Mathematical analysis of an HIV model with impulsive antiretroviral drug doses

In this paper, we incorporate the periodic therapy from antiretroviral drugs for HIV into the standard within-host virus model, and study the stability and bifurcation of the system. It is shown that when the basic reproduction number of virus is less than one, there is an infection-free equilibrium which is globally stable. Further, if it is greater than one, the HIV infection is uniformly persistent. Besides, subharmonic bifurcation occurs under suitable conditions, and chaotic attractor may emerge through period doubling routes, which can be used to explain the HIV patients’ unpredictable unstable health states, even after a long and hard treatment.     

The concept of a quasi-particle and the non-probabilistic interpretation of wave mechanics

In recent works of the author [Found. Phys. 36 (2006) 1701–1717; Math. Comput. Simul. 74 (2007) 93–103], the argument has been made that Hertz's equations of electrodynamics reflect the material invariance (indifference) of the latter. Then the principle of material invariance was postulated in lieu of Lorentz covariance, and the respective absolute medium was named the metacontinuum.     

Stochastic optimization for the calculation of the optimal critical curve from experimental data in a model of the process of regaining balance after perturbation from quiet stance

We demonstrate the successful application of ALOPEX stochastic optimization to the problem of calculating the optimal critical curve in a dynamical systems model of the process of regaining balance after perturbation from quiet stance. Experimental data provide the time series of angles for which the subjects were able to regain balance after an initial perturbation. The optimal critical curve encloses all data points and has a minimum distance from the border points of the data set. We demonstrate the results of the optimization firstly using the traditional cost function of chi-square distance. We then successfully introduce a modified cost function that fits the model to the experimental data by taking into account the specific requirements of the model. By use of the proposed cost function, combined with the efficiency of our optimization method, an optimal critical curve is calculated even in the cases of very asymmetric data sets that lie within the capabilities of the existing model.     

Using a generalized molecular dynamics force model for random microstructure generation of different aspect-ratios and orientation for use in the optical design of an LED edge-lit backlight

We propose a method for the pattern generation on the base of a light guide for application in an edge-lit backlight. This method uses the molecular dynamics method of a generalized force model as a generation scheme to produce a microstructure with a pattern combining a variable aspect ratio and a variable microstructure orientation. This generation scheme can accommodate the needs of the subsequent optical design phase, and allows for easier optical optimization to reach the equal luminance condition. The scheme is incorporated into several new schemes to meet these needs, the most important of which is the cell division technique, which allows the adjustment of the microstructure density in each sub-domain, or cell. In addition, the boundary treatments allow the precise control of the microstructure density in each cell and the ability to smooth the microstructure distribution across the cell boundary. Finally, we present an example of a backlight with one light emitting diode showing the integration of the generation scheme and the optical design phase in order to assess the validation of the proposed scheme.     

The application hosting environment: Lightweight middleware for grid-based computational science

Grid computing is distributed computing performed transparently across multiple administrative domains. Grid middleware, which is meant to enable access to grid resources, is currently widely seen as being too heavyweight and, in consequence, unwieldy for general scientific use. Its heavyweight nature, especially on the client-side, has severely restricted the uptake of grid technology by computational scientists. In this paper, we describe the Application Hosting Environment (AHE) which we have developed to address some of these problems. The AHE is a lightweight, easily deployable environment designed to allow the scientist to quickly and easily run legacy applications on distributed grid resources. It provides a higher level abstraction of a grid than is offered by existing grid middleware schemes such as the Globus Toolkit. As a result, the computational scientist does not need to know the details of any particular underlying grid middleware and is isolated from any changes to it on the distributed resources. The functionality provided by the AHE is ‘application-centric’: applications are exposed as web services with a well-defined standards-compliant interface. This allows the computational scientist to start and manage application instances on a grid in a transparent manner, thus greatly simplifying the user experience. We describe how a range of computational science codes have been hosted within the AHE and how the design of the AHE allows us to implement complex workflows for deployment on grid infrastructure.     

OOF3D: An image-based finite element solver for materials science

Recent advances in experimental techniques (micro-CT scans, automated serial sectioning, electron back-scatter diffraction, and synchrotron radiation X-rays) have made it possible to characterize the full, three-dimensional structure of real materials. Such new experimental techniques have created a need for software tools that can model the response of these materials under various kinds of loads. OOF (Object Oriented Finite Elements) is a desktop software application for studying the relationship between the microstructure of a material and its overall mechanical, dielectric, or thermal properties using finite element models based on real or simulated micrographs. OOF provides methods for segmenting images, creating meshes of complex geometries, solving PDE's using finite element models, and visualizing 3D results. We discuss the challenges involved in implementing OOF in 3D and create a finite element mesh of trabecular bone as an illustrative example.     

Au/SnO2 an excellent material for room temperature carbon monoxide sensing

Tin dioxide synthesized by the hydrothermal method, impregnated with Au has been used for the room temperature carbon monoxide sensing in air. Incorporation of poly ethylene glycol (PEG-6000) as a modifier during the synthesis procedure results in well dispersed nanosized particles of SnO₂ which influence the sensing capability dramatically. This tailored morphology leads to development of a material with improved sensor response. Incorporation of gold resulted in a composition that was capable of selectively sensing low concentrations (upto 10 ppm CO in air) at temperatures below 50 °C. The mechanism of improved sensing has been explained based on the gas sensing characteristics with support from TEM, UV-DRS, XPS and FTIR.     

