HetHetNets: Heterogeneous Traffic Distribution in Heterogeneous Wireless Cellular Networks

A recent approach in modeling and analysis of the supply and demand in heterogeneous wireless cellular networks has been the use of two independent Poisson point processes (PPPs) for the locations of base stations (BSs) and user equipments (UEs). This popular approach has two major shortcomings. First, although the PPP model may be a fitting one for the BS locations, it is less adequate for the UE locations mainly due to the fact that the model is not adjustable (tunable) to represent the severity of the heterogeneity (non-uniformity) in the UE locations. Besides, the independence assumption between the two PPPs does not capture the often-observed correlation between the UE and BS locations. This paper presents a novel heterogeneous spatial traffic modeling which allows statistical adjustment. Simple and non-parameterized, yet sufficiently accurate, measures for capturing the traffic characteristics in space are introduced. Only two statistical parameters related to the UE distribution, namely, the coefficient of variation (the normalized second-moment), of an appropriately defined inter-UE distance measure, and correlation coefficient (the normalized cross-moment) between UE and BS locations, are adjusted to control the degree of heterogeneity and the bias towards the BS locations, respectively. This model is used in heterogeneous wireless cellular networks (HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic on the network performance. This network is called HetHetNet since it has two types of heterogeneity: heterogeneity in the infrastructure (supply), and heterogeneity in the spatial traffic distribution (demand).Comment: JSA

Pair correlation functions and limiting distributions of iterated cluster point processes

We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier work by Felsenstein and Shimatani describing a reproducing population. We discuss when closed term expressions of the first and second order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument

Topological properties of hierarchical networks

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the Dyson hierarchical construction for ferromagnets, neural networks and spin-glasses, recently analyzed from a statistical-mechanics perspective, and we focus on the topological properties of the underlying structures. In particular, we find that such structures are weighted graphs that exhibit high degree of clustering and of modularity, with small spectral gap; the robustness of such features with respect to link removal is also studied. These outcomes are then discussed and related to the statistical mechanics scenario in full consistency. Lastly, we look at these weighted graphs as Markov chains and we show that in the limit of infinite size, the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of meta-stabilities in the corresponding statistical mechanical analysis

Penalized weighted low-rank approximation for robust recovery of recurrent copy number variations

2015-2016 UNCG University Libraries Open Access Publishing Fund Grant Winner. BackgroundCopy number variation (CNV) analysis has become one of the most important researchareas for understanding complex disease. With increasing resolution of array-basedcomparative genomic hybridization (aCGH) arrays, more and more raw copy numberdata are collected for multiple arrays. It is natural to realize the co-existence of bothrecurrent and individual-specific CNVs, together with the possible data contaminationduring the data generation process. Therefore, there is a great need for an efficient androbust statistical model for simultaneous recovery of both recurrent and individualspecificCNVs.ResultWe develop a penalized weighted low-rank approximation method (WPLA) for robustrecovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into arealization of a hidden low-rank matrix with some random noises and let an additionalweight matrix account for those individual-specific effects. Thus, we do not restrict therandom noise to be normally distributed, or even homogeneous. We show itsperformance through three real datasets and twelve synthetic datasets from different typesof recurrent CNV regions associated with either normal random errors or heavilycontaminated errors.ConclusionOur numerical experiments have demonstrated that the WPLA can successfully recoverthe recurrent CNV patterns from raw data under different scenarios. Compared with twoother recent methods, it performs the best regarding its ability to simultaneously detectboth recurrent and individual-specific CNVs under normal random errors. Moreimportantly, the WPLA is the only method which can effectively recover the recurrentCNVs region when the data is heavily contaminated

Analytical maximum-likelihood method to detect patterns in real networks

In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, their generation is still problematic. The existing approaches are either computationally demanding and beyond analytic control, or analytically accessible but highly approximate. Here we propose a solution to this long-standing problem by introducing an exact and fast method that allows to obtain expectation values and standard deviations of any topological property analytically, for any binary, weighted, directed or undirected network. Remarkably, the time required to obtain the expectation value of any property is as short as that required to compute the same property on the single original network. Our method reveals that the null behavior of various correlation properties is different from what previously believed, and highly sensitive to the particular network considered. Moreover, our approach shows that important structural properties (such as the modularity used in community detection problems) are currently based on incorrect expressions, and provides the exact quantities that should replace them.Comment: 26 pages, 10 figure

The Evolution of Reaction-diffusion Controllers for Minimally Cognitive Agents

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A class of pairwise models for epidemic dynamics on weighted networks

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations