On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations

In this paper we consider the estimation of population size from onesource capture–recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3, . . . contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution.We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.

The effect of paddock size on the response of seasonal anoestrous ewes to the ram effect

Many aspects of the conditions required to maximize the ewe's response to ram introduction in the late anoestrous season remain unclear. The aim of this research was to determine whether grazing space allowances could influence the efficacy of the ram effect. In August 1995, at Reading (latitude 51degrees27'N), following a 3-month isolation period from rams, two groups of nulliparous Mule ewes, aged 15 months, were introduced to four rains in a low (12 ewes/ha; treatment L, n = 124) or in a high stocking rate (84 ewes/ha; treatment H, n = 126). From the beginning of August until the end of August oestrous behaviour was recorded by daily checks of mating marks on ewes. Rams were removed and in October all ewes were scanned (day 50) for pregnancy. No significant differences were found in the parameters investigated. Eighty-two percent of the L and 75.4% of the H ewes exhibited oestrus, with a pronounced peak on day 23 following ram introduction and a compact concentration in the 21-25-day period. The oestrous synchronisation rate in this 5-day period was 69.4 and 68.3%, respectively for L and H. The mean interval from ram introduction to oestrus was 23.17+/-2.4 days in L and 23.0+/-2.2 days in the H group. Conception rates were 84.3 and 87.4% for L and H groups, respectively. These results suggest that the response of anoestrous ewes to the introduction of rams was not affected by grazing space allowances and that yearling Mule ewes respond well to the ram effect in the late anoestrus season. (C) 2003 Elsevier Science B.V. All rights reserved.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Body mass, territory size and life history tactics in a socially monogamous canid, the red fox Vulpes vulpes

Male-biased sexual size dimorphism is typical of polygynous mammals, where the degree of dimorphism in body mass is related to male intrasexual competition and the degree of polygyny. However, the importance of body mass in monogamous mammals is largely unknown. We investigated the effect of body mass on life-history parameters and territory size in the red fox (Vulpes vulpes), a socially monogamous canid with slight sexual dimorphism. Increased body size in males appeared to confer an advantage in territory acquisition and defense contests because heavier males held larger territories and exerted a greater boundary pressure on smaller neighbors. Heavier male foxes invested more effort in searching for extrapair matings by moving over a wider area and farther from their territories, leading to greater reproductive success. Males that sired cubs outside their own social group appeared to be heavier than males that only sired cubs within their social group or that were cuckolded, but our results should be treated with caution because sample sizes were small. Territory size, boundary pressure, and paternity success were not related to age of males. In comparison, body mass of females was not related to territory size, probability of breeding, litter size, or cub mass. Only age affected probability of breeding in females: younger females reproduced significantly less than did older females, although we did not measure individual nutritional status. Thus, body mass had a significant effect on life-history traits and territory size in a socially monogamous species comparable to that reported in polygynous males, even in the absence of large size dimorphism.

Hemispace differences in the visual perception of size in left hemi-Parkinson's disease

The visual perception of size in different regions of external space was studied in Parkinson's disease (PD). A group of patients with worse left-sided symptoms (LPD) was compared with a group with worse right-sided symptoms (RPD) and with a group of age-matched controls on judgements of the relative height or width of two rectangles presented in different regions of external space. The relevant dimension of one rectangle (the 'standard') was held constant, while that of the other (the 'variable') was varied in a method of constant stimuli. The point of subjective equality (PSE) of rectangle width or height was obtained by probit analysis as the mean of the resulting psychometric function. When the standard was in left space, the PSE of the LPD group occurred when the variable was smaller, and when the standard was in right space, when the variable was larger. Similarly, when the standard rectangle was presented in upper space, and the variable in lower space, the PSE occurred when the variable was smaller, an effect which was similar in both left and right spaces. In all these experiments, the PSEs for both the controls and the RPD group did not differ significantly, and were close to a physical match, and the slopes of the psychometric functions were steeper in the controls than the patients, though not significantly so. The data suggest that objects appear smaller in the left and upper visual spaces in LPD, probably because of right hemisphere impairment. (C) 2002 Elsevier Science Ltd. All rights reserved.

Estimation of distances in virtual environments using size constancy

It is reported in the literature that distances from the observer are underestimated more in virtual environments (VEs) than in physical world conditions. On the other hand estimation of size in VEs is quite accurate and follows a size-constancy law when rich cues are present. This study investigates how estimation of distance in a CAVETM environment is affected by poor and rich cue conditions, subject experience, and environmental learning when the position of the objects is estimated using an experimental paradigm that exploits size constancy. A group of 18 healthy participants was asked to move a virtual sphere controlled using the wand joystick to the position where they thought a previously-displayed virtual cube (stimulus) had appeared. Real-size physical models of the virtual objects were also presented to the participants as a reference of real physical distance during the trials. An accurate estimation of distance implied that the participants assessed the relative size of sphere and cube correctly. The cube appeared at depths between 0.6 m and 3 m, measured along the depth direction of the CAVE. The task was carried out in two environments: a poor cue one with limited background cues, and a rich cue one with textured background surfaces. It was found that distances were underestimated in both poor and rich cue conditions, with greater underestimation in the poor cue environment. The analysis also indicated that factors such as subject experience and environmental learning were not influential. However, least square fitting of Stevens’ power law indicated a high degree of accuracy during the estimation of object locations. This accuracy was higher than in other studies which were not based on a size-estimation paradigm. Thus as indirect result, this study appears to show that accuracy when estimating egocentric distances may be increased using an experimental method that provides information on the relative size of the objects used.

