Numerical and Theoretical Studies of Noise Effects in the Kauffman Model

In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a similar kind of behavior, even when the structure of their basins of attraction is quite different. This can be considered as a robust property of these models. We present numerical results for the full range of noise level and obtain approximate analytic expressions for the above crossing time as a function of the noise in the limit cases of small and large noise levels.Comment: 24 pages, 9 figures, Submitted to the Journal of Statistical Physic

An optimized analytical method for the simultaneous detection of iodoform, iodoacetic acid, and other trihalomethanes and haloacetic acids in drinking water

An optimized method is presented using liquid-liquid extraction and derivatization for the extraction of iodoacetic acid (IAA) and other haloacetic acids (HAA9) and direct extraction of iodoform (IF) and other trihalomethanes (THM4) from drinking water, followed by detection by gas chromatography with electron capture detection (GC-ECD). A Doehlert experimental design was performed to determine the optimum conditions for the five most significant factors in the derivatization step: namely, the volume and concentration of acidic methanol (optimized values  = 15%, 1 mL), the volume and concentration of Na2SO4 solution (129 g/L, 8.5 mL), and the volume of saturated NaHCO3 solution (1 mL). Also, derivatization time and temperature were optimized by a two-variable Doehlert design, resulting in the following optimized parameters: an extraction time of 11 minutes for IF and THM4 and 14 minutes for IAA and HAA9; mass of anhydrous Na2SO4 of 4 g for IF and THM4 and 16 g for IAA and HAA9; derivatization time of 160 min and temperature at 40°C. Under optimal conditions, the optimized procedure achieves excellent linearity (R2 ranges 0.9990–0.9998), low detection limits (0.0008–0.2 µg/L), low quantification limits (0.008–0.4 µg/L), and good recovery (86.6%–106.3%). Intra- and inter-day precision were less than 8.9% and 8.8%, respectively. The method was validated by applying it to the analysis of raw, flocculated, settled, and finished waters collected from a water treatment plant in China

Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

Successful Treatment of Polycystic Ovarian Syndrome, Nonalcoholic Fatty Liver Disease and Infertility with Chinese Herbal Medicine: A Case Report

This case report details a 30 year old woman with hyperlipidemia, Nonalcoholic Fatty Liver Disease (NAFLD), Polycystic Ovarian Syndrome (PCOS) and infertility. Her impaired liver function has prevented the use of pharmaceutical drugs (statins and metformin). The patient therefore underwent two stages of Chinese herbal medicine treatment: the first formula to ameliorate hyperlipidemia and amenorrhea; and the second formula to improve ovarian dysfunction as well as glucose and lipid metabolism. Over 8 months of treatment, the patient achieved pregnancy and a natural birth without developing gestational diabetes. While the treatment of coexisting metabolic syndrome conditions is often complex and difficult, this case report highlights how Chinese herbal medicine may offer a successful treatment option for women with multiple metabolic abnormalities and associated infertilit

Sex Hormone-Binding Globulin (SHBG) as an Early Biomarker and Therapeutic Target in Polycystic Ovary Syndrome.

Human sex hormone-binding globulin (SHBG) is a glycoprotein produced by the liver that binds sex steroids with high affinity and specificity. Clinical observations and reports in the literature have suggested a negative correlation between circulating SHBG levels and markers of non-alcoholic fatty liver disease (NAFLD) and insulin resistance. Decreased SHBG levels increase the bioavailability of androgens, which in turn leads to progression of ovarian pathology, anovulation and the phenotypic characteristics of polycystic ovarian syndrome (PCOS). This review will use a case report to illustrate the inter-relationships between SHBG, NAFLD and PCOS. In particular, we will review the evidence that low hepatic SHBG production may be a key step in the pathogenesis of PCOS. Furthermore, there is emerging evidence that serum SHBG levels may be useful as a diagnostic biomarker and therapeutic target for managing women with PCOS