Computational tools for comparing asymmetric GARCH models via Bayes factors

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the marginal likelihood, based on the MCMC output. From these approximations we compute Bayes factors and posterior model probabilities. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

A log-Birnbaum-Saunders regression model with asymmetric errors

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

alpha,beta-Unsaturated Diazoketones as Platforms in the Asymmetric Synthesis of Hydroxylated Alkaloids. Total Synthesis of 1-Deoxy-8,8a-diepicastanospermine and 1,6-Dideoxyepicastanospermine and Formal Synthesis of Pumiliotoxin 251D

A versatile and concise approach for the stereoselective synthesis of mono-, di-, and trihydroxylated indolizidines is presented in four to six steps from Cbz-prolinal and a diazophosphonate. The key steps involved a Wolff rearrangement, followed by a stereoselective dihydroxylation/epoxidation reaction, from an alpha,beta-unsaturated diazoketone. The strategy also permits extension to the synthesis of many natural hydroxylated indolizidine alkaloids as demonstrated in the formal synthesis of pumiliotoxin 251D.

Width of buccal and posterior corridors: differences between cases treated with asymmetric and symmetric extractions

OBJECTIVE: To verify if there is difference in the buccal and posterior corridor width in cases treated with extraction of one and four premolars. METHODS: Through posed smile photographs of 23 Class II patients, subdivision, treated with extraction of one premolar and 25 Class I and Class II patients, subdivision, treated with extraction of four premolars, the percentage of buccal and posterior corridor width was calculated. The two protocols of extractions were compared regarding the buccal and posterior corridor width by independent t tests. RESULTS: There was no statistically significant difference on the buccal and posterior corridor widths between patients treated with symmetric and asymmetric extraction. CONCLUSION: The buccal and posterior corridor did not differ between the evaluated protocols of extractions.

Nonlocal asymmetric exclusion process on a ring and conformal invariance

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram, and consequently the values of the current, depend on u and the density of particles. In the special case of half-lling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-lling value.

Large asymmetric hypertrophy of rectus abdominis muscle in professional tennis players

[EN] PURPOSE: To determine the volume and degree of asymmetry of the musculus rectus abdominis (RA) in professional tennis players. METHODS: The volume of the RA was determined using magnetic resonance imaging (MRI) in 8 professional male tennis players and 6 non-active male control subjects. RESULTS: Tennis players had 58% greater RA volume than controls (P = 0.01), due to hypertrophy of both the dominant (34% greater volume, P = 0.02) and non-dominant (82% greater volume, P = 0.01) sides, after accounting for age, the length of the RA muscle and body mass index (BMI) as covariates. In tennis players, there was a marked asymmetry in the development of the RA, which volume was 35% greater in the non-dominant compared to the dominant side (P<0.001). In contrast, no side-to-side difference in RA volume was observed in the controls (P = 0.75). The degree of side-to-side asymmetry increased linearly from the first lumbar disc to the pubic symphysis (r = 0.97, P<0.001). CONCLUSIONS: Professional tennis is associated with marked hypertrophy of the musculus rectus abdominis, which achieves a volume that is 58% greater than in non-active controls. Rectus abdominis hypertrophy is more marked in the non-dominant than in the dominant side, particularly in the more distal regions. Our study supports the concept that humans can differentially recruit both rectus abdominis but also the upper and lower regions of each muscle. It remains to be determined if this disequilibrium raises the risk of injury.

Iliopsoas and gluteal muscles are asymmetric in tennis players but not in soccer players

[EN] PURPOSE: To determine the volume and degree of asymmetry of iliopsoas (IL) and gluteal muscles (GL) in tennis and soccer players. METHODS: IL and GL volumes were determined using magnetic resonance imaging (MRI) in male professional tennis (TP) and soccer players (SP), and in non-active control subjects (CG) (n = 8, 15 and 6, respectively). RESULTS: The dominant and non-dominant IL were hypertrophied in TP (24 and 36%, respectively, P<0.05) and SP (32 and 35%, respectively, P<0.05). In TP the asymmetric hypertrophy of IL (13% greater volume in the non-dominant than in the dominant IL, P<0.01) reversed the side-to-side relationship observed in CG (4% greater volume in the dominant than in the contralateral IL, P<0.01), whilst soccer players had similar volumes in both sides (P = 0.87). The degree of side-to-side asymmetry decreased linearly from the first lumbar disc to the pubic symphysis in TP (r = -0.97, P<0.001), SP (r = -0.85, P<0.01) and CG (r = -0.76, P<0.05). The slope of the relationship was lower in SP due to a greater hypertrophy of the proximal segments of the dominant IL. Soccer and CG had similar GL volumes in both sides (P = 0.11 and P = 0.19, for the dominant and contralateral GL, respectively). GL was asymmetrically hypertrophied in TP. The non-dominant GL volume was 20% greater in TP than in CG (P<0.05), whilst TP and CG had similar dominant GL volumes (P = 0.14). CONCLUSIONS: Tennis elicits an asymmetric hypertrophy of IL and reverses the normal dominant-to-non-dominant balance observed in non-active controls, while soccer is associated to a symmetric hypertrophy of IL. Gluteal muscles are asymmetrically hypertrophied in TP, while SP display a similar size to that observed in controls. It remains to be determined whether the different patterns of IL and GL hypertrophy may influence the risk of injury.

Organocatalytic asymmetric mannich-type reactions: an easy approach to optically active amine derivatives

The topics I came across during the period I spent as a Ph.D. student are mainly two. The first concerns new organocatalytic protocols for Mannich-type reactions mediated by Cinchona alkaloids derivatives (Scheme I, left); the second topic, instead, regards the study of a new approach towards the enantioselective total synthesis of Aspirochlorine, a potent gliotoxin that recent studies indicate as a highly selective and active agent against fungi (Scheme I, right). At the beginning of 2005 I had the chance to join the group of Prof. Alfredo Ricci at the Department of Organic Chemistry of the University of Bologna, starting my PhD studies. During the first period I started to study a new homogeneous organocatalytic aza-Henry reaction by means of Cinchona alkaloid derivatives as chiral base catalysts with good results. Soon after we introduced a new protocol which allowed the in situ synthesis of N-carbamoyl imines, scarcely stable, moisture sensitive compounds. For this purpose we used α-amido sulfones, bench stable white crystalline solids, as imine precursors (Scheme II). In particular we were able to obtain the aza-Henry adducts, by using chiral phase transfer catalysis, with a broad range of substituents as R-group and excellent results, unprecedented for Mannich-type transformations (Scheme II). With the optimised protocol in hand we have extended the methodology to the other Mannich-type reactions. We applied the new method to the Mannich, Strecker and Pudovik (hydrophosphonylation of imines) reactions with very good results in terms of enantioselections and yields, broadening the usefulness of this novel protocol. The Mannich reaction was certainly the most extensively studied work in this thesis (Scheme III). Initially we developed the reaction with α-amido sulfones as imine precursors and non-commercially available malonates with excellent results in terms of yields and enantioselections.3 In this particular case we recorded 1 mol% of catalyst loading, very low for organocatalytic processes. Then we thought to develop a new Mannich reaction by using simpler malonates, such as dimethyl malonate.4 With new optimised condition the reaction provided slightly lower enantioselections than the previous protocol, but the Mannich adducts were very versatile for the obtainment of β3-amino acids. Furthermore we performed the first addition of cyclic β-ketoester to α-amido sulfones obtaining the corresponding products in good yield with high level of diastereomeric and enantiomeric excess (Scheme III). Further studies were done about the Strecker reaction mediated by Cinchona alkaloid phase-transfer quaternary ammonium salt derivatives, using acetone cyanohydrin, a relatively harmless cyanide source (Scheme IV). The reaction proceeded very well providing the corresponding α-amino nitriles in good yields and enantiomeric excesses. Finally, we developed two new complementary methodologies for the hydrophosphonylation of imines (Scheme V). As a result of the low stability of the products derived from aromatic imines, we performed the reactions in mild homogeneous basic condition by using quinine as a chiral base catalyst giving the α-aryl-α-amido phosphonic acid esters as products (Scheme V, top).6 On the other hand, we performed the addition of dialkyl phosphite to aliphatic imines by using chiral Cinchona alkaloid phase transfer quaternary ammonium salt derivatives using our methodology based on α-amido sulfones (Scheme V, bottom). The results were good for both procedures covering a broad range of α-amino phosphonic acid ester. During the second year Ph.D. studies, I spent six months in the group of Prof. Steven V. Ley, at the Department of Chemistry of the University of Cambridge, in United Kingdom. During this fruitful period I have been involved in a project concerning the enantioselective synthesis of Aspirochlorine. We provided a new route for the synthesis of a key intermediate, reducing the number of steps and increasing the overall yield. Then we introduced a new enantioselective spirocyclisation for the synthesis of a chiral building block for the completion of the synthesis (Scheme VI).

