Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions

We show short time existence and uniqueness of \C^{1,1} solutions to the mean curvature flow with obstacles, when the obstacles are of class \C^{1,1}. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface

Control of cell division in the adult brain by heparan sulfates in fractones and vascular basement membranes

Regulation of cell division in adult tissues and organs requires the coordination of growth factors at the surface of potentially-dividing cells in specific anatomic loci named germinal niches. However, the biological components and physiological system that control growth factors in the germinal niches are unknown. In the adult brain, no function has been attributed to fractones, the fractal-shaped extracellular matrix structures located in the subventricular zone (SVZ) next to neural stem and progenitor cells. Here, we show that BMP-7 (bone morphogenetic protein-7) and FGF-2 (fibroblast growth factor-2) modulate cell division in the SVZ only if the growth factors bind to heparan sulfates localized in fractones and adjoined vascular basement membranes. Our results strongly suggest that fractones and specialized basement membranes function as stem cell niche structures, capturing and potentiating growth factors to regulate cell division in the adult brain

Regular distributive efficiency and the distributive liberal social contract.

We consider abstract social systems of private property, made of n individuals endowed with non-paternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto-efficient lumpsum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is, both, Pareto-efficient relative to individual interdependent preferences, and unanimously weakly preferred to the initial market equilibrium. We elicit the global structure of the set of Pareto-efficient allocations: its relative interior is a simply connected smooth manifold of dimension n-1, homeomorphic to the relative interior of the unit-simplex of ℝn . The property obtains under three suitable conditions on the partial preordering of Pareto associated with individual interdependent preferences, which essentially state that: the social utility functions built from weighted sums of individual interdependent utilities, by means of arbitrary positive weights, exhibit a property of differentiable non-satiation and some suitably defined property of inequality aversion; and individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima. The set of market equilibrium allocations associated with the transfers of the inclusive distributive liberal social contracts consists of the allocations that are unanimously weakly preferred to the initial market equilibrium and that maximize, in the set of attainable allocations, weighted sums of individual interdependent utilities derived from suitable vectors of positive weights of ℝn ++. Its relative interior is a simply connected smooth manifold of dimension n-1 whenever the initial market equilibrium is not Pareto-efficient relative to individual interdependent preferences.Walrasian equilibrium; Pareto-efficiency; liberal social contract; individual social preferences; allocation; distribution.

VoIP Regulation in Canada

The CRTC recently released Regulatory Framework for Voice Communication Services using Internet Protocol (Decision 2005-28), Telecom Decision CRTC 2005-28, setting out the details of the appropriate regulatory regime applicable to the provision of VoIP services. We present a brief overview of Decision 2005-28, we then consider the positions of incumbents and competitors, and finally we comment on the above interventions in light of the economic theory of regulation and the theory of strategic competition. We conclude that the predominant model underlying the positions not only of the CRTC but also of the parties involved, including the firms themselves, both the incumbents and the new entrants, and their respective business consultants, do not stand the test of modern economic theory. Le CRTC a récemment publié la décision Cadre de réglementation régissant les services de communication vocale sur protocole Internet (Décision 2005-28) dans laquelle il fixe les paramètres du régime de réglementation qui régira la fourniture des services VoIP. Nous présentons d’abord un aperçu de la Décision 2005-28 ainsi que les positions des entreprises de services locaux titulaires et des nouveaux concurrents. Finalement, nous commentons ces interventions à la lumière de la théorie économique de la réglementation et de la théorie de la concurrence stratégique. Nous concluons que le modèle dominant sur lequel s’appuient non seulement la position du CRTC, mais également celles des parties intéressées, y compris les entreprises elles-mêmes, les entreprises de services locaux titulaires et les nouveaux concurrents, et leurs conseillers d’affaire, ne résiste pas à l’analyse économique moderne.regulation, strategic competition, telecommunications, VoIP, concurrence stratégique, réglementation, télécommunication VoIP