On a two urn model of Polya-type

A two urn Polya-type scheme is considered in whichr black balls (corresponding to the stable form of an element) are added to urn one at every stage and the same number of balls are removed at random at every stage from the same urn. In between these two operations, which form a stage or iteration, a fixed number of balls is exchanged at random between urns one and two. Urn one has a given initial number of white balls (corresponding to a radioactive form of the same element). The problem of interest is to study the stochastic aspect of the number of white balls remaining in urn one (and/or urn two) aftern iterations.     

A reinforcement depletion urn problem—II. Application and generalization

The urn model discussed in part is generalized so that the random depletion of balls from the urn in any cycle is not necessarily the same as the reinforcement in that cycle. This model is applied to an urn containing balls of three colors (white, red, black) for which the black balls always receive reinforcements, whereas there is only one cycle in which red balls are added. Experimental data are considered in which red balls correspond to radioactive iodine atoms, black balls to stable iodine atoms and white balls to empty space, all relating to the thyroid gland. Half-life periods for the radioactive iodine in relation to the time of uptake (ten years, fifteen years, etc.) are considered.     

On the distribution of the time required to remove white balls from an URN

Balls are removed one-at-a-time at equal time intervals from an urn initially containingw ₀ white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw ₁ from the urn. We then find the mean and variance of this distribution and also look at the special case whenw ₁ =w ₀.     

An urn model study of variability within a compartment

Formulas are derived for the mean and variance of the number of radioactive atoms present in a compartment (or urn). Initally,n ₁ radioactive atoms andb stable atoms are placed in the urn; and subsequently,r stable atoms are added and an equal number,r, of a random mixture of stable and radioactive atoms is removed per unit time. The expected number of radioactive atoms,E(t), present at timet is, as expected,n ₁ e^−λt where λ=(r/Δt)/(b+r+n ₁). The relative variance, σ²(t)/n ₁ ² , vanishes to zero forr=1, atoms per unit time and for a large number ofn ₁ radioactive atoms; but for a large number of bothr andn ₁ atoms the relative variance is ∼e ^−λt , equal to the fractional retention, fort>1/λ. Thus in studies where radionuclides are injected into animals and a single compartment represents the data, if a large variance is observed it might be due to the fact that large numbers of atoms are transferred out in unit time. When a small variance is observed, this is probably due to the fact that few atoms are transferred in smaller units of time (such that λ is the same in both cases). Research sponsored by the Energy Research and Development Administration under contract with Union Carbide Corporation.     

Development and morphology of ciliary urns in the sea cucumber Synaptula hydriformis (Echinodermata: Holothuroidea)

Sea cucumbers (holothuroids) lack the only known echinoderm immune organ, the axial organ. Holothuroids of the families Synaptidae and Chiridotidae have coelomic organs, known as ciliary urns, that gather and excrete waste and, therefore, might function in immunity. Although ciliary urns are widely reported and illustrated in the literature, the process and histology of urn development remain unknown. Development and structure of ciliary urns were examined in Synaptula hydriformis using scanning electron, brightfield, and scanning laser confocal microscopy. Mature urns occurred on all three mesenteries in 10‐tentacled young and later growth stages, and developing urns were found in post‐pentactulae, 10‐tentacled young, and released juveniles. Developing urns were circular clusters of ciliated collar cells protruding from the mesentery. The cells increased in number to form the sessile cushion stage with a shallow lumen. The subsequent spoon‐shaped stage had a stalk and a deepened lumen with an extensive ciliary field where coelomocytes began to accumulate. Mature urns had a thin stalk and cornucopia‐shaped body with an abluminal epithelium of squamous cells and an adluminal epithelium of densely packed ciliated collar cells. Cell boundaries of the rim of mature urns and of the stalk and body of developing urns were outlined on one or both sides by microvilli and an elevated cell membrane. Ciliary urns resembling the cushion‐stage urns of S. hydriformis have been described in the sea star Archaster typicus. If urns in these groups are homologous, it is likely that cushion urns are plesiomorphic and that they are present and have been overlooked in other echinoderms.     

