Finite Horizon Learning

Incorporating adaptive learning into macroeconomics requires assumptions about how agents incorporate their forecasts into their decision-making. We develop a theory of bounded rationality that we call finite-horizon learning. This approach generalizes the two existing benchmarks in the literature: Eulerequation learning, which assumes that consumption decisions are made to satisfy the one-step-ahead perceived Euler equation; and infinite-horizon learning, in which consumption today is determined optimally from an infinite-horizon optimization problem with given beliefs. In our approach, agents hold a finite forecasting/planning horizon. We find for the Ramsey model that the unique rational expectations equilibrium is E-stable at all horizons. However, transitional dynamics can differ significantly depending upon the horizon.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

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.

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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A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

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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Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.