Related papers: How beta-skeletons lose their edges
Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be…
Many edge prediction methods have been proposed, based on various local or global properties of the structure of an incomplete network. Community structure is another significant feature of networks: Vertices in a community are more densely…
We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1…
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…
In considering a social network, there are cases where people is transferred to another place. Then the physical (direct) relations among nodes are lost by the movement. In terms of a network theory, some nodes break the present connections…
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr…
In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…
We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be stable: "glide" dislocations consisting of…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…
The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
It is widely believed that central star binarity plays an important role in the formation and evolution of aspherical planetary nebulae, however observational support for this hypothesis is lacking. Here, we present the most recent results…
For the aggregation equation in $\mathbb{R}$, we consider the evolution of an initial density corresponding to the characteristic function of some set $\Omega_0$. We study the limit measure at the blow up time 1 for $\Omega_0$ open or…
The relation between neutrino oscillation parameters and neutrinoless double beta decay is studied, assuming normal and inverse hierarchies for Majorana neutrino masses. For normal hierarchy the crucial dependence on U_{e3} is explored. The…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…