Guarantees of Riemannian Optimization for Low Rank Matrix Completion

We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank $r$ matrix are sampled independently and uniformly with replacement. We first prove that with high probability the Riemannian gradient descent and conjugate gradient descent algorithms initialized by one step hard thresholding are guaranteed to converge linearly to the measured matrix provided \begin{align*} m\geq C_\kappa n^{1.5}r\log^{1.5}(n), \end{align*} where $C_\kappa$ is a numerical constant depending on the condition number of the underlying matrix. The sampling complexity has been further improved to \begin{align*} m\geq C_\kappa nr^2\log^{2}(n) \end{align*} via the resampled Riemannian gradient descent initialization. The analysis of the new initialization procedure relies on an asymmetric restricted isometry property of the sampling operator and the curvature of the low rank matrix manifold. Numerical simulation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements

Myth of Dreams

The documentary film is entitled \u27Myth of Dreams \u27. The film confronts the issue of Chinese Mainland immigration into Hong Kong. The film looks at several viewpoints, including government agencies, activists and Mainland immigrants in Hong Kong. Chinese immigrants are often overlooked simply because they are Chinese as are all Hong Kong citizens excluding cultural identifiers which lead to discriminative practices. The film investigates the cultural biases and social exclusion these immigrants face at the policy and social level

Supraspinal characterization of the thermal grill illusion with fMRI.

BackgroundSimultaneous presentation of non-noxious warm (40°C) and cold (20°C) stimuli in an interlacing fashion results in a transient hot burning noxious sensation (matched at 46°C) known as the thermal grill (TG) illusion. Functional magnetic resonance imaging and psychophysical assessments were utilized to compare the supraspinal events related to the spatial summation effect of three TG presentations: 20°C/20°C (G2020), 20°C/40°C (G2040) and 40°C/40°C (G4040) with corresponding matched thermode stimuli: 20°C (P20), 46°C (P46) and 40°C (P40) and hot pain (HP) stimuli.ResultsFor G2040, the hot burning sensation was only noted during the initial off-line assessment. In comparison to P40, G4040 resulted in an equally enhanced response from all supraspinal regions associated with both pain sensory/discriminatory and noxious modulatory response. In comparison to P20, G2020 presentation resulted in a much earlier diminished/sedative response leading to a statistically significantly (P < 0.01) higher degree of deactivation in modulatory supraspinal areas activated by G4040. Granger Causality Analysis showed that while thalamic activation in HP may cast activation inference in all hot pain related somatosensory, affective and modulatory areas, similar activation in G2040 and G2020 resulted in deactivation inference in the corresponding areas.ConclusionsIn short, the transient TG sensation is caused by a dissociated state derived from non-noxious warm and cold spatial summation interaction. The observed central dissociated state may share some parallels in certain chronic neuropathic pain states

Ten years of environmental university building

The authors have been involved in over ten years of environmental consulting and research on university buildings. Numerous simulations and measurement studies have occurred over this period of time. The intentions have always been to improve and optimise the environmental performing aspects of a building. This paper is a reporting of the implemented strategies, their pre-building research investigation as well as their operational outcomes. Their successes and failures are discussed here. This research is intended as a feedback loop to future design specification, commissioning and maintenance improvements. In hindsight many of the environmental concepts, when executed as planned, were successful. However, often those requiring extensive control, such as lighting, ventilation and mechanical air-conditioning were a failure. The observations between simulation and actual performance are also noted. The paper includes discussion about some of the obstacles in building procurement which can hinder the result of a good environmental performing building.<br /

The formation of a nanohybrid shish-kebab (NHSK) structure in melt-processed composites of poly (ethylene terephthalate) (PET) and multi-walled carbon nanotubes (MWCNTs)

The combination of synchrotron Small- and Wide-Angle X-ray scattering (SAXS/WAXS), and thermal analysis was used to follow the evolution of crystalline morphology and crystallization kinetics in a series of melt-processed composites of poly(ethylene terephthalate) (PET) and multiwall carbon nanotubes (MWCNT). The as-extruded PET-MWCNT composites underwent both hot and cold isothermal crystallizations where a final oriented nanohybrid shish-kebab (NHSK) crystalline structure was observed. An oriented NHSK structure was seen to persist even after melting and recrystallization of the composites. From the scattering data, we propose a model whereby the oriented MWCNTs act as heterogeneous nucleation surfaces (shish) and the polymer chains wrap around them and the crystallites (kebabs) grow epitaxially outwards during crystallization. However, depending on crystallization temperature, unoriented crystallites also grow in the polymer matrix, resulting in a combination of a NHSK and lamellar morphology. In contrast, the neat PET homopolymer showed the sporadic nucleation of a classic unoriented lamellar structure under the same isothermal crystallization conditions. These results provide a valuable insight into the distinctive modification of the crystalline morphology of melt-processed polymer-MWCNT composites prior to any secondary processing, having a significant impact on the use of MWCNTs as fillers in the processing and modification of the physical and mechanical properties of engineering polymers

A Contour Grouping Algorithm for 3D Reconstruction of Biological Cells

Advances in computational modelling offer unprecedented potential for obtaining insights into the mechanics of cell-cell interactions. With the aid of such models, cell-level phenomena such as cell sorting and tissue self-organization are now being understood in terms of forces generated by specific sub-cellular structural components. Three-dimensional systems can behave differently from two-dimensional ones and since models cannot be validated without corresponding data, it is crucial to build accurate three-dimensional models of real cell aggregates. The lack of automated methods to determine which cell outlines in successive images of a confocal stack or time-lapse image set belong to the same cell is an important unsolved problem in the reconstruction process. This thesis addresses this problem through a contour grouping algorithm (CGA) designed to lead to unsupervised three-dimensional reconstructions of biological cells. The CGA associates contours obtained from fluorescently-labeled cell membranes in individual confocal slices using concepts from the fields of machine learning and combinatorics. The feature extraction step results in a set of association metrics. The algorithm then uses a probabilistic grouping step and a greedy-cost optimization step to produce grouped sets of contours. Groupings are representative of imaged cells and are manually evaluated for accuracy. The CGA presented here is able to produce accuracies greater than 96% when properly tuned. Parameter studies show that the algorithm is robust. That is, acceptable results are obtained under moderately varied probabilistic constraints and reasonable cost weightings. Image properties – such as slicing distance, image quality – affect the results. Sources of error are identified and enhancements based on fuzzy-logic and other optimization methods are considered. The successful grouping of cell contours, as realized here, is an important step toward the development of realistic, three-dimensional, cell-based finite element models

Performance study of a daylight guiding system in an office building

This research developed a comprehensive evaluation of a daylight-guiding system in an Australian office building. On-site measurements, simulation and correlation studies have been carried out to identify the daylight contribution from the reflective louvre system. Results show that the system can provide up to 70% additional illuminance for the workplace.<br /

Inspiring the retirees towards active ageing : a case study of the elderly shop project

The “elderly shop” project is a project for retired elderly who are commonly identified as recipients of care and assistance, to venture into business. It provides a platform for them to be actively engaged in productive activities. This project is based on the “self-financing” business model. With the elderly as role models other social groups such as housewives and non-engaged/unemployed youths are also enlisted to provide support to this project. Together they form the service team. The transfer of “know how” and consultative support provided by the business community and professionals enable this project to provide services to those who are less privileged. “Empowerment” and “transformation” are evident among the elderly in the process of providing services. The Elderly Shop project is a platform that helps to develop “social capital” and to foster community integration in the long run

Formal verification of a microcoded VIPER microprocessor using HOL

The Royal Signals and Radar Establishment (RSRE) and members of the Hardware Verification Group at Cambridge University conducted a joint effort to prove the correspondence between the electronic block model and the top level specification of Viper. Unfortunately, the proof became too complex and unmanageable within the given time and funding constraints, and is thus incomplete as of the date of this report. This report describes an independent attempt to use the HOL (Cambridge Higher Order Logic) mechanical verifier to verify Viper. Deriving from recent results in hardware verification research at UC Davis, the approach has been to redesign the electronic block model to make it microcoded and to structure the proof in a series of decreasingly abstract interpreter levels, the lowest being the electronic block level. The highest level is the RSRE Viper instruction set. Owing to the new approach and some results on the proof of generic interpreters as applied to simple microprocessors, this attempt required an effort approximately an order of magnitude less than the previous one

An empirical study on the applicability of an augmented technology acceptance model in the context of e-government initiatives in the Hong Kong special administrative region government

The success of the Government of Hong Kong Special Administrative Region's (HKSARG) e-government initiatives is dependent on the government employees' acceptance and use of the underpinning information, internet and communication technologies (IT). Unfortunately, only a few empirical researches have been conducted to investigate the drivers of IT usage in government workplaces.To predict IT usage, the Technology Acceptance Model (TAM) has been tested and demonstrated its predictive power in various contexts. But it does not provide guidance to managers because Davis grouped the antecedents to the TAM constructs as "external factors" so as to focus on the main part of the model and to keep it robust. Hence, these factors are the ultimate drivers that determine the users' behaviors.This research aims to improve the explanatory power of TAM by identifying and including resistance to change (RTC) as a relevant external factor with the assistance from Max Weber's Theory of Bureaucracy (TB). To test the augmented TAM, an email questionnaire survey to 700 randomly selected HKSARG IT users was conducted.Additional information was gathered from senior management to validate the survey results. The results show that the IT users in HKSARG are not valuing usefulness and ease of use of IT in the same manner as employees in most other contexts. In addition, the results confirm that RTC is a relevant and strong external variable to TAM. In line with theories, HKSARG employees, as a whole, tend to have above average level of resistance to change. But statistical test results also revealed that there are heterogeneous behavioural groups within HKSARG. Specifically, younger or more educated users are more willing to change. The existence of these groups has both practical and managerial implications for implementing change.In particular, it is argued that the government should not be viewed and understood monolithically. A better strategy for management to implement change is to target the younger or more educated users first for piloting and to build up sufficient user mass and exert peer pressure to older or less educated users for a more successful implementation of IT across all staff.Because of the weaknesses of the established policies, the HKSARG has an undesirable structural composition (high percentage of older and less educated employees) in the face of change. To tackle the high level of resistance to change, it is suggested that continuous training is a must. Moreover, the training packages should be tailor-made for various groups in the civil service to suit their specific needs and to enhance their capabilities. In the long term, it is recommended that the human resources management policies should be reviewed and modified with an aim to adjust the structural composition of the civil service toward a more change ready workforce. In addition, more research on the characteristics of the public sector is required for a better understanding of the real nature of these large bureaucratic organizations