The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Pathology and immune response of the blue mussel (Mytilus edulis L.) after an exposure to the harmful dinoflagellate Prorocentrum minimum

The harmful dinoflagellate Prorocentrum minimum has different effects upon various species of grazing bivalves, and these effects also vary with life-history stage. Possible effects of this dinoflagellate upon mussels have not been reported; therefore, experiments exposing adult blue mussels, Mytilus edulis, to P. minimum were conducted. Mussels were exposed to cultures of toxic P. minimum or benign Rhodomonas sp. in glass aquaria. After a short period of acclimation, samples were collected on day 0 (before the exposure) and after 3, 6, and 9 days of continuous-exposure experiment. Hemolymph was extracted for flow-cytometric analyses of hemocyte, immune-response functions, and soft tissues were excised for histopathology. Mussels responded to P. minimum exposure with diapedesis of hemocytes into the intestine, presumably to isolate P. minimum cells within the gut, thereby minimizing damage to other tissues. This immune response appeared to have been sustained throughout the 9-day exposure period, as circulating hemocytes retained hematological and functional properties. Bacteria proliferated in the intestines of the P. minimum-exposed mussels. Hemocytes within the intestine appeared to be either overwhelmed by the large number of bacteria or fully occupied in the encapsulating response to P. minimum cells; when hemocytes reached the intestine lumina, they underwent apoptosis and bacterial degradation. This experiment demonstrated that M. edulis is affected by ingestion of toxic P. minimum; however, the specific responses observed in the blue mussel differed from those reported for other bivalve species. This finding highlights the need to study effects of HABs on different bivalve species, rather than inferring that results from one species reflect the exposure responses of all bivalves.

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Locally univalent functions, VMOA, and the Dirichlet space

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Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Weighted norm inequalities for Fourier transforms of radial functions

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Superatomic Boolean algebras constructed from strongly unbounded functions

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Welfare Maximizing Contest Success Functions when the Planner Cannot Commit

We analyze how a contest organizer chooses optimally the winner when the contestants' efforts are already exerted and commitment to the use of a given contest success function is not possible. We de…ne the notion of rationalizability in mixed-strategies to capture such a situation. Our approach allows to derive different contest success functions depending on the aims and attitudes of the decider. We derive contest success functions which are closely related to commonly used functions providing new support for them. By taking into account social welfare considerations our approach bridges the contest literature and the recent literature on political economy. Keywords: Endogenous Contests, Contest Success Function, Mixed-Strategies. JEL Classi…cation: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances)

Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results

We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties.

Candidate quality in a Downsian Model with a continuous policy space

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution over the unit interval. In our equilibrium the advantaged candidate chooses the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. We show that this equilibrium exists if the number of voters is large enough relative to the size of the advantage.

Green vs. Lempert functions: a minimal example

The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and majorizes the corresponding multi-pole pluricomplex Green function. Coman proved that both coincide in the case of sets of two poles in the unit ball. We give an example of a set of three poles in the unit ball where this equality fails.

On the system of the functions x (s) / (s-r)k

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