Cerebral malaria admissions in Papua New Guinea may show inter-annual cyclicity: An example of about a 1.5-year cycle for malaria incidence in Burundi

Best available descriptions of malaria incidence and mortality dynamics are important to better plan and evaluate the implementation of programs to monitor (e.g., remote sensing) and control the disease, especially in endemic zones. This was stressed recently by Cibulskis et al (2007) in the view of completeness of monthly reporting for cerebral malaria admissions in Papua New Guinea (latitude 6 degree S, 1987-1996). Notably, regardless of the rate of its completeness, the temporal dynamics of admissions was preserved over the years, however, neither raw data nor results on further analyses about eventual inter-annual cyclic components (periods T>1 year) were provided despite obvious graphical patterns for such a specific time structure (chronome). Interestingly, in a recent analysis by Gomez-Elipe et al (2007) on monthly malaria notifications in Burundi, at almost the same latitude (province of Karuzi, >3 degree S, 1997-2001), the data have shown neither trend not periodic oscillations beyond a 6-month (0.5-year) period. Since the graphical representation of both data sets have indicated an eventual existence of inter-annual variations, and because both are located at the same latitude zone, we have further analyzed the data from Burundi for such periodic oscillations. By using a periodogram regression analysis, we discovered a multicomponent cyclic chronome with periods above 12 months (T=17.5-18.0, 27.5 and 65.0-65.5 months, all at p<0.05). Notably, the most strong cyclic pattern at p<0.002 in the periodogram of the detrended malaria rates in Burundi remained only that with a peak at about 1.5 years (period T=17.5-18.0 months, R=0.51, z=5.3). It is possible that likely inter-annual cyclic patterns might exist also in the time structure for cerebral malaria admissions in Papua New Guinea and, if confirmed, these may be found very useful in epidemic forecasting and programs implementation. We explored these cyclic variations and also discussed possible associations with environmental factors exhibiting alike cyclicity

Ind--varieties of generalized flags as homogeneous spaces for classical ind--groups

The purpose of the present paper is twofold: to introduce the notion of a generalized flag in an infinite dimensional vector space $V$ (extending the notion of a flag of subspaces in a vector space), and to give a geometric realization of homogeneous spaces of the ind--groups $SL(\infty)$, $SO(\infty)$ and $Sp(\infty)$ in terms of generalized flags. Generalized flags in $V$ are chains of subspaces which in general cannot be enumerated by integers. Given a basis $E$ of $V$, we define a notion of $E$--commensurability for generalized flags, and prove that the set \cFl (\cF, E) of generalized flags E$--commensurable with a fixed generalized flag$\cF$in$V$has a natural structure of an ind--variety. In the case when$V$is the standard representation of$G = SL(\infty)$, all homogeneous ind--spaces$G/P$for parabolic subgroups$P$containing a fixed splitting Cartan subgroup of$G$, are of the form$\cFl (\cF, E)$. We also consider isotropic generalized flags. The corresponding ind--spaces are homogeneous spaces for$SO(\infty)$and$Sp(\infty)$. As an application of the construction, we compute the Picard group of$\cFl (\cF, E)$(and of its isotropic analogs) and show that$\cFl (\cF, E)$is a projective ind--variety if and only if$\cF$is a usual, possibly infinite, flag of subspaces in$V$

Thermal Breakage and Self-Healing of a Polymer Chain under Tensile Stress

We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer multidimensional theory and by extensive Molecular Dynamics simulations in 1D- and 3D-space. Comparison with simulation data in one- and three dimensions demonstrates that the Kramers-Langer theory provides good qualitative description of the process of bond-scission as caused by a {\em collective} unstable mode. We derive distributions of the probability for scission over the successive bonds along the chain which reveal the influence of chain ends on rupture in good agreement with theory. The breakage time distribution of an individual bond is found to follow an exponential law as predicted by theory. Special attention is focused on the recombination (self-healing) of broken bonds. Theoretically derived expressions for the recombination time and distance distributions comply with MD observations and indicate that the energy barrier position crossing is not a good criterion for true rupture. It is shown that the fraction of self-healing bonds increases with rising temperature and friction.Comment: 25 pages, 13 picture