Study of age dependent half-life of iodine in man: A reinforcement-depletion urn model

An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Shenton (1981, 1983). In this paper, the theory is applied to the biological age dependent half-life of radioactive iodine in man; the data of Cook and Snyder (1965) is used. The intake of radioactive iodine and its retention subsequently is studied. Research sponsored by the Office of Health and Environmental Research, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-840R21400 with the Martin Merietta Energy Systems. Inc.     

Dual‐energy X‐ray Absorptiometry and Anthropometric Estimates of Visceral Fat in Black and White South African Women

Visceral adipose tissue (VAT) is associated with increased risk for cardiovascular disease, and therefore, accurate methods to estimate VAT have been investigated. Computerized tomography (CT) is the gold standard measure of VAT, but its use is limited. We therefore compared waist measures and two dual‐energy X‐ray absorptiometry (DXA) methods (Ley and Lunar) that quantify abdominal regions of interest (ROIs) to CT‐derived VAT in 166 black and 143 white South African women. Anthropometry, DXA ROI, and VAT (CT at L4–L5) were measured. Black women were younger (P < 0.001), shorter (P < 0.001), and had higher body fat (P < 0.05) than white women. There were no ethnic differences in waist (89.7 ± 18.2 cm vs. 90.1 ± 15.6 cm), waist:height ratio (WHtR, 0.56 ± 0.12 vs. 0.54 ± 0.09), or DXA ROI (Ley: 2.2 ± 1.5 vs. 2.1 ± 1.4; Lunar: 2.3 ± 1.4 vs. 2.3 ± 1.5), but black women had less VAT, after adjusting for age, height, weight, and fat mass (76 ± 34 cm² vs. 98 ± 35 cm²; P < 0.001). Ley ROI and Lunar ROI were correlated in black (r = 0.983) and white (r = 0.988) women. VAT correlated with DXA ROI (Ley: r = 0.729 and r = 0.838, P < 0.01; Lunar: r = 0.739 and r = 0.847, P < 0.01) in black and white women, but with increasing ROI android fatness, black women had less VAT. Similarly, VAT was associated with waist (r = 0.732 and r = 0.836, P < 0.01) and WHtR (r = 0.721 and r = 0.824, P < 0.01) in black and white women. In conclusion, although DXA‐derived ROIs correlate well with VAT as measured by CT, they are no better than waist or WHtR. Neither DXA nor anthropometric measures are able to accurately distinguish between high and low levels of VAT between population groups.     

Racial Differences in Metabolic Predictors of Obesity among Postmenopausal Women

NICKLAS, BARBARA S., DORA M. BERMAN, DAWN C. DAVIS, C. LYNNE DOBROVOLNY, AND KAREN E. DENNIS. Racial differences in metabolic predictors of obesity among postmenopausal women. Ober Res. Objective: This study determined whether there are racial differences in resting metabolic rate (RMR), fat oxidation, and maximal oxygen consumption (VO,max) in obese [body mass index (BMI = 34±2 kg/m²)], postmenopausal (58±2 years) women. Research Methods and Procedures: Twenty black and 20 white women were matched for fat mass and lean mass (LM), as determined by dual energy X-ray absorptiometry. RMR and fat oxidation were measured by indirect calorimetry in the early morning after a 12-hour fast using the ventilated hood technique. VO₂max was measured on a treadmill during a progressive exercise test to voluntary exhaustion. Results: RMR, adjusted for differences in LM, was 5% higher in white than black women (1566±27 and 1490±26 kcal/day, respectively; p<0. 05); and fat oxidation rate was 17% higher in white than black women (87±4 and 72±3 g/day, respectively; p<0. 01). VO₂max (L/minute) was 150 mL per minute (8%) higher (p<0. 05) in white than black women. VO₂max correlated with LM in black (r = 0. 44, p = 0. 05) and white (r=0. 53, p<0. 05) women, but the intercept of the regression line was higher in white than black women (p<0. 05), with no significant difference in slopes. In a multiple regression model including race, body weight, LM, and age, LM was the only independent predictor of RMR (r² = 0. 46, p<0. 0001), whereas race was the only independent predictor of fat oxidation (r² = 0. 18,p<0. 05). The best predictors of VO,max were LM (r² = 0. 22, p<0. 05) and race (cumulative r² = 0. 30, p<0. 05). Discussion: These results show there are racial differences in metabolic predictors of obesity. Determination of whether these ethnic differences lead to, or are an effect of, obesity status or other lifestyle factors requires further study.     

