Quelques théorèmes ergodiques pour des suites de fonctions

Le théorème ergodique de Birkhoff nous renseigne sur la convergence de suites de fonctions. Nous nous intéressons alors à étudier la convergence en moyenne et presque partout de ces suites, mais dans le cas où la suite est une suite strictement croissante de nombres entiers positifs. C’est alors que nous définirons les suites uniformes et étudierons la convergence presque partout pour ces suites. Nous regarderons également s’il existe certaines suites pour lesquelles la convergence n’a pas lieu. Nous présenterons alors un résultat dû en partie à Alexandra Bellow qui dit que de telles suites existent. Finalement, nous démontrerons une équivalence entre la notion de transformatiuon fortement mélangeante et la convergence d'une certaine suite qui utilise des “poids” qui satisfont certaines propriétés.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Una rassegna di teoremi ergodici. Dal teorema ergodico di Birkhoff Khinchin al teorema ergodico quantistico di von Neumann.

La tesi tratta dei teoremi ergodici più importanti scoperti dalla fine dell'800 ad oggi.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

Reducible von Neumann models and uniqueness

This paper can be regarded as a result of basic research on the technological characteristics of the von Neumann models and their consequences. It introduces a new taxonomy of reducible technologies, explores their key distinguishing features, and specifies which ones ensure the uniqueness of von Neumann equilibrium. A comprehensive comparison is also given between the familiar (in)decomposability ideas and the reducibility concepts suggested here. All these are carried out with a modern approach. Simultaneously, the reader may also acquire a complete picture of and guidance on the fundamental von Neumann models here.

Von Neumann-Morgenstern Stable Sets in Matching Problems

The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

Non-uniqueness through duality in the von Neumann growth models

Duality can be viewed as the soul of each von Neumann growth model. This is not at all surprising because von Neumann (1955), a mathematical genius, extensively studied quantum mechanics which involves a “dual nature” (electromagnetic waves and discrete corpuscules or light quanta). This may have had some influence on developing his own economic duality concept. The main object of this paper is to restore the spirit of economic duality in the investigations of the multiple von Neumann equilibria. By means of the (ir)reducibility taxonomy in Móczár (1995) the author transforms the primal canonical decomposition given by Bromek (1974) in the von Neumann growth model into the synergistic primal and dual canonical decomposition. This enables us to obtain all the information about the steadily maintainable states of growth sustained by the compatible price-constellations at each distinct expansion factor.

Invoking a cartesian product structure on social states: new resolutions of Sen's and Gibbard's impossibility theorems

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard's and Sen's paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. We then apply these notions to Gibbard's paradox and to Sen's impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems.

Plasmatic ADAMTS-13 metalloprotease and von Willebrand factor in children with cyanotic congenital heart disease

Changes in plasma von Willebrand factor concentration (VWF:Ag) and ADAMTS-13 activity (the metalloprotease that cleaves VWF physiologically) have been reported in several cardiovascular disorders with prognostic implications. We therefore determined the level of these proteins in the plasma of children with cyanotic congenital heart disease (CCHD) undergoing surgical treatment. Forty-eight children were enrolled (age 0.83 to 7.58 years). Measurements were performed at baseline and 48 h after surgery. ELISA, collagen-binding assays and Western blotting were used to estimate antigenic and biological activities, and proteolysis of VWF multimers. Preoperatively, VWF:Ag and ADAMTS-13 activity were decreased (65 and 71% of normal levels considered as 113 (105-129) U/dL and 91 ± 24% respectively, P < 0.003) and correlated (r = 0.39, P = 0.0064). High molecular weight VWF multimers were not related, suggesting an interaction of VWF with cell membranes, followed by proteolytic cleavage. A low preoperative ADAMTS-13 activity, a longer activated partial thromboplastin time and the need for cardiopulmonary bypass correlated with postoperative bleeding (P < 0.05). Postoperatively, ADAMTS-13 activity increased but less extensively than VWF:Ag (respectively, 2.23 and 2.83 times baseline, P < 0.0001), resulting in an increased VWF:Ag/ADAMTS-13 activity ratio (1.20 to 1.54, respectively, pre- and postoperative median values, P = 0.0029). ADAMTS-13 consumption was further confirmed by decreased ADAMTS-13 antigenic concentration (0.91 ± 0.30 to 0.70 ± 0.25 µg/mL, P < 0.0001) and persistent proteolysis of VWF multimers. We conclude that, in pediatric CCHD, changes in circulating ADAMTS-13 suggest enzyme consumption, associated with abnormal structure and function of VWF.

Platelet endothelial cell adhesion molecule-1 inhibits platelet response to thrombin and von Willebrand factor by regulating the internalization of glycoprotein Ib via AKT/glycogen synthase kinase-3/dynamin and integrin αIIbβ3

OBJECTIVE: Platelet endothelial cell adhesion molecule-1 (PECAM-1) regulates platelet response to multiple agonists. How this immunoreceptor tyrosine-based inhibitory motif-containing receptor inhibits G protein-coupled receptor-mediated thrombin-induced activation of platelets is unknown. APPROACH AND RESULTS: Here, we show that the activation of PECAM-1 inhibits fibrinogen binding to integrin αIIbβ3 and P-selectin surface expression in response to thrombin (0.1-3 U/mL) but not thrombin receptor-activating peptides SFLLRN (3×10(-7)-1×10(-5) mol/L) and GYPGQV (3×10(-6)-1×10(-4) mol/L). We hypothesized a role for PECAM-1 in reducing the tethering of thrombin to glycoprotein Ibα (GPIbα) on the platelet surface. We show that PECAM-1 signaling regulates the binding of fluorescein isothiocyanate-labeled thrombin to the platelet surface and reduces the levels of cell surface GPIbα by promoting its internalization, while concomitantly reducing the binding of platelets to von Willebrand factor under flow in vitro. PECAM-1-mediated internalization of GPIbα was reduced in the presence of both EGTA and cytochalasin D or latrunculin, but not either individually, and was reduced in mice in which tyrosines 747 and 759 of the cytoplasmic tail of β3 integrin were mutated to phenylalanine. Furthermore, PECAM-1 cross-linking led to a significant reduction in the phosphorylation of glycogen synthase kinase-3β Ser(9), but interestingly an increase in glycogen synthase kinase-3α pSer(21). PECAM-1-mediated internalization of GPIbα was reduced by inhibitors of dynamin (Dynasore) and glycogen synthase kinase-3 (CHIR99021), an effect that was enhanced in the presence of EGTA. CONCLUSIONS: PECAM-1 mediates internalization of GPIbα in platelets through dual AKT/protein kinase B/glycogen synthase kinase-3/dynamin-dependent and αIIbβ3-dependent mechanisms. These findings expand our understanding of how PECAM-1 regulates nonimmunoreceptor signaling pathways and helps to explains how PECAM-1 regulates thrombosis.