Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.Comment: v1: 6 pages main text + 14 pages supplemental material, 10 figures. v2: LaTeX, 79 pages, 18 eps figures, new material (Sections 6, 10, 11 & Appendices C, E, F, G

Sinai model in presence of dilute absorbers

We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, the averaged diffusion front and return probability, the two particle meeting probability, the distribution of total distance traveled before absorption and the averaged Green's function of the associated Schrodinger operator. Our work confirms some recent results of Texier and Hagendorf obtained by Dyson-Schmidt methods, and extends them to other observables and in presence of a drift. In particular the power law density of states is found to hold in all cases. Irrespective of the drift, the asymptotic rescaled diffusion front of surviving particles is found to be a symmetric step distribution, uniform for $|x| < {1/2} \xi(t)$, where $\xi(t)$ is a new, survival length scale ($\xi(t)=T \ln t/\sqrt{\rho}$ in the absence of drift). Survival outside this sharp region is found to decay with a larger exponent, continuously varying with the rescaled distance $x/\xi(t)$. A simple physical picture based on a saddle point is given, and universality is discussed.Comment: 21 pages, 2 figure

Nature of the bad metallic behavior of Fe_{1.06}Te inferred from its evolution in the magnetic state

We investigate with angle resolved photoelectron spectroscopy the change of the Fermi Surface (FS) and the main bands from the paramagnetic (PM) state to the antiferromagnetic (AFM) occurring below 72 K in Fe_{1.06}Te. The evolution is completely different from that observed in iron-pnictides as nesting is absent. The AFM state is a rather good metal, in agreement with our magnetic band structure calculation. On the other hand, the PM state is very anomalous with a large pseudogap on the electron pocket that closes in the AFM state. We discuss this behavior in connection with spin fluctuations existing above the magnetic transition and the correlations predicted in the spin-freezing regime of the incoherent metallic state

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde

Lithic technological responses to Late Pleistocene glacial cycling at Pinnacle Point Site 5-6, South Africa

There are multiple hypotheses for human responses to glacial cycling in the Late Pleistocene, including changes in population size, interconnectedness, and mobility. Lithic technological analysis informs us of human responses to environmental change because lithic assemblage characteristics are a reflection of raw material transport, reduction, and discard behaviors that depend on hunter-gatherer social and economic decisions. Pinnacle Point Site 5-6 (PP5-6), Western Cape, South Africa is an ideal locality for examining the influence of glacial cycling on early modern human behaviors because it preserves a long sequence spanning marine isotope stages (MIS) 5, 4, and 3 and is associated with robust records of paleoenvironmental change. The analysis presented here addresses the question, what, if any, lithic assemblage traits at PP5-6 represent changing behavioral responses to the MIS 5-4-3 interglacial-glacial cycle? It statistically evaluates changes in 93 traits with no a priori assumptions about which traits may significantly associate with MIS. In contrast to other studies that claim that there is little relationship between broad-scale patterns of climate change and lithic technology, we identified the following characteristics that are associated with MIS 4: increased use of quartz, increased evidence for outcrop sources of quartzite and silcrete, increased evidence for earlier stages of reduction in silcrete, evidence for increased flaking efficiency in all raw material types, and changes in tool types and function for silcrete. Based on these results, we suggest that foragers responded to MIS 4 glacial environmental conditions at PP5-6 with increased population or group sizes, 'place provisioning', longer and/or more intense site occupations, and decreased residential mobility. Several other traits, including silcrete frequency, do not exhibit an association with MIS. Backed pieces, once they appear in the PP5-6 record during MIS 4, persist through MIS 3. Changing paleoenvironments explain some, but not all temporal technological variability at PP5-6.Social Science and Humanities Research Council of Canada; NORAM; American-Scandinavian Foundation; Fundacao para a Ciencia e Tecnologia [SFRH/BPD/73598/2010]; IGERT [DGE 0801634]; Hyde Family Foundations; Institute of Human Origins; National Science Foundation [BCS-9912465, BCS-0130713, BCS-0524087, BCS-1138073]; John Templeton Foundation to the Institute of Human Origins at Arizona State Universit

