The rank of the semigroup of transformations stabilising a partition of a finite set

Let $\mathcal{P}$ be a partition of a finite set $X$. We say that a full transformation $f:X\to X$ preserves (or stabilizes) the partition $\mathcal{P}$ if for all $P\in \mathcal{P}$ there exists $Q\in \mathcal{P}$ such that $Pf\subseteq Q$. Let $T(X,\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\mathcal{P}$. In 2005 Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is a partition in which all of its parts have the same size. In addition, Huisheng conjectured that his bound was exact. In 2009 the first and last authors used representation theory to completely solve Hisheng's conjecture. The goal of this paper is to solve the much more complex problem of finding the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is an arbitrary partition. Again we use representation theory to find the minimum number of elements needed to generate the wreath product of finitely many symmetric groups, and then use this result to solve the problem. The paper ends with a number of problems for experts in group and semigroup theories

Hydrologic Data for Urban Studies in the Austin, Texas Metropolitan Area, 1980

This report includes drainage basin maps and information from a specific storm (May 12, 1980) for the 23rd and 38th street Waller Creek locations.Waller Creek Working Grou

A New Metaheuristic Bat-Inspired Algorithm

Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and harmony search are now becoming powerful methods for solving many tough optimization problems. In this paper, we propose a new metaheuristic method, the Bat Algorithm, based on the echolocation behaviour of bats. We also intend to combine the advantages of existing algorithms into the new bat algorithm. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing algorithms, including genetic algorithms and particle swarm optimization. Simulations show that the proposed algorithm seems much superior to other algorithms, and further studies are also discussed.Comment: 10 pages, 2 figure

Can osteophagia provide giraffes with phosphorus and calcium?

The daily requirement for calcium and phosphorus by giraffes to sustain the growth and maintenance of their skeletons is large. The source of sufficient calcium is browse. The source of necessary phosphorus is obscure, but it could be osteophagia, a frequently observed behaviour in giraffes. We have assessed whether bone ingested as a result of osteophagia can be digested in the rumen. Bone samples from cancellous (cervical vertebrae) and dense bones (metacarpal shaft) were immersed in the rumens of five sheep, for a period of up to 30 days, and the effect compared to immersion in distilled water and in artificial saliva for 30 days. Distilled water had no effect on the bones. Dense bone samples were softened by exposure to the saliva and rumen fluid, but did not lose either calcium or phosphorus. In saliva and rumen fluid the cancellous bone samples also softened, and their mass and volume decreased as a result of exposure to saliva, but in neither fluid did they lose significant amounts of calcium and phosphorus. We conclude that although saliva and rumen fluid can soften ingested bones, there is an insignificant digestion of bones in the rumen

The effects of graded levels of calorie restriction : II. Impact of short term calorie and protein restriction on circulating hormone levels, glucose homeostasis and oxidative stress in male C57BL/6 mice

This work was supported by BBSRC BB009953/1 awarded to JRS and SEM. PK and CD were funded by the Erasmus exchange programme. JRS, SEM, DD, CG, LC, JJDH, YW, DELP, DL and AD are members of the BBSRC China Partnership Award, BB/J020028/1.Peer reviewedPublisher PD

Achieving Health Equity in Embedded Pragmatic Trials for People Living with Dementia and Their Family Caregivers

Embedded pragmatic clinical trials (ePCTs) advance research on Alzheimer's disease/Alzheimer's disease and related dementias (AD/ADRD) in real-world contexts; however, health equity issues have not yet been fully considered, assessed, or integrated into ePCT designs. Health disparity populations may not be well represented in ePCTs without special efforts to identify and successfully recruit sites of care that serve larger numbers of these populations. The National Institute on Aging (NIA) Imbedded Pragmatic Alzheimer's disease (AD) and AD-Related Dementias (AD/ADRD) Clinical Trials (IMPACT) Collaboratory's Health Equity Team will contribute to the overall mission of the collaboratory by developing and implementing strategies to address health equity in the conduct of ePCTs and ensure the collaboratory is a national resource for all Americans with dementia. As a first step toward meeting these goals, this article reviews what is currently known about the inclusion of health disparities populations of people living with dementia (PLWD) and their caregivers in ePCTs, highlights unique challenges related to health equity in the conduct of ePCTs, and suggests priority areas in the design and implementation of ePCTs to increase the awareness and avoidance of pitfalls that may perpetuate and magnify healthcare disparities

