Finding an optimal proximity bound in a very special scenario

Given A ∈ Zm×n and b ∈ Zm, we provide a sharp upper bound for the ℓ∞-distance from any vertex of the polyhedron P(A, b) = {x ∈ Rn ≥0: Ax = b} to a nearby feasible integral point under a strong assumption regarding the dimensions of the matrix A. It is hoped that this result provides motivation for conducting further research into providing more such upper bounds under certain additional assumptions

Identifying Job Satisfaction Parameters among the Employees in Higher Educational Institutions: A Mathematical Model

The study is conducted to evaluate the job satisfaction among the administrative and teaching faculties in higher educational institutions. Many researchers have conducted studies to evaluate differences in job perception between teaching and non-teaching staff. Despite this, none of the studies have explicitly focused on developing a formal mathematical approach for analysis. Thus, this paper aims to identify the job satisfaction parameters among staff in an educational institution by using Multi Criteria Decision Making (MCDM) tools. The factors influencing employee job satisfaction have been ascertained and hierarchically organized through the utilization of the standard deviation methodology. Analytical findings reveal that certain variables, including promotional opportunities, interpersonal relations with colleagues, managerial support, and the department of employment, exert a substantial impact on an individual's level of job satisfaction. The research posits that the strategic implementation of these variables and attributes by organizational management can significantly ameliorate challenges related to employee retention, thereby enhancing overall workforce efficiency.Comment: 12 pages, 2 Figures, 2 Tables, 1 Grap

The sweat of the brain: representations of intellectual labour in the writings of Edmund Burke, William Cobbett, William Hazlitt and Thomas Carlyle

This thesis examines representations of intellectual work in the writings of Edmund Burke, William Cobbett, William Hazlitt, and Thomas Carlyle, focusing on their tendency to draw on an analogy between mental and manual labour when representing their own work to themselves and to their readers. It is my argument that while the assimilation of intellectual to physical labour can be seen as a symptom of political bad faith - suggesting, as it does, that thinking and writing are as painful or as difficult as digging and ploughing - the primary purposes of the analogy in the works of these four cultural commentators are, first, to forge rhetorical alliances with ordinary labourers, and, second, to attack other intellectuals engaged in what are alleged to be less arduous and less valuable forms of intellectual endeavour. By blaming the irresponsible activity of disaffected literary men for the political upheaval of the French Revolution, Burke set the terms for debate about the role of educated and literate men in society, a debate in which, for the first time, intellectuals competed for the allegiance of the labouring population. The analogy with manual labour was a key rhetorical site in the struggle to define an ideology for intellectuals, since it claims to ground the speaker or writer in the labouring community at large. For each author, I undertake close readings of several key texts to demonstrate the prevalence of the comparison with manual labour in the representation of intellectual activity. The political-ideological valence of the analogy is never straightforward, I contend, and it often occurs alongside an impulse to emphasise, as well as to elide, what are assumed to be the fundamental differences between mental and manual activity. We witness in the writings of Burke, Cobbett, Hazlitt, and Carlyle a recognisable mode of self-representation, for the desire to assimilate intellectual to material work has persisted

Customer Service in Aviation Industry – An Exploratory Analysis of UAE Airports

Customer satisfaction is given top priority by all service-oriented industries. The civil aviation industry is no exception. The highly competitive global aviation arena causes various airlines to vie for the top position with lot of importance being given to the customer service. The aim of this study is to analyze the methods and tools used by the United Arab Emirates’ (UAE’s) federal government and the various local governments in the country to improve the customer satisfaction with regard to the aviation industry in the country. This paper develops a framework to assess customer service in the aviation sector in the UAE and uses the framework to analyze and compare the three main airports in the UAE based on the feedback of passengers. This study used a multi-pronged approach to collect data. In all, 78 travelers were chosen at random and they were administered a structured and a semi-structured questionnaire. Responses to the former were used to perform Chi-square test and establish the differences between the three airports; the latter were used to gain deeper insight and gauge a more in-depth opinion of the respondents. Through the analysis of the data, this study was able to learn more about the public view with regard to the innovations and ideas implemented by the government of the UAE. A new customer service model has been developed to compare the three airports in UAE and gain more insights into opportunities for improvement

The involvement of hyaluronan matrix in regulating peritoneal infection, inflammation & fibrosis

The prevalence of Chronic Kidney Disease (CKD) is rising owing to increased diabetes and obesity in our ageing populations. Hence, end-stage renal disease (ESRD) has become a major global health burden. For many ESRD patients, kidney transplantation is not possible. Hence these patients require dialysis to regulate their salt/fluid levels, and to remove toxins from the body. Peritoneal Dialysis (PD) is a well-established and effective form of treatment for ESRD. However, the longevity of PD is limited because of the constant exposure of the peritoneum to bioincompatible PD solutions. This, alongside unavoidable repeated episodes of PD peritonitis, alters the structural and functional integrity of the peritoneal membrane and plays a pivotal role in the development of peritoneal fibrosis leading to failure of the peritoneal tissue to act as a semi-permeable membrane. This results in failure of PD as a therapy for ESRD, limiting a patient’s options for renal-replacement therapy. A key process that drives peritoneal fibrosis during PD is mesothelial-to-mesenchymal transition (MMT). MMT is a process whereby mesothelial cells (known to comprise the majority of cells in the peritoneal membrane) undergo myofibroblast differentiation and lay down increased fibrous matrix. Numerous studies have demonstrated that TGF-β1 plays an established role in driving MMT and in the subsequent development of peritoneal fibrosis. Therefore, delineating the regulators of TGF-β1-driven MMT are important in identifying novel mechanisms to prevent peritoneal fibrosis and PD failure. In solid organ fibrosis (lungs, kidneys, skin) TGF-β1-driven myofibroblast differentiation is mediated through increased expression and alterations in the matrix polysaccharide, hyaluronan (HA). Previous studies demonstrate that PD therapy is associated with increased HA generation by mesothelial cells. However, the role of this in mediating TGF-β1-driven in the peritoneum has not been established and the role of increased HA generation during PD is not understood. The aim of this study was to determine the role of the increased HA generated during PD in regulating peritoneal infection, inflammation and fibrosis. This work uses primary human peritoneal mesothelial cells to study the involvement of HA in mediating TGF-β1-driven MMT in an in vitro experimental model. The role of HA in prevention and/or reversal of TGF-β1-driven MMT is also investigated in vitro. The role of HA in modulating peritoneal immunity and inflammation following acute bacterial infection is also examined using an in vivo mouse-model of PD peritonitis. Patients with PD peritonitis had significantly increased HA concentrations in their PD effluent after developing acute bacterial peritonitis compared to non-infected patients. Cell studies established that TGF-β1-driven MMT in primary human mesothelial cells significantly increased HA generation, and this was predominantly driven by Hyaluronan Synthase-1 (HAS1) isoenzyme expression. However, the increased HA was not causally related to TGF-β1- driven MMT; but was simply a consequence of this process. The increased HA also did not mediate prevention and/or reversal of TGF-β1-driven MMT in primary human mesothelial cells. Blocking HA in the peritoneum with PEP1 blocking antibody during bacterial infection lead to a delayed resolution of inflammation, characterized by increased and persistent neutrophil infiltration, dysregulated monocyte recruitment and decreased cytokine and chemokine release. In conclusion, following peritoneal injury, HA generated by mesothelial cells is predominantly HAS1 driven and promotes enhanced peritoneal inflammation and alters leukocyte recruitment following acute bacterial infection

Distance-sparsity transference for vertices of corner polyhedra

We obtain a transference bound for vertices of corner polyhedra that connects two well-established areas of research: proximity and sparsity of solutions to integer programs. In the knapsack scenario, it implies an exponential in size of support improvement on previously known proximity estimates. In addition, for general integer linear programs we obtain a resembling result that connects the minimum absolute nonzero entry of an optimal solution with the size of its support

Distances to lattice points in rational polyhedra

Let a ∈ Z n >0 , n ≥ 2 , gcd(a) := gcd(a1 , . . . , an ) = 1, b ∈ Z≥0 and denote by k · k∞ the ℓ∞-norm. Consider the knapsack polytope P(a, b) = { x ∈ R n ≥0 : a T x = b and assume that P(a, b) ∩ Z n 6= ; holds. The main result of this thesis states that for any vertex x ∗ of the knapsack polytope P(a, b) there exists a feasible integer point z ∗ ∈ P(a, b) such that, denoting by s the size of the support of z ∗ , i.e. the number of nonzero components in z ∗ and upon assuming s > 0 , the inequality kx ∗ − z ∗ k∞ 2 s−1 s < kak∞ holds. This inequality may be viewed as a transference result which allows strengthening the best known distance (proximity) bounds if integer points are not sparse and, vice versa, strengthening the best known sparsity bounds if feasible integer points are sufficiently far from a vertex of the knapsack polytope. In particular, this bound provides an exponential in s improvement on the previously best known distance bounds in the knapsack scenario. Further, when considering general integer linear programs, we show that a resembling inequality holds for vertices of Gomory’s corner polyhedra [49, 96]. In addition, we provide several refinements of the known distance and support bounds under additional assumption

The effect of work-based mentoring on patient outcome in musculoskeletal physiotherapy:study protocol for a randomised controlled trial

BACKGROUND: Despite persistent calls to measure the effectiveness of educational interventions on patient outcomes, few studies have been conducted. Within musculoskeletal physiotherapy, the effects of postgraduate clinical mentoring on physiotherapist performance have been assessed, but the impact of this mentoring on patient outcomes remains unknown. The objective of this trial is to assess the effectiveness of a work-based mentoring programme to facilitate physiotherapist clinical reasoning on patient outcomes in musculoskeletal physiotherapy. METHODS/DESIGN: A stepped wedge cluster randomised controlled trial (CRCT) has been designed to recruit a minimum of 12 senior physiotherapists who work in musculoskeletal outpatient departments of a large National Health Service (NHS) organization. Participating physiotherapists will be randomised by cluster to receive the intervention at three time periods. Patients will be blinded to whether their physiotherapist has received the intervention. The primary outcome measure will be the Patient-Specific Functional Scale; secondary outcome measures will include the EQ-5D, patient activation, patient satisfaction and physiotherapist performance. Sample size considerations used published methods describing stepped wedge designs, conventional values of 0.80 for statistical power and 0.05 for statistical significance, and pragmatic groupings of 12 participating physiotherapists in three clusters. Based on an intergroup difference of 1.0 on the PSFS with a standard deviation of 2.0, 10 patients are required to complete outcome measures per physiotherapist, at time period 1 (prior to intervention roll-out) and at each of time periods 2, 3 and 4, giving a sample size of 480 patients. To account for the potential loss to follow-up of 33%, 720 sets of patient outcomes will be collected. All physiotherapist participants will receive 150 hours of mentored clinical practice as the intervention and usual in-service training as control. Consecutive, consenting patients attending treatment by the participating physiotherapists during data collection periods will complete outcome measures at baseline, discharge and 12 months post-baseline. The lead researcher will be blinded to the allocation of the physiotherapist when analyzing outcome data; statistical analysis will involve classical linear models incorporating both an intervention effect and a random intercept term to reflect systematic differences among clusters. TRIAL REGISTRATION: Assigned 31 July 2012: ISRCTN79599220. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1745-6215-15-409) contains supplementary material, which is available to authorized users