The fully implicit stochastic-alpha method for stiff stochastic differential equations

A fully implicit integration method for stochastic differential equations with significant multiplicative noise and stiffness in both the drift and diffusion coefficients has been constructed, analyzed and illustrated with numerical examples in this work. The method has strong order 1.0 consistency and has user-selectable parameters that allow the user to expand the stability region of the method to cover almost the entire drift-diffusion stability plane. The large stability region enables the method to take computationally efficient time steps. A system of chemical Langevin equations simulated with the method illustrates its computational efficiency.

Counting the cost: Estimating the number of deaths among recently released prisoners in Australia

TO THE EDITOR: Kinner and colleagues described the high proportion of deaths among recently released prisoners in Australia...

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

The line transect method for estimating densities of large mammals in a tropical deciduous forest: An evaluation of models and field experiments

We have evaluated techniques of estimating animal density through direct counts using line transects during 1988-92 in the tropical deciduous forests of Mudumalai Sanctuary in southern India for four species of large herbivorous mammals, namely, chital (Axis axis), sambar (Cervus unicolor), Asian elephant (Elephas maximus) and gaur (Bos gauras). Density estimates derived from the Fourier Series and the Half-Normal models consistently had the lowest coefficient of variation. These two models also generated similar mean density estimates. For the Fourier Series estimator, appropriate cut-off widths for analysing line transect data for the four species are suggested. Grouping data into various distance classes did not produce any appreciable differences in estimates of mean density or their variances, although model fit is generally better when data are placed in fewer groups. The sampling effort needed to achieve a desired precision (coefficient of variation) in the density estimate is derived. A sampling effort of 800 km of transects returned a 10% coefficient of variation on estimate for chital; for the other species a higher effort was needed to achieve this level of precision. There was no statistically significant relationship between detectability of a group and the size of the group for any species. Density estimates along roads were generally significantly different from those in the interior af the forest, indicating that road-side counts may not be appropriate for most species.

Shape effect on optimal geometric conditions in surface aeration systems

The performance of surface aeration systems, among other key design variables, depends upon the geometric parameters of the aeration tank. Efficient performance and scale up or scale down of the experimental results of an aeration ystem requires optimal geometric conditions. Optimal conditions refer to the conditions of maximum oxygen transfer rate, which assists in scaling up or down the system for ommercial utilization. The present work investigates the effect of an aeration tank's shape (unbaffled circular, baffled circular and unbaffled square) on oxygen transfer. Present results demonstrate that there is no effect of shape on the optimal geometric conditions for rotor position and rotor dimensions. This experimentation shows that circular tanks (baffled or unbaffled) do not have optimal geometric conditions for liquid transfer, whereas the square cross-section tank shows a unique geometric shape to optimize oxygen transfer.

Delay Optimal Scheduling in a Two-Hop Vehicular Relay Network

We study a scheduling problem in a wireless network where vehicles are used as store-and-forward relays, a situation that might arise, for example, in practical rural communication networks. A fixed source node wants to transfer a file to a fixed destination node, located beyond its communication range. In the absence of any infrastructure connecting the two nodes, we consider the possibility of communication using vehicles passing by. Vehicles arrive at the source node at renewal instants and are known to travel towards the destination node with average speed v sampled from a given probability distribution. Th source node communicates data packets (or fragments) of the file to the destination node using these vehicles as relays. We assume that the vehicles communicate with the source node and the destination node only, and hence, every packet communication involves two hops. In this setup, we study the source node's sequential decision problem of transferring packets of the file to vehicles as they pass by, with the objective of minimizing delay in the network. We study both the finite file size case and the infinite file size case. In the finite file size case, we aim to minimize the expected file transfer delay, i.e. expected value of the maximum of the packet sojourn times. In the infinite file size case, we study the average packet delay minimization problem as well as the optimal tradeoff achievable between the average queueing delay at the source node buffer and the average transit delay in the relay vehicle.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

A new framework for solution of multidimensional population balance equations

A new framework is proposed in this work to solve multidimensional population balance equations (PBEs) using the method of discretization. A continuous PBE is considered as a statement of evolution of one evolving property of particles and conservation of their n internal attributes. Discretization must therefore preserve n + I properties of particles. Continuously distributed population is represented on discrete fixed pivots as in the fixed pivot technique of Kumar and Ramkrishna [1996a. On the solution of population balance equation by discretization-I A fixed pivot technique. Chemical Engineering Science 51(8), 1311-1332] for 1-d PBEs, but instead of the earlier extensions of this technique proposed in the literature which preserve 2(n) properties of non-pivot particles, the new framework requires n + I properties to be preserved. This opens up the use of triangular and tetrahedral elements to solve 2-d and 3-d PBEs, instead of the rectangles and cuboids that are suggested in the literature. Capabilities of computational fluid dynamics and other packages available for generating complex meshes can also be harnessed. The numerical results obtained indeed show the effectiveness of the new framework. It also brings out the hitherto unknown role of directionality of the grid in controlling the accuracy of the numerical solution of multidimensional PBEs. The numerical results obtained show that the quality of the numerical solution can be improved significantly just by altering the directionality of the grid, which does not require any increase in the number of points, or any refinement of the grid, or even redistribution of pivots in space. Directionality of a grid can be altered simply by regrouping of pivots.