Entropy Measures Quantify Global Splicing Disorders in Cancer

Most mammalian genes are able to express several splice variants in a phenomenon known as alternative splicing. Serious alterations of alternative splicing occur in cancer tissues, leading to expression of multiple aberrant splice forms. Most studies of alternative splicing defects have focused on the identification of cancer-specific splice variants as potential therapeutic targets. Here, we examine instead the bulk of non-specific transcript isoforms and analyze their level of disorder using a measure of uncertainty called Shannon's entropy. We compare isoform expression entropy in normal and cancer tissues from the same anatomical site for different classes of transcript variations: alternative splicing, polyadenylation, and transcription initiation. Whereas alternative initiation and polyadenylation show no significant gain or loss of entropy between normal and cancer tissues, alternative splicing shows highly significant entropy gains for 13 of the 27 cancers studied. This entropy gain is characterized by a flattening in the expression profile of normal isoforms and is correlated to the level of estimated cellular proliferation in the cancer tissue. Interestingly, the genes that present the highest entropy gain are enriched in splicing factors. We provide here the first quantitative estimate of splicing disruption in cancer. The expression of normal splice variants is widely and significantly disrupted in at least half of the cancers studied. We postulate that such splicing disorders may develop in part from splicing alteration in key splice factors, which in turn significantly impact multiple target genes

A whole-genome sequence and transcriptome perspective on HER2-positive breast cancers

HER2-positive breast cancer has long proven to be a clinically distinct class of breast cancers for which several targeted therapies are now available. However, resistance to the treatment associated with specific gene expressions or mutations has been observed, revealing the underlying diversity of these cancers. Therefore, understanding the full extent of the HER2-positive disease heterogeneity still remains challenging. Here we carry out an in-depth genomic characterization of 64 HER2-positive breast tumour genomes that exhibit four subgroups, based on the expression data, with distinctive genomic features in terms of somatic mutations, copy-number changes or structural variations. The results suggest that, despite being clinically defined by a specific gene amplification, HER2-positive tumours melt into the whole luminal-basal breast cancer spectrum rather than standing apart. The results also lead to a refined ERBB2 amplicon of 106 kb and show that several cases of amplifications are compatible with a breakage-fusion-bridge mechanism

A General Definition and Nomenclature for Alternative Splicing Events

Understanding the molecular mechanisms responsible for the regulation of the transcriptome present in eukaryotic cells is one of the most challenging tasks in the postgenomic era. In this regard, alternative splicing (AS) is a key phenomenon contributing to the production of different mature transcripts from the same primary RNA sequence. As a plethora of different transcript forms is available in databases, a first step to uncover the biology that drives AS is to identify the different types of reflected splicing variation. In this work, we present a general definition of the AS event along with a notation system that involves the relative positions of the splice sites. This nomenclature univocally and dynamically assigns a specific “AS code” to every possible pattern of splicing variation. On the basis of this definition and the corresponding codes, we have developed a computational tool (AStalavista) that automatically characterizes the complete landscape of AS events in a given transcript annotation of a genome, thus providing a platform to investigate the transcriptome diversity across genes, chromosomes, and species. Our analysis reveals that a substantial part—in human more than a quarter—of the observed splicing variations are ignored in common classification pipelines. We have used AStalavista to investigate and to compare the AS landscape of different reference annotation sets in human and in other metazoan species and found that proportions of AS events change substantially depending on the annotation protocol, species-specific attributes, and coding constraints acting on the transcripts. The AStalavista system therefore provides a general framework to conduct specific studies investigating the occurrence, impact, and regulation of AS

Planck 2013 results. I. Overview of products and scientific results

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Planck pre-launch status : The Planck mission

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