A closed-form solution to estimate uncertainty in non-rigid structure from motion

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.Comment: 9 pages, 2 figure

Action observation in the modification of postural sway and gait: Theory and use in rehabilitation

The discovery of cortical neurons responsive to both the observation of another individual’s movement and one’s own physical movement has spurred scientists into utilising this interplay for rehabilitation. The idea that humans can quickly transfer motor programmes or refine existing motor strategies through observation has only recently gained interest in the context of gait rehabilitation but may offer significant promise as an adjunctive therapy to routine balance training. This review is the first dedicated to action observation in postural control or gait in healthy individuals and patients. The traditional use of action observation in rehabilitation is that the observer has to carefully watch pre-recorded or physically performed actions and thereafter imitate them. Using this approach, previous studies have shown improved gait after action observation in stroke, Parkinson’s disease and knee or hip replacement patients. In healthy subjects, action observation reduced postural sway from externally induced balance perturbations. Despite this initial evidence, future studies should establish whether patients are instructed to observe the same movement to be trained (i.e., replicate the observed action(s)) or observe a motor error in order to produce postural countermeasures. The best mode of motor transfer from action observation is yet to be fully explored, and may involve observing live motor acts rather than viewing video clips. Given the ease with which action observation training can be applied in the home, it offers a promising, safe and economical approach as an adjunctive therapy to routine balance training

Postural control and adaptation to threats to balance stability

Postural control is the ability to maintain equilibrium and orientation in a gravitational environment. It is dependent on feedback and feedforward mechanisms that generate appropriate corrective movement based on body-sway motion detected primarily by visual, vestibular, and proprioceptive sensory systems. Since information from the various senses is not always accurate (e.g. by disease) or available (e.g. with eyes closed), the postural control system must adapt to maintain stance. This thesis aimed to investigate postural control and adaptation to threats of balance. Effective approaches for the clinical measurement of postural control still remains to be developed. In the past, it has been common to investigate patients’ balance by having them stand upon compliant foam blocks with eyes open and closed since standing on foam is believed to affect the accuracy of information from cutaneous mechanoreceptors on the soles of the feet. However, when assessing balance on foam blocks with different compliances and mechanical properties, it was found that postural sway was larger on firmer compliant surfaces, which also increased the importance of visual information. Postural adaptation was also investigated by repeatedly perturbing balance using muscle vibrations. In healthy, young persons, a slow adaptive change was observed. This adaptation involved decreased costs of standing including decreased energy, body movement and muscle activity and changes to the relationship between muscle activity and movement. The characteristics of the adaptation also depended on the availability of visual information. The elderly had poor postural control with and without being perturbed but were able to adapt to improve their poor balance. However, decreased mechanoreceptive sensation in the elderly prevented them from adapting their balance to the level of younger test subjects. Sleep deprivation decreased attention and alertness and resulted in decreased postural control and adaptation. The findings in this thesis extend what is known about motor learning. The adaptive learning capability of the postural control system, and hence the accurate reconstruction of the kinematics and kinetics of movement, was dependant on ones own mechanoreceptive somatosensation and availability of visual information. Decreasing attention and alertness through sleep deprivation decreased adaptive capabilities, suggesting an important role for sleep in memory and consolidation of a new motor skill

Multiscale modelling of delayed hydride cracking

A mechanistic model of delayed hydride cracking (DHC) is crucial to the nuclear industry as a predictive tool for understanding the structural failure of zirconium alloy components that are used to clad fuel pins in water-cooled reactors. Such a model of DHC failure must be both physically accurate and computationally efficient so that it can inform and guide nuclear safety assessments. However, this endeavour has so far proved to be an unsurmountable challenge because of the seemingly intractable multiscale complexity of the DHC phenomenon, which is a manifestation of hydrogen embrittlement that involves the interplay and repetition of three constituent processes: atomic scale diffusion, microscale precipitation and continuum scale fracture. This investigation aims to blueprint a novel multiscale modelling strategy to simulate the early stages of DHC initiation: stress-driven hydrogen diffusion-controlled precipitation of hydrides near loaded flaws in polycrystalline zirconium. Following a careful review of the experimental observations in the literature as well as the standard modelling techniques that are commonplace in nuclear fuel performance codes in the first part of this dissertation, the second and third parts introduce a hybrid multiscale modelling strategy that integrates concepts across a spectrum of length and time scales into one self-consistent framework whilst accounting for the complicated nuances of the zirconium-hydrogen system. In particular, this strategy dissects the DHC mechanism into three interconnected modules: (i) stress analysis, which performs defect micromechanics in hexagonal close-packed zirconium through the application of the mathematical theory of planar elasticity to anisotropic continua; (ii) stress-diffusion analysis, which bridges the classical long-range elastochemical transport with the quantum structure of the hydrogen interstitialcy in the trigonal environment of the tetrahedral site; and (iii) diffusion-precipitation analysis, which translates empirical findings into an optimised algorithm that emulates the thermodynamically favourable spatial assembly of the microscopic hydride needles into macroscopic hydride colonies at prospective nucleation sites. Each module explores several unique mechanistic modelling considerations, including a multipolar expansion of the forces exerted by hydrogen interstitials, a distributed dislocation representation of the hydride platelets, and a stoichiometric hydrogen mass conservation criterion that dictates the lifecycle of hydrides. The investigation proceeds to amalgamate the stress, stress-diffusion and diffusion-precipitation analyses into a unified theory of the mesoscale mechanics that underpin the early stages of DHC failure and a comprehensive simulation of the flaw-tip hydrogen profiles and hydride microstructures. The multiscale theory and simulation are realised within a bespoke software which incorporates computer vision to generate mesoscale micrographs that depict the geometries, morphologies and contours of key metallographic entities: cracks and notches, grains, intergranular and intragranular nucleation sites as well as regions of hydrogen enhancement and complex networks of hydride features. Computer vision mediates the balance between simulation accuracy and simulation efficiency, which is completely novel in the context of DHC research as a paradigm at the intersection of computational science and computer science. Preliminary tests show that the simulation environment of the hybrid model is significantly more accurate and efficient in comparison with the traditional finite element and phase field methodologies. Due to this unprecedented simulation accuracy-efficiency balance, realistic flaw-tip hydrogen profiles and hydride microstructures can be simulated within seconds, which naturally facilitates statistical averaging over ensembles. Such statistical capabilities are highly relevant to nuclear safety assessments and, therefore, a systematic breakdown of the model formulation is presented in the style of a code specification manual so that the bespoke software can be readily adapted within an industrial setting. As the main contribution to DHC research, the proposed multiscale model comprises a state-of-the-art microstructural solver whose unrivalled versatility is demonstrated by showcasing a series of simulated micrographs that are parametrised by flaw acuity, grain size, texture, alloy composition, and histories of thermomechanical cycles. Direct comparisons with experimental micrographs indicate good quantitative agreement and provide some justification to the known qualitative trends. Furthermore, the overall hybrid methodology is proven to scale linearly with the number of hydrides, which is computationally advantageous in its own right because it allows the bespoke software to be extended without compromising its speed. Several possible extensions are outlined which would improve the phenomological accuracy of the multiscale model whilst retaining its efficiency. In its current form, however, this hybrid multiscale model of the early stages of DHC goes far beyond existing methodologies in terms of simulation scope.Open Acces

An Econometric Analysis of Bombay Stock Exchange: Annual Returns Analysis, Day-of-the-Week Effect and Volatility of Returns

This paper investigates the presence of day-of-the-week effect, returns volatility and analyzes the annual returns of Bombay Stock Exchange. A set of parametric and nonparametric tests is used to test equality of mean returns and standard deviations of the returns across the-days-of-the-week. To supplement this analysis, graphical representation of the index annual percentage changes was explored. The results contradict the presence of the-day-of-the- week but indicate insignificant daily returns volatility in most of these Markets. The stock exchanges experienced enormous growth between 2001 and 2010. The result of the Levenes test value for Bombay Stock Exchange was 0.847 which concludes that the daily return seasonalities are not accompanied by any volatility seasonality and investing on low (high) return weekday does not necessarily mean that risk is also low or high and Index that has marginally significant Levenes statistic. Key words: Volatility of Returns, Bombay Stock Exchange, Day-of-week effec

ROLE OF CRM IN ERP ESPECIALLY FOR SELECTED ENGINEERING COMPANIES IN AHMEDABAD.

The purpose of this investigation is to identify the awareness of CRM in ERP and essential components of CRM-ERP integration and how it deals with HR concerns. CRM: The Business Focus factor and information quality of ERP solution, system quality of ERP solution, system use of ERP solution and appropriateness of ERP solutions in context to Engineering companies of Ahmedabad City. The total CRM-ERP integration oriented Engineering companies are 58 in Ahmedabad. The selection of 15 companies is made possible on the basis of five zones of Ahmedabad City. The source of data is primary and secondary. The primary data are collected through structured questionnaire administered to the respondents in person and through email; scale reliability test and Pearson correlations test are conducted as statistical tests for achieving the objectives