Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model

We propose a method for obtaining the maximum likelihood estimators of the parameters of the Markov-Modulated Diffusion Risk Model in which the inter-claim times, the claim sizes, and the volatility diffusion process are influenced by an underlying Markov jump process. We consider cases when this process has been observed in two scenarios: first, only observing the inter-claim times and the claim sizes in an interval time, and second, considering the number of claims and the underlying Markov jump process at discrete times. In both cases, the data can be viewed as incomplete observations of a model with a tractable likelihood function, so we propose to use algorithms based on stochastic Expectation-Maximization algorithms to do the statistical inference. For the second scenario, we present a simulation study to estimate the ruin probability. Moreover, we apply the Markov-Modulated Diffusion Risk Model to fit a real dataset of motor insurance.

     

Interaction of Tb(III) and hydrolyzed polyacrylamides in solution as a gel and in the solid state

Formation of the HPAM-Tb³ complex in solution was observed in the intensification of Tb(III) fluorescence, viscosity, and light scattering. The interaction is dependent on the degree of hydrolysis of the copolymer and the pH of the solution. As the pH value increases, an intensification of the interaction and formation of a gel is observed. The latter was associated with the appearance of crosslinks in which terbium, or one of its hydrolysis products, works as a binding agent between chains. After drying, the characterization of the residues of the gels was effected by analytical determination (C, H, N, Cl, Tb), fluorescence, and infrared spectrophotometry. The analysis and fluorescence revealed the existence of particles of terbium hydroxide; the infrared spectrophotometry showed the binding of terbium (III) to carboxylate of the copolymer.     

Tuning the acceptors in catalyzed cyclizations initiated by allenes. Silylstannylation/cyclization of allene-aldehydes for synthesis of polyalkylated indolizidines including 223A congeners

Starting from succinamide and 1,2-heptadiene-4-ol, a racemic allene-aldehyde substrate, 20, suitable for R(3)SiSnR'(3)-mediated cyclization was synthesized in six steps and in 21% yield. Stereoselective cyclization (relative cis configuration at the new stereogenic centers of the homoallyl alcohol generated) proceeded smoothly, giving a mixture of indolizidinols bearing five contiguous stereocenters in a combined yield of 80%. Relative configurations of each of the products were unequivocally established by a combination of 2D NMR experiments and single-crystal X-ray analysis. The major indolizidinol obtained in 32% yield was elaborated into indolizidine 5,8-epi-indolizidine 223A via a five-step reaction sequence in 32% overall yield. The second major component (24%) of the key cyclization yielded, in four steps, indolizidine 6,8-epi-223 in 14% yield. Even though revision of the initially postulated structure foiled our original synthetic plans for the natural product, indolizidine 223A, the new stereoselective cyclization strategy and several selective transformations of the indolizidine derivatives reported here may find further applications for the synthesis of highly alkylated indolizidine and other related alkaloids.     

Synthesis of 1-Aza-8-thiabicyclo[4.2.1]nona-2,4-diene 8,8-dioxide and its conversion to a strained spirocycle via photoinduced SO2-N bond cleavage

A route to the doubly unsaturated bridgehead sultam 12 has been developed. When irradiated at 350 nm, this conjugated diene is isomerized via a two-photon process to the structurally novel spiro heterocycle 17 constituted of cyclobutene, thietane dioxide, and pyrrolidine rings. A probable mechanism for the generation of 17 and select reactions thereof are reported. [reaction: see text]     

Olefins turned alkylating agents: diastereoselective intramolecular Zr-catalyzed olefin alkylations

The first examples of intramolecular Zr-catalyzed electrophilic alkylation of aryl olefins are disclosed. Substituted carbo- and heterocycles are prepared efficiently and diastereoselectively.     

First successful reaction of a silyl anion with hafnium tetrachloride

Hafnium tetrachloride reacts with the tris(trimethylsilyl)silyl potassium tmen adduct (1) to form a [tris(trimethylsilyl)silyl]trichlorohafnium tmen complex (2); reaction of 2 with 2,6-dimethylphenylisonitrile leads to insertion into the silicon hafnium bond (4).     

PROBING PHOTODYNAMIC DAMAGE IN NUCLEIC ACIDS WITH A DAMAGE-SPECIFIC DNA BINDING PROTEIN: A COMPARISON OF THE B and Z DNA CONFORMATIONS

—We have employed a damage-specific DNA binding protein from human cells as a probe for base damage in polymers irradiated with white light in the presence of methylene blue. Protein-recognizable damage is introduced only into guanine-containing polymers and quenching of damage introduction by H₂O and sodium azide suggest the involvement of a singlet oxygen mechanism. Using poly d(G-m⁵C), we have demonstrated that the left-handed double helical Z conformation is much less susceptible to guanine photooxidation than is the usual B conformation. We speculate that this difference in reactivity may reflect steric hindrance at the purine C-4 position and could provide some insight into the initial steps of the reaction between singlet oxygen and guanine in nucleic acid polymers.     

