Mixtures of probabilistic principal component analysers

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

Isotropic compression of mixtures of hard and soft spheres

The compaction behaviour of powders with soft and hard components is of particular interest to the paint processing industry. Unfortunately, at the present time, very little is known about the internal mechanisms within such systems and therefore suitable tests are required to help in the interpretative process. The TRUBAL, Distinct Element Method (D.E.M.) program was the method of investigation used in this study. Steel (hard) and rubber (soft) particles were used in the randomly-generated, binary assemblies because they provided a sharp contrast in physical properties. For reasons of simplicity, isotropic compression of two-dimensional assemblies was also initially considered. The assemblies were first subject to quasi-static compaction, in order to define their behaviour under equilibrium conditions. The stress-strain behaviour of the assemblies under such conditions was found to be adequately described by a second-order polynomial expansion. The structural evolution of the simulation assemblies was also similar to that observed for real powder systems. Further simulation tests were carried out to investigate the effects of particle size on the compaction behaviour of the two-dimensional, binary assemblies. Later work focused on the quasi-static compaction behaviour of three-dimensional assemblies, because they represented more realistic particle systems. The compaction behaviour of the assemblies during the simulation experiments was considered in terms of percolation theory concepts, as well as more familiar macroscopic and microstructural parameters. Percolation theory, which is based on ideas from statistical physics, has been found to be useful in the interpretation of the mechanical behaviour of simple, elastic lattices. However, from the evidence of this study, percolation theory is also able to offer a useful insight into the compaction behaviour of more realistic particle assemblies.

The role of experts in policy making

As public policy issues increasingly have a technical aspect to them an interactive relationship has developed between science and policy. The aim of this thesis is to investigate the two aspects of this relationship: the influence of science on policy and the influence of policy implications on science. Most existing studies in this area treat only one or other of these aspects. Furthermore, they tend to provide interesting case study material but very little theoretical analysis. This thesis attempts to overcome these problems by dealing with both aspects of the interaction between science and policy and by providing theoretical models of this relationship. The thesis combines the theoretical development of these models with the analysis of three empirical case studies: the controversy in Britain over smoking and health; the application of educational psychology to the development of education policy in Britain; the controversy over the health effect of lead in the environment. The theoretical models are developed in Part 1. In Part 2 the empirical case studies are presented and in Part 3 the theoretical material is assessed in the light of these case studies. The main thesis of this study is that there is a fundamental mismatch between science and policy-making. Criticism is always essential in science. However, when science is involved in the policy process, either scientific claims are not subjected to a significant level of criticism or they are scrutinized so closely that no view achieves general consensus and conflicting advice results. In this situation, contrary to the traditional view, science can generate uncertainty. The role which science plays in the policy process is influenced by this level of criticism, by the context of political power and by the progress of an issue through the various stages of the policy process.

Measure Refutations and Metrics on Statements of Experts (Logical Formulas) in the Models for Some Theory

* This work was financially supported by the Russian Foundation for Basic Research, project no. 04-01-00858a.

On Coordination of Experts’ Estimations of Quantitative Variable

* The work was supported by the RFBR under Grants N07-01-00331a, 08-07-00136a

Mixtures of g-priors in Generalized Linear Models

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this paper, we extend mixtures of g-priors to GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1+g) and illustrate how this prior distribution encompasses several special cases of mixtures of g-priors in the literature, such as the Hyper-g, truncated Gamma, Beta-prime, and the Robust prior. Under an integrated Laplace approximation to the likelihood, the posterior distribution of 1/(1+g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically. We discuss the local geometric properties of the g-prior in GLMs and show that specific choices of the hyper-parameters satisfy the various desiderata for model selection proposed by Bayarri et al, such as asymptotic model selection consistency, information consistency, intrinsic consistency, and measurement invariance. We also illustrate inference using these priors and contrast them to others in the literature via simulation and real examples.

New Method for the Estimation of Viscosity of Pure and Mixtures of Ionic Liquids Based on the UNIFAC–VISCO Model

A modified UNIFAC–VISCO group contribution method was developed for the correlation and prediction of viscosity of ionic liquids as a function of temperature at 0.1 MPa. In this original approach, cations and anions were regarded as peculiar molecular groups. The significance of this approach comes from the ability to calculate the viscosity of mixtures of ionic liquids as well as pure ionic liquids. Binary interaction parameters for selected cations and anions were determined by fitting the experimental viscosity data available in literature for selected ionic liquids. The temperature dependence on the viscosity of the cations and anions were fitted to a Vogel–Fulcher–Tamman behavior. Binary interaction parameters and VFT type fitting parameters were then used to determine the viscosity of pure and mixtures of ionic liquids with different combinations of cations and anions to ensure the validity of the prediction method. Consequently, the viscosities of binary ionic liquid mixtures were then calculated by using this prediction method. In this work, the viscosity data of pure ionic liquids and of binary mixtures of ionic liquids are successfully calculated from 293.15 K to 363.15 K at 0.1 MPa. All calculated viscosity data showed excellent agreement with experimental data with a relative absolute average deviation lower than 1.7%.

