Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Fast computation by block permanents of cumulative distribution functions of order statistics from several populations

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.Comment: 21 pages, 3 figure

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Acetylation of H2A.Z is a key epigenetic modification associated with gene deregulation and epigenetic remodeling in cancer

Histone H2A.Z (H2A.Z) is an evolutionarily conserved H2A variant implicated in the regulation of gene expression; however, its role in transcriptional deregulation in cancer remains poorly understood. Using genome-wide studies, we investigated the role of promoter-associated H2A.Z and acetylated H2A.Z (acH2A.Z) in gene deregulation and its relationship with DNA methylation and H3K27me3 in prostate cancer. Our results reconcile the conflicting reports of positive and negative roles for histone H2A.Z and gene expression states. We find that H2A.Z is enriched in a bimodal distribution at nucleosomes, surrounding the transcription start sites (TSSs) of both active and poised gene promoters. In addition, H2A.Z spreads across the entire promoter of inactive genes in a deacetylated state. In contrast, acH2A.Z is only localized at the TSSs of active genes. Gene deregulation in cancer is also associated with a reorganization of acH2A.Z and H2A.Z nucleosome occupancy across the promoter region and TSS of genes. Notably, in cancer cells we find that a gain of acH2A.Z at the TSS occurs with an overall decrease of H2A.Z levels, in concert with oncogene activation. Furthermore, deacetylation of H2A.Z at TSSs is increased with silencing of tumor suppressor genes. We also demonstrate that acH2A.Z anti-correlates with promoter H3K27me3 and DNA methylation. We show for the first time, that acetylation of H2A.Z is a key modification associated with gene activity in normal cells and epigenetic gene deregulation in tumorigenesis

Policy-making tool for optimization of transit priority lanes in urban network

Transit improvement is an effective way to relieve traffic congestion and decrease greenhouse gas emissions. Improvement can be in the form of new facilities or giving on-road priority to transit. Although construction of off-road mass transit is not always viable, giving priority to transit can be a low-cost alternative. A framework is introduced for optimization of bus priority at the network level. The framework identifies links on which a bus lane should be located. Allocation of a lane to transit vehicles would increase the utility of transit, although this can be a disadvantage to auto traffic. The approach balances the impact on all stakeholders. Automobile advocates would like to increase traffic road space, and the total travel time of users and total emissions of the network could be reduced by a stronger priority scheme. A bilevel optimization is applied that encompasses an objective function at the upper level and a mode choice, a traffic assignment, and a transit assignment model at the lower level. The proposed optimization helps transport authorities to quantify the outcomes of various strategies of transit priority. A detailed sensitivity analysis is carried out on the relative weight of each factor in the objective function. The proposed framework can also be applied in the context of high-occupancy-vehicle lanes and heavy-vehicle priority lanes

A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.Comment: 18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available at http://www.springerlink.co

Acetylated histone variant H2A.Z is involved in the activation of neo-enhancers in prostate cancer.

Acetylation of the histone variant H2A.Z (H2A.Zac) occurs at active promoters and is associated with oncogene activation in prostate cancer, but its role in enhancer function is still poorly understood. Here we show that H2A.Zac containing nucleosomes are commonly redistributed to neo-enhancers in cancer resulting in a concomitant gain of chromatin accessibility and ectopic gene expression. Notably incorporation of acetylated H2A.Z nucleosomes is a pre-requisite for activation of Androgen receptor (AR) associated enhancers. H2A.Zac nucleosome occupancy is rapidly remodeled to flank the AR sites to initiate the formation of nucleosome-free regions and the production of AR-enhancer RNAs upon androgen treatment. Remarkably higher levels of global H2A.Zac correlate with poorer prognosis. Altogether these data demonstrate the novel contribution of H2A.Zac in activation of newly formed enhancers in prostate cancer

Estimating Omissions from Searches

The mark-recapture method was devised by Petersen in 1896 to estimate the number of fish migrating into the Limfjord, and independently by Lincoln in 1930 to estimate waterfowl abundance. The technique applies to any search for a finite number of items by two or more people or agents, allowing the number of searched-for items to be estimated. This ubiquitous problem appears in fields from ecology and epidemiology, through to mathematics, social sciences, and computing. Here we exactly calculate the moments of the hypergeometric distribution associated with this long-standing problem, confirming that widely used estimates conjectured in 1951 are often too small. Our Bayesian approach highlights how different search strategies will modify the estimates. As an example, we assess the accuracy of a systematic literature review, an application we recommend.Comment: One figure. Supplementary Material included as an Appendi

DNA methylation is required to maintain both DNA replication timing precision and 3D genome organization integrity

DNA replication timing and three-dimensional (3D) genome organization are associated with distinct epigenome patterns across large domains. However, whether alterations in the epigenome, in particular cancer-related DNA hypomethylation, affects higher-order levels of genome architecture is still unclear. Here, using Repli-Seq, single-cell Repli-Seq, and Hi-C, we show that genome-wide methylation loss is associated with both concordant loss of replication timing precision and deregulation of 3D genome organization. Notably, we find distinct disruption in 3D genome compartmentalization, striking gains in cell-to-cell replication timing heterogeneity and loss of allelic replication timing in cancer hypomethylation models, potentially through the gene deregulation of DNA replication and genome organization pathways. Finally, we identify ectopic H3K4me3-H3K9me3 domains from across large hypomethylated domains, where late replication is maintained, which we purport serves to protect against catastrophic genome reorganization and aberrant gene transcription. Our results highlight a potential role for the methylome in the maintenance of 3D genome regulation

A new model for root growth in soil with macropores

Abstract: Background and aimsThe use of standard dynamic root architecture models to simulate root growth in soil containing macropores failed to reproduce experimentally observed root growth patterns. We thus developed a new, more mechanistic model approach for the simulation of root growth in structured soil. Methods: In our alternative modelling approach, we distinguish between, firstly, the driving force for root growth, which is determined by the orientation of the previous root segment and the influence of gravitropism and, secondly, soil mechanical resistance to root growth. The latter is expressed by its inverse, soil mechanical conductance, and treated similarly to hydraulic conductivity in Darcy’s law. At the presence of macropores, soil mechanical conductance is anisotropic, which leads to a difference between the direction of the driving force and the direction of the root tip movement. Results: The model was tested using data from the literature, at pot scale, at macropore scale, and in a series of simulations where sensitivity to gravity and macropore orientation was evaluated. Conclusions: Qualitative and quantitative comparisons between simulated and experimentally observed root systems showed good agreement, suggesting that the drawn analogy between soil water flow and root growth is a useful one