A study of the thermal and light induced spin transition in [FeL2](BF4)2 and [FeL2](ClO4)2 L=2,6-di(3-methylpyrazol-1-yl)pyrazine

The spin crossover compounds [FeL2](BF4)2, L=2,6-di(3-methylpyrazol-1-yl)pyrazine and [FeL2](ClO4)2 have very unusual two stage spin transitions which are initially steep and then become more gradual. A detailed variable temperature single crystal X-ray diffraction study has shown that the course of the spin transition is controlled by an order-disorder transition in the counter anions. The high and low spin states both crystallise in the tetragonal space group I4, the structures of the high and low spin states are presented at 290 and 30 K, respectively. The title compounds are shown to undergo LIESST (Light Induced Excited Spin State Trapping) under irradiation with either red or green laser light with wavelengths of 632.8 and 532.06 nm, respectively, at 30 K. The cell parameters for the tetragonal photo-induced metastable high spin state at this temperature are a= 9.169(6), c= 17.77(1) A for [FeL2](ClO4)2 with an increase in unit cell volume of 21 A3, and a= 9.11(1), c= 17.75(2) A and an increase in volume of 42.8 A3 for [FeL2](BF4)2.     

The first enantiomerically pure [n]triangulanes and analogues: sigma-[n]helicenes with remarkable features

(M)-(-)- and (P)-(+)-Trispiro[2.0.0.2.1.1]nonanes [(M)- and (P)-3] as well as (M)-(-)- and (P)-(+)-tetraspiro[2.0.0.0.2.1.1.1]undecanes [(M)- and (P)-4]-enantiomerically pure unbranched [4]- and [5]triangulanes-have been prepared starting from racemic bicyclopropylidenecarboxylic [(1RS)-12] and exo-dispiro[2.0.2.1]heptane-1-carboxylic [(1RS,3SR)-13] acids. The optical resolutions of rac-12 and rac-13 furnished enantiomerically pure acids (S)-(+)-12, (R)-(-)-12, (1R,3S)-(-)-13, and (1S,3R)-(+)-13. The ethyl ester (R)-25 of the acid (R)-(-)-12 was cyclopropanated to give carboxylates (1R,3R)-26 and (1R,3S)-26. The ester (1R,3S)-26 and acids (1R,3S)-13 and (1S,3R)-13 were converted into enantiomerically pure methylene[3]triangulanes (S)-(-)- and (R)-(+)-28. An alternative approach consisted of an enzymatic deracemization of endo-[(1SR,3SR)-dispiro[2.0.2.1]heptyl]methanol (rac-20) or anti-[(1SR,3RS)-4-methylenespiropentyl]methanol (rac-18). This afforded (S)-(-)- and (R)-(+)-28 (starting from rac-20), as well as enantiomerically pure (M)-(-)- and (P)-(+)-1,4-dimethylenespiropentanes [(M)- and (P)-23] starting from rac-18. The methylenetriangulanes (S)-(-)- and (R)-(+)-28 were cyclopropanated furnishing (M)- and (P)-3. The rhodium-catalyzed cycloaddition of ethyl diazoacetate onto (S)-(-)- and (R)-(+)-28 yielded four diastereomeric ethyl trispiro[2.0.0.2.1.1]nonane-1-carboxylates in approximately equal proportions. The enantiomerically pure esters (1R,3S,4S)- and (1S,3R,4R)-30 were isolated by careful distillation and then transformed into [5]triangulanes (M)- and (P)-4 using the same sequence of reactions as applied for (M)- and (P)-3. The structures of the key intermediates (R)-12 and rac-31 were confirmed by X-ray analyses. Although [4]- and [5]triangulanes have no chromophore which would lead to any significant absorption above 200 nm, they have remarkably high specific rotations even at 589 nm with [alpha](20)D=-192.7 [(M)-3, c=1.18, CHCl(3))] or +373.0 [(P)-4, c=1.18, CHCl(3))]. This remarkable optical rotatation is in line with their helical arrangement of sigma bonds, as confirmed by a full valence space single excitation configuration interaction treatment (SCI) in conjunction with DFT computations at the B3LYP/TZVP//B3LYP/6-31+G(d,p) level of theory which reproduce the ORD very well. Thus, it is appropriate to call the helically shaped unbranched [n]triangulanes the "sigma-[n]helicenes", representing the sigma-bond analogues of the aromatic [n]helicenes.