Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: A computer simulation study

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

Adsorption of quadrupolar, diatomic nitrogen onto graphitized thermal carbon black and in slit-shaped carbon pores. Effects of surface mediation

In this paper, we study the effect of solid surface mediation on the intermolecular potential energy of nitrogen, and its impact on the adsorption of nitrogen on a graphitized carbon black surface and in carbon slit-shaped pores. This effect arises from the lower effective interaction potential energy between two particles close to the surface compared to the potential energy of the same two particles when they are far away from the surface. A simple equation is proposed to calculate the reduction factor and this is used in the Grand Canonical Monte Carlo (GCMC) simulation of nitrogen adsorption on graphitized thermal carbon black. With this modification, the GCMC simulation results agree extremely well with the experimental data over a wide range of pressure; the simulation results with the original potential energy (i.e. no surface mediation) give rise to a shoulder in the neighbourhood of monolayer coverage and a significant over-prediction of the second and higher layer coverages. The influence of this surface mediation on the dependence of the pore-filling pressure on the pore width is also studied. It is shown that such surface mediation has a significant effect on the pore-filling pressure. This implies that the use of the local isotherms obtained from the potential model without surface mediation could give rise to a serious error in the determination of the pore-size distribution.

Adsorption of Lennard-Jones fluids in carbon slit pores of a finite length. A computer simulation study

The adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length was studied with Canonical Ensemble (NVT) and Gibbs Ensemble Monte Carlo Simulations (GEMC). The Canonical Ensemble was a collection of cubic simulation boxes in which a finite pore resides, while the Gibbs Ensemble was that of the pore space of the finite pore. Argon was used as a model for Lennard-Jones fluids, while the adsorbent was modelled as a finite carbon slit pore whose two walls were composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. The Lennard-Jones (LJ) 12-6 potential model was used to compute the interaction energy between two fluid particles, and also between a fluid particle and a carbon atom. Argon adsorption isotherms were obtained at 87.3 K for pore widths of 1.0, 1.5 and 2.0 nm using both Canonical and Gibbs Ensembles. These results were compared with isotherms obtained with corresponding infinite pores using Grand Canonical Ensembles. The effects of the number of cycles necessary to reach equilibrium, the initial allocation of particles, the displacement step and the simulation box size were particularly investigated in the Monte Carlo simulation with Canonical Ensembles. Of these parameters, the displacement step had the most significant effect on the performance of the Monte Carlo simulation. The simulation box size was also important, especially at low pressures at which the size must be sufficiently large to have a statistically acceptable number of particles in the bulk phase. Finally, it was found that the Canonical Ensemble and the Gibbs Ensemble both yielded the same isotherm (within statistical error); however, the computation time for GEMC was shorter than that for canonical ensemble simulation. However, the latter method described the proper interface between the reservoir and the adsorbed phase (and hence the meniscus).

Adsorption of flexible n-alkane on graphitized thermal carbon black: analysis of adsorption isotherm by means of GCMC simulation

In this paper, we investigate the suitability of the grand canonical Monte Carlo in the description of adsorption equilibria of flexible n-alkane (butane, pentane and hexane) on graphitized thermal carbon black. Potential model of n-alkane of Martin and Siepmann (J. Phys. Chem. 102 (1998) 2569) is employed in the simulation, and we consider the flexibility of molecule in the simulation. By this we study two models, one is the fully flexible molecular model in which n-alkane is subject to bending and torsion, while the other is the rigid molecular model in which all carbon atoms reside on the same plane. It is found that (i) the adsorption isotherm results of these two models are close to each other, suggesting that n-alkane model behaves mostly as rigid molecules with respect to adsorption although the isotherm for longer chain n-hexane is better described by the flexible molecular model (ii) the isotherms agree very well with the experimental data at least up to two layers on the surface.

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC.

Protein interactions studied by SAXS:effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, S-SC(q), or an attractive square-well structure factor, S-SW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I <0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.

Glucosamine-induced insulin resistance in L6 muscle cells

Background: Glucosamine increases flux through the hexosamine pathway, causing insulin resistance and disturbances similar to diabetic glucose toxicity. Aim: This study examines the effect of glucosamine on glucose uptake by cultured L6 muscle cells as a model of insulin resistance. Methods: Glucose uptake by L6 myotubes was measured using the non-metabolized glucose analogue 2-deoxy-D-glucose after incubation with glucosamine for 4 and 24 h, with and without insulin and several other agents (metformin, peroxovanadium and D-pinitol) that improve glucose uptake in diabetic states. Results: After 4 h, high concentrations of glucosamine (5 × 10-3 and 10-2 M) reduced basal and insulin-stimulated glucose uptake by up to 50%. After 24 h, the effect of insulin was completely abolished by 10-2 M glucosamine and reduced over 50% by 5 × 10-3 M glucosamine. Lower concentrations of glucosamine did not significantly alter glucose uptake. The effect of glucosamine could not be attributed to cytotoxicity assessed by the Trypan Blue test. Metformin, peroxovanadium and D-pinitol, each of which increased glucose uptake by L6 cells, did not prevent the decrease in glucose uptake with glucosamine. Conclusion: Glucosamine decreased insulin-stimulated glucose uptake by L6 muscle cells, providing a potential model of insulin resistance with similarities to glucose toxicity. Insulin resistance induced by glucosamine was not reversed by three agents (metformin, peroxovanadium and D-pinitol) known to enhance or partially mimic the effects of insulin. © 2004 Blackwell Publishing Ltd.

