Primality-testing Mersenne numbers

Report of a systematic review of Mersenne numbers 2^p-1 for p < 62982.

Modeling the variability of single-cell lag times for Listeria innocua populations after sublethal and lethal heat treatments

Optical density measurements were used to estimate the effect of heat treatments on the single-cell lag times of Listeria innocua fitted to a shifted gamma distribution. The single-cell lag time was subdivided into repair time ( the shift of the distribution assumed to be uniform for all cells) and adjustment time (varying randomly from cell to cell). After heat treatments in which all of the cells recovered (sublethal), the repair time and the mean and the variance of the single-cell adjustment time increased with the severity of the treatment. When the heat treatments resulted in a loss of viability (lethal), the repair time of the survivors increased with the decimal reduction of the cell numbers independently of the temperature, while the mean and variance of the single-cell adjustment times remained the same irrespective of the heat treatment. Based on these observations and modeling of the effect of time and temperature of the heat treatment, we propose that the severity of a heat treatment can be characterized by the repair time of the cells whether the heat treatment is lethal or not, an extension of the F value concept for sublethal heat treatments. In addition, the repair time could be interpreted as the extent or degree of injury with a multiple-hit lethality model. Another implication of these results is that the distribution of the time for cells to reach unacceptable numbers in food is not affected by the time-temperature combination resulting in a given decimal reduction.

The relationships of time and temperature to body weight and numbers of endospores in Pasteuria penetrans-infected Meloidogyne javanica females

Tomato plants inoculated with Meloidogyne javanica juveniles infected with Pasteuria penetrans were grown in a glasshouse (20-32degreesC) for 36, 53, 71 and 88 days and in a growth room (26-29degreesC) for 36, 53, 71 and 80 days. Over these periods the numbers of P penetrans endospores in infected M. javanica females and the weights of individual infected females increased. In the growth room, most spores (2.03 x 10(6)) were found after 71 days. However, in the glasshouse the rate of increase was slower and spore numbers were still increasing at the final sampling at 88 days (2.04 x 10(6)), as was the weight of the nematodes (72 mug). Weights of uninfected females reached a maximum of 36.2 and 43.1 mug after 71 days in the growth room and glasshouse, respectively.

Estimating numbers of infectious units from serial dilution assays

The paper concerns the design and analysis of serial dilution assays to estimate the infectivity of a sample of tissue when it is assumed that the sample contains a finite number of indivisible infectious units such that a subsample will be infectious if it contains one or more of these units. The aim of the study is to estimate the number of infectious units in the original sample. The standard approach to the analysis of data from such a study is based on the assumption of independence of aliquots both at the same dilution level and at different dilution levels, so that the numbers of infectious units in the aliquots follow independent Poisson distributions. An alternative approach is based on calculation of the expected value of the total number of samples tested that are not infectious. We derive the likelihood for the data on the basis of the discrete number of infectious units, enabling calculation of the maximum likelihood estimate and likelihood-based confidence intervals. We use the exact probabilities that are obtained to compare the maximum likelihood estimate with those given by the other methods in terms of bias and standard error and to compare the coverage of the confidence intervals. We show that the methods have very similar properties and conclude that for practical use the method that is based on the Poisson assumption is to be recommended, since it can be implemented by using standard statistical software. Finally we consider the design of serial dilution assays, concluding that it is important that neither the dilution factor nor the number of samples that remain untested should be too large.

