Partial Synthesis and Regioselective Reduction of Steroidal 11,12-Seco-Dioic Anhydrides

12-seco-5beta-cholane-11,12,24-trioic acid in 42% yield, along with two other compounds identified as 3alpha-hydroxy-11,12-seco-12-nor-5beta-cholane-11,24-dioic acid (25%) and 3alpha, 13-dihydroxy-11,12-seco-12-nor-5beta-cholane-11,24-dioic acid (32%). Ozonolysis of methyl 3alpha-ethoxycarbonyloxy-5beta-chol-11-enoate afforded the3alpha-ethoxycarbonyloxy-11,12-seco- 5beta -cholane-11,12,24-trioic acid 24-methyl ester, in 25% yield, which was converted to the desired 11,12-seco-dioic anhydride by treatment with acetic anhydride. Reduction of the obtained anhydride with NaBH4 in THF gave in total regioselectivity the 3alpha-ethoxycarbonvloxv-11,12-seco-12-hvdroxy-5beta-cholane-11,24-dioic acid 24-methyl ester. Treatment of the hydroxy-acid with acetic anhydride led to the corresponding acetoxy-acid, 3alpha-ethoxycarbonyioxy-11,12-seco-12-acetoxy-5beta-cholane-11,24-dioic acid 24-methyl ester. Oxidation of methyl 12beta-hydroxy-11-oxo-5beta-cholanoate with NaIO4/CrO3 afforded the corresponding 11,12-seco-dioic acid in good yield. Treatment with acetic anhydride led to the desired 11,12-seco-5beta-cholane-11,12,24-trioic acid-11,12-anhydride 24-methyl ester. Reduction of the anhydride with NaBH4 in THF gave exclusively the 11,12-seco-12-hvdroxv-5beta-cholane-11,24-dioic acid 24-methyl ester. Treatment of the latter with acetic anhydride afforded the corresponding lactone, methyl 12-oxa-C-homo-11-oxo-5beta-cholanoate, in only 6% yield and the acetoxy-acid, 11,12-seco-12-acetoxy-5beta-cholane-11,24-dioic acid 24-methyl ester, as the major product. In the 5a-series, hecogenin was chosen as the starting material. The corresponding 3beta-acetoxy- and 3beta-benzoyloxy-12-hydroxy-11-ones derivatives were prepared through the corresponding bromo-ketones. Oxidation of these ketols with NaIO4 /CrO3 gave the corresponding 11,12-seco-dioic acids which led, upon treatment with acetic anhydride, to the desired 11,12-seco-dioic anhydrides. Reduction of the obtained 3beta-acetoxy-11,12-secotigogenin-11,12-dioic anhydride with NaBH4 in THF gave in total selectivity the corresponding hydroxy-acid, 3alpha-acetoxy-11,12-secotigogenin-12- hydroxy-11-oic acid. Treatment of the latter with acetic anhydride afforded in a quantitative yield the corresponding 11,12-seco-12-acetoxy-11-oic acid derivative. When the hydroxy acid was treated with p-toluenesulphonic acid in xylene, 5% of the corresponding lactone was obtained. Treatment of the hydroxy-acid with 2,2-dipyridyl disulphide in dry benzene afforded 14% of the corresponding lactone. Gas chromatography technique has been used for qualitative and quantitative analysis. Detailed GLC data of bile acid and hecogenin derivatives, which have been studied in this work, are given in tables 1,4,5,6,7,10,11,12a, and 12b. Mass spectrometry has been also very useful for the identification of different compounds. Interpretations of mass spectral data of all new compounds are given in figures at the appropriate places in Chapter 2. Detailed mass spectral data of most of the investigated derivatives are listed in tables in the Appendix. In conclusion, 11,12-seco-dioic anhydrides, in both 5a- and 5beta-series, having different substituents at C-3 have been prepared. Treatment of those anhydrides with NaBH4 has led to the reduction in total regioselectivity at C-12. Neither the substituents at C-3 nor the type of A/B ring fusion seem to have an effect on the course of regioselectivity. A rationalisation for this selectivity, in the hydride reduction of these anhydrides, is offered in 2.16. It has also been observed that the products from the reduction process are the corresponding hydroxy-acids. These hydroxy-acids have proved to resist attempts for cyclisation to the corresponding lactones

