Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

Finitely coordinated models for low-temperature phases of amorphous systems

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behaviour of finite-dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von Karman-type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double-well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well-known universal glassy low-temperature anomalies when quantum effects are taken into account. © 2007 IOP Publishing Ltd.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Protein interactions studied by SAXS:effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, S-SC(q), or an attractive square-well structure factor, S-SW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I <0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Crystallization on the Mesoscale : Self-Assembly of Iron Oxide Nanocubes into Mesocrystals

Self-assembly of nanoparticles is a promising route to form complex, nanostructured materials with functional properties. Nanoparticle assemblies characterized by a crystallographic alignment of the nanoparticles on the atomic scale, i.e. mesocrystals, are commonly found in nature with outstanding functional and mechanical properties. This thesis aims to investigate and understand the formation mechanisms of mesocrystals formed by self-assembling iron oxide nanocubes. We have used the thermal decomposition method to synthesize monodisperse, oleate-capped iron oxide nanocubes with average edge lengths between 7 nm and 12 nm and studied the evaporation-induced self-assembly in dilute toluene-based nanocube dispersions. The influence of packing constraints on the alignment of the nanocubes in nanofluidic containers has been investigated with small and wide angle X-ray scattering (SAXS and WAXS, respectively). We found that the nanocubes preferentially orient one of their {100} faces with the confining channel wall and display mesocrystalline alignment irrespective of the channel widths.  We manipulated the solvent evaporation rate of drop-cast dispersions on fluorosilane-functionalized silica substrates in a custom-designed cell. The growth stages of the assembly process were investigated using light microscopy and quartz crystal microbalance with dissipation monitoring (QCM-D). We found that particle transport phenomena, e.g. the coffee ring effect and Marangoni flow, result in complex-shaped arrays near the three-phase contact line of a drying colloidal drop when the nitrogen flow rate is high. Diffusion-driven nanoparticle assembly into large mesocrystals with a well-defined morphology dominates at much lower nitrogen flow rates. Analysis of the time-resolved video microscopy data was used to quantify the mesocrystal growth and establish a particle diffusion-based, three-dimensional growth model. The dissipation obtained from the QCM-D signal reached its maximum value when the microscopy-observed lateral growth of the mesocrystals ceased, which we address to the fluid-like behavior of the mesocrystals and their weak binding to the substrate. Analysis of electron microscopy images and diffraction patterns showed that the formed arrays display significant nanoparticle ordering, regardless of the distinctive formation process.  We followed the two-stage formation mechanism of mesocrystals in levitating colloidal drops with real-time SAXS. Modelling of the SAXS data with the square-well potential together with calculations of van der Waals interactions suggests that the nanocubes initially form disordered clusters, which quickly transform into an ordered phase.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Double-setting alpha-tricalcium phosphate cement provided with interconection channels in rabbits after enucleation: a potential implant for the anophthalmic socket

The purpose of this study was to evaluate the macroscopy and microstructure of a double setting alpha-tricalcium phosphate bone cement sphere provided with interconnection channels (alpha-TCP-i), as well as the integration of the implant with the rabbits' orbital tissue, through macroscopic analysis and histopathology. The external and internal surfaces of the alpha-TCP-i were evaluated macroscopically and by electron microscopy. Twelve New Zealand rabbits received 12mm implants of alpha-TCP-i following enucleation of the left eye. The clinical assessment was undertaken daily during the first 15 days, followed by fortnightly assessment until the end of the study period. For the morphological analysis, exenteration was performed in 3 animals per experimental period (15, 45, 90 and 180 days). The external and internal surfaces of the implant appeared solid, smooth and compact, with six channels which interconnected centrally. The micro-architecture was characterized by the formation of columns of hexagonal crystals. No signs of infection, exposure, dehiscence of sutures or extrusion of the implant were noted in any of the animals during the entire period of the study. The morphological evaluation demonstrated the presence of a thin capsule around the implant, from whence appeared fibro-vascular projections, which penetrated it through the interconnecting channels. In the first days after the insertion of the implant, an intense inflammatory reaction was noted. At 180 days, however, there were no signs of inflammation. The alpha-tricalcium phosphate cement implant was well tolerated in this rabbit model and appeared to be relatively inert with some fibrovascular ingrowth through the large channels.

Anomalous dephasing scattering rate of two-dimensional electrons in double quantum well structures

The results on the measurement of electrical conductivity and magnetoconductivity of a GaAs double quantum well between 0.5 and 1.1 K are reported. The zero magnetic-field conductivity is well described from the point of view of contributions made by both the weak localization and electron-electron interaction. At low field and low temperature, the magnetoconductivity is dominated by the weak localization effect only. Using the weak localization method, we have determined the electron dephasing times tau(phi) and tunneling times tau(t). Concerning tunneling, we concluded that tau(t) presents a minimum around the balance point; concerning dephasing, we observed an anomalous dependence on temperature and conductivity (or elastic mean free path) of tau(phi). This anomalous behavior cannot be explained in terms of the prevailing concepts for the electron-electron interaction in high-mobility two-dimensional electron systems.

Physical signatures of discontinuities of the time-dependent exchange-correlation potential

The exact exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT) is known to develop steps and discontinuities upon change of the particle number in spatially confined regions or isolated subsystems. We demonstrate that the self-interaction corrected adiabatic local-density approximation for the XC potential has this property, using the example of electron loss of a model quantum well system. We then study the influence of the XC potential discontinuity in a real-time simulation of a dissociation process of an asymmetric double quantum well system, and show that it dramatically affects the population of the resulting isolated single quantum wells. This indicates the importance of a proper account of the discontinuities in TDDFT descriptions of ionization, dissociation or charge transfer processes.

Effects of Varenicline in Adult Smokers: A Multinational, 24-Week, Randomized, Double-Blind, Placebo-Controlled Study

Background: Prevalence rates of smoking are rising in developing countries. Previous trials evaluating the efficacy and tolerability of the smoking-cessation medication varenicline have used largely participants of Caucasian origin. Objective: This study was conducted to evaluate the efficacy and tolerability of varenicline in populations of participants from Latin America, Africa, and the Middle East to investigate potential differences in the therapeutic response to varenicline. Methods: This multinational, randomized, double-blind, placebo-controlled trial was conducted at 42 centers in 11 countries (Latin America: Brazil, Colombia, Costa Rica, Mexico, and Venezuela; Africa: Egypt and South Africa; Middle East: Jordan, Lebanon, Saudi Arabia, and the United Arab Emirates). Participants were male and female smokers aged 18 to 75 years who were motivated to stop smoking; smoked >= 10 cigarettes/d, with no cumulative period of abstinence >3 months in the previous year; and who had no serious or unstable disease within the previous 6 months. Subjects were randomized in a 2:1 ratio to receive varenicline 1 mg or placebo, BID for 12 weeks, with a 12-week nontreatment follow-up. Brief smoking-cessation counseling was provided. The main outcome measures were carbon monoxide confirmed continuous abstinence rate (CAR) at weeks 9 to 12 and weeks 9 to 24. Adverse events (AEs) were recorded for tolerability assessment. Results: Overall, 588 subjects (varenicline, 390; placebo, 198) were randomized and treated. The mean (SD) ages of subjects in the varenicline and placebo groups were 43.1 (10.8) and 43.9 (10.8) years, respectively; 57.7% and 65.7% were male; and the mean (SD) weights were 75.0 (16.0) and 76.7 (16.3) kg (range, 40.0-130.0 and 45.6-126.0 kg). CAR at weeks 9 to 12 was significantly higher with varenicline than with placebo (53.59% vs 18.69%; odds ratio [OR] = 5.76; 95% CI, 3.74-8.88; P < 0.0001), and this rate was maintained during weeks 9 to 24 (39.74% vs 13.13%; OR = 4.78; 95% CI, 2.97-7.68; P < 0.0001). Nausea, headache, and insomnia were the most commonly reported AEs with varenicline and were reported numerically more frequently in the varenicline group compared with the placebo group. Serious AEs (SAEs) were reported in 2.8% of varenicline recipients compared with 1.0% in the placebo group, with 6 subjects reporting psychiatric SAEs compared with none in the placebo group. Conclusion: Based on these data, varenicline was apparently efficacious and generally well tolerated as a smoking-cessation aid in smokers from selected sites in Latin America, Africa, and the Middle East. ClinicalTrials. gov identifier: NCT00594204. (Clin Ther. 2011;33:465-477) (C) 2011 Published by Elsevier HS Journals, Inc.

Dendrimer intercalation in layered double hydroxides

New organic/inorganic (O/I) hybrid assemblies based on Layered Double Hydroxide (LDH) with polyamide amine dendrimer (PAMAM, generation -0.5 and generation +0.5) were prepared by two different routes using either the direct coprecipitation at constant pH or the anion exchange procedure in double surfactant S(+)S(-) phases. The obtained materials were characterized by means of powder X-ray diffraction, thermal gravimetric analysis associated with mass spectrometry, and Fourier-transform infrared spectroscopy. X-ray powder diffraction pattern of the O/I LDH assembly exhibit characteristic profiles of LDH-based materials with basal spacing depending on the nature of the dendrimer. Indeed, for both synthetic procedures, interleaved PAMAM -0.5 gives rise to an interlayer space in agreement with a perpendicular molecular arrangement against the layer of the host structure. For PAMAM+0.5, considering its spherical dimension, a much smaller basal spacing was observed. This observation was interpreted as shrinkage of the molecule to accommodate the interlayer LDH gap, which was rendered possible by the bond angle twisting within PAMAM-0.5. FTIR spectra confirm the presence of both moieties inside both Zn(2)Al/PAMAM G-0.5 and Zn(2)Al/PAMAM G+0.5 assemblies. Finally, thermal analysis associated with mass spectrometry confirm this composition, and in situ temperature XRD data reveal that the highly constrained arrangement for the generation +0.5 is not accompanied by a gain in thermal structural stability; in fact, the assembly prepared from PAMAM -0.5 is more stable. Both O/I PAMAM LDH assemblies constitute well-defined materials which are candidate for catalytic applications.

A randomized, double-blind clinical trial on the efficacy of cortical direct current stimulation for the treatment of major depression

Preliminary findings suggest that transcranial direct current stimulation (tDCS) can have antidepressant effects. We sought to test this further in a parallel-group, double-blind clinical trial with 40 patients with major depression, medication-free randomized into three groups of treatment: anodal tDCS of the left dorsolateral prefrontal cortex (active group-`DLPFC`); anodal tDCS of the occipital cortex (active control group-`occipital`) and sham tDCS (placebo control group-`sham`). tDCS was applied for 10 sessions during a 2-wk period. Mood was evaluated by a blinded rater using the Hamilton Depression Rating Scale (HDRS) and Beck Depression Inventory (BDI). The treatment was well tolerated with minimal side-effects that were distributed equally across all treatment groups. We found significantly larger reductions in depression scores after DLPFC tDCS [HDRS reduction of 40.4 % (+/-25.8%)] compared to occipital [HDRS reduction of 21.3 % ( +/-12.9%)] and sham tDCS [HDRS reduction of 10.4 % (+/-36.6%)]. The beneficial effects of tDCS in the DLPFC group persisted for 1 month after the end of treatment. Our findings support further investigation on the effects of this novel potential therapeutic approach - tDCS - for the treatment of major depression.