Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Precise Asymptotics for a Random Walker's Maximum

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum E[M_n] of the walk up to n steps behaves asymptotically for large n as, E[M_n]/\sigma=\sqrt{2n/\pi}+ \gamma +O(n^{-1/2}), where \sigma^2 is the variance of the step lengths. While the leading \sqrt{n} behavior is universal and easy to derive, the leading correction term turns out to be a nontrivial constant \gamma. For the special case of uniform distribution over [-1,1], Coffmann et. al. recently computed \gamma=-0.516068...by exactly enumerating a lengthy double series. Here we present a closed exact formula for \gamma valid for arbitrary symmetric distributions. We also demonstrate how \gamma appears in the thermodynamic limit as the leading behavior of the difference variable E[M_n]-E[|x_n|] where x_n is the position of the walker after n steps. An application of these results to the equilibrium thermodynamics of a Rouse polymer chain is pointed out. We also generalize our results to L\'evy walks.Comment: new references added, typos corrected, published versio

Networked youth research for empowerment in digital society. The WYRED project

ABSTRACT The emergence of the young as a distinct social group, and their slowly increasing empowerment through the availability of digital technology, has brought with it an understanding that they have a key role to play in the digital society, as drivers of new behaviors and understandings. However, their active participation in society is not reflected sufficiently in policy and decision-making, especially in relation to digital issues. Because of this, they are not well represented and unheard, and this makes it hard for research and policy to identify and understand their needs. These issues are further complicated by the fact that the group is a swiftly moving target, it is as heterogeneous as the wider society, and young people can be unwilling to be subjects of research. The WYRED project (netWorked Youth Research for Empowerment in the Digital society) aims to provide a framework for research in which children and young people can express and explore their perspectives and interests in relation to digital society, but also a platform from which they can communicate their perspectives to other stakeholders effectively through innovative engagement processes. It will do this by implementing a generative research cycle involving networking, dialogue, participatory research and interpretation phases centered around and driven by children and young people, out of which a diverse range of outputs, critical perspectives and other insights will emerge to inform policy and decisionmaking in relation to children and young people&apos;s needs in relation to digital society. CCS Concept

Polynomial kernels for 3-leaf power graph modification problems

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005).Comment: Submitte

Virtual signatures of dark sectors in Higgs couplings

Where collider searches for resonant invisible particles loose steam, dark sectors might leave their trace as virtual effects in precision observables. Here we explore this option in the framework of Higgs portal models, where a sector of dark fermions interacts with the standard model through a strong renormalizable coupling to the Higgs boson. We show that precise measurements of Higgs-gauge and triple Higgs interactions can probe dark fermions up to the TeV scale through virtual corrections. Observation prospects at the LHC and future lepton colliders are discussed for the so-called singlet-doublet model of Majorana fermions, a generalization of the bino-higgsino scenario in supersymmetry. We advocate a two-fold search strategy for dark sectors through direct and indirect observables.Comment: 20 pages, 7 figures, 1 tabl

Thrombosis Is Reduced by Inhibition of COX-1, but Unaffected by Inhibition of COX-2, in an Acute Model of Platelet Activation in the Mouse

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Combining Phylogeography with Distribution Modeling: Multiple Pleistocene Range Expansions in a Parthenogenetic Gecko from the Australian Arid Zone

Phylogenetic and geographic evidence suggest that many parthenogenetic organisms have evolved recently and have spread rapidly. These patterns play a critical role in our understanding of the relative merits of sexual versus asexual reproductive modes, yet their interpretation is often hampered by a lack of detail. Here we present a detailed phylogeographic study of a vertebrate parthenogen, the Australian gecko Heteronotia binoei, in combination with statistical and biophysical modeling of its distribution during the last glacial maximum. Parthenogenetic H. binoei occur in the Australian arid zone and have the widest range of any known vertebrate parthenogen. They are broadly sympatric with their sexual counterparts, from which they arose via hybridization. We have applied nested clade phylogeographic, effective migration, and mismatch distribution analyses to mitochondrial DNA (mtDNA) sequences obtained for 319 individuals sampled throughout the known geographic ranges of two parthenogenetic mitochondrial lineages. These analyses provide strong evidence for past range expansion events from west to east across the arid zone, and for continuing eastward range expansion. Parthenogen formation and range expansion events date to the late Pleistocene, with one lineage expanding from the northwest of its present range around 240,000 years ago and the second lineage expanding from the far west around 70,000 years ago. Statistical and biophysical distribution models support these inferences of recent range expansion, with suitable climatic conditions during the last glacial maximum most likely limited to parts of the arid zone north and west of much of the current ranges of these lineages. Combination of phylogeographic analyses and distribution modeling allowed considerably stronger inferences of the history of this complex than either would in isolation, illustrating the power of combining complementary analytical approaches