Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

Identification of particular groups of microRNAs that positively or negatively impact on beta cell function in obese models of type 2 diabetes.

AIMS/HYPOTHESIS: MicroRNAs are key regulators of gene expression involved in health and disease. The goal of our study was to investigate the global changes in beta cell microRNA expression occurring in two models of obesity-associated type 2 diabetes and to assess their potential contribution to the development of the disease. METHODS: MicroRNA profiling of pancreatic islets isolated from prediabetic and diabetic db/db mice and from mice fed a high-fat diet was performed by microarray. The functional impact of the changes in microRNA expression was assessed by reproducing them in vitro in primary rat and human beta cells. RESULTS: MicroRNAs differentially expressed in both models of obesity-associated type 2 diabetes fall into two distinct categories. A group including miR-132, miR-184 and miR-338-3p displays expression changes occurring long before the onset of diabetes. Functional studies indicate that these expression changes have positive effects on beta cell activities and mass. In contrast, modifications in the levels of miR-34a, miR-146a, miR-199a-3p, miR-203, miR-210 and miR-383 primarily occur in diabetic mice and result in increased beta cell apoptosis. These results indicate that obesity and insulin resistance trigger adaptations in the levels of particular microRNAs to allow sustained beta cell function, and that additional microRNA deregulation negatively impacting on insulin-secreting cells may cause beta cell demise and diabetes manifestation. CONCLUSIONS/INTERPRETATION: We propose that maintenance of blood glucose homeostasis or progression toward glucose intolerance and type 2 diabetes may be determined by the balance between expression changes of particular microRNAs.

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.

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Income stratification and the measurement of interdistributional inequality between multiple groups

This paper proposes a new class of stratification indices that measure interdistributional inequality between multiple groups. The class is based on a conceptualisation of stratification as a process that results in a hierarchical ordering of groups and therefore seeks to capture not only the extent to which groups form well-defined strata in the income distribution but also the scale of the resultant differences in income standards between them, where these two factors play the same role as identification and alienation respectively in the measurement of polarisation. The properties of the class as a whole are investigated as well as those of selected members of it: zeroth and first power indices may be interpreted as measuring the overall incidence and depth of stratification respectively, while higher power indices members are directly sensitive to the severity of stratification between groups. An illustrative application provides an empirical analysis of global income stratification by regions in 1993.

On uniform conjugators in torsion-free hyperbolic groups

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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.

Testosterone Restoration by Enclomiphene Citrate in Men with Secondary Hypogonadism: a pharmacodynamic and Pharmacokinetic study.

OBJECTIVES: To determine the pharmacodynamic (PD) profile of serum total testosterone levels (TT) and luteinizing hormone (LH) in men with secondary hypogonadism following initial and chronic daily oral doses of enclomiphene citrate in comparison to transdermal testosterone. To determine the effects of daily oral doses of enclomiphene citrate (Androxal®) in comparison to transdermal testosterone on other hormones and markers in men with secondary hypogonadism. PATIENTS AND METHODS: This was a randomized, single blind, two-center phase II study to evaluate three different doses of enclomiphene citrate (6.25mg, 12.5mg and 25 mg Androxal®), versus AndroGel®, a transdermal testosterone, on 24-hour LH and TT in otherwise normal healthy men with secondary hypogonadism. Forty-eight men were enrolled in the trial (ITT Population), but 4 men had T levels >350 ng/dL at baseline. Forty-four men completed the study per protocol (PP population). All subjects enrolled in this trial had serum TT in the low range (<350 ng/dL) and had low to normal LH (<12 IU/L) on at least two occasions. TT and LH levels were assessed each hour for 24 hours to examine the effects at each of three treatment doses of enclomiphene versus a standard dose (5 grams) of transdermal testosterone (AndroGel). In the initial profile TT and LH were determined in a naïve population following a single initial oral or transdermal treatment (Day 1). This was contrasted to that seen after six weeks of continuous daily oral or transdermal treatment (Day 42). The pharmacokinetics of enclomiphene was performed in a select subpopulation. Serum samples were obtained over the course of the study to determine levels of various hormones and lipids. RESULTS: After six weeks of continuous use, the mean ± SD concentration of TT at Day 42 C0hrTT, was 604 ± 160 ng/dL for men taking the highest of dose of enclomiphene citrate (enclomiphene, 25 mg daily) and 500 ± 278 ng in those men treated with transdermal testosterone. These values were higher than Day 1 values but not different from each other (p = 0.23, T-test). All three doses of enclomiphene increased C0hrTT, CavgTT, CmaxTT, CminTT and CrangeTT. Transdermal testosterone also raised TT, albeit with more variability, and with suppressed LH levels. The patterns of TT over 24 hour period following six weeks of dosing could be fit to a non-linear function with morning elevations, mid-day troughs, and rising night-time levels. Enclomiphene and transdermal testosterone increased levels of TT within two weeks, but they had opposite effects on FSH and LH Treatment with enclomiphene did not significantly affect levels of TSH, ACTH, cortisol, lipids, or bone markers. Both transdermal testosterone and enclomiphene citrate decreased IGF-1 levels (p<0.05) but suppression was greater in the enclomiphene citrate groups. CONCLUSIONS: Enclomiphene citrate increased serum LH and TT; however, there was not a temporal association between the peak drug levels and the Cmax levels LH or TT. Enclomiphene citrate consistently increased serum TT into the normal range and increased LH and FSH above the normal range. The effects on LH and TT persisted for at least one week after stopping treatment.

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&lt;0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

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.

Vitellogenesis in insects and other groups: a review

The eggs from oviparous organisms contain large amounts of vitellus, or yolk, wich are utilized by the growing embryo. Vitellogenesis is the process of vitellus accumulation and involves massive heterosynthetic synthesis of the protein vitellogenin (Vg) and its deposition in the oocyte. This work summarizes data on Vg structure, synthesis, uptake by oocytes and its fate during embryogenesis. The hormonal control of vitellogenesis and its tissue, sex and temporal regulation are also discussed. Where it is available, data on structure and expression of Vg-coding genes are reviewed. Insect vitellogenesis is priorized although other oviparous animal groups outside insects are also treated.

Structure theorems for subgroups of homeomorphism groups

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Bounding the residual finiteness of free groups

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