The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment

We present proofs, based on the Shapley-Folkman theorem, of the convexity of the range of a strongly continuous, finitely additive measure, as well as that of an atomless, countably additive measure. We also present proofs, based on diagonalization and separation arguments respectively, of the closure of the range of a purely atomic or purely nonatomic countably additive measure. A combination of these results yields Lyapunov's celebrated theorem on the range of a countably additive measure. We also sketch, through a comprehensive bibliography, the pervasive diversity of the applications of the Shapley-Folkman theorem in mathematical economics.

On Large Games with a Bio-Social Typology

We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.

Preliminary study of feasibility of an experiment looking for excited state double beta transitions in tin

An attempt to study the feasibility of a new experiment to search for double beta decay in $^{112}$Sn and $^{124}$Sn was carried out by using ultra-low background HPGe detector (244 cm$^{3}$) inside the Gran Sasso National Laboratory (LNGS) of the INFN (Italy). A small sample of natural Sn was examined for 2367.5 h. The radioactive contamination of the sample has been estimated. The data has also been considered to calculate the present sensitivity for the proposed search; half-life limits $\sim$ $10^{17} - 10^{18}$ years for $\beta^{+}$EC and EC-EC processes in $^{112}$Sn and $\sim$ $10^{18}$ years for $\beta^{-}\beta^{-}$ transition in $^{124}$Sn were measured. In the last section of the paper the enhancement of the sensitivity for a proposed experiment with larger mass to reach theoretically estimated values of half-lives is discussed.Comment: 20 pages, 11 figures, 4 tables, accepted for publication in NIMA (in press

arrayMap 2014: an updated cancer genome resource.

Somatic copy number aberrations (CNA) represent a mutation type encountered in the majority of cancer genomes. Here, we present the 2014 edition of arrayMap (http://www.arraymap.org), a publicly accessible collection of pre-processed oncogenomic array data sets and CNA profiles, representing a vast range of human malignancies. Since the initial release, we have enhanced this resource both in content and especially with regard to data mining support. The 2014 release of arrayMap contains more than 64,000 genomic array data sets, representing about 250 tumor diagnoses. Data sets included in arrayMap have been assembled from public repositories as well as additional resources, and integrated by applying custom processing pipelines. Online tools have been upgraded for a more flexible array data visualization, including options for processing user provided, non-public data sets. Data integration has been improved by mapping to multiple editions of the human reference genome, with the majority of the data now being available for the UCSC hg18 as well as GRCh37 versions. The large amount of tumor CNA data in arrayMap can be freely downloaded by users to promote data mining projects, and to explore special events such as chromothripsis-like genome patterns

Effect of Strain of Holstein-Friesian Cow and Feed System on Reproductive Performance in Seasonal-Calving Milk Production Systems Over Four Years

In Ireland most dairy farms operate seasonal calving grass-based milk production systems. Feed demand and supply are matched by having calving highly concentrated in spring. This requires high pregnancy rates within a short time following the start of mating in late April or early May, but has become increasingly difficult to achieve due to declining fertility in Irish dairy herds (Mee, 2004). In New Zealand, cows of North American Holstein-Friesian origin have poorer fertility than New Zealand Holstein-Friesians on pasture-based seasonal calving systems (Harris & Kolver, 2001). The present study sought to determine the effect of strain of Holstein-Friesian (HF) cow and feed system on reproductive performance within Irish milk production systems