We adopt the following rules: n is a natural number and x1, x2, x3, x4, x5, y1, y2, y3 are sets. Let x1, x2, x3, x4, x5 be sets. We say that x1, x2, x3, x4, x5 are mutually different if and only if: (Def. 1) x1 6= x2 and x1 6= x3 and x1 6= x4 and x1 6= x5 and x2 6= x3 and x2 6= x4 and x2 6= x5 and x3 6= x4 and x3 6= x5 and x4 6= x5. Next we state several propositions: (1) If x1, x2, x3, x4, x5 ...

Solution. The Markov blanket of a node in a undirected graphical model equals the set of its neighbours: MB(x4) = ne(x4) = ne4 = {x1, x5}. This implies, for example, that x4 ⊥ x2, x3 | x1, x5. (e) On which minimal set of variables A do we need to condition to have x1 ⊥ x5 | A? Solution. We first identify all trails from x1 to x5. There are three such trails: (x1, x2, x5), (x1, x3, x2, x5), and ...

OBJECTIVES Tropism evolution of HIV-1 quasispecies was analysed by ultra-deep pyrosequencing (UDPS) in patients on first-line combination antiretroviral therapy (cART) always suppressed or experiencing virological failure episodes. METHODS Among ICONA patients, two groups of 20 patients on cART for ≥5 years, matched for baseline viraemia and therapy duration, were analysed [Group I, patients ...

This study compared HIV-1 genotypes shed over time (≤3.5 years) in the vaginal secretions (VS) and blood plasma (BP) of 15 chronically infected women. Analysis of predicted coreceptor tropism (CCR5=R5, CXCR4=X4) for quasispecies shedding revealed three patterns: (1) viral quasispecies shed in both VS and BP were restricted to R5-tropism at all time points, (2) quasispecies shed in VS were restr...

Dual/mixed-tropic HIV-1 strains are predominant in a significative proportion of patients, though few information is available regarding the genetic characteristics, quasispecies composition, and susceptibility against CCR5-antagonists of the primary-isolates. For this reason, we investigated in deep details, both phenotypically and genotypically, the characteristics of 54 HIV-1 primary-isolate...

OBJECTIVE The association between emergence of CXCR4-tropic HIV-1 variants (X4 variants) and disease progression of HIV-1 infection has been reported. However, it is not known whether the emergence of X4 variants is the cause or result of HIV-1 disease progression. We tried to answer this question. DESIGN HIV-1 env sequences around the V3 region were analyzed in serially stocked samples in or...

The emergence of CXCR4-using HIV variants (X4-HIV) is associated with accelerated disease progression in the absence of antiretroviral therapy. However, the effect of X4-HIV variants on the treatment response remains unclear. Here we determined whether the presence of X4-HIV variants influenced the time to undetectable viral load and CD4+ T cell reconstitution after initiation of cART in 732 pa...

BACKGROUND CCR5-using (r5) HIV-1 predominates during asymptomatic disease followed by occasional emergence of CXCR4-using (x4) or dual tropic (r5x4) virus. We examined the contribution of the x4 and r5 components to replicative fitness of HIV-1 isolates. METHODS Dual tropic r5x4 viruses were predicted from average HIV-1 env sequences of two primary subtype C HIV-1 isolates (C19 and C27) and f...

The clinical trials of maraviroc showed that treatment failure was mostly associated with lack of X4 virus detection at baseline. The detection limit for X4 in tropism assays is ill defined around 10%. In the current study, quantification of X4-tropic minority populations was assessed on artificial mixed samples and 38 clinical isolates. These mixtures were subjected to tropism "clonal genotypi...

In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).