Related papers: Critical Line in Random Threshold Networks with In…
In a series of articles published in 1986 Derrida, and his colleagues studied two mean field treatments (the quenched and the annealed) for \textit{NK}-Kauffman Networks. Their main results lead to a phase transition curve $ K_c \, 2 \, p_c…
Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and…
We develop a consolidated theory for the detectability of network-borne attacks under two canonical observation models: (i) a static graph drawn from an Erdos-Renyi background with a planted anomalous community, and (ii) a temporal…
We show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of…
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
This work explores the characteristics of financial contagion in networks whose links distributions approaches a power law, using a model that defines banks balance sheets from information of network connectivity. By varying the parameters…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
Chemical reaction networks (CRN) comprise an important class of models to understand biological functions such as cellular information processing, the robustness and control of metabolic pathways, circadian rhythms, and many more. However,…
Over the years, quantifying the similarity of nodes has been a hot topic in complex networks, yet little has been known about the distributions of node-similarity. In this paper, we consider a typical measure of node-similarity called the…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
The structure of social contact networks strongly influences the dynamics of epidemic diseases. In particular the scale-free structure of real-world social networks allows unlikely diseases with low infection rates to spread and become…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node…
Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…
Motivated by the vacuum selection problem of string/M theory, we study a new geometric invariant of a positive Hermitian line bundle $(L, h)\to M$ over a compact K\"ahler manifold: the expected distribution of critical points of a Gaussian…
Recently it was shown (I.A.Gruzberg, A. Kl\"umper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization…