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.

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

An axiomatization of difference-form contest success functions

This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Equalizing Consistency, stating that the difference between winning probabilities in the grand contest and in the smaller contest should be identical across all participants in the smaller contest. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance and zero elasticity of augmentation, are unfounded.By clarifying the properties of this family of contest success functions, this axiomatization can help researchers to find the functional form better suited to their application of interest.

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.

Macrophages from Crohn's disease patients exhibit deficient pro-repair functions

BACKGROUND: We previously reported that myeloid cells can induce mucosal healing in a mouse model of acute colitis. Promotion of mucosal repair is becoming a major goal in the treatment of Crohn's disease. Our aim in this study is to investigate the pro-repair function of myeloid cells in healthy donor (HD) and Crohn's disease patients (CD). METHODS: Peripheral blood mononuclear cells (PBMC) from HD and CD patients were isolated from blood samples by Ficoll density gradient. Monocytic CD14+ cells were positively selected by Macs procedure and then differentiated ex-vivo into macrophages (Mφ). The repair function of PBMC, CD14+ monocytic cells and macrophages were evaluated in an in vitro wound healing assay. RESULTS: PBMC and CD14+ myeloid cells from HD and CD were not able to repair at any tested cell concentration. Remarkably, HD Mφ were able to induce wound healing only at high concentration (105 added Mφ), but, if activated with heat killed bacteria, they were able to repair even at very low concentration. On the contrary, not activated CD Mφ were not able to promote healing at any rate, but this function was restored upon activation. CONCLUSION: We showed that CD Mφ in their steady state, unlike HD Mφ, are defective in promoting wound healing. Our results are in keeping with the current theory of CD as an innate immunodeficiency. Defective Mφ may be responsible to the mucosal repair defects in CD patients and to the subsequent chronic activation of the adaptive immune response.

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.

Is the coiled body involved in nucleolar functions?

Coiled bodies (CBs) are structural constituents observed in nuclei of most eukaryotic cells. They usually occur in the nucleoplasm as well as in contact with the nucleolar surface. In this work we studied the hepatocyte nuclei of hibernating dormice in order to investigate possible modifications of CBs along the seasonal cycle. CBs were abundant during hibernation and rapidly disappeared upon arousal from hibernation. Moreover, CBs were frequently found to be integrated into the nucleolar body. Immunocytochemical analyses showed that CBs contain nucleoplasmic as well as nucleolar RNA-processing factors, suggesting an "ambiguous" role for this organelle in the nuclear functions.

Fractional hepatic de novo lipogenesis in healthy subjects during near-continuous oral nutrition and bed rest: a comparison with published data in artificially fed, critically ill patients.

BACKGROUND AND AIMS: In critically ill patients, fractional hepatic de novo lipogenesis increases in proportion to carbohydrate administration during isoenergetic nutrition. In this study, we sought to determine whether this increase may be the consequence of continuous enteral nutrition and bed rest. We, therefore, measured fractional hepatic de novo lipogenesis in a group of 12 healthy subjects during near-continuous oral feeding (hourly isoenergetic meals with a liquid formula containing 55% carbohydrate). In eight subjects, near-continuous enteral nutrition and bed rest were applied over a 10 h period. In the other four subjects, it was extended to 34 h. Fractional hepatic de novo lipogenesis was measured by infusing(13) C-labeled acetate and monitoring VLDL-(13)C palmitate enrichment with mass isotopomer distribution analysis. Fractional hepatic de novo lipogenesis was 3.2% (range 1.5-7.5%) in the eight subjects after 10 h of near continuous nutrition and 1.6% (range 1.3-2.0%) in the four subjects after 34 h of near-continuous nutrition and bed rest. This indicates that continuous nutrition and physical inactivity do not increase hepatic de novo lipogenesis. Fractional hepatic de novo lipogenesis previously reported in critically ill patients under similar nutritional conditions (9.3%) (range 5.3-15.8%) was markedly higher than in healthy subjects (P<0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

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.

The neuropeptide Y Y1 receptor regulates leptin-mediated control of energy homeostasis and reproductive functions.

The orexigenic neurotransmitter neuropeptide Y (NPY) plays a central role in the hypothalamic control of food intake and energy balance. NPY also exerts an inhibition of the gonadotrope axis that could be important in the response to poor metabolic conditions. In contrast, leptin provides an anorexigenic signal to centrally control the body needs in energy. Moreover, leptin contributes to preserve adequate reproductive functions by stimulating the activity of the gonadotrope axis. It is of interest that hypothalamic NPY represents a primary target of leptin actions. To evaluate the importance of the NPY Y1 and Y5 receptors in the downstream pathways modulated by leptin and controlling energy metabolism as well as the activity of the gonadotrope axis, we studied the effects of leptin administration on food intake and reproductive functions in mice deficient for the expression of either the Y1 or the Y5 receptor. Furthermore, the role of the Y1 receptor in leptin resistance was determined in leptin-deficient ob/ob mice bearing a null mutation in the NPY Y1 locus. Results point to a crucial role for the NPY Y1 receptor in mediating the NPY pathways situated downstream of leptin actions and controlling food intake, the onset of puberty, and the maintenance of reproductive functions.

Post-translational modifications regulate distinct functions of CARMA1 and BCL10.

Activation of the transcription factor nuclear factor (NF)-kappaB is essential for the normal functioning of the immune system. Deregulated NF-kappaB signalling in lymphocytes can lead to immunodeficiency, but also to autoimmunity or lymphomas. Many of the signalling components controlling NF-kappaB activation in lymphocytes are now known, but it is less clear how distinct molecular components of this pathway are regulated. Here, we summarize recent findings on post-translational modifications of intracellular components of this pathway. Phosphorylation of the CARMA1 and BCL10 proteins and ubiquitylation of BCL10 affect the formation and stability of the CARMA1-BCL10-MALT1 (CBM) complex, and also control negative feedback regulation of the NF-kappaB signalling pathway. Moreover, the study of BCL10 phosphorylation isoforms has revealed a new mechanism controlling BCL10 nuclear translocation and an unexpected role for BCL10 in the regulation of the actin cytoskeleton.

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

"Vegeu el resum a l'inici del document del fitxer adjunt."