On some problems of random nets

The probability problems connected with random nets are restated as probabilities of drawings from an urn containing black and white balls. A partial difference equation is obtained and its solution is given. For large nets a series expression is obtained for the connectivity γ, and this is shown to be equivalent to the transcendental equation obtained by R. Solomonoff and A. Rapport (1951).     

On the taxonomy and distribution of the leaf-beetle <Emphasis Type="Italic">Macroplea japana</Emphasis> Jacoby, 1885 (Coleoptera,Chrysomelidae)

The species rank of Macroplea japana (Jacoby, 1885) is confirmed based on examination of the holotype. The main characters distinguishing this species from M. mutica are as following: the 4th antennomere is as long as the 3rd segment and somewhat longer than the 2nd segment; the pronotum is smooth, shining, with 3 black longitudinal stripes on the bottoms of 3 longitudinal impressions; the femora and tibiae black apically; the 1st metatarsomere is as long as the 2nd and the 3rd tarsomeres combined and is almost twice as long as the 2nd tarsomere; the claws bear no triangular projection near the bases; the aedeagus forms a shorter apical projection. Macroplea japana is found in Russia (Primorskii Territory) for the first time.     

Selenium concentration in blood and hair of holstein dairy cows

Four-hundred Holstein cows in 40 dairy farms in north Greece were included in this study, and blood (n=400), black hair (n=400), white hair (n=40), and feed (n=40) samples were obtained. Although the feeding regime in these farms was similar, the selenium content of feeds was variable. The Se content of concentrate feeds was 0.104±0.086 mg/kg dry matter (DM), and of silage, it was 0.025±0.018 mg/kg. A significantly positive correlation was found between the Se concentration in black hair and the Se concentration in blood (r ²=0.610, p<0.001), the Se concentration in white hair and the Se concentration in blood (r ²=0.770, p<0.001), and the Se concentration in white hair and the Se concentration in black hair (r ²=0.921, p<0.001). The Se concentration in white hair was significantly smaller than that in black hair (p<0.001).     

PHOTOCONTROL OF THE ORIENTATION OF CELL DIVISION IN ADIANTUM. I. EFFECTS OF THE DARK AND RED PERIODS IN THE APICAL CELL OF GAMETOPHYTES

When protonemata of Adiantum capillus-veneris L. which had been grown filamentously under continuous red light were transferred to continuous white light, the apical cell divided transversely twice, but the 3rd division was longitudinal. An intervening period of darkness lasting from 0 to 90 hr either between the 1st and the 2nd cell division or between the 2nd and the 3rd one did not affect the number of protonemata in which the 3rd cell division was longitudinal. The insertion of red light instead of darkness greatly decreased the percentage of 1st longitudinal divisions occurring at the 3rd division, and increased the number of transverse divisions. Fifty percent reduction of induction of 1st longitudinal division was caused by ca. 50 hr exposure to red light between 1st and 2nd division and by ca. 20 hr between 2nd and 3rd division, and total loss was induced by an exposure of ca. 100 hr or longer to red light in the former and by ca. 40 hr longer in the latter. Thus, by using an appropriate intervening dark period or exposure to red light, the orientation and timing of cell division could be controlled in apical cell of the fern protonemata.     

Racial Differences in the Tracking of Childhood BMI to Adulthood

Objective: The possibility that there are racial differences in the patterns of BMI (kilograms per meter squared) change throughout life has not been examined. For example, the high prevalence of obesity among black women could result from a higher prevalence of obesity among black girls or because normal‐weight black girls experience larger BMI increases in adolescence or adulthood than do their white counterparts. Therefore, we examined the tracking of childhood BMI into adulthood in a biracial (36% black) sample. Research Methods and Procedures: Five‐ to 14‐year‐old children (2392) were followed for (mean) 17 years. Childhood overweight was defined as BMI ≥ 95th percentile, and adult obesity was defined as BMI ≥ 30 kg/m². Results: The tracking of childhood BMI differed between whites and blacks. Among overweight children, 65% of white girls vs. 84% of black girls became obese adults, and predictive values among boys were 71% (whites) vs. 82% (blacks). These racial differences reflected contrasting patterns in the rate of BMI change. Although the initial BMI of black children was not higher than that of white children, BMI increases with age were larger among black girls and overweight black boys than among their white counterparts. In contrast, relatively thin (BMI < 50th percentile) white boys were more likely to become overweight adults than were their black counterparts. Discussion: These findings emphasize the black/white differences in BMI changes with age. Because of the adult health consequences of childhood‐onset obesity, early prevention should be given additional emphasis.     

Resting Energy Expenditure Changes With Weight Loss: Racial Differences

It is controversial whether weight loss reduces resting energy expenditure (REE) to a different magnitude in black and white women. This aim of this study was to determine whether changes in REE with weight loss were different between black and white postmenopausal women, and whether changes in body composition (including regional lean and fat mass) were associated with REE changes within each race. Black (n = 26) and white (n = 65) women (age = 58.2 ± 5.4 years, 25 < BMI < 40 kg/m²) completed a 20‐week weight‐loss intervention. Body weight, lean and fat mass (total body, limb, and trunk) via dual‐energy X‐ray absorptiometry, and REE via indirect calorimetry were measured before and after the intervention. We found that baseline REE positively correlated with body weight, lean and fat mass (total, limb, and trunk) in white women only (P < 0.05 for all). The intervention decreased absolute REE in both races similarly (1,279 ± 162 to 1,204 ± 169 kcal/day in blacks; 1,315 ± 200 to 1,209 ± 185 kcal/day in whites). REE remained decreased after adjusting for changes in total or limb lean mass in black (1,302–1,182 kcal/day, P = 0.043; 1,298–1,144 kcal/day, P = 0.006, respectively), but not in white, women. Changes in REE correlated with changes in body weight (partial r = 0.277) and fat mass (partial r = 0.295, 0.275, and 0.254 for total, limb, and trunk, respectively; P < 0.05) independent of baseline REE in white women. Therefore, with weight loss, REE decreased in proportion to the amount of fat and lean mass lost in white, but not black, women.     

Peptide‐YY Levels after a Fat Load in Black and White Women

Objective: To determine whether basal plasma peptide‐YY (PYY) levels in overweight, middle‐aged black women are different from those of white women of similar BMI and age and ascertain whether there is a difference between the two groups in plasma PYY levels in response to a liquid high fat load. Research Methods and Procedures: Using a commercial radioimmunoassay kit, the concentration of PYY was measured at baseline and at 2, 4, 6, and 8 hours after ingesting a fatty liquid meal (86.5% of the calories from fat) in 12 black and 12 white women who were matched for age and BMI. Results: PYY levels (picograms per milliliter) at baseline and at every other time‐point of the test meal were significantly lower in the black than in the white group. In addition, the change in PYY concentration from baseline was lower in the black than in the white group only at 8 hours after the meal. Discussion: The lower baseline level and the blunted PYY response of the black women to the fat load indicated that this signal for appetite suppression was reduced, which, in turn, might contribute to the enhanced obesity of the black women.     

Microsatellite mapping of the bovine roan locus: A major determinant of White Heifer Disease

In the Belgian Blue Cattle breed, coat color variation is mainly under the influence of a single autosomal locus, the roan locus, characterized by a pair of codominant alleles: r ⁺ (black) and R (white). Heterozygous r ⁺ R animals have intermingled black and white hairs, yielding the ``blue' phenotype typical of the breed. Major interest for the roan locus stems from its pleiotropic effect on fertility, owing to the critical role of the R allele in the determinism of White Heifer Disease. We describe the linkage mapping of the roan locus to bovine Chromosome (Chr) 5, in the interval between microsatellite markers BPI and AGLA293, with an associated lodscore of 11.2. Moreover, we map a candidate gene, the Steel locus coding for the mast cell growth factor, to bovine Chr 5. Received: 30 May 1995 / Accepted: 6 September 1995     

