BackgroundInternational travel plays a role in the spread of HIV-1 across Europe. It is, however, not known whether international travel is more important for spread of the epidemic as compared to endogenous infections within single countries. In this study, phylogenetic associations among HIV of newly diagnosed patients were determined across Europe.ResultsData came from the SPREAD programme which collects samples of newly diagnosed patients that are representative for national HIV epidemics. 4260 pol sequences from 25 European countries and Israel collected in 2002–2007 were included.We identified 457 clusters including 1330 persons (31.2% of all patients). The cluster size ranged between 2 and 28. A number of 987 patients (74.2%) were part of a cluster that consisted only of patients originating from the same country. In addition, 135 patients (10.2%) were in a cluster including only individuals from neighboring countries. Finally, 208 patients (15.6%) clustered with individuals from countries without a common border. Clustering with patients from the same country was less prevalent in patients being infected with B subtype (P-value <0.0001), in men who have sex with men (P-value <0.0001), and in recently infected patients (P-value =0.045).ConclusionsOur findings indicate that the transmission of HIV-1 in Europe is predominantly occurring between patients from the same country. This could have implications for HIV-1 transmission prevention programmes. Because infections through travelling between countries is not frequently observed it is important to have good surveillance of the national HIV-1 epidemics.
Stochastic fluctuations in the copy number of gene products have perceivable effects on the functioning of gene regulatory networks (GRN). The Master equation (ME) provides a theoretical basis for studying such effects. However, solving the ME can be a task that ranges from simple to difficult to impossible using conventional methods. Therefore, discovering new techniques for solving the ME is an important part of research on stochastic GRN. In this paper, we present a novel approach to obtaining the generating function (GF), which contains the same information as the ME, for a one gene system that includes multi-step post-transcription and post-translation processes. The novelty of the approach lies in the separation of the mRNAs from proteins. The GF for the mRNAs is obtained using a formalism involving operators and vector states. Using the same formalism, the GF for the proteins is solved for a particular path taken by all mRNAs in the time-copy number plane; then, the GF is summed over all possible paths. We prove a theorem that shows the summation of all paths to be equivalent to an equation similar to the ME for the mRNAs. On a system with six gene products in total and randomly selected initial conditions, we confirm the validity of our results by comparing them with Gillespie simulations.
We study the violation of the Bell-Clauser-Horne-Shimony-Holt ͑Bell-CHSH͒ inequality for two-spin systems, of arbitrary spins j 1 and j 2 , prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, 2 ͱ 2, for any choices of the spins. Over the past 30 years or more, there has been interest in the question of whether or not classical realism, as embodied in various versions of Bell's theorem, is recovered in the limit of large quantum numbers, generally assumed to be the classical limit as per the correspondence principle. Some years ago, Garg and Mermin ͓1͔ studied Bell's inequality for two-spin j particles in a singlet state, given asand found violations for measurements along almost all pairs of directions. However, the magnitude of the violation decreased with increasing j, the decrease being the result of the author's use of a slowly varying function of the spin components which made their method insensitive to the rapidly varying part of the correlations. Later, Peres ͓2͔ pointed out that the Stern-Gerlach experiment, for arbitrary angular momentum, measures the dichotomic operatorif the detectors are positioned such that the 2j + 1 beams are well separated. The operator ̂͑ j͒ is just the parity operator for the D ͑j͒ unitary irreducible representation of SU͑2͒. Using this observable, Peres found that the violations of Bell's theorem, as given in the form of the Clauser, Horne, Shimony, and Holt ͑Bell-CHSH͒ inequality ͓3͔, remains constant in the limit j → ϱ. Gerry and Albert ͓4͔ proposed an optical scheme for generating states that are very close to the spin-singlet states. These were two-mode field states that could be produced by the action of a 50:50 beam splitter on an input state containing N photons in one port and the vacuum at the other. The identification of the output state with a spin-j singletlike state, with j = N / 2, comes about by introducing a Holstein-Primakoff ͓5͔ realization of the SU͑2͒ algebra for each of the photon modes. The corresponding violations of the Bell-CHSH inequality, using displacement operations performed with beam splitters of low transmittance and a strong classical-like field at the other input port, followed by photon parity measurements, were discussed in Ref. ͓4͔.Mermin and Schwartz ͓6͔ pointed out that there really is no reason to expect classical behavior to be approached in the limit of large spin, as the measurements that discriminate between the 2j + 1 values of M, no matter how large j, have a nonclassical character. Of course, what really matters is the degree to which the two particles in the singlet state of Eq. ͑1͒ remain entangled as j → ϱ. The linear entropy for particle 1, given as S 1 =1−Tr 1 1 2 , where 1 =Tr 2 ͓ 12 ͔, and where 12 = ͉SS͗͘SS͉, is easily...
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