Related papers: Heaven & Hell II: Scale Laws and Robustness in One…
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…
Error tolerance and attack vulnerability are two common and important properties of complex networks, which are usually used to evaluate the robustness of a network. Recently, much work has been devoted to determining the network design…
The latest results of the ATLAS and CMS experiments point to a preferred narrow Higgs mass range (m_h \simeq 124 - 126 GeV) in which the effective potential of the Standard Model (SM) develops a vacuum instability at a scale 10^{9} -10^{11}…
Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
Often in the analysis of first-order methods for both smooth and nonsmooth optimization, assuming the existence of a growth/error bound or KL condition facilitates much stronger convergence analysis. Hence separate analysis is typically…
Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Hierarchical SGD (H-SGD) has emerged as a new distributed SGD algorithm for multi-level communication networks. In H-SGD, before each global aggregation, workers send their updated local models to local servers for aggregations. Despite…
Naturalness demands that the quadratic divergence of the one-loop top contribution to the Higgs mass be cancelled at a scale below 1 TeV. This can be achieved by introducing a fermionic (spin-1/2) top partner, as in, for example, Little…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
With the increasing interest in proximity and docking operations, there is a growing interest in spacecraft relative motion control. This paper extends a previously proposed constrained relative motion approach based on chained positively…
In this paper, we study the characteristic scale of transition to cosmic homogeneity of the universe, $\mathcal{R}_H$, as a standard ruler, to constrain cosmological parameters on mock galaxy catalogues. We use mock galaxy catalogues that…
Throughput scaling laws of an ad hoc network equipping directional antennas at each node are analyzed. More specifically, this paper considers a general framework in which the beam width of each node can scale at an arbitrary rate relative…
We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of…
We present an up-to-date compilation of published Hubble constant ($H_0$) measurements that are independent of the CMB sound horizon scale. This compilation is split in two distinct groups: A. Distance Ladder Measurements sample comprising…
This paper proposes the first hash opinion dynamics model, named SkyHash, that can help a P2P network quickly reach consensus on hash opinion. The model consists of a bit layer and a hash layer, each time when a node shapes its new opinion,…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling…