Poisson trees, succession lines and coalescing random walks

We give a deterministic algorithm to construct a graph with no loops (a tree or a forest) whose vertices are the points of a d-dimensional stationary Poisson process S, subset of R^d. The algorithm is independent of the origin of coordinates. We show that (1) the graph has one topological end --that is, from any point there is exactly one infinite self-avoiding path; (2) the graph has a unique connected component if d=2 and d=3 (a tree) and it has infinitely many components if d\ge 4 (a forest); (3) in d=2 and d=3 we construct a bijection between the points of the Poisson process and Z using the preorder-traversal algorithm. To construct the graph we interpret each point in S as a space-time point (x,r)\in\R^{d-1}\times R. Then a (d-1) dimensional random walk in continuous time continuous space starts at site x at time r. The first jump of the walk is to point x', at time r'>r, (x',r')\in S, where r' is the minimal time after r such that |x-x'|<1. All the walks jumping to x' at time r' coalesce with the one starting at (x',r'). Calling (x',r') = \alpha(x,r), the graph has vertex set S and edges {(s,\alpha(s)), s\in S}. This enables us to shift the origin of S^o = S + \delta_0 (the Palm version of S) to another point in such a way that the distribution of S^o does not change (to any point if d = 2 and d = 3; point-stationarity).Comment: 15 pages. Second version with minor correction

Identity in research infrastructure and scientific communication: Report from the 1st IRISC workshop, Helsinki Sep 12-13, 2011

Motivation for the IRISC workshop came from the observation that identity and digital identification are increasingly important factors in modern scientific research, especially with the now near-ubiquitous use of the Internet as a global medium for dissemination and debate of scientific knowledge and data, and as a platform for scientific collaborations and large-scale e-science activities.&#xd;&#xa;&#xd;&#xa;The 1 1/2 day IRISC2011 workshop sought to explore a series of interrelated topics under two main themes: i) unambiguously identifying authors/creators &#x26; attributing their scholarly works, and ii) individual identification and access management in the context of identity federations. Specific aims of the workshop included:&#xd;&#xa;&#xd;&#xa;&#x2022; Raising overall awareness of key technical and non-technical challenges, opportunities and developments.&#xd;&#xa;&#x2022; Facilitating a dialogue, cross-pollination of ideas, collaboration and coordination between diverse &#x2013; and largely unconnected &#x2013; communities.&#xd;&#xa;&#x2022; Identifying &#x26; discussing existing/emerging technologies, best practices and requirements for researcher identification.&#xd;&#xa;&#xd;&#xa;This report provides background information on key identification-related concepts &#x26; projects, describes workshop proceedings and summarizes key workshop findings

The strong weak convergence of the quasi-EA

In this paper, we investigate the convergence of a novel simulation scheme to the target diffusion process. This scheme, the Quasi-EA, is closely related to the Exact Algorithm (EA) for diffusion processes, as it is obtained by neglecting the rejection step in EA. We prove the existence of a myopic coupling between the Quasi-EA and the diffusion. Moreover, an upper bound for the coupling probability is given. Consequently we establish the convergence of the Quasi-EA to the diffusion with respect to the total variation distance

Relational reasoning via probabilistic coupling

Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings are powerful tools proving properties about the relation between two processes, include reasoning about convergence of distributions and stochastic dominance---a probabilistic version of a monotonicity property. While the mathematical definition of coupling looks rather complex and cumbersome to manipulate, we show that the relational program logic pRHL---the logic underlying the EasyCrypt cryptographic proof assistant---already internalizes a generalization of probabilistic coupling. With this insight, constructing couplings is no harder than constructing logical proofs. We demonstrate how to express and verify classic examples of couplings in pRHL, and we mechanically verify several couplings in EasyCrypt

Interaction between Cape hake spawning and the circulation in the northern Benguela upwelling ecosystem

