What Monte Carlo models can do and cannot do efficiently?

The question "what Monte Carlo models can do and cannot do efficiently" is discussed for some functional spaces that define the regularity of the input data. Data classes important for practical computations are considered: classes of functions with bounded derivatives and Holder type conditions, as well as Korobov-like spaces. Theoretical performance analysis of some algorithms with unimprovable rate of convergence is given. Estimates of computational complexity of two classes of algorithms - deterministic and randomized for both problems - numerical multidimensional integration and calculation of linear functionals of the solution of a class of integral equations are presented. (c) 2007 Elsevier Inc. All rights reserved.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.

Syntheses, structures, some reactions, and electrochemical oxidation of ferrocenylethynyl complexes of iron, ruthenium, and osmium

The syntheses and characterizations of several complexes containing ferrocenylethynyl and ferrocene-1,1'-bis(ethynyl) groups attached to M(PP)Cp'[M = Fe, Ru, PP = dppe, Cp'= Cp*; M = Ru, Os, PP = (PPh3)(2), dppe, Cp' = Cp] are described. Reactions with tetracyanoethene have given either tetracyanobuta-1,3-dienyl or eta(3)-allylic derivatives, while addition of Me+ afforded the corresponding vinylidene derivatives. Some electrochemical measurements are discussed in terms of electronic communication between the redox-active M(PP)Cp' groups through the ferrocene nucleus. The molecular structures of 14 of these complexes have been determined by crystallographic methods.

Synthesis and biological evaluation of a polyglutamic acid-dopamine conjugate: a new antiangiogenic agent

Dopamine has previously been shown to inhibit angiogenesis in vitro and in vivo, but its clinical applications in this context are severely limited by its short half-life. Here we report the synthesis of a polyglutamic acid-dopamine conjugate and show that conjugation significantly extends (from 1 to 24 h) dopamine’s antiangiogenic activity in vitro and in vivo. These findings form the basis for the development of a new class of agents for the treatment of angiogenesis-dependent diseases.