Related papers: Discrete surface growth process as a synchronizati…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
We consider whether distributed subgradient methods can achieve a linear speedup over a centralized subgradient method. While it might be hoped that distributed network of $n$ nodes that can compute $n$ times more subgradients in parallel…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the…
The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…
The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents…
We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…
We give a simple proof for the global convergence of gradient descent in training deep ReLU networks with the standard square loss, and show some of its improvements over the state-of-the-art. In particular, while prior works require all…
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…
Depth completion, inferring dense depth maps from sparse measurements, is crucial for robust 3D perception. Although deep learning based methods have made tremendous progress in this problem, these models cannot generalize well across…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs), whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the…
We investigate mechanisms of the typically observed recoverable prevalence in epidemic spreading. Assuming the time-independent connectivity correlations, we analyze the dynamics of spreading on linearly growing scale-free (SF) networks,…
Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…
We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…