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In this work we study reciprocal classes of Markov walks on graphs. Given a continuous time reference Markov chain on a graph, its reciprocal class is the set of all probability measures which can be represented as a mixture of the bridges of the reference walks. We characterize reciprocal classes with two different approaches. With the first approach we found it as the set of solutions to duality formulae on path space, where the differential operators have the interpretation of the addition of infinitesimal random loops to the paths of the canonical process. With the second approach we look at short time asymptotics of bridges. Both approaches allow an explicit computation of reciprocal characteristics, which are divided into two families, the loop characteristics and the arc characteristics. They are those specific functionals of the generator of the reference chain which determine its reciprocal class. We look at the specific examples such as Cayley graphs, the hypercube and planar graphs. Finally we establish the first concentration of measure results for the bridges of a continuous time Markov chain based on the reciprocal characteristics.
In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.
The conservation of rare plant species as living collections in botanic gardens and arboreta has become an established tool in the battle against worldwide species' extinctions. However, the establishment of ex situ collections with a high conservation value requires a sound understanding of the evolutionary processes that may reduce the suitability of these collections for future reintroductions. Particularly, risks such as fitness decline of cultivated plants over time, trait shifts and loss of adaptation to the original habitat due to changes in selection regimes have rarely been addressed so far. Based on a literature review and results of our own project we show that genetic drift can lead to fitness decline in ex situ cultivated plants, but these drift effects strongly depend on the conditions and cultivation history in the ex situ facility. Furthermore, we provide evidence that shifts in traits such as germination and flowering time, and a decrease in stress tolerance to drought and competition can reduce the conservation value of ex situ collections. These threats associated with ex situ conditions require more attention by researchers, curators and conservationists. We need to increase knowledge on traits that are subject to novel selection pressures in ex situ collections, and to define population sizes that prevent genetic drift. Establishing conservation networks with replicated collections across gardens and balancing the seed contribution of mother plants to the next generation within a collection are suggested as first steps to increase the conservation value of ex situ plant collections. (C) 2015 Elsevier Ltd. All rights reserved.
The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.
We argue that the theories of Volokitin and Persson (2014 New J. Phys. 16 118001), Dedkov and Kyasov (2008 J. Phys.: Condens. Matter 20 354006), and Pieplow and Henkel (2013 New J. Phys. 15 023027) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of the Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is 'diluted' to obtain the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.
Many perceptual and cognitive tasks permit or require the integrated cooperation of specialized sensory channels, detectors, or other functionally separate units. In compound detection or discrimination tasks, 1 prominent general mechanism to model the combination of the output of different processing channels is probability summation. The classical example is the binocular summation model of Pirenne (1943), according to which a weak visual stimulus is detected if at least 1 of the 2 eyes detects this stimulus; as we review briefly, exactly the same reasoning is applied in numerous other fields. It is generally accepted that this mechanism necessarily predicts performance based on 2 (or more) channels to be superior to single channel performance, because 2 separate channels provide "2 chances" to succeed with the task. We argue that this reasoning is misleading because it neglects the increased opportunity with 2 channels not just for hits but also for false alarms and that there may well be no redundancy gain at all when performance is measured in terms of receiver operating characteristic curves. We illustrate and support these arguments with a visual detection experiment involving different spatial uncertainty conditions. Our arguments and findings have important implications for all models that, in one way or another, rest on, or incorporate, the notion of probability summation for the analysis of detection tasks, 2-alternative forced-choice tasks, and psychometric functions.
International organisations as research subject. Or: "About Blind and the Shape of the Elephant"
(2014)
Removing spatial responses reveals spatial concepts even in a culture with mixed reading habits
(2014)
Comment on "Bias correction, quantile mapping, and downscaling: revisiting the inflation issue"
(2014)
In a recent paper, Maraun describes the adverse effects of quantile mapping on downscaling. He argues that when large-scale GCM variables are rescaled directly to small-scale fields or even station data, genuine small-scale covariability is lost and replaced by uniform variability inherited from the larger scales. This leads to a misrepresentation mainly of areal means and long-term trends. This comment acknowledges the former point, although the argument is relatively old, but disagrees with the latter, showing that grid-size long-term trends can be different from local trends. Finally, because it is partly incorrectly addressed, some clarification is added regarding the inflation issue, stressing that neither randomization nor inflation is free of unverified assumptions.
Advance in geocomputation
(2014)
Should I stay or should I go - The challenges and opportunities of moving between University systems
(2014)
Allyl alkyl carbonates
(2014)
Editiorial
(2014)
We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
Costing natural hazards
(2014)
This commentary argues that, rather than providing an "exhaustive review," Elson and Ferguson (2013) discuss a selective sample of empirical studies on violent video game use which corroborate their claim that there is no systematic evidence for a link between violent video game play and aggression. In evaluating the evidence, the authors portray a biased picture of the current state of knowledge about media violence effects. They fail to distinguish between aggression and violence and between everyday and clinical forms of aggression. Furthermore, they misrepresent key constructs, such as mediation, moderation, and external validity, to discredit methodologies used to assess aggression and media violence use. The paper moves the debate backward rather than forward, falling behind existing meta-analytic studies that consider a much wider and more balanced range of studies.