The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Conditional Probability-Based Significance Tests for Sequential Patterns in Multineuronal Spike Trains

We consider the problem of detecting statistically significant sequential patterns in multineuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data-mining scheme to efficiently discover such patterns, which occur often enough in the data. Here we propose a method to determine the statistical significance of such repeating patterns. The novelty of our approach is that we use a compound null hypothesis that not only includes models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to derive a test of significance for rejecting such a compound null hypothesis. The structure of our null hypothesis also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated with a simulator.

Structural Studies on the Second Mycobacterium smegmatis Dps: Invariant and Variable Features of Structure, Assembly and Function

A second DNA binding protein from stationary-phase cells of Mycobacterium smegmatis (MsDps2) has been identified from the bacterial genome. It was cloned, expressed and characterised and its crystal structure was determined. The core dodecameric structure of MsDps2 is the same as that of the Dps from the organism described earlier (MsDps1). However, MsDps2 possesses a long N-terminal tail instead of the C-terminal tail in MsDps1. This tail appears to be involved in DNA binding. It is also intimately involved in stabilizing the dodecamer. Partly on account of this factor, MsDps2 assembles straightway into the dodecamer, while MsDps1 does so on incubation after going through an intermediate trimeric stage. The ferroxidation centre is similar in the two proteins, while the pores leading to it exhibit some difference. The mode of sequestration of DNA in the crystalline array of molecules, as evidenced by the crystal structures, appears to be different in MsDps1 and MsDps2, highlighting the variability in the mode of Dps–DNA complexation. A sequence search led to the identification of 300 Dps molecules in bacteria with known genome sequences. Fifty bacteria contain two or more types of Dps molecules each, while 195 contain only one type. Some bacteria, notably some pathogenic ones, do not contain Dps. A sequence signature for Dps could also be derived from the analysis.

Seismic response of wrap-faced reinforced soil-retaining wall models using shaking table tests

This paper presents the results of shaking table tests on geotextile-reinforced wrap-faced soil-retaining walls. Construction of model retaining walls in a laminar box mounted on a shaking table, instrumentation, and results from the shaking table tests are discussed in detail. The base motion parameters, surcharge pressure and number of reinforcing layers are varied in different model tests. It is observed from these tests that the response of the wrap-faced soil-retaining walls is significantly affected by the base acceleration levels, frequency of shaking, quantity of reinforcement and magnitude of surcharge pressure on the crest. The effects of these different parameters on acceleration response at different elevations of the retaining wall, horizontal soil pressures and face deformations are also presented. The results obtained from this study are helpful in understanding the relative performance of reinforced soil-retaining walls under different test conditions used in the experiments.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Tests of a Roman Pot Prototype for the TOTEM Experiment

The TOTEM collaboration has developed and tested the first prototype of its Roman Pots to be operated in the LHC. TOTEM Roman Pots contain stacks of 10 silicon detectors with strips oriented in two orthogonal directions. To measure proton scattering angles of a few microradians, the detectors will approach the beam centre to a distance of 10 sigma + 0.5 mm (= 1.3 mm). Dead space near the detector edge is minimised by using two novel "edgeless" detector technologies. The silicon detectors are used both for precise track reconstruction and for triggering. The first full-sized prototypes of both detector technologies as well as their read-out electronics have been developed, built and operated. The tests took place first in a fixed-target muon beam at CERN's SPS, and then in the proton beam-line of the SPS accelerator ring. We present the test beam results demonstrating the successful functionality of the system despite slight technical shortcomings to be improved in the near future.

Loading of itraconazole into porous silica and silicon microparticles: characterization and dissolution tests

Most new drug molecules discovered today suffer from poor bioavailability. Poor oral bioavailability results mainly from poor dissolution properties of hydrophobic drug molecules, because the drug dissolution is often the rate-limiting event of the drug’s absorption through the intestinal wall into the systemic circulation. During the last few years, the use of mesoporous silica and silicon particles as oral drug delivery vehicles has been widely studied, and there have been promising results of their suitability to enhance the physicochemical properties of poorly soluble drug molecules. Mesoporous silica and silicon particles can be used to enhance the solubility and dissolution rate of a drug by incorporating the drug inside the pores, which are only a few times larger than the drug molecules, and thus, breaking the crystalline structure into a disordered, amorphous form with better dissolution properties. Also, the high surface area of the mesoporous particles improves the dissolution rate of the incorporated drug. In addition, the mesoporous materials can also enhance the permeability of large, hydrophilic drug substances across biological barriers. T he loading process of drugs into silica and silicon mesopores is mainly based on the adsorption of drug molecules from a loading solution into the silica or silicon pore walls. There are several factors that affect the loading process: the surface area, the pore size, the total pore volume, the pore geometry and surface chemistry of the mesoporous material, as well as the chemical nature of the drugs and the solvents. Furthermore, both the pore and the surface structure of the particles also affect the drug release kinetics. In this study, the loading of itraconazole into mesoporous silica (Syloid AL-1 and Syloid 244) and silicon (TOPSi and TCPSi) microparticles was studied, as well as the release of itraconazole from the microparticles and its stability after loading. Itraconazole was selected for this study because of its highly hydrophobic and poorly soluble nature. Different mesoporous materials with different surface structures, pore volumes and surface areas were selected in order to evaluate the structural effect of the particles on the loading degree and dissolution behaviour of the drug using different loading parameters. The loaded particles were characterized with various analytical methods, and the drug release from the particles was assessed by in vitro dissolution tests. The results showed that the loaded drug was apparently in amorphous form after loading, and that the loading process did not alter the chemical structure of the silica or silicon surface. Both the mesoporous silica and silicon microparticles enhanced the solubility and dissolution rate of itraconazole. Moreover, the physicochemical properties of the particles and the loading procedure were shown to have an effect on the drug loading efficiency and drug release kinetics. Finally, the mesoporous silicon particles loaded with itraconazole were found to be unstable under stressed conditions (at 38 qC and 70 % relative humidity).

Effect of relative density and confining pressure on Poisson ratio from bender and extender elements tests

By using the bender and extender elements tests, together with measurements of the travel times of shear (S) and primary (P) waves, the variation of Poisson ratio (nu) was determined for dry sands with respect to changes in relative densities and effective confining pressures (sigma(3)). The tests were performed for three different ranges of particle sizes. The magnitude of the Poisson ratio decreases invariably with an increase in both the relative density and the effective confining pressure. The effect of the confining pressure on the Poisson ratio was found to become relatively more significant for fine-grained sand as compared with the coarse-grained sand. For a given material, at a particular value of sigma(3), the magnitude of the Poisson ratio decreases, almost in a linear fashion, with an increase in the value of maximum shear modulus (G(max)). The two widely used correlations in literature, providing the relationships among G(max), void ratio (e) and effective confining pressure (sigma(3)), applicable for angular granular materials, were found to compare reasonably well with the present experimental data for the fine- and medium-grained sands. However, for the coarse-grained sand, these correlations tend to overestimate the values of G(max).

Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.