Continuity of the measure of the spectrum for quasiperiodic Schrodinger operators with rough potentials

We study discrete quasiperiodic Schr\"odinger operators on \ell^2(\zee) with potentials defined by $\gamma$-H\"older functions. We prove a general statement that for $\gamma >1/2$ and under the condition of positive Lyapunov exponents, measure of the spectrum at irrational frequencies is the limit of measures of spectra of periodic approximants. An important ingredient in our analysis is a general result on uniformity of the upper Lyapunov exponent of strictly ergodic cocycles.Comment: 15 page

Agent-based modeling of the impact of advertising on the regional economic cluster lifecycle

The aim of the study is the development and testing of an algorithm for modeling the impact of advertising on various stages of the life cycle of economic clusters. It is assumed, that the life cycle of the cluster consists of the stages: a diffuse group, a hidden cluster, an evolving cluster, a mature cluster, a collapsing cluster. Using the agent-based simulation methods, hierarchical clustering and chaos theory, the following results were obtained: a conceptual model of the behavior of cluster members for cluster formation processes at each stage of the cluster life cycle and an imitation model of the influence of advertising on the life cycle of the economic cluster; the patterns of various stages of the life cycle of the economic cluster and the functioning of the cluster without influence and under the influence of advertising were revealed. Advertising reduces the time at the stages of the associated life cycle of the cluster, increases the stage of maturity of the cluster. Companies that do not comply with the principles of clustering are under the influence of advertising and promotional activities. Such enterprises most often arise in the cluster at the stages of its formation

HIV-1 envelope, integrins and co-receptor use in mucosal transmission of HIV

It is well established that HIV-1 infection typically involves an interaction between the viral envelope protein gp120/41 and the CD4 molecule followed by a second interaction with a chemokine receptor, usually CCR5 or CXCR4. In the early stages of an HIV-1 infection CCR5 using viruses (R5 viruses) predominate. In some viral subtypes there is a propensity to switch to CXCR4 usage (X4 viruses). The receptor switch occurs in ~ 40% of the infected individuals and is associated with faster disease progression. This holds for subtypes B and D, but occurs less frequently in subtypes A and C. There are several hypotheses to explain the preferential transmission of R5 viruses and the mechanisms that lead to switching of co-receptor usage; however, there is no definitive explanation for either. One important consideration regarding transmission is that signaling by R5 gp120 may facilitate transmission of R5 viruses by inducing a permissive environment for HIV replication. In the case of sexual transmission, infection by HIV requires the virus to breach the mucosal barrier to gain access to the immune cell targets that it infects; however, the immediate events that follow HIV exposure at genital mucosal sites are not well understood. Upon transmission, the HIV quasispecies that is replicating in an infected donor contracts through a “genetic bottleneck”, and often infection results from a single infectious event. Many details surrounding this initial infection remain unresolved. In mucosal tissues, CD4+ T cells express high levels of CCR5, and a subset of these CD4+/CCR5high cells express the integrin α4β7, the gut homing receptor. CD4+/CCR5high/ α4β7high T cells are highly susceptible to infection by HIV-1 and are ideal targets for an efficient productive infection at the point of transmission. In this context we have demonstrated that the HIV-1 envelope protein gp120 binds to α4β7 on CD4+ T cells. On CD4+/CCR5high/ α4β7high T cells, α4β7 is closely associated with CD4 and CCR5. Furthermore, α4β7 is ~3 times the size of CD4 on the cell surface, that makes it a prominent receptor for an efficient virus capture. gp120-α4β7 interactions mediate the activation of the adhesion-associated integrin LFA-1. LFA-1 facilitates the formation of virological synapses and cell-to-cell spread of HIV-1. gp120 binding to α4β7 is mediated by a tripeptide located in the V1/V2 domain of gp120. Of note, the V1/V2 domain of gp120 has been linked to variations in transmission fitness among viral isolates raising the intriguing possibility that gp120-α4β7 interactions may be linked to transmission fitness. Although many details remain unresolved, we hypothesize that gp120-α4β7 interactions play an important role in the very early events following sexual transmission of HIV and may have important implication in the design of vaccine strategies for the prevention of acquisition of HIV infectio

Different Pattern of Immunoglobulin Gene Usage by HIV-1 Compared to Non-HIV-1 Antibodies Derived from the Same Infected Subject

A biased usage of immunoglobulin (Ig) genes is observed in human anti-HIV-1 monoclonal antibodies (mAbs) resulting probably from compensation to reduced usage of the VH3 family genes, while the other alternative suggests that this bias usage is due to antigen requirements. If the antigen structure is responsible for the preferential usage of particular Ig genes, it may have certain implications for HIV vaccine development by the targeting of particular Ig gene-encoded B cell receptors to induce neutralizing anti-HIV-1 antibodies. To address this issue, we have produced HIV-1 specific and non-HIV-1 mAbs from an infected individual and analyzed the Ig gene usage. Green-fluorescence labeled virus-like particles (VLP) expressing HIV-1 envelope (Env) proteins of JRFL and BaL and control VLPs (without Env) were used to select single B cells for the production of 68 recombinant mAbs. Ten of these mAbs were HIV-1 Env specific with neutralizing activity against V3 and the CD4 binding site, as well as non-neutralizing mAbs to gp41. The remaining 58 mAbs were non-HIV-1 Env mAbs with undefined specificities. Analysis revealed that biased usage of Ig genes was restricted only to anti-HIV-1 but not to non-HIV-1 mAbs. The VH1 family genes were dominantly used, followed by VH3, VH4, and VH5 among anti-HIV-1 mAbs, while non-HIV-1 specific mAbs preferentially used VH3 family genes, followed by VH4, VH1 and VH5 families in a pattern identical to Abs derived from healthy individuals. This observation suggests that the biased usage of Ig genes by anti-HIV-1 mAbs is driven by structural requirements of the virus antigens rather than by compensation to any depletion of VH3 B cells due to autoreactive mechanisms, according to the gp120 superantigen hypothesis

On the abominable properties of the almost Mathieu operator with well approximated frequencies

We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of critical coupling, we show that the Hausdorff measure of the spectrum may vanish (for appropriately chosen frequencies) whenever the gauge function tends to zero faster than logarithmically. For arbitrary coupling, we show that modulus of continuity of the integrated density of states can be arbitrary close to logarithmic; we also prove a similar result for the Lyapunov exponent as a function of the spectral parameter. Finally, we show that (for any coupling) there exist frequencies for which the spectrum is not homogeneous in the sense of Carleson, and, moreover, fails the Parreau-Widom condition. The frequencies for which these properties hold are explicitly described in terms of the growth of the denominators of the convergents

Kinetics of early T cell receptor signaling regulate the pathway of lytic granule delivery to the secretory domain.

Cytolytic granules mediate killing of virus-infected cells by cytotoxic T lymphocytes. We show here that the granules can take long or short paths to the secretory domain. Both paths utilized the same intracellular molecular events, which have different spatial and temporal arrangements and are regulated by the kinetics of Ca(2+)-mediated signaling. Rapid signaling caused swift granule concentration near the microtubule-organizing center (MTOC) and subsequent delivery by the polarized MTOC directly to the secretory domain-the shortest path. Indolent signaling led to late recruitment of granules that moved along microtubules to the periphery of the synapse and then moved tangentially to fuse at the outer edge of the secretory domain-a longer path. The short pathway is associated with faster granule release and more efficient killing than the long pathway. Thus, the kinetics of early signaling regulates the quality of the T cell cytolytic response