Numbers of antral follicles during follicular waves in cattle: Evidence for high variation among animals, very high repeatability in individuals, and an inverse association with serum follicle-stimulating hormone concentrations

The extent, causes, and physiological significance of the variation in number of follicles growing during ovarian follicular waves in human beings and cattle are unknown. Therefore, the present study examined the variability and repeatability in numbers of follicles 3 mm or greater in diameter during the follicular waves in bovine estrous cycles, and we determined if the variation in number of follicles during waves was associated with alterations in secretion of FSH, estradiol, inhibin, and insulin-like growth factor I (IGF-I). Dairy cattle were subjected to twice-daily ultrasound analysis to count total number of antral follicles 3 mm or greater in diameter throughout 138 different follicular waves. In another study, blood samples were taken at frequent intervals from cows that consistently had low or very high numbers of follicles during waves and were subjected to immunoassays. Results indicate the following: First, despite an approximately sevenfold variation in number of follicles during waves among animals and marked differences in age, stage of lactation, and season of the year, a very highly repeatable (0.95) number of follicles 3 mm or greater in diameter is maintained during the ovulatory and nonovulatory follicular waves of individuals. Second, variation in number of follicles 3 mm or greater in diameter during waves and the inverse association of number of follicles during waves with FSH are not directly explained by alterations in the patterns of secretion of estradiol, inhibin, or IGF-I. Third, ovarian ultrasound analysis can be used reliably by investigators to identify cattle that consistently have low or high numbers of follicles during waves, thus providing a novel experimental model to determine the causes and physiological significance of the high variation in antral follicle number during follicular waves among single-ovulating species, such as cattle or humans.

Hepatozoon griseisciuri in grey squirrels (Sciurus carolinensis): changes of blood leucocyte numbers resulting from infection

Numbers of leucocytes in squirrels with gametocytes of Hepatozoon in their blood (infected) were compared with animals without gametocytes (uninfected). Typical values for leucocytes/mm(3) blood in uninfected squirrels were: leucocytes 5-7 x 10(3), granulocytes 3-4 x 10(3), lymphocytes 2-0 x 10(3) and monocytes 0-3 x 10(3) cells. Infection caused an increase in monocytes, lymphocytes and granulocytes, and there was a significant positive association between parasitaemia level and numbers of both total leucocytes and monocytes. Infected animals had more uninfected monocytes/mm(3) blood than did uninfected animals. The proportions of monocytes were more variable over time in infected animals, but no shift between infected and uninfected status was detected. Transfer of serum from infected squirrels to mice resulted in elevated counts of total blood leucocytes, monocytes and granulocytes, but not of lymphocytes, as compared with controls. Serum from squirrels with high parasitaemias had a more marked effect than serum from squirrels with low parasitaemias. Results indicate an infection - related monocytosis, possibly controlled by cytokines, that increases the number of cells available for invasion by gametocytes, thus enhancing the chances of parasite transmission.

A novel galactooligosaccharide mixture increases the bifidobacterial population numbers in a continuous in vitro fermentation system and in the proximal colonic contents of pigs in vivo

Prebiotics are nondigestible food ingredients that encourage proliferation of selected groups of the colonic microflora, thereby altering the composition toward a more beneficial community. In the present study, the prebiotic potential of a novel galactooligosaccharide (GOS) mixture, produced by the activity of galactosyltransferases from Bifidobacterium bifidum 41171 on lactose, was assessed in vitro and in a parallel continuous randomized pig trial. In situ fluorescent hybridization with 16S rRNA-targeted probes was used to investigate changes in total bacteria, bifidobacteria, lactobacilli, bacteroides, and Clostridium histolyticum group in response to supplementing the novel GOS mixture. In a 3-stage continuous culture system, the bifidobacterial numbers for the first 2 vessels, which represented the proximal and traverse colon, increased (P < 0.05) after the addition of the oligosaccharide mixture. In addition, the oligosaccharide mixture strongly inhibited the attachment of enterohepatic Escherichia coli (P < 0.01) and Salmonella enterica serotype Typhimurium (P < 0.01) to HT29 cells. Addition of the novel mixture at 4% (wt:wt) to a commercial diet increased the density of bificlobacteria (P < 0.001) and the acetate concentration (P < 0.001), and decreased the pH (P < 0.001) compared with the control diet and the control diet supplemented with inulin, suggesting a great prebiotic potential for the novel oligosaccharide mixture. J. Nutr. 135: 1726-1731, 2005.