Identification of domestication-related loci associated with flowering time and seed size in soybean with the RAD-seq genotyping method

Flowering time and seed size are traits related to domestication. However, identification of domestication-related loci/genes of controlling the traits in soybean is rarely reported. In this study, we identified a total of 48 domestication-related loci based on RAD-seq genotyping of a natural population comprising 286 accessions. Among these, four on chromosome 12 and additional two on chromosomes 11 and 15 were associated with flowering time, and four on chromosomes 11 and 16 were associated with seed size. Of the five genes associated with flowering time and the three genes associated with seed size, three genes Glyma11g18720, Glyma11g15480 and Glyma15g35080 were homologous to Arabidopsis genes, additional five genes were found for the first time to be associated with these two traits. Glyma11g18720 and Glyma05g28130 were co-expressed with five genes homologous to flowering time genes in Arabidopsis, and Glyma11g15480 was co-expressed with 24 genes homologous to seed development genes in Arabidopsis. This study indicates that integration of population divergence analysis, genome-wide association study and expression analysis is an efficient approach to identify candidate domestication-related genes.

Variance in male reproductive success and sexual size dimorphism in pinnipeds: testing an assumption of sexual selection theory

The theory of evolution by sexual selection for sexual size dimorphism (SSD) postulates that SSD primarily reflects the adaptation of males and females to their different reproductive roles. For example, competition among males for access to females increases male body size because larger males are better able to maintain dominant status than smaller males. Larger dominant males sire most offspring while smaller subordinate males are unsuccessful, leading to skew in reproductive success. Therefore, species with male-biased SSD are predicted to have greater variance in male reproductive success than those in which both sexes are similar in size. We tested this prediction among the Pinnipedia, a mammalian group with a great variation in SSD. From a literature review, we identified genetic estimates of male reproductive success for 10 pinniped taxa (eight unique species and two subspecies of a ninth species) that range from seals with similarly sized males and females to species in which males are more than four times as large as females. We found no support for a positive relationship between variance in reproductive success and SSD among pinnipeds after excluding the elephant seals Mirounga leonina and Mirounga angustirostris, which we discuss as distinctive cases. Several explanations for these results are presented, including the revival of one of Darwin's original ideas. Darwin proposed that natural selection may explain SSD based on differences in energetic requirements between sexes and the potential for sexual niche segregation. Males may develop larger bodies to exploit resources that remain unavailable to females due to the energetic constraints imposed on female mammals by gestation and lactation. The importance of this alternative explanation remains to be tested.

Comparison of the portion size and frequency of consumption of 156 foods across seven European countries: insights from the Food4ME study

There are no standardised serving/portion sizes defined for foods consumed in the European Union (EU). Typical serving sizes can deviate significantly from the 100 g/100 ml labelling specification required by the EU legislation. Where the nutritional value of a portion is specified, the portion size is determined by the manufacturers. Our objective was to investigate the potential for standardising portion sizes for specific foods, thereby ensuring complementarity across countries. We compared portion size for 156 food items measured using a food frequency questionnaire across the seven countries participating in the Food4me study. The probability of consuming a food and the frequency of consumption differed across countries for 93% and 58% of the foods, respectively. However, the individual country mean portion size differed from the average across countries in only 16% of comparisons. Thus, although dietary choices vary markedly across countries, there is much less variation in portion sizes. Our results highlight the potential for standardisation of portion sizes on nutrition labels in the EU

Sexual System, Sex Ratio, and Group Living in the Shrimp Thor amboinensis (De Man): Relevance to Resource-Monopolization and Sex-Allocation Theories

The sexual system of the symbiotic shrimp Thor amboinensis is described, along with observations on sex ratio and host-use pattern of different populations. We used a comprehensive approach to elucidate the previously unknown sexual system of this shrimp. Dissections, scanning electron microscopy, size-frequency distribution analysis, and laboratory observations demonstrated that T amboinensis is a protandric hermaphrodite: shrimp first mature as males and change into females later in life. Thor amboinensis inhabited the large and structurally heterogeneous sea anemone Stichoclactyla helianthus in large groups (up to 11 individuals) more frequently than expected by chance alone. Groups exhibited no particularly complex social structure and showed male-biased sex ratios more frequently than expected by chance alone. The adult sex ratio was male-biased in the four separate populations studied, one of them being thousands of kilometers apart from the others. This study supports predictions central to theories of resource monopolization and sex allocation. Dissections demonstrated that unusually large males were parasitized by an undescribed species of isopod (family Entoniscidae). Infestation rates were similarly low in both sexes (approximate to 11%-12%). The available information suggests that T. amboinensis uses pure search promiscuity as a mating system. This hypothesis needs to be formally tested with mating behavior observations and field measurements on the movement pattern of both sexes of the species. Further detailed studies on the lifestyle and sexual system of all the species within this genus and the development of a molecular phylogeny are necessary to elucidate the evolutionary history of gender expression in the genus Thor.

