The automorphism group of a free-by-cyclic group in rank 2

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On the weights of nations: assigning voting weights in a heterogenous union

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model.

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

CM points and weight 3=2 modular forms

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Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Real rank zero algebras have the corona factorization property

The purpose of this short note is to prove that a stable separable C*-algebra with real rank zero has the so-called corona factorization property, that is, all the full multiplier projections are properly in finite. Enroute to our result, we consider conditions under which a real rank zero C*-algebra admits an injection of the compact operators (a question already considered in [21]).

Payoff-dependent balancedness and cores (revised version)

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Weight loss and survival of Biomphalaria Glabrata deprived of water

Immature and mature Biomphalaria glabrata are kept out of water at relative humidities varying from 0 to 100%. When snails are submitted to a saturated atmosphere, they show a slow weight loss and survival may be long. If relative humidity (RH) decreases, weight loss becomes important and survival is short. A reduced RH (0 to 65%) produces similar effects. During desiccation, fasting has no noticeable effect; survival depends essentially on weight loss.

Loss of Cutaneous TSLP-Dependent Immune Responses Skews the Balance of Inflammation from Tumor Protective to Tumor Promoting.

Inflammation can promote or inhibit cancer progression. In this study we have addressed the role of the proinflammatory cytokine thymic stromal lymphopoietin (TSLP) during skin carcinogenesis. Using conditional loss- and gain-of-function mouse models for Notch and Wnt signaling, respectively, we demonstrate that TSLP-mediated inflammation protects against cutaneous carcinogenesis by acting directly on CD4 and CD8 T cells. Genetic ablation of TSLP receptor (TSLPR) perturbs T-cell-mediated protection and results in the accumulation of CD11b(+)Gr1(+) myeloid cells. These promote tumor growth by secreting Wnt ligands and augmenting β-catenin signaling in the neighboring epithelium. Epithelial specific ablation of β-catenin prevents both carcinogenesis and the accumulation of CD11b(+)Gr1(+) myeloid cells, suggesting tumor cells initiate a feed-forward loop that induces protumorigenic inflammation.

Glucose-dependent insulinotropic polypeptide receptor deficiency leads to modifications of trabecular bone volume and quality in mice.

A role for the gastro-intestinal tract in controlling bone remodeling is suspected since serum levels of bone remodeling markers are affected rapidly after a meal. Glucose-dependent insulinotropic polypeptide (GIP) represents a suitable candidate in mediating this effect. The aim of the present study was to investigate the effect of total inhibition of GIP signaling on trabecular bone volume, microarchitecture and quality. We used GIP receptor (GIPR) knockout mice and investigated trabecular bone volume and microarchitecture by microCT and histomorphometry. GIPR-deficient animals at 16 weeks of age presented with a significant (20%) increase in trabecular bone mass accompanied by an increase (17%) in trabecular number. In addition, the number of osteoclasts and bone formation rate was significantly reduced and augmented, respectively in these animals when compared with wild-type littermates. These modifications of trabecular bone microarchitecture are linked to a remodeling in the expression pattern of adipokines in the GIPR-deficient mice. On the other hand, despite significant enhancement in bone volume, intrinsic mechanical properties of the bone matrix was reduced as well as the distribution of bone mineral density and the ratio of mature/immature collagen cross-links. Taken together, these results indicate an increase in trabecular bone volume in GIPR KO animals associated with a reduction in bone quality.

Conjunctival MALT lymphoma: utility of FDG PET/CT for diagnosis, staging, and evaluation of treatment response.

A 67-year-old woman was referred for staging of a mucosa-associated lymphoid tumor lymphoma involving the left conjunctiva. CT scan had shown paravertebral and pelvic masses, and a breast nodule. FDG PET/CT demonstrated moderately increased uptake in the left ocular conjunctiva and confirmed the paravertebral and pelvic masses and the breast nodule. Moreover, abnormal FDG uptake was shown in 2 breast nodules, the flank, the gluteus maximus, and the gastric cardia. The patient received 6 cycles of rituximab-bendamustine chemotherapy with a complete clinical and metabolic response at the 6-month follow-up PET/CT and remained relapse-free without visual acuity problem after a 36-month follow-up.

Insulin secretion is regulated by the glucose-dependent production of islet beta cell macrophage migration inhibitory factor.

Macrophage migration inhibitory factor (MIF), originally identified as a cytokine secreted by T lymphocytes, was found recently to be both a pituitary hormone and a mediator released by immune cells in response to glucocorticoid stimulation. We report here that the insulin-secreting beta cell of the islets of Langerhans expresses MIF and that its production is regulated by glucose in a time- and concentration-dependent manner. MIF and insulin colocalize by immunocytochemistry within the secretory granules of the pancreatic islet beta cells, and once released, MIF appears to regulate insulin release in an autocrine fashion. In perifusion studies performed with isolated rat islets, immunoneutralization of MIF reduced the first and second phase of the glucose-induced insulin secretion response by 39% and 31%, respectively. Conversely, exogenously added recombinant MIF was found to potentiate insulin release. Constitutive expression of MIF antisense RNA in the insulin-secreting INS-1 cell line inhibited MIF protein synthesis and decreased significantly glucose-induced insulin release. MIF is therefore a glucose-dependent, islet cell product that regulates insulin secretion in a positive manner and may play an important role in carbohydrate metabolism.