Perspex machine XI: topology of the transreal numbers

The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and, possibly, for physical theories. We define the topology of the transreal numbers and show that it gives a more coherent interpretation of two's complement arithmetic than the conventional integer model. Trans-two's-complement arithmetic handles the infinities and 0/0 more coherently, and with very much less circuitry, than floating-point arithmetic. This reduction in circuitry is especially beneficial in parallel computers, such as the Perspex machine, and the increase in functionality makes Digital Signal Processing chips better suited to general computation.

A hypoplastic model of skeletal muscle development displaying reduced foetal myoblast cell numbers, increased oxidative myofibres and improved specific tension capacity

The major component of skeletal muscle is the myofibre. Genetic intervention inducing over-enlargement of myofibres beyond a certain threshold through acellular growth causes a reduction in the specific tension generating capacity of the muscle. However the physiological parameters of a genetic model that harbours reduced skeletal muscle mass have yet to be analysed. Genetic deletion of Meox2 in mice leads to reduced limb muscle size and causes some patterning defects. The loss of Meox2 is not embryonically lethal and a small percentage of animals survive to adulthood making it an excellent model with which to investigate how skeletal muscle responds to reductions in mass. In this study we have performed a detailed analysis of both late foetal and adult muscle development in the absence of Meox2. In the adult, we show that the loss of Meox2 results in smaller limb muscles that harbour reduced numbers of myofibres. However, these fibres are enlarged. These myofibres display a molecular and metabolic fibre type switch towards a more oxidative phenotype that is induced through abnormalities in foetal fibre formation. In spite of these changes, the muscle from Meox2 mutant mice is able to generate increased levels of specific tension compared to that of the wild type.

A sequential two meal challenge reveals abnormalities in postprandial TAG but not glucose in men with increasing numbers of metabolic syndrome components

Objective To examine the impact of increasing numbers of metabolic syndrome (MetS) components on postprandial lipaemia. Methods Healthy men (n = 112) underwent a sequential meal postprandial investigation, in which blood samples were taken at regular intervals after a test breakfast (0 min) and lunch (330 min). Lipids and glucose were measured in the fasting sample, with triacylglycerol (TAG), non-esterified fatty acids and glucose analysed in the postprandial samples. Results Subjects were grouped according to the number of MetS components regardless of the combinations of components (0/1, 2, 3 and 4/5). As expected, there was a trend for an increase in body mass index, blood pressure, fasting TAG, glucose and insulin, and a decrease in fasting high-density lipoprotein cholesterol with increasing numbers of MetS components (P≤0.0004). A similar trend was observed for the summary measures of the postprandial TAG and glucose responses. For TAG, the area under the curve (AUC) and maximum concentration (maxC) were significantly greater in men with ≥ 3 than < 3 components (P < 0.001), whereas incremental AUC was greater in those with 3 than 0/1 and 2, and 4/5 compared with 2 components (P < 0.04). For glucose, maxC after the test breakfast (0-330 min) and total AUC (0-480 min) were higher in men with ≥ 3 than < 3 components (P≤0.001). Conclusions Our data analysis has revealed a linear trend between increasing numbers of MetS components and magnitude (AUC) of the postprandial TAG and glucose responses. Furthermore, the two meal challenge discriminated a worsening of postprandial lipaemic control in subjects with ≥ 3 MetS components.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Software-based study of a non-sorting method for median calculation on a set of integer numbers

This paper presents a software-based study of a hardware-based non-sorting median calculation method on a set of integer numbers. The method divides the binary representation of each integer element in the set into bit slices in order to find the element located in the middle position. The method exhibits a linear complexity order and our analysis shows that the best performance in execution time is obtained when slices of 4-bit in size are used for 8-bit and 16-bit integers, in mostly any data set size. Results suggest that software implementation of bit slice method for median calculation outperforms sorting-based methods with increasing improvement for larger data set size. For data set sizes of N > 5, our simulations show an improvement of at least 40%.