On the construction of a nonlinear recursive predictor

In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.     

Phase Conjugation with Picosecond Pulses in BaTi03

The self-pumped phase conjugate signal of picosecond laser pulses is observed. The width of the incident laser pulses is about 1.5 ps and their repetition rate is 82 MHz. The wavelength of the pulses can be tuned in the range from 710 nm to 850 nm. The pulse character of the conjugate signal is determined by an autocorrelator. The quality of the conjugate pulses is found to be good by the well-known phase distorter method.     

Large-volume sample stacking with polarity switching for the analysis of bacteria by capillary electrophoresis with laser-induced fluorescence detection

Capillary electrophoresis has been utilized for the rapid analysis of bacteria under specific experimental conditions. In this work, a method of large-volume sample stacking with polarity switching was evaluated for the analysis of bacteria by capillary electrophoresis with laser-induced fluorescence detection in order to enhance the detection sensitivity. The results indicated that the proposed method is not only effective for the focusing of bacterial cells, but also for the separation of mixtures of bacteria. With the optimized conditions, an enhancement factor of around 60-fold was obtained when long sample plug (up to 39.6% of capillary volume) was injected. Moreover, with the help of such stacking method, single, sharp, intense peak with high efficiency was observed without multiple peaks attributable to irregular clusters and aggregates of bacterial cells. This simple stacking approach appears to be promising as a rapid sterility test in various fields of applications.     

Simplicial Ricci Flow

We construct a discrete form of Hamilton’s Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, ${{\mathcal S}}$ . These new algebraic equations are derived using the discrete formulation of Einstein’s theory of general relativity known as Regge calculus. A Regge–Ricci flow (RRF) equation can be associated to each edge, ?, of a simplicial lattice. In defining this equation, we find it convenient to utilize both the simplicial lattice ${{\mathcal S}}$ and its circumcentric dual lattice, ${{\mathcal S}^*}$ . In particular, the RRF equation associated to ? is naturally defined on a d-dimensional hybrid block connecting ? with its (d?1)-dimensional circumcentric dual cell, ? ^*. We show that this equation is expressed as the proportionality between (1) the simplicial Ricci tensor, Rc _? , associated with the edge ${\ell\in{\mathcal S}}$ , and (2) a certain volume weighted average of the fractional rate of change of the edges, ${\lambda\in \ell^*}$ , of the circumcentric dual lattice, ${{\mathcal S}^*}$ , that are in the dual of ?. The inherent orthogonality between elements of ${\mathcal S}$ and their duals in ${{\mathcal S}^*}$ provide a simple geometric representation of Hamilton’s RF equations. In this paper we utilize the well established theories of Regge calculus, or equivalently discrete exterior calculus, to construct these equations. We solve these equations for a few illustrative examples.     

Screening and rank ordering of reversible mechanism‐based inhibitors of Hepatitis C virus NS3 protease using electrospray ionization mass spectrometry

An affinity‐selection study using size exclusion chromatography (SEC) combined with off‐line electrospray ionization mass spectrometry (ESI‐MS) was performed on libraries of peptidic α‐ketoamide inhibitors directed against the hepatitis C virus (HCV) NS3 protease. A limiting amount of HCV NS3 protease (25 µM ) was incubated with equimolar amounts (100 µM ) of 49 reversible mechanism‐based ketoamide inhibitors, previously grouped into seven sets to ensure clearly distinguishable mass differences of the enzyme‐inhibitor complexes (>10 Da). The unbound compounds were separated rapidly from the protease and the protease‐inhibitor complexes by SEC spin columns. The eluate of the SEC was immediately analyzed by direct‐infusion ESI‐MS. An enzyme‐inhibitor complex, with a molecular mass corresponding to the NS3 protease binding to the preferred inhibitor, SCH212986, was the only molecular species detected. By increasing the molar ratio of HCV NS3 protease to inhibitors to 1:2 while keeping the inhibitors' concentration constant, the complex of the second most tightly bound inhibitor, SCH215426, was also identified. Although the potencies of these inhibitors were virtually un‐measurable by kinetic assays, a rank order of CVS4441 > SCH212986 > SCH215426 was deduced for their inhibition potencies by direct competition experiment with CVS4441 ( M ). As discussed in the article, through judicious application of this strategy, even large libraries of fairly weak, reversible and slow‐binding inhibitors could be rapidly screened and rank ordered to provide critical initial structure‐activity insights. Copyright © 2011 John Wiley & Sons, Ltd.     

The Alive Particle Filter and Its Use in Particle Markov Chain Monte Carlo

In the following article, we investigate a particle filter for approximating Feynman–Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require the use of advanced particle filter or MCMC algorithms to perform estimation. One of the drawbacks of existing particle filters is that they may “collapse,” in that the algorithm may terminate early, due to the indicator potentials. In this article, using a newly developed special case of the locally adaptive particle filter, we use an algorithm that can deal with this latter problem, while introducing a random cost per-time step. In particular, we show how this algorithm can be used within MCMC, using particle MCMC. It is established that, when not taking into account computational time, when the new MCMC algorithm is applied to a simplified model it has a lower asymptotic variance in comparison to a standard particle MCMC algorithm. Numerical examples are presented for ABC approximations of HMMs.     

First-order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimension d ≥ 3

It is well-known that the hydrodynamic limit of the asymmetric simple exclusion is governed by a viscousless Burgers equation in the Euler scale [15]. We prove that, in the same scale, the next-order correction is given by a viscous Burgers equation up to a fixed time T for dimension d ≥ 3 provided that the corresponding viscousless Burger equation has a smooth solution up to time T. The diffusion coefficient was characterized via a variation of the Green-Kubo formula by [17, 18, 6]. Within the framework of asymmetric simple exclusion, this provides a rigorous verification in a simplified setting that the correction to the Euler equation is given by the Navier-Stokes equation if the time scale is within the Euler scale. © 1997 John Wiley & Sons, Inc.