Qualitative assessment of the role of public health education program on HIV transmission dynamics

© The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.This paper presents a nonlinear deterministic model for assessing the impact of public health education campaign on curtailing the spread of the HIV pandemic in a population. Rigorous qualitative analysis of the model reveals that it exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the 'effective reproduction number' (Reff), is less than unity. The epidemiological implication of BB is that a public health education campaign could fail to effectively control HIV, even when the classical requirement of having the associated reproduction number less than unity is satisfied. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden), and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries.Kano State Government of Nigeria (N.H.); Natural Science and Engineering Research Council and Mathematics of Information Technology and Complex Systems of Canada (A.B.G.

Preliminary design of a test rig for combining passive nonlinear isolation with active control

Resilient elements are typically used to isolate delicate equipment from a vibrating host structure. Conventionally, these isolators are designed to operate in their linear region, but more recently nonlinear isolators have been employed to increase the frequency over which vibration isolation can be achieved. Another way of improving the performance of an isolator has been to use active control in conjunction with a passive linear system. The work presented in this paper concerns the development of an experimental rig for vibration isolation and is motivated by the intention to combine the advantages of passive nonlinear isolation with active control.The structure consists of a mass suspended on four tensioned wires to form a single-degree-of-freedom system. The nonlinear stiffness of the wires is such that the system behaves like a hardening Duffing oscillator. Firstly, a static analysis is carried out, both analytically and experimentally, where the nonlinearity of the system is determined by the tension, length, cross-sectional area and Young’s modulus of the wires. For the dynamic analysis, harmonic base excitation is considered. The magnitude of the base displacement is fixed for all excitation frequencies and the level of nonlinearity is adjusted by varying the tension in the wires, a higher tension leading to a milder system nonlinearity. Finally, the motion transmissibility of the system is measured and appears to agree with the theoretical result. The rig forms a suitable platform for subsequent incorporation of an active control system for combining the benefits of passive nonlinear isolation with, for example, skyhook damping

Reference incidence angles in constant stagger cascades

Fortran 4 computer program for design application of stagger angle replacing inlet flow angle for given blade cascad

Delta-Nabla Optimal Control Problems

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Contro

Derived equivalence classification of the cluster-tilted algebras of Dynkin type E

We obtain a complete derived equivalence classification of the cluster-tilted algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and E8 which turn out to fall into 6, 14, 15 derived equivalence classes, respectively. This classification can be achieved computationally and we outline an algorithm which has been implemented to carry out this task. We also make the classification explicit by giving standard forms for each derived equivalence class as well as complete lists of the algebras contained in each class; as these lists are quite long they are provided as supplementary material to this paper. From a structural point of view the remarkable outcome of our classification is that two cluster-tilted algebras of Dynkin type E are derived equivalent if and only if their Cartan matrices represent equivalent bilinear forms over the integers which in turn happens if and only if the two algebras are connected by a sequence of "good" mutations. This is reminiscent of the derived equivalence classification of cluster-tilted algebras of Dynkin type A, but quite different from the situation in Dynkin type D where a far-reaching classification has been obtained using similar methods as in the present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr. Represent. Theory. v3: Main theorem strengthened by including "good" mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third author added. Major revision. All questions left open in the earlier version by the first two authors are now settled in v2 and the derived equivalence classification is completed. arXiv admin note: some text overlap with arXiv:1012.466

OpenACC Based GPU Parallelization of Plane Sweep Algorithm for Geometric Intersection

Line segment intersection is one of the elementary operations in computational geometry. Complex problems in Geographic Information Systems (GIS) like finding map overlays or spatial joins using polygonal data require solving segment intersections. Plane sweep paradigm is used for finding geometric intersection in an efficient manner. However, it is difficult to parallelize due to its in-order processing of spatial events. We present a new fine-grained parallel algorithm for geometric intersection and its CPU and GPU implementation using OpenMP and OpenACC. To the best of our knowledge, this is the first work demonstrating an effective parallelization of plane sweep on GPUs. We chose compiler directive based approach for implementation because of its simplicity to parallelize sequential code. Using Nvidia Tesla P100 GPU, our implementation achieves around 40X speedup for line segment intersection problem on 40K and 80K data sets compared to sequential CGAL library

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Predicted peak expiratroy flow in human and the clinical implications of differences across related formulae: a proposed guideline standard reference for Asthma

In an attempt to examine the differences between Peak Expiratory Flow (PEF) formulae in the literature so as to assess the potential impact of those differences on the interpretation of clinical guidelines for asthma management, the present study was carried out. We calculated 100% PEF values using formula developed by (Gregg, 1973) at 50th percentile for age, height and weight obtained from our study (Salisu et al., 2007) and classified the percent predicted PEF in to severity groups according to national asthma guidelines (NAEPP, 1991 and 1997). Choosing different formulae could give an individual in the age range of 15-19 years a 100% predicted PEF as low as 402 L/min and as high as 412 L/min; and another woman in the age range of 30-34years a classification of severe (47%) using one, but moderate (71%) using another. This indicates that predicted PEF varied widely across formulae and choice of a particular formula may alter guidelinebase care. This work has therefore accepted a recently published population-base equation proposed as the reference standard for future asthma guidelines. Keywords Peak expiratory flow, Asthma, Practice guidelines, reference value

Firms' Main Market, Human Capital and Wages

Recent international trade literature emphasizes two features in characterizing the current patterns of trade: efficiency heterogeneity at the firm level and quality differentiation. This paper explores human capital and wage differences across firms in that context. We build a partial equilibrium model predicting that firms selling in more-remote markets employ higher human capital and pay higher wages to employees within each education group. The channel linking these variables is firms’ endogenous choice of quality. Predictions are tested using Spanish employer-employee matched data that classify firms according to four main destination markets: local, national, European Union, and rest of the World. Employees’ average education is increasing in the remoteness of firm’s main output market. Market–destination wage premia are large, increasing in the remoteness of the market, and increasing in individual education. These results suggest that increasing globalization may play a significant role in raising wage inequality within and across education groups