Nucleotide Frequencies in Human Genome and Fibonacci Numbers

This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff's second parity rule should be valid, and, second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. It is noteworthy, that the predicted values are solutions of an optimization problem, which is commonplace in many nature's phenomena.Comment: 12 pages, 2 figure

Allometric analysis of the giraffe cardiovascular system

There has been co-evolution of a long neck and high blood pressure in giraffes. How the cardiovascular system (CVS) has adapted to produce a high blood pressure, and how it compares with other similar sized mammals largely is unknown. We have measured body mass and heart structure in 56 giraffes of both genders ranging in body mass from 18 kg to 1500 kg, and developed allometric equations that relate changes in heart dimensions to growth and to cardiovascular function. Predictions made from these equations match measurements made in giraffes. We have found that heart mass increases as body mass increases but it has a relative mass of 0.51±0.7% of body mass which is the same as that in other mammals. The left ventricular and interventricular walls are hypertrophied and their thicknesses are linearly related to neck length. Systemic blood pressure increases as body mass and neck length increase and is twice that of mammals of the same body mass. Cardiac output is the same as, but peripheral resistance double that predicted for similar sized mammals. We have concluded that increasing hydrostatic pressure of the column of blood during neck elongation results in cardiac hypertrophy and concurrent hypertrophy of arteriole walls raising peripheral resistance, with an increase in blood pressure following.The Bubye Valley Conservancy, Zimbabwe and the Don Craib Trust (JDS), from a personal research grant (JDS) and the University of Wyoming (GM).http://www.elsevier.com/locate/cbpamn201

A measurement of parity-violating gamma-ray asymmetries in polarized cold neutron capture on 35Cl, 113Cd, and 139La

An apparatus for measuring parity-violating asymmetries in gamma-ray emission following polarized cold neutron capture was constructed as a 1/10th scale test of the design for the forthcoming n+p->d+gamma experiment at LANSCE. The elements of the polarized neutron beam, including a polarized 3He neutron spin filter and a radio frequency neutron spin rotator, are described. Using CsI(Tl) detectors and photodiode current mode readout, measurements were made of asymmetries in gamma-ray emission following neutron capture on 35Cl, 113Cd, and 139La targets. Upper limits on the parity-allowed asymmetry $s_n \cdot (k_{\gamma} \times k_n)$ were set at the level of 7 x 10^-6 for all three targets. Parity-violating asymmetries $s_n \cdot k_{\gamma}$ were observed in 35Cl, A_gamma = (-29.1 +- 6.7) x 10^-6, and 139La, A_gamma = (-15.5 +- 7.1) x 10^-6, values consistent with previous measurements.Comment: 19 pages, 4 figures, submitted to Nucl. Instr. and Meth.

Parity Nonconservation in Neutron Resonances in 133Cs

Spatial parity nonconservation (PNC) has been studied in the compound-nuclear states of 134Cs by measuring the helicity dependence of the neutron total cross section. Transmission measurements on a thick 133Cs target were performed by the time-of-flight method at the Manuel Lujan Neutron Scattering Center with a longitudinally polarized neutron beam in the energy range from 5 to 400 eV. A total of 28 new p-wave resonances were found, their neutron widths determined, and the PNC longitudinal asymmetries of the resonance cross sections measured. The value obtained for the root-mean-square PNC element M=(0.06-0.02+0.25) meV in 133Cs is the smallest among all targets studied. This value corresponds to a weak spreading width Γw=(0.006-0.003+0.154)×10-7 eV