Modelling human dynamics in-situ for rehabilitation and therapy robots

This paper outlines some rehabilitation applications of manipulators and identifies that new approaches demand that the robot make an intimate contact with the user. Design of new generations of manipulators with programmable compliance along with higher level controllers that can set the compliance appropriately for the task, are both feasible propositions. We must thus gain a greater insight into the way in which a person interacts with a machine, particularly given that the interaction may be non-passive. We are primarily interested in the change in wrist and arm dynamics as the person co-contracts his/her muscles. It is observed that this leads to a change in stiffness that can push an actuated interface into a limit cycle. We use both experimental results gathered from a PHANToM haptic interface and a mathematical model to observe this effect. Results are relevant to the fields of rehabilitation and therapy robots, haptic interfaces, and telerobotics

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

A prospective longitudinal study of the impact of early postnatal vs. chronic maternal depressive symptoms on child development

Background Few studies of the effects of postnatal depression on child development have considered the chronicity of depressive symptoms. We investigated whether early postnatal depressive symptoms (PNDS) predicted child developmental outcome independently of later maternal depressive symptoms. Methods In a prospective, longitudinal study, mothers and children were followed-up from birth to 2 years; repeated measures of PNDS were made using the Edinburgh Postnatal Depression Scale (EPDS); child development was assessed using the Bayley Scales II. Multilevel modelling techniques were used to examine the association between 6 week PNDS, and child development, taking subsequent depressive symptoms into account. Results Children of mothers with 6 week PNDS were significantly more likely than children of non-symptomatic mothers to have poor cognitive outcome; however, this association was reduced to trend level when adjusted for later maternal depressive symptoms. Conclusion Effects of early PNDS on infant development may be partly explained by subsequent depressive symptoms.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Oxygen/Glucose deprivation induces a reduction in synaptic AMPA receptors on hippocampal CA3 neurons mediated by mGluR1 and adenosine A3 receptors

Hippocampal CA1 pyramidal neurons are highly sensitive to ischemic damage, whereas neighboring CA3 pyramidal neurons are less susceptible. It is proposed that switching of AMPA receptor (AMPAR) subunits on CA1 neurons during an in vitro model of ischemia, oxygen/glucose deprivation (OGD), leads to an enhanced permeability of AMPARs to Ca2+, resulting in delayed cell death. However, it is unclear whether the same mechanisms exist in CA3 neurons and whether this underlies the differential sensitivity to ischemia. Here, we investigated the consequences of OGD for AMPAR function in CA3 neurons using electrophysiological recordings in rat hippocampal slices. Following a 15 min OGD protocol, a substantial depression of AMPAR-mediated synaptic transmission was observed at CA3 associational/commissural and mossy fiber synapses but not CA1 Schaffer collateral synapses. The depression of synaptic transmission following OGD was prevented by metabotropic glutamate receptor 1 (mGluR1) or A3 receptor antagonists, indicating a role for both glutamate and adenosine release. Inhibition of PLC, PKC, or chelation of intracellular Ca2+ also prevented the depression of synaptic transmission. Inclusion of peptides to interrupt the interaction between GluA2 and PICK1 or dynamin and amphiphysin prevented the depression of transmission, suggesting a dynamin and PICK1-dependent internalization of AMPARs after OGD. We also show that a reduction in surface and total AMPAR protein levels after OGD was prevented by mGluR1 or A3 receptor antagonists, indicating that AMPARs are degraded following internalization. Thus, we describe a novel mechanism for the removal of AMPARs in CA3 pyramidal neurons following OGD that has the potential to reduce excitotoxicity and promote neuroprotection

Modelling phosphorus dynamics in multi-branch river systems: A study of the Black River, Lake Simcoe, Ontario, Canada

