Fine Tunable,Redox Active Octapalladium Chains Supported by Linear Tetraphosphines,Leading to Dynamically 1D Self-Assembled Coordination Polymers

A series of the octapalladium chains supported by meso-Ph₂PCH₂P(Ph)CH₂P(Ph)CH₂PPh₂ (meso-dpmppm) ligands, [Pd₈(meso-dpmppm)₄(L)₂](BF₄)₄ (L=none ( 1 ), solvents: CH₃CN ( 2 a ), dmf ( 2 b ), dmso ( 2 c ), RN≡C: R=Xyl ( 3 a ), Mes ( 3 b ), Dip ( 3 c ), ^tBu ( 3 d ), Cy ( 3 e ), CH₃(CH₂)₇ ( 3 f ), CH₃(CH₂)₁₁ ( 3 g ), CH₃(CH₂)₁₇ ( 3 h )) and [Pd₈(meso-dpmppm)₄(X)₂](BF₄)₂ (X=Cl ( 4 a ), N₃ ( 4 b ), CN ( 4 c ), SCN ( 4 d )), were synthesized by using 2 a as a stable good precursor, and characterized by spectroscopic (IR, ¹H and ³¹P NMR, UV-vis-NIR, ESI-MS) measurements and X-ray crystallographic analyses (for 1 , 2 a , b , 3 a , b , e , f , 4 a – d ). On the basis of DFT calculations on the X-ray determined structure of 2 b ( [2b-Pd₈]⁴⁺ ) and the optimized models [Pd₈(meso-Ph₂PCH₂P(H)CH₂P(H)CH₂PH₂)₄(CH₃CN)₂]⁴⁺ ( [Pd₈Ph₈]⁴⁺ ) and [Pd₈(meso-H₂PCH₂P(H)CH₂P(H)CH₂PH₂)₄(CH₃CN)₂]⁴⁺ ( [Pd₈H₈]⁴⁺ ), with and without empirically calculating dispersion force stabilization energy (B3LYP-D3, B3LYP), the formation energy between the two Pd₄ fragments is assumed to involve mainly noncovalent interactions (ca. −70 kcal/mol) with four sets of interligand C−H/π interactions and Pd⋅⋅⋅Pd metallophilic one, while electron shared covalent interactions are almost canceled out within the Pd₈ chain. All the compounds isolated are stable in solution and exhibit characteristic absorption at ∼900 nm, which is assignable to a spin allowed HOMO to LUMO transition, and shows temperature dependent intensity change with variable absorption coefficients presumably due to coupling with some thermal vibrations. The structures and electronic states of the Pd₈ chains are found finely tunable by varying the terminal capping ligands. In particular, theoretical calculations elucidated that the HOMO-LUMO energy gap is systematically related to the central Pd−Pd distance (2.7319(6)–2.7575(6) Å) by two ways with neutral ligands L ( 1 , 2 , 3 ) and with anionic ligands X ( 4 ), which are reflected on the NIR absorption energy of 867–954 nm. The isocyanide terminated Pd₈ complexes ( 3 ) further reacted with excess of RNC (6 eq) to afford the Pd₄ complexes, [Pd₄(meso-dpmppm)₂(RNC)₂](BF₄)₂ ( 13 ), and the cyclic voltammograms of 2 a (L=CH₃CN), 3 , and 13 (R=Xyl, Mes, ^tBu, Cy) demonstrated wide range redox behaviors from 2{Pd₄}⁴⁺ to 2{Pd₄}⁰ through 2{Pd₄}²⁺↔{Pd₈}⁴⁺, {Pd₈}³⁺, and {Pd₈}²⁺ strings. The oxidized complexes, [Pd₄(meso-dpmppm)₂(RNC)₃](BF₄)₄ ( 16 ), were characterized by X-ray analyses, and the two-electron reduced chain of [Pd₈(meso-dpmppm)₄](BF₄)₂ ( 7 ) was analyzed by spectroscopic and electrochemical techniques and DFT calculations. Reactions of 2 a with 1 equiv. of aromatic linear bisisocyanide (BI) in CH₂Cl₂ deposited insoluble coordination polymers, {[Pd₈(meso-dpmppm)₄(BI)](BF₄)₄}_n ( 5 ), and interestingly, they were soluble in acetonitrile, ³¹P{¹H} and ¹H DOSY NMR spectra as well as SAXS curves suggesting that the coordination polymers may exist in acetonitrile as dynamically 1D self-assembled coordination polymers comprising ca. 50 units of the Pd₈ rod averaged within the timescale.     