On the Reduction of Singularly-Perturbed Linear Differential Systems

In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is based on the reduction criterion introduced for linear singular differential systems by Moser. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations, giving rise to the package ISOLDE, as well as in the perturbed algebraic eigenvalue problem. Our algorithm, implemented in the computer algebra system Maple, paves the way for efficient symbolic resolution of singularly-perturbed linear differential systems as well as further applications of Moser-based reduction over bivariate (differential) fields.Comment: Keywords: Moser-based Reduction, Perturbed linear Differential systems, turning points, Computer algebr

Sample-Efficient Learning of Mixtures

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total variation distance. Let $\mathcal F$ be an arbitrary class of probability distributions, and let $\mathcal{F}^k$ denote the class of $k$-mixtures of elements of $\mathcal F$. Assuming the existence of a method for learning $\mathcal F$ with sample complexity $m_{\mathcal{F}}(\epsilon)$, we provide a method for learning $\mathcal F^k$ with sample complexity $O({k\log k \cdot m_{\mathcal F}(\epsilon) }/{\epsilon^{2}})$. Our mixture learning algorithm has the property that, if the $\mathcal F$-learner is proper/agnostic, then the $\mathcal F^k$-learner would be proper/agnostic as well. This general result enables us to improve the best known sample complexity upper bounds for a variety of important mixture classes. First, we show that the class of mixtures of $k$ axis-aligned Gaussians in $\mathbb{R}^d$ is PAC-learnable in the agnostic setting with $\widetilde{O}({kd}/{\epsilon ^ 4})$ samples, which is tight in $k$ and $d$ up to logarithmic factors. Second, we show that the class of mixtures of $k$ Gaussians in $\mathbb{R}^d$ is PAC-learnable in the agnostic setting with sample complexity $\widetilde{O}({kd^2}/{\epsilon ^ 4})$, which improves the previous known bounds of $\widetilde{O}({k^3d^2}/{\epsilon ^ 4})$ and $\widetilde{O}(k^4d^4/\epsilon ^ 2)$ in its dependence on $k$ and $d$. Finally, we show that the class of mixtures of $k$ log-concave distributions over $\mathbb{R}^d$ is PAC-learnable using $\widetilde{O}(d^{(d+5)/2}\epsilon^{-(d+9)/2}k)$ samples.Comment: A bug from the previous version, which appeared in AAAI 2018 proceedings, is fixed. 18 page

Formal Solutions of a Class of Pfaffian Systems in Two Variables

In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in (Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE, implemented in the computer algebra system Maple.Comment: Keywords: Linear systems of partial differential equations, Pfaffian systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal for

Development of new transition metal catalyzed C-C bond forming reactions and their application toward natural product synthesis

textIn Michael J. Krische research group we are developing new transition metal catalyzed Carbon-Carbon (C-C) forming reactions focusing on atom economy and byproduct free, environmental friendly approaches. We have developed a broad family of C-C bond forming hydrogenations with relative and absolute stereocontrol which provide an alternative to stoichiometric organometallic reagents in certain carbonyl and imine additions. Inspiring from the group work my goal was to develop new reactions, extend the scope of our group chemistry and their application towards synthesis of biologically active natural products. I have been part of enantioselective Rh catalyzed Aldol reaction of vinyl ketones to different aldehydes. Also, we have found that iridium catalyzed transfer hydrogenation of allylic acetates in the presence of aldehydes or alcohols results in highly enantioselective carbonyl allylation under the conditions of transfer hydrogenative. Based on this reactivity a concise enantio- and diastereoselective synthesis of 1,3-polyols was achieved via iterative chain elongation and bidirectional iterative asymmetric allylation was performed, which enables the rapid assembly of 1,3-polyol substructures with exceptional levels of stereocontrol. The utility of this approach stems from the ability to avoid the use of chirally modified allylmetal reagents, which require multistep preparation, and the ability to perform chain elongation directly from the alcohol oxidation level. This approach was utilized for the total synthesis of (+)-Roxaticin from 1,3-propanediol in 20 longest linear steps and a total number of 29 manipulations. Further, advancements were made in iridium catalyzed C-C bond formation under transfer hydrogenation. While methallyl acetate does not serve as an efficient allyl donor, the use of more reactive leaving group in methallyl chloride compensate for the shorter lifetime of the more highly substituted olefin π-complex. Based on this insight into the requirements of the catalytic process, highly enantioselective Grignard-Nozaki-Hiyama methallylation is achieved from the alcohol or aldehyde oxidation levels. Also, a catalytic method for enantioselective vinylogous Reformatsky- type aldol addition was developed in which asymmetric carbonyl addition occurs with equal facility from the alcohol or aldehyde oxidation level. Good to excellent levels of regioselectivity and uniformly high levels of enantioselectivity were observed across a range of alcohols and aldehydes.Chemistr

