Monte Carlo algorithms: performance analysis for some computer architectures

AbstractThe paper deals with the performance analysis of three Monte Carlo algorithms for some models of computer architectures. To estimate the performance and the speedup of these algorithms, we introduce a special modification of the criterion for the time required to achieve a preset probable error and consider a serial (von Neumann) architecture, a pipeline architecture, and two MIMD (Multiple Instruction stream, Multiple Data stream) parallel architectures. An approach to constructing Monte Carlo vector algorithms to be efficiently run on pipeline computers has also been considered

Exact Error Estimates and Optimal Randomized Algorithms for Integration ⋆

Abstract. Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Hölder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

High capacitance freestanding PEDOT:PSS electrodes for low-frequency electric field delivery

Since the 18th century, the use of electrical stimulation has been widely used to treat disease and control the development of cells, tissues, and organ growth. Electric fields and currents are used to mimic endogenous signals that regulate cell behavior to both better understand their mechanism of action and provide control for bio-engineering and therapeutics. While delivery of electric fields has proven useful, low frequency field delivery remains inaccessible with standard metal electrodes. This delivery of low frequency electric fields is limited by areal capacitance, resulting in low charge injection capacities or Faradaic reactions, which can generate cytotoxic by-products. Here, we demonstrate freestanding poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) electrodes, which conduct both ions and electrons, resulting in electrode capacitance that scales with volume rather than area. We show that these electrodes can be used to generate electric fields in an aqueous medium at frequencies as low as 0.1 Hz. Specifically, we demonstrate persistent electric fields in aqueous media without exceeding the electrochemical window of water, previously unattainable using standard electrodes. Finally, we show that thick PEDOT:PSS electrodes are not cytotoxic. This work opens the path toward delivery of low frequency stimulating electric fields to cells and tissues both in vitro and in vivo