Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Dislocation Analysis for Large-sized Sapphire Single Crystal Grown by SAPMAC Method

In this paper,large-sized sapphire (230×210 mm,27.5 kg) was grown by SAPMAC method (sapphire growth technique with micro-pulling and shoulder-expanding at the cooled center). Dislocation peculiarity in large sapphire boule (0001) basal plane was investigated by chemical etching,scanning electron microscopy and X-ray topography method. The triangular dislocation etch pit measured is 7.6×101～8.0×102 cm-2,in which relative high-density dislocations were generated at both initial and final stages of crystal growth. The analysis of single-crystal X-ray topography shows that there are no apparent sub-grain boundaries; the dislocation lines are isolated and straight. Finally,the origins of low-density dislocation in sapphire crystal are discussed by numerical analysis method.     

Aligning Text and Phonemes for Speech Technology Applications Using an EM-Like Algorithm

A common requirement in speech technology is to align two different symbolic representations of the same linguistic ‘message’. For instance, we often need to align letters of words listed in a dictionary with the corresponding phonemes specifying their pronunciation. As dictionaries become ever bigger, manual alignment becomes less and less tenable yet automatic alignment is a hard problem for a language like English. In this paper, we describe the use of a form of the expectation-maximization (EM) algorithm to learn alignments of English text and phonemes, starting from a variety of initializations. We use the British English Example Pronunciation (BEEP) dictionary of almost 200,000 words in this work. The quality of alignment is difficult to determine quantitatively since no ‘gold standard’ correct alignment exists. We evaluate the success of our algorithm indirectly from the performance of a pronunciation by analogy system using the aligned dictionary data as a knowledge base for inferring pronunciations. We find excellent performance—the best so far reported in the literature. There is very little dependence on the start point for alignment, indicating that the EM search space is strongly convex. Since the aligned BEEP dictionary is a potentially valuable resource, it is made freely available for research use.     

Pion absorption by16O using realistic interactions—II: Free pion absorption followed by emission of proton

Matrix element of the Gallilean invariant nonrelativistic reduction of the pseudoscalar-pseudovector interaction has been calculated for free pion absorption by a single nucleon inside the nucleus of¹⁶O. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon interaction have been used for the π-capturing nucleon in the initial state. The initial pion distortion in the presence of nuclear field of the absorbing nucleus prior to its absorption together with the Coulomb interaction with the finite nuclear size has been taken into account. The distortion of the emitted proton in the field of the residual nucleus has also been considered. The differential cross-sections have been obtained and calculated results are compared with the previous experimental and theoretical work.     

An evaluation of molecular models of the cytochrome P450 Streptomyces griseolus enzymes P450SU1 and P450SU2

Summary P450SU1 and P450SU2 are herbicide-inducible bacterial cytochrome P450 enzymes from Streptomyces griseolus. They have two of the highest sequence identities to camphor hydroxylase (P450cam from Pseudomonas putida), the cytochrome P450 with the first known crystal structure. We have built several models of these two proteins to investigate the variability in the structures that can occur from using different modeling protocols. We looked at variability due to alignment methods, backbone loop conformations and refinement methods. We have constructed two models for each protein using two alignment algorithms, and then an additional model using an identical alignment but different loop conformations for both buried and surface loops. The alignments used to build the models were created using the Needleman-Wunsch method, adapted for multiple sequences, and a manual method that utilized both a dotmatrix search matrix and the Needleman-Wunsch method. After constructing the initial models, several energy minimization methods were used to explore the variability in the final models caused by the choice of minimization techniques. Features of cytochrome P450cam and the cytochrome P450 superfamily, such as the ferredoxin binding site, the heme binding site and the substrate binding site were used to evaluate the validity of the models. Although the final structures were very similar between the models with different alignments, active-site residues were found to be dependent on the conformations of buried loops and early stages of energy minimization. We show which regions of the active site are the most dependent on the particular methods used, and which parts of the structures seem to be independent of the methods.     