Asymmetric synthesis of benzylic and heterobenzylic amines

C2-Symmetrical, enantiopure 2,6-di[1-(1-aziridinyl)alkyl]pyridines (DIAZAPs) were prepared by a high-yielding, three-step sequence starting from 2,6-pyridinedicarbaldehyde and (S)-valinol or (S)-phenylglycinol. The new compounds were tested as ligands in palladium-catalyzed allylation of carbanions in different solvents. Almost quantitative yield and up to 99% enantiomeric excess were obtained in the reactions of the enolates derived from malonate, phenyl- and benzylmalonate dimethyl esters with 1,3-diphenyl-2-propenyl ethyl carbonate. Asymmetric synthesis of 2-(2-pyridyl)aziridines from chiral 2-pyridineimines bearing a stereogenic center at the nitrogen atom was development. The envisioned route involves the addition of chloromethyllithium to the imine derived from 2-pyridinealdehyde and (S)-valinol, protected as O-trimethylsilyl ether. The analogous reaction performed on the imine derived from (S)-valine methyl ester gave the product containing the aziridine ring as well as the α-chloro ketone group coming from the attack of chloromethyllithium to the ester function. Other stereogenic alkyl substituents at nitrogen gave less satisfactory results. Moreover, the aziridination protocol did not work on other aromatic imines, e.g. 3-pyridineimine and benzaldimine, which are not capable of bidentate chelation. The N-substituent could not be removed, but aziridine underwent ring-opening by attack of nitrogen, sulfur, and oxygen nucleophiles. Complete or prevalent regioselectivity was obtained using cerium trichloride heptahydrate as a catalyst. In some cases, the N-substituent could be removed by an oxidative protocol. The addition of organometallic (lithium, magnesium, zinc) reagents to 2-pyrroleimines derived from (S)-valinol and (S)-phenylglycinol gave the N-substituted-1-(2-pyrrolyl)alkylamines with high yields and diastereoselectivities. The (S,S)-diastereomers were useful intermediates for the preparation of enantiopure 1-[1-(2-pyrrolyl)alkyl]aziridines by routine cyclization of the β-aminoalcohol moiety and of (S)-N-benzoyl 1-[1-(2-pyrrolyl)alkyl]amines and their N-substituted derivatives by oxidative cleavage of the chiral auxiliary. 1-Allyl-2-pyrroleimines obtained from (S)-phenylglycinol and (S)-valinol underwent highly diastereoselective addition of allylmetal reagents, used in excess amounts, to give the corresponding secondary amines with concomitant allyl to 1-propenyl isomerisation of the 1-pyrrole substituent. Protection of the 2-aminoalcohol moiety as oxazolidinone, amide or Boc derivate followed by ring closing metathesis of the alkene groups gave the unsaturated bicyclic compound, whose hydrogenation afforded the indolizidine derivative as a mixture of separable diastereomers. The absolute configuration of the main diastereomer was assessed by X-ray crystallographic analysis.

Asymmetric aminocatalysis: a modern strategy for molecules, challenges and life

The studies conducted during my Phd thesis were focused on two different directions: 1. In one case we tried to face some long standing problems of the asymmetric aminocatalysis as the activation of encumbered carbonyl compounds and the control of the diastereoisomeric ratio in the diastero- and enantioselective construction of all carbon substituted quaternary stereocenters adjacent a tertiary one. In this section (Challenges) was described the asymmetric aziridination of ,-unsaturated ketones, the activation of ,-unsaturated -branched aldehydes and the Michael addition of oxindoles to enals and enones. For the activation via iminium ion formation of sterically demanding substrates, as ,-unsaturated ketones and ,-unsaturated -branched aldehydes, we exploited a chiral primary amine in order to overcome the problem of the iminium ion formation between the catalyst and encumbered carbonylic componds. For the control of diastereoisomeric ratio in the diastero- and enantioselective construction of all carbon substituted quaternary stereocenters adjacent a tertiary one we envisaged that a suitable strategy was the Michael addition to 3 substituted oxindoles to enals activated via LUMO-lowering catalysis. In this synthetic protocol we designed a new bifunctional catalyst with an amine moiety for activate the aldehyde and a tioureidic fragment for direct the approach of the oxindole. This part of the thesis (Challenges) could be considered pure basic research, where the solution of the synthetic problem was the goal itself of the research. 2. In the other hand (Molecules) we applied our knowledge about the carbonylic compounds activation and about cascade reaction to the synthesis of three new classes of spirooxindole in enantiopure form. The construction of libraries of these bioactive compounds represented a scientific bridge between medicinal chemistry or biology and the asymmetric catalysis.

Dynamic resolution of alpha-substituted dihydrocinnamic aldehydes. A new asymmetric synthesis of pharmaceutically important amine building blocks.

Crystallization-induced diastereoisomer transformation (CIDT) was successfully employed in the enantioselective synthesis of 2-alkyl-3-aryl-propan-1-amines. These products are seen as potentially useful building blocks in the field of asymmetric organic chemistry, notably for pharmaceutically relevant compounds. The procedure was based on a recently reported protocol for deracemization of dihydrocinnamic aldehydes in which enantiomerically enriched 1-(amino(phenyl)methyl)naphthalen-2-ol (Betti base) is employed as a resolving agent. Additionally, fenpropimorph, a biologically active substance which contains the 2-alkyl-3-aryl-propan-1-amine moiety was synthetized, as an attempt to assess the usefulness of the enantiomerically enriched amines.