High rates of nutrient loading from agricultural and urban development have resulted in surface water eutrophication and groundwater contamination in regions of Ontario. In Lake Simcoe (Ontario, Canada), anthropogenic nutrient contributions have contributed to increased algal growth, low hypolimnetic oxygen concentrations, and impaired fish reproduction. An ambitious programme has been initiated to reduce phosphorus loads to the lake, aiming to achieve at least a 40% reduction in phosphorus loads by 2045. Achievement of this target necessitates effective remediation strategies, which will rely upon an improved understanding of controls on nutrient export from tributaries of Lake Simcoe as well as improved understanding of the importance of phosphorus cycling within the lake. In this paper, we describe a new model structure for the integrated dynamic and process-based model INCA-P, which allows fully-distributed applications, suited to branched river networks. We demonstrate application of this model to the Black River, a tributary of Lake Simcoe, and use INCA-P to simulate the fluxes of P entering the lake system, apportion phosphorus among different sources in the catchment, and explore future scenarios of land-use change and nutrient management to identify high priority sites for implementation of watershed best management practises.

Participative modelling and big issues: defining features of system dynamics?

In this article the author discusses participative modelling in system dynamics and issues underlying it. It states that in the heart of system dynamics is the servo-mechanism theory. It argues that it is wrong to see an optimal solution being applied by the empowered parties just because it exhibits self-evident truth and an analysis is not enough to encourage people to do things in different way. It mentions other models including the simulation models used for developing strategy discussions.

Modelling QoS of a pervasive MVNO/M2M using semi-group theory

This paper aims to develop a mathematical model based on semi-group theory, which allows to improve quality of service (QoS), including the reduction of the carbon path, in a pervasive environment of a Mobile Virtual Network Operator (MVNO). This paper generalise an interrelationship Machine to Machine (M2M) mathematical model, based on semi-group theory. This paper demonstrates that using available technology and with a solid mathematical model, is possible to streamline relationships between building agents, to control pervasive spaces so as to reduce the impact in carbon footprint through the reduction of GHG.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

A three-compartment model of the hemodynamic response and oxygen delivery to brain

We describe a mathematical model linking changes in cerebral blood flow, blood volume and the blood oxygenation state in response to stimulation. The model has three compartments to take into account the fact that the cerebral blood flow and volume as measured concurrently using laser Doppler flowmetry and optical imaging spectroscopy have contributions from the arterial, capillary as well as the venous compartments of the vasculature. It is an extension to previous one-compartment hemodynamic models which assume that the measured blood volume changes are from the venous compartment only. An important assumption of the model is that the tissue oxygen concentration is a time varying state variable of the system and is driven by the changes in metabolic demand resulting from changes in neural activity. The model takes into account the pre-capillary oxygen diffusion by flexibly allowing the saturation of the arterial compartment to be less than unity. Simulations are used to explore the sensitivity of the model and to optimise the parameters for experimental data. We conclude that the three-compartment model was better than the one-compartment model at capturing the hemodynamics of the response to changes in neural activation following stimulation.

Surface water temperature observations of large lakes by optimal estimation

Optimal estimation (OE) and probabilistic cloud screening were developed to provide lake surface water temperature (LSWT) estimates from the series of (advanced) along-track scanning radiometers (ATSRs). Variations in physical properties such as elevation, salinity, and atmospheric conditions are accounted for through the forward modelling of observed radiances. Therefore, the OE retrieval scheme developed is generic (i.e., applicable to all lakes). LSWTs were obtained for 258 of Earth's largest lakes from ATSR-2 and AATSR imagery from 1995 to 2009. Comparison to in situ observations from several lakes yields satellite in situ differences of −0.2 ± 0.7 K for daytime and −0.1 ± 0.5 K for nighttime observations (mean ± standard deviation). This compares with −0.05 ± 0.8 K for daytime and −0.1 ± 0.9 K for nighttime observations for previous methods based on operational sea surface temperature algorithms. The new approach also increases coverage (reducing misclassification of clear sky as cloud) and exhibits greater consistency between retrievals using different channel–view combinations. Empirical orthogonal function (EOF) techniques were applied to the LSWT retrievals (which contain gaps due to cloud cover) to reconstruct spatially and temporally complete time series of LSWT. The new LSWT observations and the EOF-based reconstructions offer benefits to numerical weather prediction, lake model validation, and improve our knowledge of the climatology of lakes globally. Both observations and reconstructions are publically available from http://hdl.handle.net/10283/88.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.