The use of binary mixtures of 1-butyl-1-methylpyrrolidinium bis{(trifluoromethyl)sulfonyl}imide and aliphatic nitrile solvents as electrolyte for supercapacitors

Abstract The development of high voltage electrolytes is one of the key aspects for increasing both energy and power density of electrochemical double layer capacitors (EDLCs). The usage of blends of ionic liquids and organic solvents has been considered as a feasible strategy since these electrolytes combine high usable voltages and good transport properties at the same time. In this work, the ionic liquid 1-butyl-1-methylpyrrolidinium bis{(trifluoromethyl)sulfonyl}imide ([Pyrr14][TFSI]) was mixed with two nitrile-based organic solvents, namely butyronitrile and adiponitrile, and the resulting blends were investigated regarding their usage in electrochemical double layer capacitors. Both blends have a high electrochemical stability, which was confirmed by prolonged float tests at 3.2 V, as well as, good transport properties. In fact, the butyronitrile blend reaches a conductivity of 17.14 mS·cm−1 and a viscosity of 2.46 mPa·s at 20 °C, which is better than the state-of-the-art electrolyte (1 mol·dm−3 of tetraethylammonium tetrafluoroborate in propylene carbonate).

Binary Mixtures of 1-Butyl-1-Methylpyrrolidinium Bis{(trifluoromethyl)Sulfonyl}Imide and Aliphatic Nitrile Solvents As Electrolyte for Electrochemical Double Layer Capacitors (Invited).

Electrochemical double layer capacitors (EDLCs), also known as supercapacitors, are promising energy storage devices, especially when considering high power applications [1]. EDLCs can be charged and discharged within seconds [1], feature high power (10 kW·kg-1) and an excellent cycle life (>500,000 cycles). All these properties are a result of the energy storage process of EDLCs, which relies on storing energy by charge separation instead of chemical redox reactions, as utilized in battery systems. Upon charging, double layers are forming at the electrode/electrolyte interface consisting of the electrolyte’s ions and electric charges at the electrode surface.In state-of-the-art EDLC systems activated carbons (AC) are used as active materials and tetraethylammonium tetrafluoroborate ([Et4N][BF4]) dissolved in organic solvents like propylene carbonate (PC) or acetonitrile (ACN) are commonly used as the electrolyte [2]. These combinations of materials allow operative voltages up to 2.7 V - 2.8 V and an energy in the order of 5 Wh·kg-1[3]. The energy of EDLCs is dependent on the square of the operative voltage, thus increasing the usable operative voltage has a strong effect on the delivered energy of the device [1]. Due to their high electrochemical stability, ionic liquids (ILs) were thoroughly investigated as electrolytes for EDLCs, as well as, batteries, enabling high operating voltages as high as 3.2 V - 3.5 V for the former [2]. While their unique ionic structure allows the usage of neat ILs as electrolyte in EDLCs, ILs suffer from low conductivity and high viscosity increasing the intrinsic resistance and, as a result, a lower power output of the device. In order to overcome this issue, the usage of blends of ionic liquids and organic solvents has been considered a feasible strategy as they combine high usable voltages, while still retaining good transport properties at the same time.In our recent work the ionic liquid 1-butyl-1-methylpyrrolidinium bis{(trifluoromethyl)sulfonyl}imide ([Pyrr14][TFSI]) was combined with two nitrile-based organic solvents, namely butyronitrile (BTN) and adiponitrile (ADN), and the resulting blends were investing regarding their usage in electrochemical double layer capacitors [4,5]. Firstly, the physicochemical properties were investigated, showing good transport properties for both blends, which are similar to the state-of-the-art combination of [Et4N][BF4] in PC. Secondly, the electrochemical properties for EDLC application were studied in depth revealing a high electrochemical stability with a maximum operative voltage as high as 3.7 V. In full cells these high voltage organic solvent based electrolytes have a good performance in terms of capacitance and an acceptable equivalent series resistance at cut-off voltages of 3.2 and 3.5 V. However, long term stability tests by float testing revealed stability issues when using a maximum voltage of 3.5 V for prolonged time, whereas at 3.2 V no such issues are observed (Fig. 1).Considering the obtained results, the usage of ADN and BTN blends with [Pyrr14][TFSI] in EDLCs appears to be an interesting alternative to state-of-the-art organic solvent based electrolytes, allowing the usage of higher maximum operative voltages while having similar transport properties to 1 mol∙dm-3 [Et4N][BF4] in PC at the same time.

Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of $\Rb{87}$ vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in $\Rb{87}$ with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use $\Rb{87}$ to sympathetically cool $\Yb{171}$ to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation.