Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function

It is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of two Bessel bridges, in which noncolliding condition is imposed. We show that the moments of the maximum value is then expressed using the double Dirichlet series, or using the integrals of products of the Jacobi theta functions and its derivatives. Since the present system will be provided as a diffusion scaling limit of a version of vicious walker model, the ensemble of 2-watermelons with a wall, the dominant terms in long-time asymptotics of moments of height of 2-watermelons are completely determined. For the height of 2-watermelons with a wall, the average value was recently studied by Fulmek by a method of enumerative combinatorics.Comment: v2: LaTeX, 19 pages, 2 figures, minor corrections made for publication in J. Stat. Phy

Limit distributions of two-dimensional quantum walks

One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two components of walker's pseudovelocity, $X_t/t$ and $Y_t/t$, is proved and the probability density of limit distribution is derived. Dependence of the two-dimensional limit density function on the parameter of quantum coin and initial four-component qudit of quantum walker is determined. Symmetry of limit distribution on a plane and localization around the origin are completely controlled. Comparison with numerical results of direct computer-simulations is also shown.Comment: v3: REVTeX4, 20 pages, 6 figures, minor corrections made for publicatio

Effect of extracted garlic powder ingestion for two months on exercise-induced immunological responses

Introduction. Exhaustive exercise is associated with an increased risk of upper respiratory tract infection. Previously, allicin supplementation has been reported to reduce the incidence of common cold symptoms and production of exercise-induced interleukin (IL)-6. However, it is not clear if daily ingestion of the edible portion of whole garlic (Allium sativum) alters the exercise-induced immunological response. The present study investigated the effects of extracted garlic powder ingestion for 2 months on immune cell counts, natural killer cell activity (NKCA), as well as changes in cytokines, cortisol, and lactic acid in response to high-intensity cycling exercise. Methods. The present study employed a before-after study design. Six sedentary male participants (age, 22.0±0.3 years) consumed extracted garlic powder for 2 months, and underwent 45 minutes of cycling exercise at 80% of the heart rate reserve once before and once after the supplementation period. A thousand milligrams of extracted garlic powder, comparable to 6 g (1 clove) of raw garlic, was ingested every day. Blood samples were obtained at the following five time points: before exercise, 0 min, 30 min, 60 min, and 120 min after exercise. We measured NKCA, leukocyte counts, neutrophil counts, lymphocyte counts, as well as levels of serum IL-6, IL-10, cortisol, and lactic acid. Repeated measures ANOVA was used for statistical analyses. When interaction effects were significant, measurement values at the various time points were compared between pre- and post-supplementation period using the paired t-test. Changes were deemed statistically significant when p\u3c0.05. Results. We observed no significant difference in pre-exercise measurements between pre- and post-supplementation periods. In addition, we found no significant interaction effect for leukocytes, neutrophils, NKCA, IL-10, and cortisol. However, we did identify a significant interaction effect for lymphocytes, IL-6, and lactic acid (p=0.033, p=0.030, and p\u3c0.001, respectively). Lymphocyte counts were significantly lower post-supplementation relative to pre-supplementation immediately after exercise (p=0.014). In addition, IL-6 was significantly lower post-supplementation relative to pre-supplementation immediately and 30 minutes after exercise (p=0.015 and p=0.018, respectively). Lactic acid levels were significantly lower post-supplementation relative to pre-supplementation immediately after exercise (p=0.018). Conclusions. The extracted garlic powder did not significantly influence exercise-induced responses by leukocytes, neutrophils, NKCA, IL-10, or cortisol. However, exercise-induced responses by lymphocytes, IL-6, and lactic acid were suppressed after ingestion of extracted garlic powder. Thus, daily ingestion of the edible portion of whole garlic may suppress exercise-induced immunological responses and lactic acid levels

“Live-Autoradiography” Technique Reveals Genetic Variation in the Rate of Fe Uptake by Barley Cultivars

Iron (Fe) is an essential trace element in plants; however, the available Fe in soil solution does not always satisfy the demand of plants. Genetic diversity in the rate of Fe uptake by plants has not been broadly surveyed among plant species or genotypes, although plants have developed various Fe acquisition mechanisms. The “live-autoradiography” technique with radioactive 59Fe was adopted to directly evaluate the uptake rate of Fe by barley cultivars from a nutrient solution containing a very low concentration of Fe. The uptake rate of Fe measured by live autoradiography was consistent with the accumulation of Fe-containing proteins on the thylakoid membrane. The results revealed that the ability to acquire Fe from the low-Fe solution was not always the sole determinant of tolerance to Fe deficiency among barley genotypes. The live-autoradiography system visualizes the distribution of β-ray-emitting nuclides and has flexibility in the shape of the field of view. This technique will strongly support phenotyping with regard to the long-distance transport of nutrient elements in the plant body