Statistics on continuous IBD data: Exact distribution evaluation for a pair of full(half)-sibs and a pair of a (great-) grandchild with a (great-) grandparent

BACKGROUND: Pairs of related individuals are widely used in linkage analysis. Most of the tests for linkage analysis are based on statistics associated with identity by descent (IBD) data. The current biotechnology provides data on very densely packed loci, and therefore, it may provide almost continuous IBD data for pairs of closely related individuals. Therefore, the distribution theory for statistics on continuous IBD data is of interest. In particular, distributional results which allow the evaluation of p-values for relevant tests are of importance. RESULTS: A technology is provided for numerical evaluation, with any given accuracy, of the cumulative probabilities of some statistics on continuous genome data for pairs of closely related individuals. In the case of a pair of full-sibs, the following statistics are considered: (i) the proportion of genome with 2 (at least 1) haplotypes shared identical-by-descent (IBD) on a chromosomal segment, (ii) the number of distinct pieces (subsegments) of a chromosomal segment, on each of which exactly 2 (at least 1) haplotypes are shared IBD. The natural counterparts of these statistics for the other relationships are also considered. Relevant Maple codes are provided for a rapid evaluation of the cumulative probabilities of such statistics. The genomic continuum model, with Haldane's model for the crossover process, is assumed. CONCLUSIONS: A technology, together with relevant software codes for its automated implementation, are provided for exact evaluation of the distributions of relevant statistics associated with continuous genome data on closely related individuals

Born-Infeld black holes coupled to a massive scalar field

Born-Infeld black holes in the Scalar-Tensor Theories of Gravity, in the case of massless scalar field, have been recently obtained. The aim of the current paper is to study the effect from the inclusion of a potential for the scalar field in the theory, through a combination of analytical techniques and numerical methods. The black holes coupled to a massive scalar field have richer causal structure in comparison to the massless scalar field case. In the latter case, the black holes may have a second, inner horizon. The presence of potential for the scalar field allows the existence of extremal black holes for certain values of the mass of the scalar field and the magnetic (electric) charge of the black hole. The linear stability against spherically symmetric perturbations is studied. Arguments in favor of the general stability of the solutions coming from the application of the "turning point" method are also presented.Comment: 26 pages, 16 figure

Quantitative Photo-acoustic Tomography with Partial Data

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and improve an earlier result of Bal and Uhlmann to the partial date case. We show that the reconstruction can be uniquely determined by the knowledge of 4 internal data based on well-chosen partial boundary conditions. Stability of this reconstruction is ensured if a convexity condition is satisfied. Similar stability result is obtained without this geometric constraint if 4n well-chosen partial boundary conditions are available, where $n$ is the spatial dimension. The set of well-chosen boundary measurements is characterized by some complex geometric optics (CGO) solutions vanishing on a part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250

Case Study on Limits and Consequences of Agricultural Technologies in the North-East Region of the People's Republic of Bulgaria

The Food and Agriculture Program at IIASA focuses its research activities on understanding the nature and dimension of the world's food situation and problems, on exploring possible alternative policies which could improve the present situation in the short and long term, and on investigating the consequences of such policies at various levels -- global, national and regional -- and in various time horizons. One part of the research activities focussed on investigations of alternative paths of technology transformation in agriculture with respect to resource limitations and environmental consequences in the long term. The general approach and methodology developed for this investigation is being applied in several case studies on the regional level. The reason for the studies is not only to validate the general methodology but also to develop an applicable tool for detailed investigations for a particular region which could then be applied on a number of similar regions. Furthermore, some specific aspects are being addressed in all these case studies which has been initiated within the IIASA's Food and Agriculture Program. This will allow the behavior of various systems to be compared, according to the selected aspects, and analyzed (in different social, economic and natural resource conditions) according to the selected aspects. One of the case studies is being carried out for the north-east region of Bulgaria. This paper describes the first phase of the study, the problem identification, the formulation of goals, and the basic methodological framework