Related papers: Weakly reinforced P\'olya urns on countable networ…
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…
This work deals with a system of interacting reinforced stochastic processes, where each process $X^j=(X_{n,j})_n$ is located at a vertex $j$ of a finite weighted direct graph, and it can be interpreted as the sequence of "actions" adopted…
Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for…
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…
We give bounds for (central) moments for balanced P\'olya urns under very general conditions. In some cases, these bounds imply that moment convergence holds in earlier known results on asymptotic distribution. The results overlap with…
In a network of reinforced stochastic processes, for certain values of the parameters, all the agents' inclinations synchronize and converge almost surely toward a certain random variable. The present work aims at clarifying when the agents…
This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…
It is known that in an irreducible small P\'olya urn process, the composition of the urn after suitable normalization converges in distribution to a normal distribution. We show that if the urn also is balanced, this normal convergence…
We introduce the P\'olya threshold graph model and derive its stochastic and algebraic properties. This random threshold graph is generated sequentially via a two-color P\'olya urn process. Starting from an empty graph, each time step…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
In view of the node importance in weighted networks, weighted expected method (WEM), was proposed in this paper, which take an advantages of uncertain graph algorithm. First, a weight processing method is proposed based on the relationship…
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is…
We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
Generalized Friedman urn is one of the simplest and most useful models considered in probability theory. Since Athreya and Ney (1972) showed the almost sure convergence of urn proportions in a randomized urn model with irreducible…
Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process.…
Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…