相关论文: Growing Cayley trees described by Fermi distributi…

A generalization of the coherent-noise models [M. E. J. Newman and K. Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in the model are subjected to a multitude of stresses, generated in a hierarchy of different…

The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed focousing on the directed distance of nodes from the origin. The topology of the netwoks strongly depends on the dynamical parameter $T$,…

We analytically investigate the heat current $I$ and its thermal fluctuations $\Delta$ in a branching network without loops (Cayley tree). The network consists of two type of harmonic masses: vertex masses $M$ placed at the branching points…

The most general single species autonomous reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced. The stationary solutions of such models, as well as their dynamics, are discussed. To study dynamics of…

We study the mathematical aspects of the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non homogeneous networks. The graphs under investigation are obtained by adding density zero…

The numerical integration of stochastic growth equations on non-Euclidean networks presents unique challenges due to the nonlinearities that occur in many relevant models and of the structural constraints of the networks. In this work, we…

The behavior of two interacting populations, ``hosts''and ``parasites'', is investigated on Cayley trees and scale-free networks. In the former case analytical and numerical arguments elucidate a phase diagram, whose most interesting…

We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…

We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits…

The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…

Understanding the flow dynamics of yield stress fluids in porous media presents a substantial challenge. Both experiments and extensive numerical simulations frequently show a non-linear relationship between the flow rate and the pressure…

Attacks on networks is a very important issue in developing strategies of eradicating spreads of malicious phenomena in networks, such as epidemics and fake information, which are generally named in the research networks immunization. The…

Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…

There are few exactly solvable lattice models and even fewer solvable quantum lattice models. Here we address the problem of finding the spectrum of the tight-binding model (equivalently, the spectrum of the adjacency matrix) on Cayley…

Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…

We describe an ensemble of growing scale-free networks in an equilibrium framework, providing insight into why the exponent of empirical scale-free networks in nature is typically robust. In an analogy to thermostatistics, to describe the…

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool…

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the…

We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of…