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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.
Scheck-Wenderoth, Magdalena ; Schmeißer, Dieter ; Mutti, Maria ; Kolditz, Olaf ; Hünges, Ernst ; Schultz, Hans-Martin ; Liebscher, Axel ; Bock, Michaela
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.
Kreft, Jan-Ulrich ; Plugge, Caroline M. ; Grimm, Volker ; Prats, Clara ; Leveau, Johan H. J. ; Banitz, Thomas ; Baines, Stephen ; Clark, James ; Ros, Alexandra ; Klapper, Isaac ; Topping, Chris J. ; Field, Anthony J. ; Schuler, Andrew ; Litchman, Elena ; Hellweger, Ferdi L.
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.
Kaufmann, Liane ; Mazzocco, Michele M. ; Dowker, Ann ; von Aster, Michael G. ; Goebel, Silke M. ; Grabner, Roland H. ; Henik, Avishai ; Jordan, Nancy C. ; Karmiloff-Smith, Annette D. ; Kucian, Karin ; Rubinsten, Orly ; Szucs, Denes ; Shalev, Ruth ; Nuerk, Hans-Christoph
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.