A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Fiscal Sustainability in a New Keynesian Model

Recent work on optimal monetary and fiscal policy in New Keynesian models suggests that it is optimal to allow steady-state debt to follow a random walk. Leith and Wren-Lewis (2012) consider the nature of the timeinconsistency involved in such a policy and its implication for discretionary policy-making. We show that governments are tempted, given inflationary expectations, to utilize their monetary and fiscal instruments in the initial period to change the ultimate debt burden they need to service. We demonstrate that this temptation is only eliminated if following shocks, the new steady-state debt is equal to the original (efficient) debt level even though there is no explicit debt target in the government’s objective function. Analytically and in a series of numerical simulations we show which instrument is used to stabilize the debt depends crucially on the degree of nominal inertia and the size of the debt-stock. We also show that the welfare consequences of introducing debt are negligible for precommitment policies, but can be significant for discretionary policy. Finally, we assess the credibility of commitment policy by considering a quasi-commitment policy which allows for different probabilities of reneging on past promises. This on-line Appendix extends the results of this paper.

Fiscal Sustainability in a New Keynesian Model

Recent work on optimal monetary and fiscal policy in New Keynesian models suggests that it is optimal to allow steady-state debt to follow a random walk. Leith and Wren-Lewis (2012) consider the nature of the timeinconsistency involved in such a policy and its implication for discretionary policy-making. We show that governments are tempted, given inflationary expectations, to utilize their monetary and fiscal instruments in the initial period to change the ultimate debt burden they need to service. We demonstrate that this temptation is only eliminated if following shocks, the new steady-state debt is equal to the original (efficient) debt level even though there is no explicit debt target in the government’s objective function. Analytically and in a series of numerical simulations we show which instrument is used to stabilize the debt depends crucially on the degree of nominal inertia and the size of the debt-stock. We also show that the welfare consequences of introducing debt are negligible for precommitment policies, but can be significant for discretionary policy. Finally, we assess the credibility of commitment policy by considering a quasi-commitment policy which allows for different probabilities of reneging on past promises. This on-line Appendix extends the results of this paper.

The Inflation Risk Premium on Government Debt in an Overlapping Generations Model

This paper presents a general equilibrium model in which nominal government debt pays an inflation risk premium. The model predicts that the inflation risk premium will be higher in economies which are exposed to unanticipated inflation through nominal asset holdings. In particular, the inflation risk premium is higher when government debt is primarily nominal, steady-state inflation is low, and when cash and nominal debt account for a large fraction of consumers' retirement portfolios. These channels do not appear to have been highlighted in previous models or tested empirically. Numerical results suggest that the inflation risk premium is comparable in magnitude to standard representative agent models. These findings have implications for management of government debt, since the inflation risk premium makes it more costly for governments to borrow using nominal rather than indexed debt. Simulations of an extended model with Epstein-Zin preferences suggest that increasing the share of indexed debt would enable governments to permanently lower taxes by an amount that is quantitatively non-trivial.

The Optimal Degree of Monetary-Discretion in a New Keynesian Model with Private Information

This paper considers the optimal degree of discretion in monetary policy when the central bank conducts policy based on its private information about the state of the economy and is unable to commit. Society seeks to maximize social welfare by imposing restrictions on the central bank's actions over time, and the central bank takes these restrictions and the New Keynesian Phillips curve as constraints. By solving a dynamic mechanism design problem we find that it is optimal to grant "constrained discretion" to the central bank by imposing both upper and lower bounds on permissible inflation, and that these bounds must be set in a history-dependent way. The optimal degree of discretion varies over time with the severity of the time-inconsistency problem, and, although no discretion is optimal when the time-inconsistency problem is very severe, our numerical experiment suggests that no-discretion is a transient phenomenon, and that some discretion is granted eventually.

An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

Complex landslide behaviour and structural controlled by the structures: A 3D conceptual model example of Åknes rockslide, Norway

Åknes is an active complex large rockslide of approximately 30?40 Mm3 located within the Proterozoic gneisses of western Norway. The observed surface displacements indicate that this rockslide is divided into several blocks moving in different directions at velocities of between 3 and 10 cm year?1. Because of regional safety issues and economic interests this rockslide has been extensively monitored since 2004. The understanding of the deformation mechanism is crucial for the implementation of a viable monitoring system. Detailed field investigations and the analysis of a digital elevation model (DEM) indicate that the movements and the block geometry are controlled by the main schistosity (S1) in gneisses, folds, joints and regional faults. Such complex slope deformations use pre-existing structures, but also result in new failure surfaces and deformation zones, like preferential rupture in fold-hinge zones. Our interpretation provides a consistent conceptual three-dimensional (3D) model for the movements measured by various methods that is crucial for numerical stability modelling. In addition, this reinterpretation of the morphology confirms that in the past several rockslides occurred from the Åknes slope. They may be related to scars propagating along the vertical foliation in folds hinges. Finally, a model of the evolution of the Åknes slope is presented.

Oscillations in a molecular structured cell population model

We consider a nonlinear cyclin content structured model of a cell population divided into proliferative and quiescent cells. We show, for particular values of the parameters, existence of solutions that do not depend on the cyclin content. We make numerical simulations for the general case obtaining, for some values of the parameters convergence to the steady state but also oscillations of the population for others.

A decision-making Fokker-Planck model in computational neuroscience

Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

High-resolution numerical modelling of flow-vegetation interactions

In this paper, we present and apply a new three-dimensional model for the prediction of canopy-flow and turbulence dynamics in open-channel flow. The approach uses a dynamic immersed boundary technique that is coupled in a sequentially staggered manner to a large eddy simulation. Two different biomechanical models are developed depending on whether the vegetation is dominated by bending or tensile forces. For bending plants, a model structured on the Euler-Bernoulli beam equation has been developed, whilst for tensile plants, an N-pendula model has been developed. Validation against flume data shows good agreement and demonstrates that for a given stem density, the models are able to simulate the extraction of energy from the mean flow at the stem-scale which leads to the drag discontinuity and associated mixing layer.

Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers

Recent technological advances in remote sensing have enabled investigation of the morphodynamics and hydrodynamics of large rivers. However, measuring topography and flow in these very large rivers is time consuming and thus often constrains the spatial resolution and reach-length scales that can be monitored. Similar constraints exist for computational fluid dynamics (CFD) studies of large rivers, requiring maximization of mesh-or grid-cell dimensions and implying a reduction in the representation of bedform-roughness elements that are of the order of a model grid cell or less, even if they are represented in available topographic data. These ``subgrid'' elements must be parameterized, and this paper applies and considers the impact of roughness-length treatments that include the effect of bed roughness due to ``unmeasured'' topography. CFD predictions were found to be sensitive to the roughness-length specification. Model optimization was based on acoustic Doppler current profiler measurements and estimates of the water surface slope for a variety of roughness lengths. This proved difficult as the metrics used to assess optimal model performance diverged due to the effects of large bedforms that are not well parameterized in roughness-length treatments. However, the general spatial flow patterns are effectively predicted by the model. Changes in roughness length were shown to have a major impact upon flow routing at the channel scale. The results also indicate an absence of secondary flow circulation cells in the reached studied, and suggest simpler two-dimensional models may have great utility in the investigation of flow within large rivers. Citation: Sandbach, S. D. et al. (2012), Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers, Water Resour. Res., 48, W12501, doi: 10.1029/2011WR011284.

Predictors of HIV-protection behaviour in HIV-positive men who have sex with casual male partners: a test of the explanatory power of an extended Information-Motivation-Behavioural Skills model.

This prospective study applies an extended Information-Motivation-Behavioural Skills (IMB) model to establish predictors of HIV-protection behaviour among HIV-positive men who have sex with men (MSM) during sex with casual partners. Data have been collected from anonymous, self-administered questionnaires and analysed by using descriptive and backward elimination regression analyses. In a sample of 165 HIV-positive MSM, 82 participants between the ages of 23 and 78 (M=46.4, SD=9.0) had sex with casual partners during the three-month period under investigation. About 62% (n=51) have always used a condom when having sex with casual partners. From the original IMB model, only subjective norm predicted condom use. More important predictors that increased condom use were low consumption of psychotropics, high satisfaction with sexuality, numerous changes in sexual behaviour after diagnosis, low social support from friends, alcohol use before sex and habitualised condom use with casual partner(s). The explanatory power of the calculated regression model was 49% (p<0.001). The study reveals the importance of personal and social resources and of routines for condom use, and provides information for the research-based conceptualisation of prevention offers addressing especially people living with HIV ("positive prevention").

Sexual protection behavior in HIV-positive gay men: testing a modified information-motivation-behavioral skills model.

This study on determinants of sexual protection behavior among HIV-positive gay men used the empirically tested information-motivation-behavioral skills (IMB) model. HIV-specific variables were added to the model to determine factors decisive for condom use with steady and casual partners. Data were collected using an anonymous, standardized self-administered questionnaire. Study participants were recruited at HIV outpatient clinics associated with the Eurosupport Study Group and the Swiss HIV Cohort Study. To identify factors associated with condom use, backward elimination regression analyses were performed. Overall, 838 HIV-infected gay men from 14 European countries were included in this analysis. About 53% of them reported at least one sexual contact with a steady partner; 62.5% had sex with a casual partner during the last 6 months. Forty-three percent always used condoms with steady partners and 44% with casual partners. High self-efficacy and subjective norms in favor of condom-use were associated with increased condom use with casual and steady partners, whereas feeling depressed was associated with decreased condom use with casual partners. Condoms were used less often with HIV-positive partners. Self-efficacy as an important behavioral skill to perform protection behavior was influenced by lower perceived vulnerability, higher subjective norms, and more positive safer sex attitudes. The IMB-model constructs appeared to be valid; however, not all the model predictors could be determined as hypothesized. Besides the original IMB constructs, HIV-specific variables, including sexual partners' serostatus and mental health, explained condom use. Such factors should be considered in clinical interventions to promote "positive prevention."