condensation phenomenon in a zero range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase…