Related papers: Mean field approximation for biased diffusion on J…
We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if $d>2(\alpha\wedge2)$ for self-avoiding walk and the Ising model, and…
This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control.…
We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and…
Predicting the behavior of a wireless link in terms of, e.g., the frame delivery ratio, is a critical task for optimizing the performance of wireless industrial communication systems. This is because industrial applications are typically…
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models…
In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate. In this paper, we propose a novel diffusion model -- the Pressure Threshold model (PT)…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
We present a detailed analysis of the Connecting Nearest Neighbors (CNN) model by V\'azquez. We show that the degree distribution follows a power law, but the scaling exponent can vary with the parameter setting. Moreover, the…
Murray's cubic branching law ($\alpha=3$) predicts a universal diameter scaling exponent for all hierarchical transport networks, yet arterial trees yield $\alpha \sim 2.7-2.9$. We show that this discrepancy has a structural origin:…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…
This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = \delta \varphi$. They…
Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores non-linear charge tunneling in nanoparticle networks, controlled by external…
Mean-field limits have been used now as a standard tool in approximations, including for networks with a large number of nodes. Statistical inference on mean-filed models has attracted more attention recently mainly due to the rapid…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
In this paper we study data from financial markets using an information-theory tool that we call the normalised Mutual Information Rate and show how to use it to infer the underlying network structure of interrelations in foreign currency…
The discrepancy between the upper bound on throughput in wireless networks and the throughput scaling in random networks which is also known as the connectivity-throughput trade-off is analyzed. In a random network with $\lambda$ nodes per…
The formation of interface from an initial sharp interface in polydisperse A/B blends is studied using the external potential dynamic method. The present model is a nonlocal coupling model as we take into account the correlation between…
In the last years efforts in econophysics have been shifted to study how network theory can facilitate understanding of complex financial markets. Main part of these efforts is the study of correlation-based hierarchical networks. This is…
Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are many variants of label spreading, nearly all of them are…