Optimal Strategies in Markov Games

This thesis intends to explore the optimal strategies in Markov chain games and their relevance to applications. For this, the present study not only analyses the classic optimal bold strategies that gamblers bet everything they can afford, but also takes into account the strategies for capital portfolios and certain criteria that outperform traditional bold strategies. In addition, this thesis builds a P-adic number version by modifying the original model and proposes its associated algorithms. Speci?cally, it presents a case of the 2-adic version after listing all the algorithms for the 64 strategies, and proves that the bold strategies are optimal in this case(with three strategies exceptionally optimal and still bold). While applying Probability Generating Function (PGF) approach enables us to successfully solve the gambler's ruin process, the solution of the process involving investment is not immediately obvious. Furthermore, this study introduces various Markov mouse models and ?nds that the survival probability is generally larger under the horizontal splitting context. To develop a general version of an in?nite two- and three-dimensional Markov mouse model, we have ?rst processed the versions of the mouse in both vertical and horizontal models, during the former of which the optimality depends on the probability of being caught, whereas the latter case always outperforms when the number of grids increases. We have also applied the lumped Markov process and the perturbation theory to explore the transition matrix of the in?nite three-dimensional game, and ?nally,have developed a continuous version of the Markov mouse model that can produce the same results with the discrete version in terms of the absorption probability.</p

Additional file 1 of Methyl 3,4-dihydroxybenzoate alleviates oxidative damage in granulosa cells by activating Nrf2 antioxidant pathway

Supplementary Material 1

Comparison of the Kato-Katz methods and ELISA for diagnosis <i>Clonorchis sinensis</i> infection in Heilongjiang Province.

<p>The Kappa value between the two methods was 0.564, <i>P</i><0.001.</p

Test properties of the Kato-Katz methods and ELISA as estimated by Bayesian analysis.

*<p>CI, credibility intervals.</p

Flowchart for the diagnosis of 2359 patients.

<p>KK = Kato-Katz technique.</p

Regional distribution of <i>Clonorchis sinensis</i> infection in Heilongjiang Province by Kato-Katz and ELISA examinations.

<p>A. by Kato-Katz B. by ELISA.</p

Prevalence of Clonorchis sinensis infection in different age group by Kato-Katz and ELISA examinations.

<p>Prevalence of Clonorchis sinensis infection in different age group by Kato-Katz and ELISA examinations.</p

Values of priors and corresponding beta distributions used to estimate the test parameters in the diagnosis of <i>Clonorchis sinensis</i>.

<p>Se = sensitivity.</p><p>Sp = specificity.</p

DataSheet_2_Getting pregnant with congenital adrenal hyperplasia: Assisted reproduction and pregnancy complications. A systematic review and meta-analysis.docx

Many patients with congenital adrenal hyperplasia (CAH) refrain from seeking pregnancy, suffer from infertility or worry about pregnancy complications, mainly due to genitalia abnormalities, anovulation, unreceptive endometrium and metabolic disturbances. Despite those challenges, many live births have been reported. In this systematic review, we focused on the key to successful assisted reproduction strategies and the potential pregnancy complications. We did a systematic literature search of Pubmed, Medline and Scopus for articles reporting successful pregnancies in CAH other than 21-hydroxylase deficiency, and found 25 studies reporting 39 pregnancies covering deficiency in steroidogenic acute regulatory protein, 17α-hydroxylase/17,20-lyase, 11β-hydroxylase, P450 oxidoreductase, cytochrome b5 and 3β-hydroxysteroid dehydrogenase. We summarized various clinical manifestations and tailored reproduction strategy for each subtype. Furthermore, a meta-analysis was performed to evaluate the pregnancy complications of CAH patients. A total of 19 cross-sectional or cohort studies involving 1311 pregnancies of classic and non-classic CAH patients were included. Surprisingly, as high as 5.5% (95% CI 2.3%-9.7%) of pregnancies were electively aborted, and the risk was significantly higher in those studies with a larger proportion of classic CAH than those with only non-classical patients (8.43% (4.1%-13.81%) VS 3.75%(1.2%-7.49%)), which called for better family planning. Pooled incidence of miscarriage was 18.2% (13.4%-23.4%) with a relative risk (RR) of 1.86 (1.27-2.72) compared to control. Glucocorticoid treatment in non-classical CAH patients significantly lowered the miscarriage rate when compared to the untreated group (RR 0.25 (0.13-0.47)). CAH patients were also more susceptible to gestational diabetes mellitus, with a prevalence of 7.3% (2.4%-14.1%) and a RR 2.57 (1.29-5.12). However, risks of preeclampsia, preterm birth and small for gestational age were not significantly different. 67.8% (50.8%-86.9%) CAH patients underwent Cesarean delivery, 3.86 (1.66-8.97) times the risk of the control group. These results showed that fertility is possible for CAH patients but special care was necessary when planning, seeking and during pregnancy.Systematic Review RegistrationPROSPERO https://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=342642, CRD42022342642.</p

The Effect of Peritoneal Fluid from Patients with Endometriosis on Mitochondrial Function and Development of Early Mouse Embryos

<div><p>Background</p><p>Peritoneal fluid (PF) from patients with endometriosis can inhibit early embryo development via probable functional changes of embryo mitochondria in the early stage of embryo development. The purpose of this study was to determine the effect of PF from patients with endometriosis on mitochondrial function and development of early mouse embryos.</p><p>Methodology/Principal Findings</p><p>PF was collected from patients with infertility and endometriosis, infertility due to tubal factors, and normal control subjects, and the level of NO was measured. Early murine embryos were then cultured with PF from normal control subjects, those with endometriosis, and with human tubal fluid (HTF), respectively. Cleavage and blastulation rates, mitochondrial DNA (mtDNA) copy numbers, adenosine triphosphate (ATP) level, and mitochondrial membrane potential (ΔΨm) of the different groups were compared. The NO level in the PF of patients with endometriosis was significantly greater than in those without endometriosis and control patients. The embryos cultures with PF from patients with endometriosis had a lower cleavage rate and blastulation rate, and higher ATP and ΔΨm level at the 2- and 4-cell stages. No significant difference was found in mtDNA copies among the 3 groups.</p><p>Conclusions/Significance</p><p>PF from patients with endometriosis can inhibit early embryo development via probable functional changes of embryo mitochondria in the early stage of embryo development. Understanding the effects of PF on embryo development may assist in developing new methods of treatment for infertility.</p></div