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In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.

We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.

Reciprocal processes, whose concept can be traced back to E. Schrödinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. Léonard.

By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.

We are interested in modeling the Darwinian evolution of a population described by two levels of biological parameters: individuals characterized by an heritable phenotypic trait submitted to mutation and natural selection and cells in these individuals influencing their ability to consume resources and to reproduce. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We are looking for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses.

Serial and parallel processes in eye movement control - current controversies and future directions
(2013)

In this editorial for the Special Issue on Serial and Parallel Processing in Reading we explore the background to the current debate concerning whether the word recognition processes in reading are strictly serialsequential or take place in an overlapping parallel fashion. We consider the history of the controversy and some of the underlying assumptions, together with an analysis of the types of evidence and arguments that have been adduced to both sides of the debate, concluding that both accounts necessarily presuppose some weakening of, or elasticity in, the eyemind assumption. We then consider future directions, both for reading research and for scene viewing, and wrap up the editorial with a brief overview of the following articles and their conclusions.

Simplicity is a mindset, a way of looking at solutions, an extremely wide-ranging philosophical stance on the world, and thus a deeply rooted cultural paradigm. The culture of "less" can be profoundly disruptive, cutting out existing "standard" elements from products and business models, thereby revolutionizing entire markets.

In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.

Intimate partner violence as a global problem - international and interdisciplinary perspectives
(2013)

This editorial introduces the Focus Section on Intimate Partner Violence (IPV) as a worldwide problem, which brings together six papers that are truly international and interdisciplinary. They provide insights into IPV from nine different cultures - China, Germany, Italy, Japan, Mexico, Northern Ireland, Sweden, Turkey, and the United States - from scholars in the fields of psychology, gender studies, political science, and economics. The first three papers look at how widespread the experience of IPV is among different groups of women, examine selected risk factors associated with heightened vulnerability to victimization, and discuss consequences of intimate partner victimization. Another two papers place the problem of IPV in the wider context of societal perceptions and attitudes about victims and perpetrators of IPV in different countries, whereas the last paper examines the role of individual differences in the management of emotions in the escalation or de-escalation of relationship conflict. In combination, the papers highlight the interplay between the macro level of social and cultural norms condoning the use of violence, the micro level of family relations and construction of couple relationships, and the individual level of attitudes and behaviors that precipitate IPV.

Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.

Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.

We consider an SDE driven by a Lévy noise on a foliated manifold, whose trajectories stay on compact leaves. We determine the effective behavior of the system subject to a small smooth transversal perturbation of positive order epsilon. More precisely, we show that the average of the transversal component of the SDE converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to the invariant measures on the leaves (of the unpertubed system) as epsilon goes to 0. In particular we give upper bounds for the rates of convergence. The main results which are proved for pure jump Lévy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to Lévy driven SDEs of Marcus type.

Preclinical work indicates that calcitriol restores vascular function by normalizing the endothelial expression of cyclooxygenase-2 and thromboxane-prostanoid receptors in conditions of estrogen deficiency and thus prevents the thromboxane-prostanoid receptor activation-induced inhibition of nitric oxide synthase. Since endothelial dysfunction is a key factor in the pathogenesis of cardiovascular diseases, this finding may have an important translational impact. It provides a clear rationale to use endothelial function in clinical trials aiming to find the optimal dose of vitamin D for the prevention of cardiovascular events in postmenopausal women.

We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Lévy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.

Special issue on graph transformation and visual modeling techniques - guest editors' introduction
(2013)

Language processing changes with the knowledge and use of two languages. The advantage of being bilingual comes at the expense of increased processing demands and processing costs. I suggest considering bilingual complexity including these demands and costs. The proposed model claims effortless monolingual processing. By integrating individual and situational variability, the model would lose its idealistic touch, even for monolinguals.

Introduction
(2013)

Filming illegals
(2013)

This account presents information on all aspects of the biology of Robinia pseudoacacia L. that are relevant to understanding its ecological characteristics and behaviour. The main topics are presented within the standard framework of the Biological Flora of the British Isles: distribution, habitat, communities, responses to biotic factors, responses to environment, structure and physiology, phenology, floral and seed characters, herbivores and disease, and history and conservation.Robinia pseudoacacia, false acacia or black locust, is a deciduous, broad-leaved tree native to North America. The medium-sized, fast-growing tree is armed with spines, and extensively suckering. It has become naturalized in grassland, semi-natural woodlands and urban habitats. The tree is common in the south of the British Isles and in many other regions of Europe.Robinia pseudoacacia is a light-demanding pioneer species, which occurs primarily in disturbed sites on fertile to poor soils. The tree does not tolerate wet or compacted soils. In contrast to its native range, where it rapidly colonizes forest gaps and is replaced after 15-30years by more competitive tree species, populations in the secondary range can persist for a longer time, probably due to release from natural enemies.Robinia pseudoacacia reproduces sexually, and asexually by underground runners. Disturbance favours clonal growth and leads to an increase in the number of ramets. Mechanical stem damage and fires also lead to increased clonal recruitment. The tree benefits from di-nitrogen fixation associated with symbiotic rhizobia in root nodules. Estimated symbiotic nitrogen fixation rates range widely from 23 to 300kgha(-1)year(-1). The nitrogen becomes available to other plants mainly by the rapid decay of nitrogen-rich leaves.Robinia pseudoacacia is host to a wide range of fungi both in the native and introduced ranges. Megaherbivores are of minor significance in Europe but browsing by ungulates occurs in the native range. Among insects, the North American black locust gall midge (Obolodiplosis robiniae) is specific to Robinia and is spreading rapidly throughout Europe. In parts of Europe, Robinia pseudoacacia is considered an invasive non-indigenous plant and the tree is controlled. Negative impacts include shading and changes of soil conditions as a result of nitrogen fixation.

Preface to the special issue "Triggered and induced seismicity: probabilities and discrimination"
(2013)

We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.

The main goal of our target article was to provide concrete recommendations for improving the replicability of research findings. Most of the comments focus on this point. In addition, a few comments were concerned with the distinction between replicability and generalizability and the role of theory in replication. We address all comments within the conceptual structure of the target article and hope to convince readers that replication in psychological science amounts to much more than hitting the lottery twice.

We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.

Introducing the CTA concept
(2013)

The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.