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PubMed1979

Allocation of doctors to health centres in Haryana state of India--a case study.

Medical Administrators are usually confronted with the problem of determining the number of doctors to be posted at different health centres within their jurisdiction. In India the number of doctors allocated to a health centre is normally decided without any proper study of the health needs of the area served by the centre. In certain areas the number of doctors posted is considerably different from the requirement of the area. Also, in certain health centres situated in villages lacking in modern amenities, absenteeism among doctors poses a very serious problem in day to day running of the health centres. The problem of allocation is formulated and a heuristic method is suggested for determining the optimum number of doctors to be posted at each health centre in order to maximise the number of patients seen by the doctor per day. The heuristic method is applied to nine health centres of Haryana state of India in order to demonstrate the potential benefits.

Community Health Centers↗

PubMed1997

Nonintegrability of two problems in vortex dynamics.

An analysis is presented of two problems in vortex dynamics whose equations can be written in the Hamiltonian form. They are: the interaction of three coaxial vortex rings and the motion of four point vortices on a sphere. The nonintegrability of these problems in the restricted formulation is demonstrated analytically by the method of split separatrices, using a small parameter. (c) 1997 American Institute of Physics.

Journal Article↗

PubMed2004

Modeling diffusion in miscible polymer blend films.

Recent experiments designed to probe polymer transport in the bulk and in the vicinity of surfaces have examined the interdiffusion of multilayer sandwiches of isotopically labeled polymers. The measured time dependent concentration profiles normal to the surface are typically fit to Fick's law, with a single fitting parameter, the mutual binary diffusion coefficient (MBDC). The resulting MBDCs are found to vary over a broad range of film thicknesses and time, with the time dependence being viewed as a unique signature of the reptation mechanism of long chain motion, and the thickness dependence being attributed to the slowing down of chain dynamics near surfaces. Since the experiments are conducted at finite concentration, the MBDC, which is a product of the bare mobility and the concentration derivative of the chemical potential, could be dominated by the time and thickness dependence of this second term (which is ignored in Fick's law). To quantify this conjecture we consider the more rigorous Cahn formulation of the diffusion problem in terms of chemical potential gradients. We use square gradient theory to evaluate chemical potentials, and fit the resulting time dependent concentration profiles to the analytical solution of Fick's law. By thus mimicking the experimental analysis we find that the apparent MBDCs vary with time as t(-1/2) at short times, in good agreement with existing experiments. We show that this time dependence reflects the system's desire to minimize concentration gradients, a fact ignored in Fick's law. Since these arguments make no reference to the mechanism of chain motion, we argue that the time dependence of MBDC derived from interdiffusion experiments does not provide unequivocal support for the reptation mechanism of long chain transport. The MBDC values, which also vary with the degree of confinement, are predicted to increase with decreasing thickness for model parameters corresponding to experimental systems. In contrast, since the experimental fits yield an opposite trend, we suggest that the bare mobility of the chains decreases strongly with decreasing thickness. These findings strongly support the idea that the chains are "pinned" irreversibly to the surfaces, in good agreement with other, independent experiments.

Journal Article↗

PubMed2004

Coping with the node problem in quantum hydrodynamics: the covering function method.

A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet.

Biophysics↗

PubMed2006

A line integral reaction path approximation for large systems via nonlinear constrained optimization: application to alanine dipeptide and the beta hairpin of protein G.

A variation of the line integral method of Elber with self-avoiding walk has been implemented using a state of the art nonlinear constrained optimization procedure. The new implementation appears to be robust in finding approximate reaction paths for small and large systems. Exact transition states and intermediates for the resulting paths can easily be pinpointed with subsequent application of the conjugate peak refinement method [S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992)] and unconstrained minimization, respectively. Unlike previous implementations utilizing a penalty function approach, the present implementation generates an exact solution of the underlying problem. Most importantly, this formulation does not require an initial guess for the path, which makes it particularly useful for studying complex molecular rearrangements. The method has been applied to conformational rearrangements of the alanine dipeptide in the gas phase and in water, and folding of the beta hairpin of protein G in water. In the latter case a procedure was developed to systematically sample the potential energy surface underlying folding and reconstruct folding pathways within the nearest-neighbor hopping approximation.

Alanine↗

PubMed2003

Transfer of a passive additive in a turbulent boundary layer at very large Reynolds numbers.

We formulate the mass transfer problem for a passive additive in a turbulent boundary layer based on the recently proposed model of the turbulent boundary layer at very large Reynolds numbers. The solutions of three basic problems are obtained. These solutions are self-similar asymptotics describing the mass exchange at its initial stages. The solutions obtained can be used for the construction (in particular, the numerical construction) of the solution to the more general problems of passive admixture transfer in the developed turbulent wall-bounded shear flows.

Journal Article↗

PubMed2005

Using fingerprint image quality to improve the identification performance of the U.S. Visitor and Immigrant Status Indicator Technology Program.

Motivated by the difficulty of biometric systems to correctly match fingerprints with poor image quality, we formulate and solve a game-theoretic formulation of the identification problem in two settings: U.S. visa applicants are checked against a list of visa holders to detect visa fraud, and visitors entering the U.S. are checked against a watchlist of criminals and suspected terrorists. For three types of biometric strategies, we solve the game in which the U.S. Government chooses the strategy's optimal parameter values to maximize the detection probability subject to a constraint on the mean biometric processing time per legal visitor, and then the terrorist chooses the image quality to minimize the detection probability. At current inspector staffing levels at ports of entry, our model predicts that a quality-dependent two-finger strategy achieves a detection probability of 0.733, compared to 0.526 under the quality-independent two-finger strategy that is currently implemented at the U.S. border. Increasing the staffing level of inspectors offers only minor increases in the detection probability for these two strategies. Using more than two fingers to match visitors with poor image quality allows a detection probability of 0.949 under current staffing levels, but may require major changes to the current U.S. biometric program. The detection probabilities during visa application are approximately 11-22% smaller than at ports of entry for all three strategies, but the same qualitative conclusions hold.

Biometry↗

PubMed1992

On assessment of bioequivalence under a higher-order crossover design.

In bioavailability studies of two formulations of a drug, the standard two-sequence, two-period crossover design is usually considered to assess bioequivalence. The standard two-sequence, two-period crossover design, however, may not be useful when differential carryover effects are present. In addition, it does not provide independent estimates of intrasubject variabilities for the two formulations. To overcome these problems, alternatively, a higher-order crossover design may be considered. In this paper, we derive statistical methods based on Schuirmann's two one-sided tests procedure for assessing bioequivalence for some commonly used higher-order crossover designs. Four designs, including Balaam's design, the two-sequence dual design, and two four-period designs (with two and four sequences), are considered. The relative merits of these designs as compared to the standard two-sequence, two-period design are discussed. Two examples concerning bioequivalence are used to illustrate the use of these methods.

Biological Availability↗

PubMed1996

Bayesian reconstruction of PET images: methodology and performance analysis.

We describe a practical statistical methodology for the reconstruction of PET images. Our approach is based on a Bayesian formulation of the imaging problem. The data are modelled as independent Poisson random variables and the image is modelled using a Markov random field smoothing prior. We describe a sequence of calibration procedures which are performed before reconstruction: (i) calculation of accurate attenuation correction factors from re-projected Bayesian reconstructions of the transmission image; (ii) estimation of the mean of the randoms component in the data; and (iii) computation of the scatter component in the data using a Klein-Nishina-based scatter estimation method. The Bayesian estimate of the PET image is then reconstructed using a pre-conditioned conjugate gradient method. We performed a quantitation study with a multi-compartment chest phantom in a Siemens/CTI ECAT931 system. Using 40 1 min frames, we computed the ensemble mean and variance over several regions of interest from images reconstructed using the Bayesian and a standard filtered backprojection (FBP) protocol. The values for the region of interest were compared with well counter data for each compartment. These results show that the Bayesian protocol can produce substantial improvements in relative quantitation over the standard FBP protocol, particularly when short transmission scans are used. An example showing the application of the method to a clinical chest study is also given.

Algorithms↗

PubMed1999

Forward problem solution of electromagnetic source imaging using a new BEM formulation with high-order elements.

Representations of the active cell populations on the cortical surface via electric and magnetic measurements are known as electromagnetic source images (EMSIs) of the human brain. Numerical solution of the potential and magnetic fields for a given electrical source distribution in the human brain is an essential part of electromagnetic source imaging. In this study, the performance of the boundary element method (BEM) is explored with different surface element types. A new BEM formulation is derived that makes use of isoparametric linear, quadratic or cubic elements. The surface integration is performed with Gauss quadrature. The potential fields are solved assuming a concentric three-shell model of the human head for a tangential dipole at different locations. In order to achieve 2% accuracy in potential solutions, the number of quadratic elements is of the order of hundreds. However, with linear elements, this number is of the order of ten thousand. The relative difference measures (RDMs) are obtained for the numerical models that use different element types. The numerical models that employ quadratic and cubic element types provide superior performance over linear elements in terms of accuracy in solutions. Assuming a homogeneous sphere model of the head, the RDMs are also obtained for the three components (radial and tangential) of the magnetic fields. The RDMs obtained for the tangential fields are, in general, much higher than those obtained for the radial fields. Both quadratic and cubic elements provide superior performance compared with linear elements for a wide range of dipole locations.

Algorithms↗

PubMed2005

A comparison of Monte Carlo dose calculation denoising techniques.

Recent studies have demonstrated that Monte Carlo (MC) denoising techniques can reduce MC radiotherapy dose computation time significantly by preferentially eliminating statistical fluctuations ('noise') through smoothing. In this study, we compare new and previously published approaches to MC denoising, including 3D wavelet threshold denoising with sub-band adaptive thresholding, content adaptive mean-median-hybrid (CAMH) filtering, locally adaptive Savitzky-Golay curve-fitting (LASG), anisotropic diffusion (AD) and an iterative reduction of noise (IRON) method formulated as an optimization problem. Several challenging phantom and computed-tomography-based MC dose distributions with varying levels of noise formed the test set. Denoising effectiveness was measured in three ways: by improvements in the mean-square-error (MSE) with respect to a reference (low noise) dose distribution; by the maximum difference from the reference distribution and by the 'Van Dyk' pass/fail criteria of either adequate agreement with the reference image in low-gradient regions (within 2% in our case) or, in high-gradient regions, a distance-to-agreement-within-2% of less than 2 mm. Results varied significantly based on the dose test case: greater reductions in MSE were observed for the relatively smoother phantom-based dose distribution (up to a factor of 16 for the LASG algorithm); smaller reductions were seen for an intensity modulated radiation therapy (IMRT) head and neck case (typically, factors of 2-4). Although several algorithms reduced statistical noise for all test geometries, the LASG method had the best MSE reduction for three of the four test geometries, and performed the best for the Van Dyk criteria. However, the wavelet thresholding method performed better for the head and neck IMRT geometry and also decreased the maximum error more effectively than LASG. In almost all cases, the evaluated methods provided acceleration of MC results towards statistically more accurate results.

Algorithms↗

PubMed1992

Conductivity interface modelling with dipoles by means of optimal control and boundary element methods in impedance tomography.

Optimal control techniques have been combined with Alessandrini's singular perturbation method and Wexler's algorithm to reconstruct images in impedance imaging. We have also considered an integral formulation of the potential problem, which has led us to introduce an array of dipoles whose position, orientation and length can be optimised to model the conductivity discontinuities.

Algorithms↗

PubMed1998

Assembling genes from predicted exons in linear time with dynamic programming.

In a number of programs for gene structure prediction in higher eukaryotic genomic sequences, exon prediction is decoupled from gene assembly: a large pool of candidate exons is predicted and scored from features located in the query DNA sequence, and candidate genes are assembled from such a pool as sequences of nonoverlapping frame-compatible exons. Genes are scored as a function of the scores of the assembled exons, and the highest scoring candidate gene is assumed to be the most likely gene encoded by the query DNA sequence. Considering additive gene scoring functions, currently available algorithms to determine such a highest scoring candidate gene run in time proportional to the square of the number of predicted exons. Here, we present an algorithm whose running time grows only linearly with the size of the set of predicted exons. Polynomial algorithms rely on the fact that, while scanning the set of predicted exons, the highest scoring gene ending in a given exon can be obtained by appending the exon to the highest scoring among the highest scoring genes ending at each compatible preceding exon. The algorithm here relies on the simple fact that such highest scoring gene can be stored and updated. This requires scanning the set of predicted exons simultaneously by increasing acceptor and donor position. On the other hand, the algorithm described here does not assume an underlying gene structure model. Indeed, the definition of valid gene structures is externally defined in the so-called Gene Model. The Gene Model specifies simply which gene features are allowed immediately upstream which other gene features in valid gene structures. This allows for great flexibility in formulating the gene identification problem. In particular it allows for multiple-gene two-strand predictions and for considering gene features other than coding exons (such as promoter elements) in valid gene structures.

Algorithms↗

PubMed2001

Construction of DNA restriction maps based on a simplified experiment.

MOTIVATION: A formulation of a new problem of the restriction map construction based on a simplified digestion experiment and a development of an algorithm for solving both ideal and noisy data cases of the introduced problem. RESULTS: A simplified partial digest problem and a branch and cut algorithm for finding the solution of the problem.

Algorithms↗

PubMed2004

Reconstructing tumor amplisomes.

MOTIVATION: Duplication of genomic sequences is a common phenomenon in tumor cells. While many duplications associated with tumors have been identified (e.g. via techniques such as CGH), both the organization of the duplicated sequences and the process that leads to these duplications are less clear. One mechanism that has been observed to lead to duplication is the extraction of DNA from the chromosomes and aggregation of this DNA into small, independently replicating linear or circular DNA sequences (amplisomes). Parts of these amplisomes may later be reinserted back into the main chromosomes leading to duplication. Although amplisomes are known to play an important role in tumorigenesis, their architecture and even size remain largely unknown. RESULTS: We reconstruct the structure of tumor amplisomes by analyzing duplications in the tumor genome. Our approach relies on recently generated data from End Sequence Profiling (ESP) experiments, which allow us to examine the fine structure of duplications in a tumor on a genome-wide scale. Using ESP data, we formulate the Amplisome Reconstruction Problem, describe an algorithm for its solution, and derive a putative architecture of a tumor amplisome that is the source for duplicated material in the MCF7 breast tumor cell line.

Algorithms↗

PubMed2004

Evolutionary optimization with data collocation for reverse engineering of biological networks.

MOTIVATION: Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. RESULTS: We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Algorithms↗

PubMed2005

Divide-and-conquer approach for the exemplar breakpoint distance.

MOTIVATION: A one-to-one correspondence between the sets of genes in the two genomes being compared is necessary for the notions of breakpoint and reversal distances. To compare genomes where there are paralogous genes, Sankoff formulated the exemplar distance problem as a general version of the genome rearrangement problem. Unfortunately, the problem is NP-hard even for the breakpoint distance. RESULTS: This paper proposes a divide-and-conquer approach for calculating the exemplar breakpoint distance between two genomes with multiple gene families. The combination of our approach and Sankoff's branch-and-bound technique leads to a practical program to answer this question. Tests with both simulated and real datasets show that our program is much more efficient than the existing program that is based only on the branch-and-bound technique. AVAILABILITY: Code for the program is available from the authors.

Algorithms↗

PubMed2002

Practical aspects of experimental design in animal research.

A brief overview is presented of the key steps involved in designing a research animal experiment, with reference to resources that specifically address each topic of discussion in more detail. After an idea for a research project is conceived, a thorough review of the literature and consultation with experts in that field are pursued to refine the problem statement and to assimilate background information that is necessary for the experimental design phase. A null and an alternate hypothesis that address the problem statement are then formulated, and only then is the specific design of the experiment developed. Likely the most critical step in designing animal experiments is the identification of the most appropriate animal model to address the experimental question being asked. Other practical considerations include defining the necessary control groups, randomly assigning animals to control/treatment groups, determining the number of animals needed per group, evaluating the logistics of the actual performance of the animal experiments, and identifying the most appropriate statistical analyses and potential collaborators experienced in the area of study. All of these factors are critical to designing an experiment that will generate scientifically valid and reproducible data, which should be considered the ultimate goal of any scientific investigation.

Animal Welfare↗