Cape hake in Namibian waters are demersal and mesopelagic spawners, spawning peaking offshore between 100 and 400 m deep, depending on local environmental conditions. The cross-shelf circulation, low-oxygen layers and mesoscale gyres are three important environmental factors influencing hake spawning behaviour and subsequent transport of the spawning products. Normally, hake spawn offshore near the bottom at depths of 150–400 m. However, during one cruise, spawning was concentrated below several subsurface mesoscale gyres, resulting in reduced dispersion of the eggs and larvae. When the low-oxygen layer above the bottom is pronounced, hake spawning has been observed close to the top of the layer at oxygen concentrations as low as 0.2–0.3 ml l-1. The relatively small size of the eggs and their high specific gravity make them ascend quite slowly from the spawning depths, 10–40 m per day. Consequently, hake eggs spawned deeper than 200 m hatch before they reach the upper mixed layer. The newly hatched larvae are relatively undeveloped, without functional eyes or mouth, and display little swimming activity during their first hours, but laboratory observations have revealed subsequent periods of downward swimming activity. Based on current field observations, on buoyancy measurements of eggs and larvae and on observed larval behaviour, it is concluded that hake eggs and larvae are transported onshore by features of the upwelling subsurface circulation that compensate for offshore movement of surface water. This may be the basic mechanism concentrating early juvenile hake nearshore. Spawning activity near the low-oxygen layer might be a behavioural adaptation to minimize egg predation, because few other species are expected to survive such low concentrations of oxygen.Keywords: buoyancy, eggs, larvae, recruitment processes, retention, vertical distributionAfrican Journal of Marine Science 2001, 23: 317–33

Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology

This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called "contextuality-by-default," and then discuss a possible generalization of the theory from binary to arbitrary measurements.Comment: Lecture Notes in Computer Science 9535 (with the corrected list of authors) (2016

Aspects of nitrogen and mineral nutrition in Icelandic reindeer, Rangifer tarandus

Nitrogen and mineral (Fe, Mg, Na, K, and Ca) compositions of foodstuffs consumed by and dung produced by male, pregnant and lactating female adult Icelandic reindeer and calves were determined during May of 1992. Iron levels in foodstuffs are consistently above the reported toxicity level for similar-sized sheep (0.5 ppt) and may lead to iron toxicity when consumed by reindeer during periods of high lean body mass catabolism. Male and female reindeer meet nutrient requirements for all measured elements and nitrogen with the possible exception of calcium for males during antler growth.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31343/1/0000253.pd

IGVBrowser–a genomic variation resource from diverse Indian populations

The Indian Genome Variation Consortium (IGVC) project, an initiative of the Council for Scientific and Industrial Research, has been the first large-scale comprehensive study of the Indian population. One of the major aims of the project is to study and catalog the variations in nearly thousand candidate genes related to diseases and drug response for predictive marker discovery, founder identification and also to address questions related to ethnic diversity, migrations, extent and relatedness with other world population. The Phase I of the project aimed at providing a set of reference populations that would represent the entire genetic spectrum of India in terms of language, ethnicity and geography and Phase II in providing variation data on candidate genes and genome wide neutral markers on these reference set of populations. We report here development of the IGVBrowser that provides allele and genotype frequency data generated in the IGVC project. The database harbors 4229 SNPs from more than 900 candidate genes in contrasting Indian populations. Analysis shows that most of the markers are from genic regions. Further, a large fraction of genes are implicated in cardiovascular, metabolic, cancer and immune system-related diseases. Thus, the IGVC data provide a basal level variation data in Indian population to study genetic diseases and pharmacology. Additionally, it also houses data on ∼50 000 (Affy 50 K array) genome wide neutral markers in these reference populations. In IGVBrowser one can analyze and compare genomic variations in Indian population with those reported in HapMap along with annotation information from various primary data sources

IGVBrowser–a genomic variation resource from diverse Indian populations

The Indian Genome Variation Consortium (IGVC) project, an initiative of the Council for Scientific and Industrial Research, has been the first large-scale comprehensive study of the Indian population. One of the major aims of the project is to study and catalog the variations in nearly thousand candidate genes related to diseases and drug response for predictive marker discovery, founder identification and also to address questions related to ethnic diversity, migrations, extent and relatedness with other world population. The Phase I of the project aimed at providing a set of reference populations that would represent the entire genetic spectrum of India in terms of language, ethnicity and geography and Phase II in providing variation data on candidate genes and genome wide neutral markers on these reference set of populations. We report here development of the IGVBrowser that provides allele and genotype frequency data generated in the IGVC project. The database harbors 4229 SNPs from more than 900 candidate genes in contrasting Indian populations. Analysis shows that most of the markers are from genic regions. Further, a large fraction of genes are implicated in cardiovascular, metabolic, cancer and immune system-related diseases. Thus, the IGVC data provide a basal level variation data in Indian population to study genetic diseases and pharmacology. Additionally, it also houses data on ∼50 000 (Affy 50 K array) genome wide neutral markers in these reference populations. In IGVBrowser one can analyze and compare genomic variations in Indian population with those reported in HapMap along with annotation information from various primary data sources

Billiards in a general domain with random reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord "picked at random" in ${\mathcal D}$, and we study the angle of intersection of the process with a $(d-1)$-dimensional manifold contained in ${\mathcal D}$.Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains