Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Phase transitions from the solid state of monatomic elements

The principle aims of this thesis include the development of models of sublimation and melting from first principles and the application of these models to the rare gases.

A simple physical model is constructed to represent the sublimation of monatomic elements. According to this model, the solid and gas phases are two states of a single physical system. The nature of the phase transition is clearly revealed, and the relations between the vapor pressure, the latent heat, and the transition temperature are derived. The resulting theory is applied to argon, krypton, and xenon, and good agreement with experiment is found.

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus-Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is Boltzmann's constant, T is the temperature, and e is the well depth of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick equation were found for ρσ³ above 1.3, where ρ is the particle density and σ is the radial parameter of the Lennard-Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50 percent low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.

Uptake and factors that influence the use of 'sit less, move more' occupational intervention strategies in Spanish office employees

Background: Little is known about the types of 'sit less, move more' strategies that appeal to office employees, or what factors influence their use. This study assessed the uptake of strategies in Spanish university office employees engaged in an intervention, and those factors that enabled or limited strategy uptake. Methods: The study used a mixed method design. Semi-structured interviews were conducted with academics and administrators (n = 12; 44 +/- 12 mean SD age; 6 women) at three points across the five-month intervention, and data used to identify factors that influenced the uptake of strategies. Employees who finished the intervention then completed a survey rating (n = 88; 42 +/- 8 mean SD age; 51 women) the extent to which strategies were used [never (1) to usually (4)]; additional survey items (generated from interviewee data) rated the impact of factors that enabled or limited strategy uptake [no influence (1) to very strong influence (4)]. Survey score distributions and averages were calculated and findings triangulated with interview data. Results: Relative to baseline, 67% of the sample increased step counts post intervention (n = 59); 60% decreased occupational sitting (n = 53). 'Active work tasks' and 'increases in walking intensity' were the strategies most frequently used by employees (89% and 94% sometimes or usually utilised these strategies); 'walk-talk meetings' and ` lunchtime walking groups' were the least used (80% and 96% hardly ever or never utilised these strategies). 'Sitting time and step count logging' was the most important enabler of behaviour change (mean survey score of 3.1 +/- 0.8); interviewees highlighted the motivational value of being able to view logged data through visual graphics in a dedicated website, and gain feedback on progress against set goals. 'Screen based work' (mean survey score of 3.2 +/- 0.8) was the most significant barrier limiting the uptake of strategies. Inherent time pressures and cultural norms that dictated sedentary work practices limited the adoption of 'walk-talk meetings' and ` lunch time walking groups'. Conclusions: The findings provide practical insights into which strategies and influences practitioners need to target to maximise the impact of 'sit less, move more' occupational intervention strategies.

Optical transitions and upconversion luminescence of Er3+/Yb3+-codoped halide modified tellurite glasses

Er3+-doped halide modified tellurite glasses were synthesized by conventional melting and quenching method. The Judd-Ofelt analysis was performed on the absorption spectra and the transition probabilities, excited state lifetimes, and the branching ratios were calculated and discussed. The intense infrared and visible fluorescence spectra under 980 nm excitation were obtained. Strong upconversion signal was observed at pumping power as low as 30 mW in the glasses with halide ions. The upconversion mechanisms and power dependent intensities were discussed, which showed two-photon process are involved for the green and red emissions. The decay times of the emitting states and the corresponding quantum efficiency were determined and explained. (C) 2004 American Institute of Physics.

Optical transitions of Er3+ and Yb3+ ions in novel oxyfluoride bismuth-germanium glass: Observation of up-conversion

Er3+/Yb3+-codoped novel oxyfluoride bismuth-germanium glass was prepared and its up-conversion fluorescence property under 975 nm excitation has been studied. Intense green and weak red emissions centered at 525, 546, and 657 nm, corresponding to the transitions 2H(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The possible up-conversion mechanism was also evaluated. The optimal Yb3+-Er3+ concentration ratio is found based on the direct lifetime measurements of excited levels for Er3+ ion. The structure of this novel oxyfluoride bismuth-germanium glass has been investigated by peak-deconvolution of FT-Raman spectrum, and the structural information was obtained from the peak wavenumbers. This novel oxyfluoride bismuth-germanium glass with relatively lower maximum phonon energy (similar to 731 cm(-1)) can be used as potential host material for up-conversion lasers. (c) 2005 Elsevier B.V. All rights reserved.

Transitions in the morphological features, habitat use, and diet of young-of-the-year goosefish (Lophius americanus)

This study was designed to improve our understanding of transitions in the early life history and the distribution, habitat use, and diets for young-of-the-year (YOY) goosefish (Lophius americanus) and, as a result, their role in northeastern U.S. continental shelf ecosystems. Pelagic juveniles (>12 to ca. 50 mm total length [TL]) were distributed over most portions of the continental shelf in the Middle Atlantic Bight, Georges Bank, and into the Gulf of Maine. Most individuals settled by 50−85 mm TL and reached approximately 60−120 mm TL by one year of age. Pelagic YOY fed on chaetognaths, hyperiid amphipods, calanoid copepods, and ostracods, and benthic YOY had a varied diet of fishes and benthic crustaceans. Goosefish are widely scattered on the continental shelf in the Middle Atlantic Bight during their early life history and once settled, are habitat generalists, and thus play a role in many continental shelf habit

Two Glass Transitions Associated to Different Dynamic Disorders in the Nematic Glassy State of a Non-Symmetric Liquid Crystal Dimer Dopped with gamma-Alumina Nanoparticles

In the present work, the nematic glassy state of the non-symmetric LC dimer -(4-cyanobiphenyl-4-yloxy)--(1-pyrenimine-benzylidene-4-oxy) undecane is studied by means of calorimetric and dielectric measurements. The most striking result of the work is the presence of two different glass transition temperatures: one due to the freezing of the flip-flop motions of the bulkier unit of the dimer and the other, at a lower temperature, related to the freezing of the flip-flop and precessional motions of the cyanobiphenyl unit. This result shows the fact that glass transition is the consequence of the freezing of one or more coupled dynamic disorders and not of the disordered phase itself. In order to avoid crystallization when the bulk sample is cooled down, the LC dimer has been confined via the dispersion of -alumina nanoparticles, in several concentrations.

Analysis of multivariate stochastic signals sampled by on-line particle analyzers: Application to the quantitative assessment of occupational exposure to NOAA in multisource industrial scenarios (MSIS)

In multisource industrial scenarios (MSIS) coexist NOAA generating activities with other productive sources of airborne particles, such as parallel processes of manufacturing or electrical and diesel machinery. A distinctive characteristic of MSIS is the spatially complex distribution of aerosol sources, as well as their potential differences in dynamics, due to the feasibility of multi-task configuration at a given time. Thus, the background signal is expected to challenge the aerosol analyzers at a probably wide range of concentrations and size distributions, depending of the multisource configuration at a given time. Monitoring and prediction by using statistical analysis of time series captured by on-line particle analyzers in industrial scenarios, have been proven to be feasible in predicting PNC evolution provided a given quality of net signals (difference between signal at source and background). However the analysis and modelling of non-consistent time series, influenced by low levels of SNR (Signal-Noise Ratio) could build a misleading basis for decision making. In this context, this work explores the use of stochastic models based on ARIMA methodology to monitor and predict exposure values (PNC). The study was carried out in a MSIS where an case study focused on the manufacture of perforated tablets of nano-TiO2 by cold pressing was performed

Occupational exposure to nano-TiO2 in the life cycle steps of new depollutant mortars used in construction

The present work is focused on the measurement of workers exposure to nano-TiO2 in the life cycle steps of depollutant mortars. It has been done in the framework of the SCAFFOLD project, which aims at the management of potential risks arising from the use of manufactured nanomaterials in construction. Main findings can be summarized as follows: (1) The occupational exposure to nano-TiO2 is below 0.3 mg/m(3) for all measured scenarios. The highest concentrations were measured during the cleaning task (in the nano-TiO2 manufacturing process) and during the application (spraying) of depollutant coatings on a wall. (2) It was found a high release of particles above the background in several tasks as expected due to the nature of the activities performed. The maximum concentration was measured during drilling and during adding powder materials (mean total particle concentration up to 5.591E+04 particles/cm(3) and 5.69E+04 particles/cm(3)). However, considering data on total particle concentration released, no striking differences have been observed when tasks have been performed using conventional materials in the sector (control) and when using materials doped with nano-objects.