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to demonstrate the performance of the algorithm.     

One-pot ligation strategy for atypical ubiquitin chains synthesis by using the trifluoroacetamidomethyl-protected isopeptide-linked Ub (Tfacm-isoUb) unit

Protein chemical synthesis can provide the homogeneous atypical ubiquitin chains that are usually difficult to obtain by other methods. Herein, we report a new one-pot ligation approach for the synthesis of atypical Ub chains based on the Tfacm-protected isoUb building block with operational simplicity and high efficiency. The key intermediate, the Tfacm-protected isoUb building block can be readily prepared by Fmoc SPPS. The practicality and efficiency of the new method is demonstrated by the successful preparation of K11-linked di-Ub.     

Continuous time markov decision processes with interventions

We study Markov jump decision processes with both continuously and instantaneouslyacting decisions and with deterministic drift between jumps. Such decision processes were recentlyintroduced and studied from discrete time approximations point of view by Van der Duyn Schouten.Weobtain necessary and sufficient optimality conditions for these decision processes in terms of equations and inequalities of quasi-variational type. By means of the latter we find simple necessaryand sufficient conditions for the existence of stationary optimal policies in such processes with finite state and action spaces, both in the discounted and average per unit time reward cases.     

Random frog: An efficient reversible jump Markov Chain Monte Carlo-like approach for variable selection with applications to gene selection and disease classification

The identification of disease-relevant genes represents a challenge in microarray-based disease diagnosis where the sample size is often limited. Among established methods, reversible jump Markov Chain Monte Carlo (RJMCMC) methods have proven to be quite promising for variable selection. However, the design and application of an RJMCMC algorithm requires, for example, special criteria for prior distributions. Also, the simulation from joint posterior distributions of models is computationally extensive, and may even be mathematically intractable. These disadvantages may limit the applications of RJMCMC algorithms. Therefore, the development of algorithms that possess the advantages of RJMCMC methods and are also efficient and easy to follow for selecting disease-associated genes is required. Here we report a RJMCMC-like method, called random frog that possesses the advantages of RJMCMC methods and is much easier to implement. Using the colon and the estrogen gene expression datasets, we show that random frog is effective in identifying discriminating genes. The top 2 ranked genes for colon and estrogen are Z50753, U00968, and Y10871_at, Z22536_at, respectively. (The source codes with GNU General Public License Version 2.0 are freely available to non-commercial users at: http://code.google.com/p/randomfrog/.)     

A numerical algorithm for pricing electricity derivatives for jump-diffusion processes based on continuous time lattices

We present a numerical algorithm for pricing derivatives on electricity prices. The algorithm is based on approximating the generator of the underlying price process on a lattice of prices, resulting in an approximation of the stochastic process by a continuous time Markov chain. We numerically study the rate of convergence of the algorithm for the case of the Merton jump-diffusion model and apply the algorithm to calculate prices and sensitivities of both European and Bermudan electricity derivatives when the underlying price follows a stochastic process which exhibits both fast mean-reversion and jumps of large magnitude.     

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

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In this paper, we mainly studied the limit properties for the countable nonhomogeneous Markov chains. We established some limit properties for the functions of the countable nonhomogeneous Markov chains with variables under the convergence in the sense, which extended the similar conclusions for the functions with two variables. At last, as a corollary, we given the similar result in the homogeneous Markov stock market.     

A Note on Convergence of the Equi-Energy Sampler

This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.