An optimal weighted-average congestion based pricing scheme for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes under a single service class and multiple queues, and present a multi-layered pricing scheme. We propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. The pricing policy used depends on a weighted average queue length at each node. This helps in reducing frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks. We observe in our numerical results a considerable improvement in performance using our scheme over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our approach exhibits a throughput improvement in the range of 34 to 69 percent in all cases studied (over all routes) over the above scheme.

DNA looping and translocation provide an optimal cleavage mechanism for the type III restriction enzymes

EcoP15I is a type III restriction enzyme that requires two recognition sites in a defined orientation separated by up to 3.5 kbp to efficiently cleave DNA. The mechanism through which site- bound EcoP15I enzymes communicate between the two sites is unclear. Here, we use atomic force microscopy to study EcoP15I-DNA pre-cleavage complexes. From the number and size distribution of loops formed, we conclude that the loops observed do not result from translocation, but are instead formed by a contact between site- bound EcoP15I and a nonspecific region of DNA. This conclusion is confirmed by a theoretical polymer model. It is further shown that translocation must play some role, because when translocation is blocked by a Lac repressor protein, DNA cleavage is similarly blocked. On the basis of these results, we present a model for restriction by type III restriction enzymes and highlight the similarities between this and other classes of restriction enzymes.

Individualized immunosuppression after renal transplantation in childhood

Pediatric renal transplantation (TX) has evolved greatly during the past few decades, and today TX is considered the standard care for children with end-stage renal disease. In Finland, 191 children had received renal transplants by October 2007, and 42% of them have already reached adulthood. Improvements in treatment of end-stage renal disease, surgical techniques, intensive care medicine, and in immunosuppressive therapy have paved the way to the current highly successful outcomes of pediatric transplantation. In children, the transplanted graft should last for decades, and normal growth and development should be guaranteed. These objectives set considerable requirements in optimizing and fine-tuning the post-operative therapy. Careful optimization of immunosuppressive therapy is crucial in protecting the graft against rejection, but also in protecting the patient against adverse effects of the medication. In the present study, the results of a retrospective investigation into individualized dosing of immunosuppresive medication, based on pharmacokinetic profiles, therapeutic drug monitoring, graft function and histology studies, and glucocorticoid biological activity determinations, are reported. Subgroups of a total of 178 patients, who received renal transplants in 1988 2006 were included in the study. The mean age at TX was 6.5 years, and approximately 26% of the patients were <2 years of age. The most common diagnosis leading to renal TX was congenital nephrosis of the Finnish type (NPHS1). Pediatric patients in Finland receive standard triple immunosuppression consisting of cyclosporine A (CsA), methylprednisolone (MP) and azathioprine (AZA) after renal TX. Optimal dosing of these agents is important to prevent rejections and preserve graft function in one hand, and to avoid the potentially serious adverse effects on the other hand. CsA has a narrow therapeutic window and individually variable pharmacokinetics. Therapeutic monitoring of CsA is, therefore, mandatory. Traditionally, CsA monitoring has been based on pre-dose trough levels (C0), but recent pharmacokinetic and clinical studies have revealed that the immunosuppressive effect may be related to diurnal CsA exposure and blood CsA concentration 0-4 hours after dosing. The two-hour post-dose concentration (C2) has proved a reliable surrogate marker of CsA exposure. Individual starting doses of CsA were analyzed in 65 patients. A recommended dose based on a pre-TX pharmacokinetic study was calculated for each patient by the pre-TX protocol. The predicted dose was clearly higher in the youngest children than in the older ones (22.9±10.4 and 10.5±5.1 mg/kg/d in patients <2 and >8 years of age, respectively). The actually administered oral doses of CsA were collected for three weeks after TX and compared to the pharmacokinetically predicted dose. After the TX, dosing of CsA was adjusted according to clinical parameters and blood CsA trough concentration. The pharmacokinetically predicted dose and patient age were the two significant parameters explaining post-TX doses of CsA. Accordingly, young children received significantly higher oral doses of CsA than the older ones. The correlation to the actually administered doses after TX was best in those patients, who had a predicted dose clearly higher or lower (> ±25%) than the average in their age-group. Due to the great individual variation in pharmacokinetics standardized dosing of CsA (based on body mass or surface area) may not be adequate. Pre-Tx profiles are helpful in determining suitable initial CsA doses. CsA monitoring based on trough and C2 concentrations was analyzed in 47 patients, who received renal transplants in 2001 2006. C0, C2 and experienced acute rejections were collected during the post-TX hospitalization, and also three months after TX when the first protocol core biopsy was obtained. The patients who remained rejection free had slightly higher C2 concentrations, especially very early after TX. However, after the first two weeks also the trough level was higher in the rejection-free patients than in those with acute rejections. Three months after TX the trough level was higher in patients with normal histology than in those with rejection changes in the routine biopsy. Monitoring of both the trough level and C2 may thus be warranted to guarantee sufficient peak concentration and baseline immunosuppression on one hand and to avoid over-exposure on the other hand. Controlling of rejection in the early months after transplantation is crucial as it may contribute to the development of long-term allograft nephropathy. Recently, it has become evident that immunoactivation fulfilling the histological criteria of acute rejection is possible in a well functioning graft with no clinical sings or laboratory perturbations. The influence of treatment of subclinical rejection, diagnosed in 3-month protocol biopsy, to graft function and histology 18 months after TX was analyzed in 22 patients and compared to 35 historical control patients. The incidence of subclinical rejection at three months was 43%, and the patients received a standard rejection treatment (a course of increased MP) and/or increased baseline immunosuppression, depending on the severity of rejection and graft function. Glomerular filtration rate (GFR) at 18 months was significantly better in the patients who were screened and treated for subclinical rejection in comparison to the historical patients (86.7±22.5 vs. 67.9±31.9 ml/min/1.73m2, respectively). The improvement was most remarkable in the youngest (<2 years) age group (94.1±11.0 vs. 67.9±26.8 ml/min/1.73m2). Histological findings of chronic allograft nephropathy were also more common in the historical patients in the 18-month protocol biopsy. All pediatric renal TX patients receive MP as a part of the baseline immunosuppression. Although the maintenance dose of MP is very low in the majority of the patients, the well-known steroid-related adverse affects are not uncommon. It has been shown in a previous study in Finnish pediatric TX patients that steroid exposure, measured as area under concentration-time curve (AUC), rather than the dose correlates with the adverse effects. In the present study, MP AUC was measured in sixteen stable maintenance patients, and a correlation with excess weight gain during 12 months after TX as well as with height deficit was found. A novel bioassay measuring the activation of glucocorticoid receptor dependent transcription cascade was also employed to assess the biological effect of MP. Glucocorticoid bioactivity was found to be related to the adverse effects, although the relationship was not as apparent as that with serum MP concentration. The findings in this study support individualized monitoring and adjustment of immunosuppression based on pharmacokinetics, graft function and histology. Pharmacokinetic profiles are helpful in estimating drug exposure and thus identifying the patients who might be at risk for excessive or insufficient immunosuppression. Individualized doses and monitoring of blood concentrations should definitely be employed with CsA, but possibly also with steroids. As an alternative to complete steroid withdrawal, individualized dosing based on drug exposure monitoring might help in avoiding the adverse effects. Early screening and treatment of subclinical immunoactivation is beneficial as it improves the prospects of good long-term graft function.