Effect of conformational rigidity on the glass transition and initial decomposition temperatures of polyimides

The dependence of the glass transition and initial decomposition temperatures of polyperyleneimide and polynaphthylimide on the conformational rigidity was studied by the Monte Carlo, Kuhn segment, and quantum chemical AM1 methods. The corresponding linear plots can be used for estimation of the glass transition and initial decomposition temperatures when experimental determination is difficult.     

Hydrophobic Molecular Similarity from MST Fractional Contributions to the Octanol/water Partition Coefficient

Summary The use of a recently proposed hydrophobic similarity index for the alignment of molecules and the prediction of their differences in biological activity is described. The hydrophobic similarity index exploits atomic contributions to the octanol/water transfer free energy, which are evaluated by means of the fractional partitioning scheme developed within the framework of the Miertus-Scrocco-Tomasi continuum model. Those contributions are used to define global and local measures of hydrophobic similarity. The suitability of this computational strategy is examined for two series of compounds (ACAT inhibitors and 5-HT₃ receptor agonists), which are aligned to maximize the global hydrophobic similarity using a Monte Carlo-simulated protocol. Indeed, the concept of local hydrophobic similarity is used to explore structure–activity relationships in a series of COX-2 inhibitors. Inspection of the 3D distribution of hydrophobic/hydrophilic contributions in the aligned molecules is valuable to identify regions of very similar hydrophobicity, which can define pharmacophoric recognition patterns. Moreover, low similar regions permit to identify structural elements that modulate the differences in activity between molecules. Finally, the quantitative relationships found between the pharmacological activity and the hydrophobic similarity index points out that not only the global hydrophobicity, but its 3D distribution, is important to gain insight into the activity of molecules. J.M.M. and S.P. have contributed equally to this study.     

Thermocapillary Alignment of Gas Bubbles Induced by Convective Transport

The effect of a weak convective heat transfer on the thermocapillary interaction of two bubbles with an arbitrary orientation relative to an externally imposed temperature gradient is examined. Asymptotic analysis of the case of large separation distances, Z, suggests that the corrections to the bubbles' velocities are of (Pe/Z²), rather than (Pe²) previously found for an isolated bubble. Equal-sized bubbles are known to move with the same velocities, as if they were isolated, when heat conduction is the only transport mechanism. However, the convective transport results in a relative motion of the bubbles. The tendency of equal bubbles to line up in a plane perpendicular to the applied thermal gradient is shown analytically in the weakly nonlinear limit of small Pe numbers, and an interesting interaction behavior in the case of unequal bubbles is discussed.     

New liquid‐crystal alignment agents based on fluorinated polyimides with trifluoromethyl‐substituted benzene or diphenylether in the side chain

Fluorinated copolyimides derived from 4,4′‐oxydiphthalic anhydride (ODPA) with 4,4′‐oxydianline (ODA) and trifluoromethyl‐containing aromatic diamines have been synthesized and characterized. The trifluoromethyl‐containing diamines include 2,4‐diamino‐3′‐trifluoromethylazobenzene, 2,4‐diamino‐1‐[(4′‐trifluoromethylphenoxy) phenyl] aniline, 3,5‐diamino‐1‐[(4′‐trifluoromethylphenoxy) phenyl] benzamide, 3,5‐diamino‐1‐[(3′‐trifluoromethyl) phenyl] benzamide, 1,4‐bis(4′‐aminophenoxy)‐2‐(3′‐trifluoromethylphenyl) benzene, 3,5‐diaminobenzenetrifluoride, 4,4′‐diamino‐4″‐(p‐trifluoromethyl phenoxy) triphenylamine, and 4‐[(4′‐trifluoromethylphenoxy) phenyl]‐2,6‐bis(4″‐aminophenyl)pyridine. Strong and flexible copolyimide films, produced by casting the polyamic acid solution followed by thermal imidization, exhibited great thermal stability and high mechanical properties. The polyimides had an ultraviolet–visible absorption cutoff at 330–340 nm and pretilt angles as high as 20° for nematic liquid crystals, making them great potential candidates for advanced liquid‐crystal display applications. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1583–1593, 2002