Structural stability and robustness to bounded rationality for non-compact cases

We study the model M consisting of “general games” with noncompact action space, together with an associated abstract rationality function. We prove that M is structurally stable and robust to ϵ-equilibria for “almost all” parameters. As applications, we investigate structural stability and robustness to bounded rationality for noncooperative games, multiobjective optimizations and fixed point problems satisfying existence and some continuity conditions. Specifically, we introduce concrete rationality functions for such three kinds of problems with both payoffs and strategy sets, objective functions and domain spaces, and correspondence and domain spaces as parameters, respectively, and show the generic structural stability and robustness to bounded rationality for the corresponding model Ms.     

Cotorsion pairs associated with Auslander categories

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝⁿ. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes. Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590     

Correction to the paper “on the curvature of a generalization of a contact metric manifolds”

We considered in Example 3.1 of the paper [1] an S-structure on R^2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.     

Generation of Multiple-Atom Entangled States with Weak Cross-Kerr Nonlinearity

We propose a scheme to generate multiple-atom entangled states in separate cavities. In our scheme, only weak cross-Kerr mediums, homodyne measurement, and some linear elements are employed. With the help of homodyne measurement, four-atom GHZ state can be obtained with high probability and fidelity, and the proposal can be easily scaled to prepare multiple-atom GHZ state. Under ideal conditions, the success probability will not be affected by atomic numbers.     

Which Fine-Tuning Arguments Are Fine?

Fine-tuning arguments are a frequent find in the literature on quantum field theory. They are based on naturalness—an aesthetic criterion that was given a precise definition in the debates on the Higgs mechanism. We follow the history of such definitions and of their application at the scale of electroweak symmetry breaking. They give rise to a special interpretation of probability, which we call Gedankenfrequency. Finally, we show that the argument from naturalness has been extended to comparing different models of the physics beyond the Standard Model and that naturalness in this case can at best be understood a socio-historic heuristic.     

Effects of acceleration on the collision of particles in the rotating black hole spacetime

We study the collision of two geodesic particles in the accelerating and rotating black hole spacetime and probe the effects of the acceleration of black hole on the center-of-mass energy of the colliding particles and on the high-velocity collision belts. We find that the dependence of the center-of-mass energy on the acceleration in the near event-horizon collision is different from that in the near acceleration-horizon case. Moreover, the presence of the acceleration changes the shape and position of the high-velocity collision belts. Our results show that the acceleration of black holes brings about richer physics for the collision of particles.     

Wave functions and decay constants of <Emphasis Type="Italic">B</Emphasis> and <Emphasis Type="Italic">D</Emphasis> mesons in the relativistic potential model

With the decay constants of D and D _s mesons measured in experiment recently, we revisit the study of the bound states of quark and antiquark in B and D mesons in the relativistic potential model. The relativistic bound state wave equation is solved numerically. The masses, decay constants and wave functions of B and D mesons are obtained. Both the masses and decay constants obtained here can be seen as consistent with the experimental data. The wave functions can be used in the study of B and D meson decays.     

Morphology and bilayer integrity of small liposomes during aerosol generation by air-jet nebulisation

Small liposome suspensions (hydrodynamic diameter, 80–130 nm) were nebulised, and the resulting changes in morphology and bilayer integrity were found to be related to surface properties controlled by bilayer composition. Four separate liposome compositions (or liposome types) were investigated using three different phospholipids with unique properties. Morphological changes were studied using light scattering and imaging of liposomes before and after nebulisation, and structural integrity was investigated on the basis of the retention of an encapsulated dye (probe molecule). Nebulisation generated droplets contained liposomes. The liposome particles generated on droplet evaporation had a hollow structure as evidenced by electron imaging, indicating that the lipid bilayer does not collapse on evaporation. The particles of all compositions had mobility diameters between 50 and 90 nm, 1.4–1.6 times smaller than their diameters (hydrodynamic) measured before nebulisation, implying considerable volume shrinkage. Liposomes that had polymer-conjugated lipids covering their external surface underwent aggregation during nebulisation, evidenced by increased diameter after nebulisation. Incorporation of charged lipids reduced nebulisation-induced aggregation, but induced greater membrane rupture during aerosol generation, causing leakage of encapsulated probe molecules. Incorporation of both cholesterol and charged lipids prevented aggregation, but also preserved bilayer integrity, evidenced by the maximum retention of encapsulated dye observed in these conditions (>85%). The findings suggest that liposome bilayer composition can be manipulated to improve the efficiency of liposome aerosol delivery.     

Gender effect on neurodegeneration and myelin markers in an animal model for multiple sclerosis

Background  

Multiple sclerosis (MS) varies considerably in its incidence and progression in females and males. In spite of clinical evidence, relatively few studies have explored molecular mechanisms possibly involved in gender-related differences. The present study describes possible cellular- and molecular-involved markers which are differentially regulated in male and female rats and result in gender-dependent EAE evolution and progression. Attention was focused on markers of myelination (MBP and PDGFαR) and neuronal distress and/or damage (GABA synthesis enzymes, GAD65 and GAD67, NGF, BDNF and related receptors), in two CNS areas, i.e. spinal cord and cerebellum, which are respectively severely and mildly affected by inflammation and demyelination. Tissues were sampled during acute, relapse/remission and chronic phases and results were analysed by two-way ANOVA.