Sensitivity of Eigen Value to Damage and Its Identification

The reduction in natural frequencies,however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamentalmodes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an endbearing pile, modelled as an axial rod and a simply supported plate as a continuum dynamic system. A discrete structure, like a building frame is solved for damage using Eigen-sensitivity derived by a computationalmodel. Lastly, neural network based damage identification is also demonstrated for a simply supported bridge beam, where the known-pairs of damage-frequency vector is used to train a neural network. The performance of these methods under the influence of measurement error is outlined. It is hoped that the developed method could be integrated in a typical infra-structural management program, such that magnitudes of damage and their positions can be obtained using acquired natural frequencies, synthesized from the excited/ambient vibration signatures.

Jointly optimal power control and routing for a single cell, dense, ad hoc wireless network

We consider a dense, ad hoc wireless network confined to a small region, such that direct communication is possible between any pair of nodes. The physical communication model is that a receiver decodes the signal from a single transmitter, while treating all other signals as interference. Data packets are sent between source-destination pairs by multihop relaying. We assume that nodes self-organise into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention based multiaccess scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, we seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. We first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc network (described above) as a single cell, we study the optimal hop length and power control that maximizes the transport capacity for a given network power constraint. More specifically, for a fading channel and for a fixed transmission time strategy (akin to the IEEE 802.11 TXOP), we find that there exists an intrinsic aggregate bit rate (Theta(opt) bits per second, depending on the contention mechanism and the channel fading characteristics) carried by the network, when operating at the optimal hop length and power control. The optimal transport capacity is of the form d(opt)((P) over bar (t)) x Theta(opt) with d(opt) scaling as (P) over bar (1/eta)(t), where (P) over bar (t) is the available time average transmit power and eta is the path loss exponent. Under certain conditions on the fading distribution, we then provide a simple characterisation of the optimal operating point.