Selective hydrogenation of citral over mesoporous Ru/TiO2/SiO2 catalysts

Thesis (Master)--Izmir Institute of Technology, Chemical Engineering, Izmir, 2013Includes bibliographical references (leaves: 68-72)Text in English; Abstract: Turkish and Englishxiii, 84 leavesThe liquid phase citral hydrogenation was investigated over Ru/SiO2, Ru/TiO2 and Ru/TiO2/SiO2 catalysts. TiO2/SiO2 supports were prepared by sol-gel deposition, impregnation and absorption methods. The effect of the supports and catalyst reduction temperature, 300 ï‚°C (LTR) and 450 ï‚°C (HTR) on citral conversion and selectivity to unsaturated alcohols were examined. A well-defined crystalline anatase phase was only observed on the support prepared by absorption method, TiO2/SiO2-ABS. A high dispersion and interaction of Ru were observed over TiO2 for Ru/TiO2. Ru/TiO2/SiO2-ABS also displayed similar properties but to a lower extent. Ru/TiO2/SiO2-ABS catalyst showed the highest citral conversion (57.7 %) at LTR among the different Ru/TiO2/SiO2 catalysts. Its selectivity to UA was also high (70.2 %). This was attributed to a better metal support interaction and dispersion obtained by this method. However, a selectivity of 62.6 % was obtained over Ru/TiO2. Activity of the catalysts was mostly observed to decrease as reduction temperature increased from 300 ï‚°C to 450 ï‚°C. Citral conversion decreased from 57.7 % to 42.3 % over Ru/TiO2/SiO2-ABS. However, selectivities to unsaturated alcohol (nerol and geraniol) over Ru/TiO2 and Ru/TiO2/SiO2 catalysts were increased at HTR, reaching about 80 %. This was suggested to be due to more interaction of TiO2 with the Ru (strong metal support interaction). There was no significant change in the selectivity to UA obtained at HTR for Ru/SiO2. This was related to the inert nature of SiO2

What is Multiphysics? Definition and Examples

Academic presentation at the International Conference on the Cooperation and Integration of Industry, Education, Research and Application, arranged by Henan University of Science and Technology, Luoyang, 21. - 23.11.23

Evaluation of the Surgical and Pharmacological Treatment of Diabetic Foot Infection: A Retrospective Study

BACKGROUND: Diabetic foot infection is a major cause of patient disabilities and lowers limb amputations, with high treatment costs and hospitalisation requirements. AIM: Aim of this study was to evaluate surgical wound care plus antibiotic effects in the treatment of mild and moderate diabetic foot infections. METHODS: This retrospective study involved 60 patients with diabetic foot infections with or without osteomyelitis. The patients were categorised as group 1 mild and group 2 moderate. Both groups were treated using local wound debridement and the systemic administration of antibiotics. Group 1 (16) patients were treated with two regimens of oral antibiotics in two regimens, A (amoxicillin/clavulanate + metronidazole) and B (clindamycin + metronidazole), for 10-14 days. Group 2 (42) patients were treated with oral plus intravenous antibiotics in two regimens, A (ampicillin + cloxacillin + metronidazole) and B (lincomycin + metronidazole), for 6 weeks. The patients followed-up with local wound care specialists for 3 months to evaluate the treatment outcomes (cure, improvement, or failure). RESULTS: Group 1 had an 80% cure rate under regimen A and a 100% cure rate under regimen B. Group 2 regimen A patients had a 61.5% cure rate and 11.53% improved, while regimen B patients had a 68.75% cure rate and 12.5% improved. Failure in both regimens was 23.8% in 20 patients with osteomyelitis, while 35% were cured and 20% improved during the study period. CONCLUSION: Local surgical wound care for 3 months with antibiotic regimens for 6 weeks resulted in good response and cure rates, with lower costs and fewer instances of hospitalisation. Intravenous lincomycin and oral metronidazole achieved higher cure responses for moderate diabetic foot infections