Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

A new multivariable 6-psi-6 summation formula

By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynomial argument this 8-phi-7 summation is transformed to another multivariable 8-phi-7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6-phi-5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6-psi-6 summation formula.Comment: 16 page

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

Emerging Issues in Virus Taxonomy

Viruses occupy a unique position in biology. Although they possess some of the properties of living systems such as having a genome, they are actually nonliving infectious entities and should not be considered microorganisms. A clear distinction should be drawn between the terms virus, virion, and virus species. Species is the most fundamental taxonomic category used in all biological classification. In 1991, the International Committee on Taxonomy of Viruses (ICTV) decided that the category of virus species should be used in virus classification together with the categories of genus and family. More than 50 ICTV study groups were given the task of demarcating the 1,550 viral species that were recognized in the 7th ICTV report, which was published in 2000. We briefly describe the changes in virus classification that were introduced in that report. We also discuss recent proposals to introduce a nonlatinized binomial nomenclature for virus species

Heterogeneity of luminal breast cancer characterised by immunohistochemical expression of basal markers

Background: Luminal A breast cancer defined as hormone receptor positive and human epidermal growth factor receptor 2 (HER2) negative is known to be heterogeneous. Previous study showed that luminal A tumours with the expression of basal markers ((cytokeratin (CK) 5 or CK5/6) or epidermal growth factor receptor (EGFR)) were associated with poorer prognosis compared with those that stained negative for basal markers. Prompted by this study, we assessed whether tumour characteristics and risk factors differed by basal marker status within luminal A tumours. Methods: We pooled 5040 luminal A cases defined by immunohistochemistry (4490 basal-negative ((CK5 (or CK5/6))− and EGFR−) and 550 basal-positive ((CK5 (or CK5/6+)) or EGFR+)) from eight studies participating in the Breast Cancer Association Consortium. Case–case comparison was performed using unconditional logistic regression. Results: Tumour characteristics and risk factors did not vary significantly by the expression of basal markers, although results suggested that basal-positive luminal tumours tended to be smaller and node negative, and were more common in women with a positive family history and lower body mass index. Conclusions: Most established breast cancer risk factors were similar in basal-positive and basal-negative luminal A tumours. The non-significant but suggestive differences in tumour features and family history warrant further investigations

Crowdsourcing the General Public for Large Scale Molecular Pathology Studies in Cancer

Background: Citizen science, scientific research conducted by non-specialists, has the potential to facilitate biomedical research using available large-scale data, however validating the results is challenging. The Cell Slider is a citizen science project that intends to share images from tumors with the general public, enabling them to score tumor markers independently through an internet-based interface. Methods: From October 2012 to June 2014, 98,293 Citizen Scientists accessed the Cell Slider web page and scored 180,172 sub-images derived from images of 12,326 tissue microarray cores labeled for estrogen receptor (ER). We evaluated the accuracy of Citizen Scientist's ER classification, and the association between ER status and prognosis by comparing their test performance against trained pathologists. Findings: The area under ROC curve was 0.95 (95% CI 0.94 to 0.96) for cancer cell identification and 0.97 (95% CI 0.96 to 0.97) for ER status. ER positive tumors scored by Citizen Scientists were associated with survival in a similar way to that scored by trained pathologists. Survival probability at 15 years were 0.78 (95% CI 0.76 to 0.80) for ER-positive and 0.72 (95% CI 0.68 to 0.77) for ER-negative tumors based on Citizen Scientists classification. Based on pathologist classification, survival probability was 0.79 (95% CI 0.77 to 0.81) for ER-positive and 0.71 (95% CI 0.67 to 0.74) for ER-negative tumors. The hazard ratio for death was 0.26 (95% CI 0.18 to 0.37) at diagnosis and became greater than one after 6.5 years of follow-up for ER scored by Citizen Scientists, and 0.24 (95% CI 0.18 to 0.33) at diagnosis increasing thereafter to one after 6.7 (95% CI 4.1 to 10.9) years of follow-up for ER scored by pathologists. Interpretation: Crowdsourcing of the general public to classify cancer pathology data for research is viable, engages the public and provides accurate ER data. Crowdsourced classification of research data may offer a valid solution to problems of throughput requiring human input

High-throughput automated scoring of Ki67 in breast cancer tissue microarrays from the Breast Cancer Association Consortium (BCAC)

Automated methods are needed to facilitate high-throughput and reproducible scoring of Ki67 and other markers in breast cancer tissue microarrays (TMAs) in large-scale studies. To address this need, we developed an automated protocol for Ki67 scoring and evaluated its performanc

Bounds on the possible evolution of the Gravitational Constant from Cosmological Type-Ia Supernovae

Recent high-redshift Type Ia supernovae results can be used to set new bounds on a possible variation of the gravitational constant $G$. If the local value of $G$ at the space-time location of distant supernovae is different, it would change both the kinetic energy release and the amount of $^{56}$Ni synthesized in the supernova outburst. Both effects are related to a change in the Chandrasekhar mass $M_{Ch} \propto G^{-3/2}$. In addition, the integrated variation of $G$ with time would also affect the cosmic evolution and therefore the luminosity distance relation. We show that the later effect in the magnitudes of Type Ia supernovae is typically several times smaller than the change produced by the corresponding variation of the Chandrasekhar mass. We investigate in a consistent way how a varying $G$ could modify the Hubble diagram of Type Ia supernovae and how these results can be used to set upper bounds to a hypothetical variation of $G$. We find G/G_0 \la 1.1 and G'/G \la 10^{-11} yr^{-1} at redshifts $z\simeq 0.5$. These new bounds extend the currently available constrains on the evolution of $G$ all the way from solar and stellar distances to typical scales of Gpc/Gyr, i.e. by more than 15 orders of magnitudes in time and distance.Comment: 9 pages, 4 figures, Phys. Rev. D. in pres