General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi

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

Towards Autopoietic Computing

A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems increasingly difficult. Biological systems are thought to possess robust, scalable processing paradigms that can automatically manage complex, dynamic problem spaces, possessing several properties that may be useful in computer systems. The biological properties of self-organisation, self-replication, self-management, and scalability are addressed in an interesting way by autopoiesis, a descriptive theory of the cell founded on the concept of a system's circular organisation to define its boundary with its environment. In this paper, therefore, we review the main concepts of autopoiesis and then discuss how they could be related to fundamental concepts and theories of computation. The paper is conceptual in nature and the emphasis is on the review of other people's work in this area as part of a longer-term strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure

Pain outcomes in patients with bone metastases from advanced cancer: assessment and management with bone-targeting agents

Bone metastases in advanced cancer frequently cause painful complications that impair patient physical activity and negatively affect quality of life. Pain is often underreported and poorly managed in these patients. The most commonly used pain assessment instruments are visual analogue scales, a single-item measure, and the Brief Pain Inventory Questionnaire-Short Form. The World Health Organization analgesic ladder and the Analgesic Quantification Algorithm are used to evaluate analgesic use. Bone-targeting agents, such as denosumab or bisphosphonates, prevent skeletal complications (i.e., radiation to bone, pathologic fractures, surgery to bone, and spinal cord compression) and can also improve pain outcomes in patients with metastatic bone disease. We have reviewed pain outcomes and analgesic use and reported pain data from an integrated analysis of randomized controlled studies of denosumab versus the bisphosphonate zoledronic acid (ZA) in patients with bone metastases from advanced solid tumors. Intravenous bisphosphonates improved pain outcomes in patients with bone metastases from solid tumors. Compared with ZA, denosumab further prevented pain worsening and delayed the need for treatment with strong opioids. In patients with no or mild pain at baseline, denosumab reduced the risk of increasing pain severity and delayed pain worsening along with the time to increased pain interference compared with ZA, suggesting that use of denosumab (with appropriate calcium and vitamin D supplementation) before patients develop bone pain may improve outcomes. These data also support the use of validated pain assessments to optimize treatment and reduce the burden of pain associated with metastatic bone disease

Palaeoproterozoic magnesite: lithological and isotopic evidence for playa/sabkha environments

Magnesite forms a series of 1- to 15-m-thick beds within the approximate to2.0 Ga (Palaeoproterozoic) Tulomozerskaya Formation, NW Fennoscandian Shield, Russia. Drillcore material together with natural exposures reveal that the 680-m-thick formation is composed of a stromatolite-dolomite-'red bed' sequence formed in a complex combination of shallow-marine and non-marine, evaporitic environments. Dolomite-collapse breccia, stromatolitic and micritic dolostones and sparry allochemical dolostones are the principal rocks hosting the magnesite beds. All dolomite lithologies are marked by delta C-13 values from +7.1 parts per thousand to +11.6 parts per thousand (V-PDB) and delta O-18 ranging from 17.4 parts per thousand to 26.3 parts per thousand (V-SMOW). Magnesite occurs in different forms: finely laminated micritic; stromatolitic magnesite; and structureless micritic, crystalline and coarsely crystalline magnesite. All varieties exhibit anomalously high delta C-13 values ranging from +9.0 parts per thousand to +11.6 parts per thousand and delta O-18 values of 20.0-25.7 parts per thousand. Laminated and structureless micritic magnesite forms as a secondary phase replacing dolomite during early diagenesis, and replaced dolomite before the major phase of burial. Crystalline and coarsely crystalline magnesite replacing micritic magnesite formed late in the diagenetic/metamorphic history. Magnesite apparently precipitated from sea water-derived brine, diluted by meteoric fluids. Magnesitization was accomplished under evaporitic conditions (sabkha to playa lake environment) proposed to be similar to the Coorong or Lake Walyungup coastal playa magnesite. Magnesite and host dolostones formed in evaporative and partly restricted environments; consequently, extremely high delta C-13 values reflect a combined contribution from both global and local carbon reservoirs. A C- 13-rich global carbon reservoir (delta C-13 at around +5 parts per thousand) is related to the perturbation of the carbon cycle at 2.0 Ga, whereas the local enhancement in C-13 (up to +12 parts per thousand) is associated with evaporative and restricted environments with high bioproductivity

A pilot Internet "Value of Health" Panel: recruitment, participation and compliance

Objectives To pilot using a panel of members of the public to provide preference data via the Internet Methods A stratified random sample of members of the general public was recruited and familiarised with the standard gamble procedure using an Internet based tool. Health states were perdiodically presented in "sets" corresponding to different conditions, during the study. The following were described: Recruitment (proportion of people approached who were trained); Participation (a) the proportion of people trained who provided any preferences and (b) the proportion of panel members who contributed to each "set" of values; and Compliance (the proportion, per participant, of preference tasks which were completed). The influence of covariates on these outcomes was investigated using univariate and multivariate analyses. Results A panel of 112 people was recruited. 23% of those approached (n = 5,320) responded to the invitation, and 24% of respondents (n = 1,215) were willing to participate (net = 5.5%). However, eventual recruitment rates, following training, were low (2.1% of those approached). Recruitment from areas of high socioeconomic deprivation and among ethnic minority communities was low. Eighteen sets of health state descriptions were considered over 14 months. 74% of panel members carried out at least one valuation task. People from areas of higher socioeconomic deprivation and unmarried people were less likely to participate. An average of 41% of panel members expressed preferences on each set of descriptions. Compliance ranged from 3% to 100%. Conclusion It is feasible to establish a panel of members of the general public to express preferences on a wide range of health state descriptions using the Internet, although differential recruitment and attrition are important challenges. Particular attention to recruitment and retention in areas of high socioeconomic deprivation and among ethnic minority communities is necessary. Nevertheless, the panel approach to preference measurement using the Internet offers the potential to provide specific utility data in a responsive manner for use in economic evaluations and to address some of the outstanding methodological uncertainties in this field

DNA models of trinucleotide frameshift deletions: the formation of loops and bulges at the primer–template junction

Although mechanisms of single-nucleotide residue deletion have been investigated, processes involved in the loss of longer nucleotide sequences during DNA replication are poorly understood. Previous reports have shown that in vitro replication of a 3′-TGC TGC template sequence can result in the deletion of one 3′-TGC. We have used low-energy circular dichroism (CD) and fluorescence spectroscopy to investigate the conformations and stabilities of DNA models of the replication intermediates that may be implicated in this frameshift. Pyrrolocytosine or 2-aminopurine residues, site-specifically substituted for cytosine or adenine in the vicinity of extruded base sequences, were used as spectroscopic probes to examine local DNA conformations. An equilibrium mixture of four hybridization conformations was observed when template bases looped-out as a bulge, i.e. a structure flanked on both sides by duplex DNA. In contrast, a single-loop structure with an unusual unstacked DNA conformation at its downstream edge was observed when the extruded bases were positioned at the primer–template junction, showing that misalignments can be modified by neighboring DNA secondary structure. These results must be taken into account in considering the genetic and biochemical mechanisms of frameshift mutagenesis in polymerase-driven DNA replication