Physiology-based dynamic muscle fatigue model for upper limbs during construction tasks

Due to physically demanding construction tasks, workers frequently suffer from significant levels of muscle fatigue that can cause diverse detrimental effects on safety, health, and productivity. In this regard, evaluating the level of muscle fatigue prior to work is essential to take proper preventive actions before severe fatigue takes place. Although previous research efforts have quantified muscle fatigue using surveys, instruments, and mathematical models, most of them do not take into account irregularly varying muscle activation and fatigue recovery during a task. They are thus limited, especially for construction tasks that have varying forces and intermittent idling/resting periods. This study thus proposes a physiology-based modeling approach to computationally model and empirically validate dynamic muscle fatigue generation and recovery for construction workers through laboratory testing. Specifically, a muscle fatigue estimation model for upper limbs based on System Dynamics, which is a differential equation-based continuous simulation, is developed based on fundamental physiological mechanisms of the accumulation and clearance of intramuscular metabolites during muscle exertion and their effects on muscle contractile processes. Then the model is refined and validated through laboratory experiments. The results demonstrated the immense potential for the developed elbow and shoulder models to evaluate workers' muscle fatigue in upper limbs under varying workloads. The contribution of this study is to provide an analytic tool for understanding the physiological mechanisms of muscle fatigue and estimating workers' muscle fatigue levels during construction tasks, which can help to design appropriate interventions prior to work, thereby reducing undesirable results from muscle fatigue.     

On the application of the Cole-Hopf transformation to hyperbolic equations based on second-sound models

We point out and examine two nonlinear, hyperbolic equations, both of which arise in kinematic-wave theory, that can be solved exactly using a conditional application of the Cole-Hopf transformation. Both of these equations are based on flux relations that were originally proposed as models of thermal wave phenomena, also known as second-sound. We then show how this method can be extended and used to obtain a particular type of exact solution to a class of nonlinear, hyperbolic PDEs.     

Nonlocality as well as rejection of realism are only sufficient (but non-necessary!) conditions for violation of Bell’s inequality

In this review we remind the viewpoint that violation of Bell’s inequality might be interpreted not only as an evidence of the alternative - either nonlocality or “death of reality” (under the assumption the quantum mechanics is incomplete). Violation of Bell’s type inequalities is a well known sufficient condition of probabilistic incompatibility of random variables - impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell’s inequality - a few pairs of random variables (two-dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus, one can choose between: (a) completeness of quantum mechanics; (b) nonlocality; (c) “ death of reality”; (d) non-Kolmogorovness. In any event, violation of Bell’s inequality has a variety of possible interpretations. Hence, it could not be used to obtain the definite conclusion on the relation between quantum and classical models.     

Influence of the condensate and inverse cascade on the direct cascade in wave turbulence

During direct numerical simulation of the isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations formation of the long wave background or condensate was observed. Exponents of the direct cascade spectra at the different levels of an artificial condensate suppression show a tendency to become closer to the prediction of the wave turbulence theory at lower levels of condensate. A simple qualitative explanation of the mechanism of this phenomenon is proposed.     

An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes

An accurate conservative interpolation (remapping) algorithm is an essential component of most Arbitrary Lagrangian-Eulerian (ALE) methods. In this paper, we describe an efficient linearity and bound preserving method for polyhedral meshes. The algorithm is based on reconstruction, approximate integration and conservative redistribution. We validate our method with a suite of numerical examples, analyzing the results from the viewpoint of accuracy and order of convergence.     

New models for region of interest reader classification analysis in chest radiographs

In several computer-aided diagnosis (CAD) applications of image processing, there is no sufficiently sensitive and specific method for determining what constitutes a normal versus an abnormal classification of a chest radiograph. In the case of lung nodule detection or in classifying the perfusion of pneumoconiosis, multiple radiograph readers (radiologists) are asked to examine and score specific regions of interest (ROIs). The readers provide size, shape and perfusion grades for the presence of opacities in each region and then use all the ROI grades to classify the lung as normal or abnormal. The combined grades from all readers are then used to arrive at a consensus normal or abnormal classification. In this paper, using area under the ROC curve, we evaluate new mathematical models that are based on mathematical statistics, logic functions, and several statistical classifiers to analyze reader performance in grading chest radiographs for pneumoconiosis as the first step toward applying this technique to early detection of nodules found in lung cancer. In pneumoconiosis, rounded opacities are on the order of 1-10 mm in size, while lung nodules are often not diagnosed until they reach a size on the order of 1 cm.     

An exponential model of isometric muscular fatigue as a function of age and muscle groups

Despite the recommendations that an important design criterion is not to exceed 15% of an operator's maximum voluntary contraction (MVC) with any muscle that must be used for a long period of time, many tasks involve the exertion of much higher forces coupled with long-term contractions. Many studies have investigated the force-time relationship of isometric muscle contractions to determine the endurance time of a given relative force. To date, however, direct studies of muscle performance throughout fatiguing tasks have not been conducted to the same degree. This research was concerned with studying the effects of different muscle groups (biceps vs quadriceps) of subjects with different age groups (20·29 vs 50·59 years of age) on long-term muscular isometric contractions at different levels of %MVC (20%, 40%, 60%, 80%, and 100% MVC), and modelling the functional data to describe the time course of strength decrement. The data revealed that the time course of strength decrement was best modelled by the function:

An experiment, using 20 subjects with each subject performing 10 conditions (two muscle groups × five levels of %MVC), showed that this function accounted for over 95% of the variance of strength decrement. AH parameter estimates were statistically significant.     

On identification of the arterial model parameters from experiments applicable “in vivo”

We present a parameter identification procedure developed for a composite model of arterial wall which is characterized by collagen viscoelastic fibres embedded in hyperelastic incompressible matrix. The structure undergoes large deformation described using the total Lagrangian formulation. In the paper the identification procedure is tested numerically when applied to a simulated vessel dynamic inflation test, which can be performed in vivo. A stability test of the identification method is pursued as illustrated by two examples: the creep and relaxation tests.