An Unrestricted Hartree-Fock Self-consistent Huckel-like Procedure. Application to the Magnetic Properties of Radicals and Metallic Clusters

The Huckel method, which can be considered an SCF method on the orthogonalized Lowdin basis, is extended to the UHF model. Some applications to :re-radicals and to metallic clusters are given. A strong magnetization can appear, even in small size clusters. Correlation with the Hund rule is discussed. A calculation carried out on a tetrahedral cluster explains the origin of the strong magnetization in elements located in the middle of the transition elements period. Examples of antiferro- and ferrimagnetic clusters are given

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

Predicting protein decomposition: the case of aspartic-acid racemization kinetics

The increase in proportion of the non-biological (D-) isomer of aspartic acid (Asp) relative to the L- isomer has been widely used in archaeology and geochemistry as a tool for dating. The method has proved controversial, particularly when used for bones. The non-linear kinetics of Asp racemization have prompted a number of suggestions as to the underlying mechanism(s) and have led to the use of mathe- matical transformations which linearize the increase in D-Asp with respect to time. Using one example, a suggestion that the initial rapid phase of Asp racemization is due to a contribution from asparagine (Asn), we demonstrate how a simple model of the degradation and racemization of Asn can be used to predict the observed kinetics. A more complex model of peptide bound Asx (Asn+Asp) racemization, which occurs via the formation of a cyclic succinimide (Asu), can be used to correctly predict Asx racemi- zation kinetics in proteins at high temperatures (95-140 °C). The model fails to predict racemization kinetics in dentine collagen at 37 °C. The reason for this is that Asu formation is highly conformation dependent and is predicted to occur extremely slowly in triple helical collagen. As conformation strongly in£uences the rate of Asu formation and hence Asx racemization, the use of extrapolation from high temperatures to estimate racemization kinetics of Asx in proteins below their denaturation temperature is called into question. In the case of archaeological bone, we argue that the D:L ratio of Asx re£ects the proportion of non- helical to helical collagen, overlain by the e¡ects of leaching of more soluble (and conformationally unconstrained) peptides. Thus, racemization kinetics in bone are potentially unpredictable, and the proposed use of Asx racemization to estimate the extent of DNA depurination in archaeological bones is challenged

Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravit

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on ${\mathbb C}P^3\times \Sigma_g \times {\mathbb T}^2$ with torsion $H-$flux and demonstrate in details the conjectured T-duality to ${\mathbb R}P^7\times X^3$ with no flux. In the simple case of $X^3 = {\mathbb T}^3$, T-dualizing the circles reduces to duality between ${\mathbb C}P^3\times {\mathbb T}^2 \times {\mathbb T}^2$ with $H-$flux and ${\mathbb R}P^7\times {\mathbb T}^3$ with no flux.Comment: 27 pages, tex file, no figure

A Short Survey of Noncommutative Geometry

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the Riemann-Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illustration of the spectral formulation of geometry in the ordinary commutative case, we give a polynomial equation for geometries on the four dimensional sphere with fixed volume. The equation involves an idempotent e, playing the role of the instanton, and the Dirac operator D. It expresses the gamma five matrix as the pairing between the operator theoretic chern characters of e and D. It is of degree five in the idempotent and four in the Dirac operator which only appears through its commutant with the idempotent. It determines both the sphere and all its metrics with fixed volume form. We also show using the noncommutative analogue of the Polyakov action, how to obtain the noncommutative metric (in spectral form) on the noncommutative tori from the formal naive metric. We conclude on some questions related to string theory.Comment: Invited lecture for JMP 2000, 45

HIV Types, Groups, Subtypes and Recombinant Forms: Errors in Replication, Selection Pressure and Quasispecies

HIV-1 is a chimpanzee virus which was transmitted to humans by several zoonotic events resulting in infection with HIV-1 groups M P, and in parallel transmission events from sooty mangabey monkey viruses leading to infections with HIV-2 groups A H. Both viruses have circulated in the human population for about 80 years. In the infected patient, HIV mutates, and by elimination of some of the viruses by the action of the immune system individual quasispecies are formed. Along with the selection of the fittest viruses, mutation and recombination after superinfection with HIV from different groups or subtypes have resulted in the diversity of their patterns of geographic distribution. Despite the high variability observed, some essential parts of the HIV genome are highly conserved. Viral diversity is further facilitated in some parts of the HIV genome by drug selection pressure and may also be enhanced by different genetic factors, including HLA in patients from different regions of the world. Viral and human genetic factors influence pathogenesis. Viral genetic factors are proteins such as Tat, Vif and Rev. Human genetic factors associated with a better clinical outcome are proteins such as APOBEC, langerin, tetherin and chemokine receptor 5 (CCR5) and HLA B27, B57, DRB1{*}1303, KIR and PARD3B. Copyright (C) 2012 S. Karger AG, Base

Factors Predicting Discordant Virological and Immunological Responses to Antiretroviral Therapy in HIV-1 Clade C Infected Zulu/Xhosa in South Africa

Factors predicting suboptimal CD4 cell recovery have been studied in HIV clade-B infected US and European populations. It is, however, uncertain to what extent these results are applicable to HIV clade-C infected African populations. Multivariate analysis using logistic regression and longitudinal analyses using mixed models were employed to assess the impact of age, gender, baseline CD4 cell count, hemoglobin, body mass index (BMI), tuberculosis and other opportunistic co-infections, and frequencies of regimen change on CD4 cell recovery at 12 and 30 months and on overtime change in CD4 cells among 442 virologically suppressed South Africans. Despite adequate virological response 37% (95% CI:32%–42%) and 83% (95% CI:79%–86%) of patients on antiretroviral therapy failed to restore CD4 cell counts ≥200 cells/mm3 after 12 and ≥500 cells/mm3 after 30 months, respectively, in this South African cohort. Critical risk factors for inadequate recovery were older age (p = 0.001) and nadir CD4 cell count at ART initiation (p<0.0001), while concurrent TB co-infection, BMI, baseline hemoglobin, gender and antiretroviral regimen were not significant risk factors. These data suggest that greater efforts are needed to identify and treat HAART-eligible patients prior to severe CD4 cell decline or achievement of advanced age

Unique CRF01_AE Gag CTL Epitopes Associated with Lower HIV-Viral Load and Delayed Disease Progression in a Cohort of HIV-Infected Thais

Cytotoxic T Lymphocytes (CTLs) play a central role in controlling HIV-replication. Although numerous CTL epitopes have been described, most are in subtype B or C infection. Little is known about CTL responses in CRF01_AE infection. Gag CTL responses were investigated in a cohort of 137 treatment-naïve HIV-1 infected Thai patients with high CD4+ T cell counts, using gIFN Enzyme-Linked Immunospot (ELISpot) assays with 15-mer overlapping peptides (OLPs) derived from locally dominant CRF01_AE Gag sequences. 44 OLPs were recognized in 112 (81.8%) individuals. Both the breadth and magnitude of the CTL response, particularly against the p24 region, positively correlated with CD4+ T cell count and inversely correlated with HIV viral load. The breadth of OLP response was also associated with slower progression to antiretroviral therapy initiation. Statistical analysis and single peptide ELISpot assay identified at least 17 significant associations between reactive OLP and HLA in 12 OLP regions; 6 OLP-HLA associations (35.3%) were not compatible with previously reported CTL epitopes, suggesting that these contained new CTL Gag epitopes. A substantial proportion of CTL epitopes in CRF01_AE infection differ from subtype B or C. However, the pattern of protective CTL responses is similar; Gag CTL responses, particularly against p24, control viral replication and slow clinical progression