Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes

Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every time birth or death occurs, which makes fluctuations in the rates inevitable. The differential-difference equation governing the time evolution of such a birth-death process is well established, but it resists solving for a non-asymptotic solution. In this work, we present the analytic solution of the differential-difference equation for birth-death processes without approximation. The time-dependent solution we obtain leads to an analytical expression for counting statistics of products (or customers). We further examine the relationship between the system size fluctuations and the birth and death rates, and find that statistical properties (variance subtracted by mean) of the system size are determined by the mean death rate as well as the covariance of the system size and the net growth rate (i.e., the birth rate minus the death rate). This work suggests a promising new direction for quantitative investigations into birth-death processes

Generalized gravity model for human migration

The gravity model (GM) analogous to Newton's law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but powerful approach relies only on the 'mass' factor represented by the scale of the regions and the 'geometrical' factor represented by the geographical distance. However, when the population has a subpopulation structure distinguished by different attributes, the estimation of the flow solely from the coarse-grained geographical factors in the GM causes the loss of differential geographical information for each attribute. To exploit the full information contained in the geographical information of subpopulation structure, we generalize the GM for population flow by explicitly harnessing the subpopulation properties characterized by both attributes and geography. As a concrete example, we examine the marriage patterns between the bride and the groom clans of Korea in the past. By exploiting more refined geographical and clan information, our generalized GM properly describes the real data, a part of which could not be explained by the conventional GM. Therefore, we would like to emphasize the necessity of using our generalized version of the GM, when the information on such nongeographical subpopulation structures is available.Comment: 14 pages, 6 figures, 2 table

Identification of keratinolytic function in Chryseobacterium camelliae Dolsongi-HT1 isolated from Green Tea

Keratin forms a major component of the epidermis, hair, feathers, nails, scales and etc. However, old keratins on the skin are not preferred for the beauty purpose. Therefore, in the highly efficient and low irritative method to remove old keratin on the skin is highly desired. For this purpose, one of the appropriate methods is the enzymatic lysis of keratin. To screen a novel keratinase, a novel microorganism having keratinolytic activity was isolated by enrichment culture. Newly screened microorganism was isolated from green tea in dolsong-i tea garden, Jeju and identified as Chryseobacterium camelliae Dolsongi-HT1. The keratinase activity of C. camelliae Dolsongi-HT1 was confirmed in the culture media. The effect of pH and temperature were studied using cell culture media. Crude keratinase showed high activity over a wide range of temperature (37 to 60°C) and showed the highest activity at 50°C. Optimum pH of keratinase activity of crude keratinase was pH 8. Interestingly, this enzyme activity was maintained over 50% at pH 6. This feature is promising for the application to cosmetics. The effect of nitrogen source for cell culture was also investigated. Among the various nitrogen sources, the highest keratinase activity (relative activity of 366.4%) was detected when cells were cultured using tryptone extract. To study the keratinolytic activity effect of keratin on the skin, the keratin of skin was obtained using tape stripping. It was found that the structure of keratin was degraded by crude keratinase. To identify the keratinase, the complete genome of C. camelliae Dolsongi-HT1 was sequenced. Because keratinases are regarded as serine or metalloprotease group, we searched for those proteases in the C. camelliae Dolsongi-HT1 genome sequence. As s result, over twenty putative keratinases could be identified. Further research to identify desired keratinases should be performed

Simulation of Flood Propagation Due to Levee Break Using the Cartesian Cut Cell Method

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv