Bilinear Coagulation Equations

We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of conserved quantities $\pi$, generalising the multiplicative kernel. For these kernels, a gelation transition occurs at a finite time $t_\mathrm{g}\in (0,\infty)$, which can be given exactly in terms of an eigenvalue problem in finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant, including a corresponding phase transition for the largest particle, and exploit a coupling to random graphs to extend analysis of the limiting process beyond the gelation time.Comment: Generalises the previous version to focus on general coagulation processes of bilinear type, without restricting to the single example of the previous version. The previous results are mentioned as motivation, and all results of the previous version can be obtained from this more general versio

Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries

Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of $d$-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit

Traffic flow densities in large transport networks

We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing domain, we present an asymptotic formula expressing the local traffic flow density at any given location in the domain in terms of three fundamental characteristics of the underlying network: the spatial intensity of the nodes together with their traffic generation rates, and of the links induced by the navigation. This formula holds for a general class of navigations satisfying a link-density and a sub-ballisticity condition. As a specific example, we verify these conditions for navigations arising from a directed spanning tree on a Poisson point process with inhomogeneous intensity function.Comment: 20 pages, 7 figure

Large deviations in relay-augmented wireless networks

We analyze a model of relay-augmented cellular wireless networks. The network users, who move according to a general mobility model based on a Poisson point process of continuous trajectories in a bounded domain, try to communicate with a base station located at the origin. Messages can be sent either directly or indirectly by relaying over a second user. We show that in a scenario of an increasing number of users, the probability that an atypically high number of users experiences bad quality of service over a certain amount of time, decays at an exponential speed. This speed is characterized via a constrained entropy minimization problem. Further, we provide simulation results indicating that solutions of this problem are potentially non-unique due to symmetry breaking. Also two general sources for bad quality of service can be detected, which we refer to as isolation and screening.Comment: 28 pages, 5 figures; corrected several misprint

Large-deviation principles for connectable receivers in wireless networks

We study large-deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers, respectively. To each transmitter we associate a family of connectable receivers whose signal-to-interference-and-noise ratio is larger than a certain connectivity threshold. First, we show a large-deviation principle for the empirical measure of connectable receivers associated with transmitters in large boxes. Second, making use of the observation that the receivers connectable to the origin form a Cox point process, we derive a large-deviation principle for the rescaled process of these receivers as the connection threshold tends to zero. Finally, we show how these results can be used to develop importance-sampling algorithms that substantially reduce the variance for the estimation of probabilities of certain rare events such as users being unable to connectComment: 29 pages, 2 figure

The Dwarf Nova PQ Andromedae

We report a photometric study of the WZ Sagittae-type dwarf nova PQ Andromedae. The light curve shows strong (0.05 mag full amplitude) signals with periods of 1263(1) and 634(1) s, and a likely double-humped signal with P=80.6(2) min. We interpret the first two as nonradial pulsation periods of the underlying white dwarf, and the last as the orbital period of the underlying binary. We estimate a distance of 150(50) pc from proper motions and the two standard candles available: the white dwarf and the dwarf-nova outburst. At this distance, the K magnitude implies that the secondary is probably fainter than any star on the main sequence -- indicating a mass below the Kumar limit at 0.075 M_sol. PQ And may be another "period bouncer", where evolution now drives the binary out to longer period.Comment: PDF, 13 pages, 2 figures; accepted, in press, to appear September 2005, PASP; more info at http://cba.phys.columbia.edu

Ancient human genomes suggest three ancestral populations for present-day Europeans

We sequenced the genomes of a 7,000-year-old farmer from Germany and eight 8,000-year-old hunter-gatherers from Luxembourg and Sweden. We analysed these and other ancient genomes¹-₄ with 2,345 contemporary humans to show that most present-day Europeans derive from at least three highly differentiated populations:west European hunter-gatherers, who contributed ancestry to all Europeans but not to Near Easterners; ancient north Eurasians related to Upper Palaeolithic Siberians³, who contributed to both Europeans and Near Easterners; and early European farmers, who were mainly of Near Eastern origin but also harboured west European hunter-gatherer related ancestry.We model these populations’ deep relationships and show that early European farmers had 44% ancestry from a ‘basal Eurasian’ population that split before the diversification of other non-African lineage

SMaSH: A Benchmarking Toolkit for Human Genome Variant Calling

Motivation: Computational methods are essential to extract actionable information from raw sequencing data, and to thus fulfill the promise of next-generation sequencing technology. Unfortunately, computational tools developed to call variants from human sequencing data disagree on many of their predictions, and current methods to evaluate accuracy and computational performance are ad-hoc and incomplete. Agreement on benchmarking variant calling methods would stimulate development of genomic processing tools and facilitate communication among researchers. Results: We propose SMaSH, a benchmarking methodology for evaluating human genome variant calling algorithms. We generate synthetic datasets, organize and interpret a wide range of existing benchmarking data for real genomes, and propose a set of accuracy and computational performance metrics for evaluating variant calling methods on this benchmarking data. Moreover, we illustrate the utility of SMaSH to evaluate the performance of some leading single nucleotide polymorphism (SNP), indel, and structural variant calling algorithms. Availability: We provide free and open access online to the SMaSH toolkit, along with detailed documentation, at smash.cs.berkeley.edu