The Number of Group Homomorphisms from DmD_m into DnD_n

Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into a dihedral group of order $2n$. While the solution requires only elementary group theory, the result does not appear in the literature or in the usual texts. As the solution may be of interest, particularly to those teaching undergraduate abstract algebra, it is provided in this note

Blood group typing in five Afghan populations in the North Hindu-Kush region: implications for blood transfusion practice.

International audienceBACKGROUND AND OBJECTIVES: Blood incompatibility arises from individual and ethnic differences in red blood cell (RBC) antigen profiles. This underlines the importance of documenting RBC antigen variability in various ethnic groups. Central Asia is an area with a long and complex migratory history. The purpose of this article is to describe key antigen frequencies of Afghan ethnic groups in the Hindu-Kush region of Afghanistan as a basis for improving blood transfusion practices in that area. MATERIALS AND METHODS: The key ABO, Rh and Kell antigens were investigated in five Afghan populations. In order to depict accurately the blood group gene diversity in the area, DNA from eight additional Pakistani populations were included, and the entire sample set screened using two multiplex polymerase chain reactions sensitive for 17 alleles in 10 blood group genetic systems (MNS, Kell, Duffy, Kidd, Cartwright, Dombrock, Indian, Colton, Diego and Landsteiner-Wiener). RESULTS: Phenotype and allele frequencies fell within the ranges observed in Western European and East Asian populations. Occurrence of DI*01, IN*01, LW*07 and FY*02N.01 and prevalence of ABO*B were consistent with migratory history as well as with putative environmental adaptation in the subtropical environment Hindu-Kush region. CONCLUSION: These findings expand the current knowledge about key antigen frequencies. Regarding occurrence of viral markers, further blood transfusion in the region requires rigorous typing

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.Comment: 16 pages, 2 figure

Effective spin physics in two-dimensional cavity QED arrays

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya's enumeration theorem

Evaluation of Convalescent Plasma for Ebola Virus Disease in Guinea

: In the wake of the recent outbreak of Ebola virus disease (EVD) in several African countries, the World Health Organization prioritized the evaluation of treatment with convalescent plasma derived from patients who have recovered from the disease. We evaluated the safety and efficacy of convalescent plasma for the treatment of EVD in Guinea. : In this nonrandomized, comparative study, 99 patients of various ages (including pregnant women) with confirmed EVD received two consecutive transfusions of 200 to 250 ml of ABO-compatible convalescent plasma, with each unit of plasma obtained from a separate convalescent donor. The transfusions were initiated on the day of diagnosis or up to 2 days later. The level of neutralizing antibodies against Ebola virus in the plasma was unknown at the time of administration. The control group was 418 patients who had been treated at the same center during the previous 5 months. The primary outcome was the risk of death during the period from 3 to 16 days after diagnosis with adjustments for age and the baseline cycle-threshold value on polymerase-chain-reaction assay; patients who had died before day 3 were excluded. The clinically important difference was defined as an absolute reduction in mortality of 20 percentage points in the convalescent-plasma group as compared with the control group. : A total of 84 patients who were treated with plasma were included in the primary analysis. At baseline, the convalescent-plasma group had slightly higher cycle-threshold values and a shorter duration of symptoms than did the control group, along with a higher frequency of eye redness and difficulty in swallowing. From day 3 to day 16 after diagnosis, the risk of death was 31% in the convalescent-plasma group and 38% in the control group (risk difference, -7 percentage points; 95% confidence interval [CI], -18 to 4). The difference was reduced after adjustment for age and cycle-threshold value (adjusted risk difference, -3 percentage points; 95% CI, -13 to 8). No serious adverse reactions associated with the use of convalescent plasma were observed. : The transfusion of up to 500 ml of convalescent plasma with unknown levels of neutralizing antibodies in 84 patients with confirmed EVD was not associated with a significant improvement in survival. (Funded by the European Union's Horizon 2020 Research and Innovation Program and others; ClinicalTrials.gov number, NCT02342171.).<br/

A focus on selected perspectives of the NUMEN project

The use of double charge exchange reactions is discussed in view of their application to extract information that may be helpful to determinate the nuclear matrix elements entering in the expression of neutrinoless double beta decay half-life. The strategy adopted in the experimental campaigns performed at INFN - Laboratori Nazionali del Sud and in the analysis methods within the NUMEN project is briefly described, emphasizing the advantages of the multi-channel approach to nuclear reaction data analysis. An overview on the research and development activities on the MAGNEX magnetic spectrometer is also given, with a focus on the chosen technological solutions for the focal plane detector which will guarantee the performances at high-rate conditions