A class of infinitely divisible multivariate negative binomial distributions

AbstractA particular class of multivariate negative binomial distributions has probability generating functions of the form |I−Q|α|I−QS|−α, where α>0 and S=diag(s1, …, sn). The main results of this paper concern characterizations of the infinitely divisible distributions of this class

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure

Einstein energy associated with the Friedmann -Robertson -Walker metric

Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general formula for the total matter plus gravitational field energy ($P_0$) of an arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C., {\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962)); Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in quasi-Cartesian coordinates, this formula leads to the well known result $P_0 = \int \sqrt{-g} (T_0^0 - T_1^1 -T_2^2 -T_3^3) ~d^3 x$, where $g$ is the determinant of the metric tensor and $T^a_b$ is the energy momentum tensor of the {\em matter}. Though in the literature, this is known as "Tolman Mass", it must be realized that this is essentially "Einstein Mass" because the underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz obtained the same expression for the "inertial mass" of a static isolated system without using any pseudo-tensor at all and which points to physical significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz, E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed., 1962)! For the first time we apply this general formula to find an expression for $P_0$ for the Friedmann- Robertson -Walker (FRW) metric by using the same quasi-Cartesian basis. As we analyze this new result, physically, a spatially flat model having no cosmological constant is suggested. Eventually, it is seen that conservation of $P_0$ is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the journal version is uploade

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Novel PLS3 variants in X-linked osteoporosis: Exploring bone material properties

BACKGROUND: Idiopathic Juvenile Osteoporosis (IJO) refers to significantly lower than expected bone mass manifesting in childhood with no identifiable aetiology. IJO classically presents in early pubertal period with multiple fractures including metaphyseal and vertebral crush fractures, and low bone-mass. METHODS: Here we describe two patients and provide information on their clinical phenotype, genotype and bone material analysis in one of the patients. RESULTS: Patient 1: 40-year old adult male diagnosed with IJO in childhood who re-presented with a hip fracture as an adult. Genetic analysis identified a pathogenic PLS3 hemizygous variant, c.1765del in exon 16. Patient 2: 15-year old boy with multiple vertebral fractures and bone biopsy findings suggestive of IJO who also has a diagnosis of autism spectrum disorder. Genetic analysis identified a maternally inherited PLS3 pathogenic c.1295T>A variant in exon 12. Analyses of the transiliac bone sample revealed severe reduction of trabecular volume and bone turnover indices and elevated bone matrix mineralisation. DISCUSSION: We propose that genetic testing for PLS3 should be undertaken in patients presenting with a current or previous history of IJO as this has implications for genetic counselling and cascade screening. The extensive evaluation of the transiliac biopsy sample of Patient 2 revealed a novel bone phenotype. CONCLUSION: This report includes a review of IJO and genetic causes of osteoporosis, and suggests that existing cases of IJO should be screened for PLS3. Through analysis of bone material properties in Patient 2, we can conclude that PLS3 does have a role in bone mineralisation

Genetically Determined Height and Risk of Non-hodgkin Lymphoma

Although the evidence is not consistent, epidemiologic studies have suggested that taller adult height may be associated with an increased risk of some non-Hodgkin lymphoma (NHL) subtypes. Height is largely determined by genetic factors, but how these genetic factors may contribute to NHL risk is unknown. We investigated the relationship between genetic determinants of height and NHL risk using data from eight genome-wide association studies (GWAS) comprising 10,629 NHL cases, including 3,857 diffuse large B-cell lymphoma (DLBCL), 2,847 follicular lymphoma (FL), 3,100 chronic lymphocytic leukemia (CLL), and 825 marginal zone lymphoma (MZL) cases, and 9,505 controls of European ancestry. We evaluated genetically predicted height by constructing polygenic risk scores using 833 height-associated SNPs. We used logistic regression to estimate odds ratios (OR) and 95% confidence intervals (CI) for association between genetically determined height and the risk of four NHL subtypes in each GWAS and then used fixed-effect meta-analysis to combine subtype results across studies. We found suggestive evidence between taller genetically determined height and increased CLL risk (OR = 1.08, 95% CI = 1.00\u20131.17, p = 0.049), which was slightly stronger among women (OR = 1.15, 95% CI: 1.01\u20131.31, p = 0.036). No significant associations were observed with DLBCL, FL, or MZL. Our findings suggest that there may be some shared genetic factors between CLL and height, but other endogenous or environmental factors may underlie reported epidemiologic height associations with other subtypes

Distinct germline genetic susceptibility profiles identified for common non-Hodgkin lymphoma subtypes

Lymphoma risk is elevated for relatives with common non-Hodgkin lymphoma (NHL) subtypes, suggesting shared genetic susceptibility across subtypes. To evaluate the extent of mutual heritability among NHL subtypes and discover novel loci shared among subtypes, we analyzed data from eight genome-wide association studies within the InterLymph Consortium, including 10,629 cases and 9505 controls. We utilized Association analysis based on SubSETs (ASSET) to discover loci for subsets of NHL subtypes and evaluated shared heritability across the genome using Genome-wide Complex Trait Analysis (GCTA) and polygenic risk scores. We discovered 17 genome-wide significant loci (P < 5 × 10−8) for subsets of NHL subtypes, including a novel locus at 10q23.33 (HHEX) (P = 3.27 × 10−9). Most subset associations were driven primarily by only one subtype. Genome-wide genetic correlations between pairs of subtypes varied broadly from 0.20 to 0.86, suggesting substantial heterogeneity in the extent of shared heritability among subtypes. Polygenic risk score analyses of established loci for different lymphoid malignancies identified strong associations with some NHL subtypes (P < 5 × 10−8), but weak or null associations with others. Although our analyses suggest partially shared heritability and biological pathways, they reveal substantial heterogeneity among NHL subtypes with each having its own distinct germline genetic architecture