Data-inspired advances in geometric measure theory: generalized surface and shape metrics

Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and decomposition in generalized surface space) hold interest from a theoretical perspective but computational infeasibility prevented practical use. Others, like nonasymptotic densities as shape signatures, have been developed independently for data analysis (e.g., the integral area invariant). The flat norm measures distance between currents (generalized surfaces) by decomposing them in a way that is robust to noise. The simplicial deformation theorem shows currents can be approximated on a simplicial complex, generalizing the classical cubical deformation theorem and proving sharper bounds than Sullivan's convex cellular deformation theorem. Computationally, the discretized flat norm can be expressed as a linear programming problem and solved in polynomial time. Furthermore, the solution is guaranteed to be integral for integral input if the complex satisfies a simple topological condition (absence of relative torsion). This discretized integrality result yields a similar statement for the continuous case: the flat norm decomposition of an integral 1-current in the plane can be taken to be integral, something previously unknown for 1-currents which are not boundaries of 2-currents. Nonasymptotic densities (integral area invariants) taken along the boundary of a shape are often enough to reconstruct the shape. This result is easy when the densities are known for arbitrarily small radii but that is not generally possible in practice. When only a single radius is used, variations on reconstruction results (modulo translation and rotation) of polygons and (a dense set of) smooth curves are presented.Comment: 123 pages, dissertation, includes chapters based on arXiv:1105.5104 and arXiv:1308.245

Non-invasive and minimally invasive techniques for urodynamic stress incontinence of urine in women

1. Extra-corporeal magnetic energy stimulation of pelvic floor muscles for urodynamic stress incontinence;Objective: To assess the efficacy and practicalities of extra-corporeal magnetic energy stimulation of pelvic floor muscles as a non-invasive technique for urodynamic stress incontinence of urine in women.Design: Prospective non-controlled study.Setting: 2 district general hospitals.Population: Female patients with urodynamic stress incontinence of urine.Main outcome measures: Pad test, continence diary, quality of life assessment using the King's health and EuroQol questionnaires as well as side effects and drop out.Method; 18, twice weekly sessions. Assessment was made on recruitment, at the end of treatment and at 3 months follow up.Results: 48 patients were recruited, 31 completed treatment sessions and 27 attended for follow up at 3 months. There was no significant change in outcome measures at the end of treatment as well as at 3 months follow up. Side effects were encountered by 52.1 % of patients and the drop out rate was 35.4%. Relevant side effects were significantly more common in those who dropped out.Conclusions; Extra-corporeal magnetic energy stimulation of pelvic floor muscles seems unlikely to improve urodynamic stress incontinence of urine. This appears to be due to the passive nature of the contractions evoked. Side effects are prominent and appear to contribute to the drop out rate.2. Transvaginal radiofreguency remodelling of the endopelvic fascia for urodynamic stress incontinence due to urethral hypermobility:Objective: To assess the efficacy and safety of transvaginal radiofrequency remodelling of the endopelvic fascia as a minimally invasive technique for urodynamic stress incontinence of urine due to urethral hypermobility in women.Design: Prospective non-controlled study.Setting: 3 district general hospitals and 1 university hospital.Population: Female patients with urodynamic stress incontinence of urine due to urethral hypermobility.Main outcome measures: Pad test, urodynamic assessment, continence diary, pain scores and operative as well as post-operative complications.Method: Transvaginal radiofrequency of the endopelvic fascia. Assessment was made on recruitment, during hospital admission and at 3,6 and 12 months follow up.Results: 24 patients were available for analysis. A rising failure rate was noted as early as 3 months, leading to a cumulative cure rate of 36% at 12 months follow up. No major complications were encountered and pain scores were mild.Conclusions: The effectiveness of transvaginal radiofrequency remodelling of the endopelvic fascia for urodynamic stress incontinence of urine due to urethral hypermobility appears to be low. Inherent weakness of the endopelvic fascia appears to be the main reason. The technique has a low complication and pain profile.3. Comparison between the tension·free vaginal tape (TVT), pelvicol as well as short autologous slings for urodynamic stress incontinence:Objective: To compare the efficacy and morbidity of the tension·free vaginal tape (TVT), pelvicol as well as short autologous slings, as minimally invasive technique for urodynamic stress incontinence of urine in women.Design: Muticentre randomised controlled single blind study.Setting: 4 district general hospitals and 2 teaching university hospitals.Population: Female patients with urodynamic stress incontinence of urine.Main outcome measures: Quality of life and symptom assessment using Bristol Female Lower Urinary Tract Symptoms as well as EuroQol questionnaires, pad test, continence diary, operating time, stay in hospital, operative as well as post-operative complications.Method: Tension-free vaginal tape (TVT) , pelvicol or short autologous sling insertion. Assessment was made on recruitment, during hospital stay and at 6 weeks as well as 6 and 12 months follow up.Results: A total of 181 patients were recruited. An interim analysis of re-operation rate showed a significantly higher rate with pelvicol, necessitating closure of this arm. All pelvicol failures appeared after 6 months, raising the possibility of a delayed reaction. No significant difference was observed between the tension-free vaginal tape (TVT) and short autologous slings in terms of operative as well as post-operative complications, pad test and continence diary. Operating time and post-operative stay in hospital were significantly shorter following the tension-free vaginal tape (TVT) sling than after the short autologous one. This reduces the higher capital cost of the tension free vaginal tape (TVT) sling. There was also a short term advantage in quality of life assessment.Conclusions: Pelvicol slings are associated with a delayed failure, and should not therefore be used for continence surgery. Although both the tension-free vaginal tape (TVT) and short autologous slings are equally effective and have a comparable complications profile, the tension-free vaginal tape (TVT) sling is quicker to insert and is followed by a shorter stay in hospital; 2 features that reduce its higher cost. It is also associated with a better quality of life change in the short term

Inventory risk based technique for spare parts utilization

The equipment breakdown due to unavailability of spare parts has incurred challenges for the manufacturing industry in managing the inventory. Consequently, the problem of spare parts unavailability has lead the organization towards unproductive and eventually impact the financial performance.Therefore, maintaining good system has direct connection with spare parts availability. The inventory planner always strive hard to ensure that the spare parts are always available for the maintenance used.Nevertheless, maintaining high inventories of spare parts often conflict from meeting the needs of equipment reliability for the manufacturing plant.In view of this situation, management of spare parts become critical in ensuring the equipment reliability.This paper describes an innovative risk quantification technique using Binary Decision Diagram (BDD) for the spare parts inventory control.The technique modified the BDD concept by translating the failure history into binary decision.From the binary process, the data will be converted into spare parts probability table and failure impact is analyzed. These two functions of risk, will be calculated in order gain the risk in monetary value

Evaluation of knowledge of vitamin D aspects among pharmacy and engineering students in University of Sharjah, United Arab Emirates

Background: Vitamin D plays a major role in health. Several health disorders have been associated with its deficiency. The objectives of this study were to evaluate the knowledge of and attitude towards vitamin D of pharmacy and engineering students in the University of Sharjah, United Arab Emirates.Methods: A descriptive cross-sectional study was conducted during February-April, 2018. A 30 questions survey in English was designed, pre-validated and distributed to 250 students. The questionnaire was designed to evaluate and compare student’s knowledge and awareness of vitamin D.Results: 213 participants completed the survey producing a response rate of 85.2%. The majority of students were Arabs, females and of age ranging 21-23 years. Almost all pharmacy students were familiar with many aspects of vitamin D. Unlike engineering (66; 66.6%), most (113; 99.1%) pharmacy students know the meaning of osteoporosis. Knowledge of pharmacy students on vitamin D was generally better than that of engineering students particularly with questions on technical parameters of vitamin D levels and dosage. Students who took vitamin D test were advised by a physician. Most of the students from both colleges have a positive attitude to receive information on vitamin D through brochures, lectures/seminars and workshops.Conclusions: Awareness of non-health sciences and to some extent of pharmacy students seems to be inadequate and efforts are needed to increase awareness of the public in general of the importance of vitamin to health status

Flat Norm Decomposition of Integral Currents

Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a $d$-dimensional current into $d$- and (the boundary of) $(d+1)$-dimensional pieces in an optimal way. Given an integral current, can we expect its flat norm decomposition to be integral as well? This is not known in general, except in the case of $d$-currents that are boundaries of $(d+1)$-currents in $\mathbb{R}^{d+1}$ (following results from a corresponding problem on the $L^1$ total variation ($L^1$TV) of functionals). On the other hand, for a discretized flat norm on a finite simplicial complex, the analogous statement holds even when the inputs are not boundaries. This simplicial version relies on the total unimodularity of the boundary matrix of the simplicial complex -- a result distinct from the $L^1$TV approach. We develop an analysis framework that extends the result in the simplicial setting to one for $d$-currents in $\mathbb{R}^{d+1}$, provided a suitable triangulation result holds. In $\mathbb{R}^2$, we use a triangulation result of Shewchuk (bounding both the size and location of small angles), and apply the framework to show that the discrete result implies the continuous result for $1$-currents in $\mathbb{R}^2$.Comment: 17 pages, adds some related work and application

Simplicial Flat Norm with Scale

We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the multiscale simplicial flat norm as an instance of integer linear optimization. Following recent results on related problems, the multiscale simplicial flat norm integer program can be solved in polynomial time by solving its linear programming relaxation, when the simplicial complex satisfies a simple topological condition (absence of relative torsion). Our most significant contribution is the simplicial deformation theorem, which states that one may approximate a general current with a simplicial current while bounding the expansion of its mass. We present explicit bounds on the quality of this approximation, which indicate that the simplicial current gets closer to the original current as we make the simplicial complex finer. The multiscale simplicial flat norm opens up the possibilities of using flat norm to denoise or extract scale information of large data sets in arbitrary dimensions. On the other hand, it allows one to employ the large body of algorithmic results on simplicial complexes to address more general problems related to currents.Comment: To appear in the Journal of Computational Geometry. Since the last version, the section comparing our bounds to Sullivan's has been expanded. In particular, we show that our bounds are uniformly better in the case of boundaries and less sensitive to simplicial irregularit

Examining the Export-Led Growth Hypothesis: Empirical Evidence from Sudan

The current study analyzes the relationship between Sudan's income growth and exports from 1970 to 2020. The system of equations using the Autoregressive Distributed Lag (ARDL) approach has been employed. The ARDL results showed that there exists a long-run relationship between the variables considered in the estimated model. The researchers observed a negative lagged error-correction term coefficient, which is highly significant in all cases supporting cointegration. The result reveals the existence of a long-run equilibrium relationship between GDP, export, import, labor force, and trade policy. This confirms that the export-led growth hypothesis is valid for Sudan. Thus, the most essential conclusion is that the economy’s export expansion strategy is completely dependent on the imports of raw materials and capital inputs and the kind of goods being exported. The coefficient of import is of significance, which offers strong support for the import compression hypothesis. The most important policy implication of the findings is the implementation of an appropriate and optimal approach that can boost exports to increase economic growth substantially. Policy-makers should focus on export diversification strategies and invest more in Sudan’s ability to provide value-added services to meet international export demand

Novel one-pot multi-bond forming reaction processes for the preparation of biologically active heterocycles

During the course of this PhD, a new one-pot thermal Overman rearrangement and ring-closing metathesis process was developed for the preparation of polycyclic compounds. In this method, commercially available phenols and anilines were converted to alkene derived allylic alcohols and then transformed via a one-pot process into 5-amino 2,5-dihydro-1-benzoxepines and 5-amino 2,5-dihydro-1H-benzazepines. The synthetic utility of these compounds was explored with the preparation of highly substituted hydroxylated analogues as well as a highly active hypotensive agent. A novel one-pot process was also developed for the synthesis of allylic amide derived 2H-chromenes. The key substrates, propargyloxy cinnamyl alcohols were rapidly prepared from readily available salicylaldehydes. One-pot thermal Overman rearrangement of the corresponding allylic trichloroacetimidates, followed by a gold(I)-catalysed hydroarylation gave the 2H-chromenes in high yields. A mild chemoselective method for the oxidation of the 2H-chromenes to give coumarins was also discovered