Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Methodology for studying the numerical speed of sound in finite differences schemes

The space and time discretization inherent to all FDTD schemesintroduce non-physical dispersion errors, i.e. deviations ofthe speed of sound from the theoretical value predicted bythe governing Euler differential equations. A generalmethodologyfor computing this dispersion error via straightforwardnumerical simulations of the FDTD schemes is presented.The method is shown to provide remarkable accuraciesof the order of 1/1000 in a wide variety of twodimensionalfinite difference schemes.

Steel Diaphragms in Prestressed Concrete Girder Bridges, September 2004

Over the years, bridge engineers have been concerned about the response of prestressed concrete (PC) girder bridges that had been hit by over-height vehicles or vehicle loads. When a bridge is struck by an over-height vehicle or vehicle load, usually the outside and in some instances one of the interior girders are damaged in a bridge. The effect of intermediate diaphragms in providing damage protection to the PC girders of a bridge is not clearly defined. This analytical study focused on the role of intermediate diaphragms in reducing the occurrence of damage in the girders of a PC-girder bridge that has been struck by an over-height vehicle or vehicle load. The study also investigated whether a steel, intermediate diaphragm would essentially provide the same degree of impact protection for PC girders as that provided by a reinforced-concrete diaphragm. This investigation includes the following: a literature search and a survey questionnaire to determine the state-of-the-art in the use and design of intermediate diaphragms in PC-girder bridges. Comparisons were made between the strain and displacement results that were experimentally measured for a large-scale, laboratory, model bridge during previously documented work and those results that were obtained from analyses of the finite-element models that were developed during this research for that bridge. These comparisons were conducted to calibrate the finite element models used in the analyses for this research on intermediate diaphragms. Finite-element models were developed for non-skewed and skewed PC-girder bridges. Each model was analyzed with either a reinforced concrete or two types of steel, intermediate diaphragms that were located at mid-span of an interior span for a PC-girder bridge. The bridge models were analyzed for lateral-impact loads that were applied to the bottom flange of the exterior girders at the diaphragms location and away from the diaphragms location. A comparison was conducted between the strains and displacements induced in the girders for each intermediate-diaphragm type. These results showed that intermediate diaphragms have an effect in reducing impact damage to the PC girders. When the lateral impact-load was applied at the diaphragm location, the reinforced-concrete diaphragms provided more protection for the girders than that provided by the two types of steel diaphragms. The three types of diaphragms provided essentially the same degree of protection to the impacted, PC girder when the lateral-impact load was applied away from the diaphragm location.

Sleep deprivation effects on circadian clock gene expression in the cerebral cortex parallel electroencephalographic differences among mouse strains.

Sleep deprivation (SD) results in increased electroencephalographic (EEG) delta power during subsequent non-rapid eye movement sleep (NREMS) and is associated with changes in the expression of circadian clock-related genes in the cerebral cortex. The increase of NREMS delta power as a function of previous wake duration varies among inbred mouse strains. We sought to determine whether SD-dependent changes in circadian clock gene expression parallel this strain difference described previously at the EEG level. The effects of enforced wakefulness of incremental durations of up to 6 h on the expression of circadian clock genes (bmal1, clock, cry1, cry2, csnk1epsilon, npas2, per1, and per2) were assessed in AKR/J, C57BL/6J, and DBA/2J mice, three strains that exhibit distinct EEG responses to SD. Cortical expression of clock genes subsequent to SD was proportional to the increase in delta power that occurs in inbred strains: the strain that exhibits the most robust EEG response to SD (AKR/J) exhibited dramatic increases in expression of bmal1, clock, cry2, csnkIepsilon, and npas2, whereas the strain with the least robust response to SD (DBA/2) exhibited either no change or a decrease in expression of these genes and cry1. The effect of SD on circadian clock gene expression was maintained in mice in which both of the cryptochrome genes were genetically inactivated. cry1 and cry2 appear to be redundant in sleep regulation as elimination of either of these genes did not result in a significant deficit in sleep homeostasis. These data demonstrate transcriptional regulatory correlates to previously described strain differences at the EEG level and raise the possibility that genetic differences underlying circadian clock gene expression may drive the EEG differences among these strains.

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

On equilibria in duopolies with finite strategy spaces

We will call a game a reachable (pure strategy) equilibria game if startingfrom any strategy by any player, by a sequence of best-response moves weare able to reach a (pure strategy) equilibrium. We give a characterizationof all finite strategy space duopolies with reachable equilibria. Wedescribe some applications of the sufficient conditions of the characterization.

Finite horizon bargaining and the consistent field

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

Secretion of an endogenous subtilisin by Pichia pastoris strains GS115 and KM71.

The methylotrophic yeast Pichia pastoris is widely used for the expression of heterologous enzymes. While the purity of the desired expression product is of major importance for many applications, we found that recombinant enzymes produced in methanol medium were contaminated by a 37-kDa endogenous yeast protease. This enzyme was completely inhibited by phenylmethanesulfonyl fluoride (PMSF) but not by 1,10-phenanthroline, EDTA, and pepstatin A, suggesting the nature of a serine protease. Its secretion was abolished in P. pastoris strains GS115 and KM71 by specific mutagenesis of a subtilisin gene (SUB2) but not by inactivation of the gene encoding vacuolar proteinase B (PRB). Bioinformatic comparisons of Sub2 protein with subtilisins from other fungal genomes and phylogenetic analyses indicated that this enzyme is not an orthologue of the vacuolar protease cerevisin generally present in yeasts but is more closely related to another putative subtilisin found in a small number of yeast genomes. During growth of P. pastoris, Sub2 was produced as a secreted enzyme at a concentration of 10 microg/ml of culture supernatant after overexpression of the full-length SUB2 gene. During fermentative production of recombinant enzymes in methanol medium, 1 ml of P. pastoris culture supernatant was found to contain approximately 3 ng of Sub2, while the enzyme was not detected during growth in a medium containing glycerol as a carbon source. The mutant strain GS115-sub2 was subsequently used as a host for the production of recombinant proteases without endogenous subtilisin contamination.

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.