Analysis Of Random Networks Research Articles

Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.

A Latency and Reliability Guaranteed Resource Allocation Scheme for LTE V2V Communication Systems

By leveraging direct device-to-device interaction, LTE vehicle-to-vehicle (V2V) communication becomes a promising solution to meet the stringent requirements of vehicular communication. In this paper, we propose jointly optimizing the radio resource, power allocation, and modulation/coding schemes of the V2V communications, in order to guarantee the latency and reliability requirements of vehicular user equipments (VUEs) while maximizing the information rate of cellular user equipment (CUE). To ensure the solvability of this optimization problem, the packet latency constraint is first transformed into a data rate constraint based on random network analysis by adopting the Poisson distribution model for the packet arrival process of each VUE. Then, utilizing the Lagrange dual decomposition and binary search, a resource management algorithm is proposed to find the optimal solution of joint optimization problem with reasonable complexity. Simulation results show that the proposed radio resource management scheme can reduce the interference from V2V communication to CUEs and ensure the latency and reliability requirements of V2V communication.

Secrecy Outage Analysis in Cellular Networks

The study of the inherent secrecy capacity of wireless networks of random topologies is currently of great interest to the communication and information theory communities. Indeed, a good amount of work exists on the secrecy analysis of random networks, the majority of which relies on Poisson point processes to model the spatial distribution of devices. It has been recently demonstrated, however, that Matern hard-core point processes—rather than Poisson point processes—are better suited to characterize the random location of users and base stations of cellular systems. In this letter, we therefore offer an analysis of the secrecy outage of random networks under the Matern hard-core point process model, with the objective of shedding some light on the security limitations/capabilities inherent encountered in cellular systems.

Construction and Analysis of Random Networks with Explosive Percolation

The existence of explosive phase transitions in random (Erdös Rényi-type) networks has been recently documented by Achlioptas, D'Souza, and Spencer [Science 323, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism behind these first-order phase transitions and develop tools that allow us to identify (and predict) when a random network will exhibit an explosive transition. Several interesting new models displaying explosive transitions are also presented.

Probabilistic analysis of efficiency and vulnerability in the Erdös–Rénji model

New analytic estimates for efficiency and vulnerability in the Erdös–Rénji model are presented using probabilistic properties and diameter bounds that are specific for this model and its topology. These estimates for random networks improve the known deterministic lower estimates for efficiency and vulnerability. The probabilistic technique provides a sharper approach to parametric analysis of random networks and allows us to report some new results concerning the efficiency–vulnerability relationship. Several numerical tests are presented to compare the lower estimates obtained with the empirical Erdös–Rénji random networks. These estimates illustrate how the new probabilistic estimates improve on the generic estimates reported in the literature.

From Riemann's metric to the graph metric, or applying Occam's razor to entanglements

In 1854 Riemann prophesied: ‘Either the reality underlying space must form a discrete manifold, or the reason for measurability must be sought externally, through forces acting thereon to constrain it.’ Matter is in a graph-like state if its particle coordinates have been or are being randomized in all dimensions but one, by Brownian motions induced by random forces which maintain equipartition of kinetic energy. The graph-like particle generates a graph metric, which is one-dimensional and discrete. Physical theories of amorphous polymers generally evolve intuitively by embedding the particles in a three-dimensional continuum regarded as physically real, or in a configuration space regarded as an auxiliary. After integration over random coordinates, it appears that the end results no longer depend on the embedding space at all. The historical theories of amorphous polymer systems by Hermans and Kramers, Debye, Zimm and Stockmayer, Rouse, Fixman and some others may have the added advantage of demonstrating how the Riemann metric degenerates to the non-trivial graph-metric. The analysis of random networks, embedded in a three dimensional space with all the complications arising from chain entanglements, generally seems to result in small semi-empirical corrections which graph-like-state theories could readily develop without such complications. A programme for establishing a new axiomatic basis is suggested along these lines. The benefits would include not only a clearer relation between strikingly different theories and between their geometric and physical ingredients, but substantially simpler calculations and algorithms. Simplifications, especially some inspired by the achievements of Chompff and of Forsman, are briefly sketched. An analogy is drawn with the early programme culminating in the proof that, by virtue of their metric structures, the continum and discrete (matrix) formulations of quantum theory are isomorphic. It is suggested that the operator calculus of Rota, especially as recently perfected in his work with Roman, should be helpful in making explicit the isomorphism sought for the graph-like state.