Task sharing within a managed clinical network to improve child health in Malawi

BACKGROUND: Eighty per cent of Malawi's 8 million children live in rural areas, and there is an extensive tiered health system infrastructure from village health clinics to district hospitals which refers patients to one of the four central hospitals. The clinics and district hospitals are staffed by nurses, non-physician clinicians and recently qualified doctors. There are 16 paediatric specialists working in two of the four central hospitals which serve the urban population as well as accepting referrals from district hospitals. In order to provide expert paediatric care as close to home as possible, we describe our plan to task share within a managed clinical network and our hypothesis that this will improve paediatric care and child health.

PRESENTATION OF THE HYPOTHESIS: Managed clinical networks have been found to improve equity of care in rural districts and to ensure that the correct care is provided as close to home as possible. A network for paediatric care in Malawi with mentoring of non-physician clinicians based in a district hospital by paediatricians based at the central hospitals will establish and sustain clinical referral pathways in both directions. Ultimately, the plan envisages four managed paediatric clinical networks, each radiating from one of Malawi's four central hospitals and covering the entire country. This model of task sharing within four hub-and-spoke networks may facilitate wider dissemination of scarce expertise and improve child healthcare in Malawi close to the child's home.

TESTING THE HYPOTHESIS: Funding has been secured to train sufficient personnel to staff all central and district hospitals in Malawi with teams of paediatric specialists in the central hospitals and specialist non-physician clinicians in each government district hospital. The hypothesis will be tested using a natural experiment model. Data routinely collected by the Ministry of Health will be corroborated at the district. This will include case fatality rates for common childhood illness, perinatal mortality and process indicators. Data from different districts will be compared at baseline and annually until 2020 as the specialists of both cadres take up posts.

IMPLICATIONS OF THE HYPOTHESIS: If a managed clinical network improves child healthcare in Malawi, it may be a potential model for the other countries in sub-Saharan Africa with similar cadres in their healthcare system and face similar challenges in terms of scarcity of specialists.

Solar magnetic carpet I: simulation of synthetic magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×1016 - 1019 Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×1016 Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.

Studies of Protein-Protein and Protein-Water Interactions by Small Angle X-Ray Scattering, Terahertz Spectroscopy, ASMOS, And Computer Simulation

The protein folding problem has been one of the most challenging subjects in biological physics due to its complexity. Energy landscape theory based on statistical mechanics provides a thermodynamic interpretation of the protein folding process. We have been working to answer fundamental questions about protein-protein and protein-water interactions, which are very important for describing the energy landscape surface of proteins correctly. At first, we present a new method for computing protein-protein interaction potentials of solvated proteins directly from SAXS data. An ensemble of proteins was modeled by Metropolis Monte Carlo and Molecular Dynamics simulations, and the global X-ray scattering of the whole model ensemble was computed at each snapshot of the simulation. The interaction potential model was optimized and iterated by a Levenberg-Marquardt algorithm. Secondly, we report that terahertz spectroscopy directly probes hydration dynamics around proteins and determines the size of the dynamical hydration shell. We also present the sequence and pH-dependence of the hydration shell and the effect of the hydrophobicity. On the other hand, kinetic terahertz absorption (KITA) spectroscopy is introduced to study the refolding kinetics of ubiquitin and its mutants. KITA results are compared to small angle X-ray scattering, tryptophan fluorescence, and circular dichroism results. We propose that KITA monitors the rearrangement of hydrogen bonding during secondary structure formation. Finally, we present development of the automated single molecule operating system (ASMOS) for a high throughput single molecule detector, which levitates a single protein molecule in a 10 µm diameter droplet by the laser guidance. I also have performed supporting calculations and simulations with my own program codes.

Sustained release and osteogenic potential of heparan sulfate-doped fibrin glue scaffolds within a rat cranial model

This paper explores the potential therapeutic role of the naturally occurring sugar heparan sulfate (HS) for the augmentation of bone repair. Scaffolds comprising fibrin glue loaded with 5 lg of embryonically derived HS were assessed, firstly as a release-reservoir, and secondly as a scaffold to stimulate bone regeneration in a critical size rat cranial defect. We show HS-loaded scaffolds have a uniform distribution of HS, which was readily released with a typical burst phase, quickly followed by a prolonged delivery lasting several days. Importantly, the released HS contributed to improved wound healing over a 3-month period as determined by microcomputed tomography (lCT) scanning, histology, histomorphometry, and PCR for osteogenic markers. In all cases, only minimal healing was observed after 1 and 3 months in the absence of HS. In contrast, marked healing was observed by 3 months following HS treatment, with nearly full closure of the defect site. PCR analysis showed significant increases in the gene expression of the osteogenic markers Runx2, alkaline phosphatase, and osteopontin in the heparin sulfate group compared with controls. These results further emphasize the important role HS plays in augmenting wound healing, and its successful delivery in a hydrogel provides a novel alternative to autologous bone graft and growth factorbased therapies.

Structural equation model of construction contract dispute potential

This paper presents the results of a structural equation model (SEM) for describing and quantifying the fundamental factors that affect contract disputes between owners and contractors in the construction industry. Through this example, the potential impact of SEM analysis in construction engineering and management research is illustrated. The purpose of the specific model developed in this research is to explain how and why contract related construction problems occur. This study builds upon earlier work, which developed a disputes potential index, and the likelihood of construction disputes was modeled using logistic regression. In this earlier study, questionnaires were completed on 159 construction projects, which measured both qualitative and quantitative aspects of contract disputes, management ability, financial planning, risk allocation, and project scope definition for both owners and contractors. The SEM approach offers several advantages over the previously employed logistic regression methodology. The final set of structural equations provides insight into the interaction of the variables that was not apparent in the original logistic regression modeling methodology.

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.