Exercise changes the size of cardiac neurons and protects them from age-related neurodegeneration

Aging leads to changes in cardiac structure and function. Evidence suggests that the practice of regular exercise may prevent disturbances in the cardiovascular system during aging. We studied the effects of aging on the morphology and morphometry of cardiac neurons in Wistar rats and investigated whether a lifelong moderate exercise program could exert a protective effect toward some deleterious effects of aging. Aging caused a significant decline (28%) in the number of NADH-diaphorase-stained cardiac Animals submitted to a daily session of 60 min, 5 day/week, at 1.1 km/h of running in treadmill over the entire life span exhibited a reversion of the observed decline in the number of cardiac neurons. However, most interesting was that the introduction of this lifelong exercise protocol dramatically altered the sizes of cardiac neurons. There was a notable increase in the percentage of small neurons in the rats of the exercise group compared to the sedentary animals. This is the first time that a protective effect of lifelong regular aerobic exercise has been demonstrated on the deleterious effects of aging in cardiac neurons. (C) 2009 Elsevier GmbH. All rights reserved.

The Antiapoptotic Effect of Granulocyte Colony-stimulating Factor Reduces Infarct Size and Prevents Heart Failure Development in Rats

Background/Aim. Granulocyte colony-stimulating factor (G-CSF) reduces myocardial injury and improves cardiac function after myocardial infarction (MI). We investigated the early alterations provided by G-CSF and the chronic repercussions in infarcted rats. Methods. Male Wistar rats (200-250g) received vehicle (MI) or G-CSF (MI-GCSF) (50 mu g/kg, sc) at 7, 3 and 1 days before MI surgery. Afterwards MI was produced and infarct size was measured 1 and 15 days after surgery. Expression of anti-and proapoptotic proteins was evaluated immediately before surgery. 24 hours after surgery, apoptotic nuclei were evaluated. Two weeks after MI, left ventricular (LV) function was evaluated, followed by in situ LV diastolic pressure-volume evaluation. Results. Infarct size was decreased by 1 day pretreatment before occlusion (36 +/- 2.8 vs. 44 +/- 2.1% in MI; P<0.05) and remained reduced at 15 days after infarction (28 +/- 2.2 vs. 36 +/- 1.4% in MI; P<0.05). G-CSF pretreatment increased Bcl-2 and Bcl-xL protein expression, but did not alter Bax in LV. Apoptotic nuclei were reduced by treatment (Sham: 0.46 +/- 0.42, MI: 15.5 +/- 2.43, MI-GCSF: 5.34 +/- 3.34%; P<0.05). Fifteen days after MI, cardiac function remained preserved in G-CSF pretreated rats. The LV dilation was reduced in MI-G-CSF group as compared to MI rats, being closely associated with infarct size. Conclusion. The early beneficial effects of G-CSF were essentials to preserve cardiac function at a chronic stage of myocardial infarction. Copyright (C) 2011 S. Karger AG, Basel

Analysis of the genome of Spodoptera frugiperda nucleopolyhedrovirus (SfMNPV-19) and of the high genomic heterogeneity in group II nucleopolyhedroviruses

The genome of the most virulent among 22 Brazilian geographical isolates of Spodoptera frugiperda nucleopolyhedrovirus, isolate 19 (SfMNPV-1 9), was completely sequenced and shown to comprise 132 565 bp and 141 open reading frames (ORFs). A total of 11 ORFs with no homology to genes in the GenBank database were found. Of those, four had typical baculovirus; promoter motifs and polyadenylation sites. Computer-simulated restriction enzyme cleavage patterns of SfMNPV-1 9 were compared with published physical maps of other SfMNPV isolates. Differences were observed in terms of the restriction profiles and genome size. Comparison of SfMNPV-1 9 with the sequence of the SfMNPV isolate 3AP2 indicated that they differed due to a 1427 bp deletion, as well as by a series of smaller deletions and point mutations. The majority of genes of SfMNPV-1 9 were conserved in the closely related Spodoptera exigua NPV (SeMNPV) and Agrotis segetum NPV (AgseMNPV-A), but a few regions experienced major changes and rearrangements. Synthenic maps for the genomes of group 11 NPVs revealed that gene collinearity was observed only within certain clusters. Analysis of the dynamics of gene gain and loss along the phylogenetic tree of the NPVs showed that group 11 had only five defining genes and supported the hypothesis that these viruses form ten highly divergent ancient lineages. Crucially, more than 60% of the gene gain events followed a power-law relation to genetic distance among baculoviruses, indicative of temporal organization in the gene accretion process.

Recruiting a Diverse Student Body at Mid-Size Public Master’s Universities

As student demographics change, admissions officers are increasingly recruiting a diverse group of incoming students, including underrepresented minorities. We outline how five public institutions identify and recruit potential applicants and review recruitment strategies and methodologies for expanding target recruitment populations.