On the Stability of a Cournot Dynamic Game Under the Influence of Information

In this paper we study the impact of information on the stability of a dynamic Cournot – type duopoly game. We suppose that one player searches for information about his rival before he makes his decision. We study how the amount of information acquired by player, influences the stability of Nash equilibrium. The game is modeled with a system of two difference equations. Existence and stability of equilibrium of this system are studied. We show numerically that the model gives chaotic and unpredictable trajectories as a consequence of change in the information parameter, but in our case there are also stable trajectories for each value of the information parameter. To provide some numerical evidence for the chaotic behavior of the system we present various numerical results including bifurcation diagrams, strange attractors, Lyapunov numbers and sensitive dependence on initial conditions.     Keywords: Cournot dynamic game, Nash equilibrium, Stability, Chaos

IL-6-mediated MHC class II induction on RIN-5AH insulinoma cells by IFN-γ occurs via the G-protein pathway

Major histocompatibility complex (MHC) class II antigen expression has been implicated in the pathogenesis of autoimmune type 1 diabetes. In this study we examined the role of various cytoldnes that may induce MHC class II surface antigen expression, using the rat insulinoma line RIN-5AH as a pertinent model system. As in another study, the ability of IFN-γ to amplify MHC class II antigen expression 4-fold is demonstrated. At the same time we noted a 5-fold increase of these histocompatibility antigens by IL-6. Signal transduction analysis reveals that IL-6-induced MHC class II expression is specifically mediated by the G-protein system (activation of p21ras by IL-6) since mevalonic acid lactone (a Gprotein inhibitor) abolishes the action of IL-6. In contrast, IFN-γ, which does not activate p21ras, is not inhibited by protein kinase C (PKC) inhibitors but by those of the G-protein pathway. This finding raises the possibility that IFN-γ induces RIN cells to secrete IL-6 (as shown previously, as well as in this paper) which, in turn, increases class II antigen expression via the G-protein pathway. This action may be unique to IL-6 or in synergy with IFN-γ. Other cytokines such as IL-1α and β, and TNF-α induce a smaller increase in MHC class II antigens on RIN cells, and appear to activate both the G-protein and the PKC signal transduction pathways to varying degrees. Therefore, injury of pancreatic β-cells and possible induction of autoimmune type 1 diabetes via various cytokines may be caused by IL-6 or IFN-γ, or by their ability to induce MHC class II antigen upregulation

Modelling of thrombin generation under flow in realistic left anterior descending geometries

Currently there are no available methods for prediction of thrombotic complications in Coronary Artery disease. Additionally, blood coagulation tests are mainly performed in a steady system while coagulation in vivo occurs under flow conditions. In this work, a phenomenological model for coagulation up-to thrombin generation is proposed; the model is mainly based on the results of thrombin generation assays and therefore it can account for the variation of the coagulability that is observed in different individuals. The model is applied on 3 cases of left anterior descending arteries (LAD) with 50% maximum stenosis placed at a different location and have been statistically assessed as of different complication risk. The simulations showed that parameters of thrombin generation assays obtain different values when they refer to thrombin generation under realistic coronary flow conditions. The flow conditions prevailing locally because of the geometric differences among the arterial trees can lead to different initiation times and thrombin production rates and it also alters the spatial distribution of the coagulation products. Similarly, small changes of the coagulation characteristics of blood under identical flow conditions can allow or prevent the initiation of coagulation. The results indicate that combined consideration of geometry and coagulation characteristics of blood can lead to entirely different conclusions compared to independent assessment of each factor

Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^2 a/a_u$ and $\gamma/N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

Properties of Intersecting p-branes in Various Dimensions

General properties of intersecting extremal p-brane solutions of gravity coupled with dilatons and several different d-form fields in arbitrary space-time dimensions are considered. It is show that heuristically expected properties of the intersecting p-branes follow from the explicit formulae for solutions. In particular, harmonic superposition and S-duality hold for all p-brane solutions. Generalized T-duality takes place under additional restrictions on the initial theory parameters .Comment: 14 pages, RevTeX, misprints are corrected and more Comments are added, information about one of the authors (M.G.I.) available at http://www.geocities.com/CapeCanaveral/Lab/419