PURPOSE OF REVIEW The persistence of HIV within infected CD4 T cells is a major obstacle to eradication, and assessment of the strategies to reduce HIV reservoirs is one of the major challenges. Measuring HIV reservoirs accurately will be necessary to assess those strategies. The objective of this review is to present the most recent studies that may help to define the best markers to measure H...

We construct a random matrix model for the bijection Ψ between classical and free infinitely divisible distributions: for every d ≥ 1, we associate in a quite natural way to each ∗-infinitely divisible distribution μ a distribution Pμd on the space of d×d hermitian matrices such that Pμd ∗ Pνd = P μ∗ν d . The spectral distribution of a random matrix with distribution Pμd converges in probabilit...

We give necessary and sufficient conditions for existence and infinite divisibility of α-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.

We clarify the relationship between higher étale wild kernels of a number field at the prime 2 and the Galois-coinvariants of Tate-twisted class groups in the 2cyclotomic tower of the field. We also determine the relationship between the étale wild kernel and the group of infinitely divisible elements of H(F, Z2(j + 1)){2}.

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

Let G be a finite group. We prove that every rational G-connected Hopf G-space with two nontrivial homotopy group systems is G-homotopy equivalent to an infinite loop G-space.

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID d...

We prove that many of beta, beta prime, gamma, inverse gamma, Student tand ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, many of ultraspherical and Student t-distributions have free divisibility indicator 1.