Trends of Abdominal Adiposity in White,Black, and Mexican‐American Adults, 1988 to 2000

Objective: To describe changes in the distribution of waist circumference (WC) and abdominal obesity (AO) in white, black, and Mexican‐American adults from 1988 through 2000. Research Methods and Procedures: Nationally representative cross‐sectional surveys of adults 20 to 79 years of age were examined using data from U.S. National Health and Nutrition Examination Surveys of 1988 to 1994 and 1999 to 2000. AO was defined as WC ≥102 cm in men and ≥88 cm in women. Results: There was a gradient of increasing WC and AO with increasing age in both study periods in whites and blacks. In men, the average increase between the study periods in overall WC in whites, blacks, and Mexican Americans were 3, 3.3, and 3.4 cm, respectively. The corresponding values in women were 2.4, 5.3, and 3.7 cm, respectively. In men, the percentage change in prevalence of AO between 1988 and 2000 ranged from 5.5% in Mexican‐American men to 8.2% in white men. In women, there was a 1.7% decrease in AO in Mexican Americans, whereas there was an increase of 6.3% for whites and 7% for blacks. Discussion: Despite increased understanding of the need for screening and treatment for obesity, this study indicates increasing prevalence of AO in white and black Americans. Without concerted effort to reduce the prevalence of overall obesity, the increasing prevalence of AO is likely to lead to increased prevalence of metabolic syndromes in the United States. Our results highlight the need to design evidence‐based programs that show promise for long‐term health behavior changes to facilitate the prevention of AO and related comorbidities.     

Modeling species dispersal with occupancy urn models

Models for species dispersal make various simplifications to facilitate analysis, such as ignoring spatial correlations or assuming equal probability of colonization among all sites within a dispersal neighborhood. Here we introduce a variation of the basic contact process (BCP) which allows us to separate the number of offspring produced from the neighborhood size, which are confounded in the original BCP. We then use classical results arising from probability models involving placing balls in urns to study our modified BCP, obtaining bounds for the critical value of the survival probability needed for the population to persist. We also use the probability urn calculations with a local-dispersal mean-field approximation to estimate equilibrium population density. These methods are able to include features such as unequal dispersal probabilities to different sites in the neighborhood, e.g., as would arise when dispersers have a fixed rate of mortality per distance traveled from the parent site. We also show how urn models allow one to generalize these results to two species competing for space.     

Effect of Glycemic Load on Peptide‐YY Levels in a Biracial Sample of Obese and Normal Weight Women

Black women suffer a disproportionately higher rate of obesity than their white counterparts. Reasons for this racial disparity may reflect underlying differences in the appetite suppressing peptide‐YY (PYY). The PYY response to food is differentially influenced by macronutrient content but the effect of glycemic load on PYY response is unknown. This study examined whether glycemic load influences fasting and postprandial PYY levels and whether fasting and postprandial PYY levels are lower in obese black women compared to normal weight black women and to white women. Data were collected from 40 women (20 black, 20 white; 10 each normal weight vs. obese) at the University of North Carolina Clinical and Translational Research Center (CTRC). Participants completed in counterbalanced order two 4½‐day weight‐maintenance, mixed macronutrient high vs. low glycemic load diets followed by a test meal of identical composition. Total PYY levels were assessed before and after each test meal. Results show no differences in fasting PYY levels but significantly less postprandial PYY area under the curve (PYY_AUC) in the group of obese black women compared to each other group (race × obesity interaction, P < 0.04). PYY_AUC was positively related to insulin sensitivity (P < 0.004) but was not affected by glycemic load (main and interactive effects, P > 0.27). These findings indicate that postprandial PYY secretion is not affected by glycemic load but is blunted in obese black women compared with normal weight black women and with white women; additionally, they begin to address whether blunted PYY secretion contributes uniquely to the pathogenesis of obesity in black women.