SHIMMER (1.0): a novel mathematical model for microbial and biogeochemical dynamics in glacier forefield ecosystems

SHIMMER (Soil biogeocHemIcal Model for Microbial Ecosystem Response) is a new numerical modelling framework designed to simulate microbial dynamics and biogeochemical cycling during initial ecosystem development in glacier forefield soils. However, it is also transferable to other extreme ecosystem types (such as desert soils or the surface of glaciers). The rationale for model development arises from decades of empirical observations in glacier forefields, and enables a quantitative and process focussed approach. Here, we provide a detailed description of SHIMMER, test its performance in two case study forefields: the Damma Glacier (Switzerland) and the Athabasca Glacier (Canada) and analyse sensitivity to identify the most sensitive and unconstrained model parameters. Results show that the accumulation of microbial biomass is highly dependent on variation in microbial growth and death rate constants, Q10 values, the active fraction of microbial biomass and the reactivity of organic matter. The model correctly predicts the rapid accumulation of microbial biomass observed during the initial stages of succession in the forefields of both the case study systems. Primary production is responsible for the initial build-up of labile substrate that subsequently supports heterotrophic growth. However, allochthonous contributions of organic matter, and nitrogen fixation, are important in sustaining this productivity. The development and application of SHIMMER also highlights aspects of these systems that require further empirical research: quantifying nutrient budgets and biogeochemical rates, exploring seasonality and microbial growth and cell death. This will lead to increased understanding of how glacier forefields contribute to global biogeochemical cycling and climate under future ice retreat.

A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

A mathematical model for Banana Xanthomonas Wilt (BXW) spread by insect is presented. The model incorporates inflorescence infection and vertical transmission from the mother corm to attached suckers, but not tool-based transmission by humans. Expressions for the basic reproduction number R0 are obtained and it is verified that disease persists, at a unique endemic level, when R0 > 1. From sensitivity analysis, inflorescence infection rate and roguing rate were the parameters with most influence on disease persistence and equilibrium level. Vertical transmission parameters had less effect on persistence threshold values. Parameters were approximately estimated from field data. The model indicates that single stem removal is a feasible approach to eradication if spread is mainly via inflorescence infection. This requires continuous surveillance and debudding such that a 50% reduction in inflorescence infection and 2–3 weeks interval of surveillance would eventually lead to full recovery of banana plantations and hence improved production.

Development of a mathematical model for solar module in photovoltaic systems

A mathematical model of a solar module is presented. This model takes into account solar model temperature and solar radiation. The experimental data of a solar module under natural environment condition (NEC) have been obtained to determine the model parameters. The experimental results are compared with those calculated by using a mathematical model. It shows that the mathematical model accurately simulates the current-voltage characteristics of the solar module under the NEC and therefore is suitable for photovoltaic system design and performance analysis.

A mathematical model of neuromuscular adaptation to resistance training and its application in a computer simulation of accommodating loads

A large corpus of data obtained by means of empirical study of neuromuscular adaptation is currently of limited use to athletes and their coaches. One of the reasons lies in the unclear direct practical utility of many individual trials. This paper introduces a mathematical model of adaptation to resistance training, which derives its elements from physiological fundamentals on the one side, and empirical findings on the other. The key element of the proposed model is what is here termed the athlete’s capability profile. This is a generalization of length and velocity dependent force production characteristics of individual muscles, to an exercise with arbitrary biomechanics. The capability profile, a two-dimensional function over the capability plane, plays the central role in the proposed model of the training-adaptation feedback loop. Together with a dynamic model of resistance the capability profile is used in the model’s predictive stage when exercise performance is simulated using a numerical approximation of differential equations of motion. Simulation results are used to infer the adaptational stimulus, which manifests itself through a fed back modification of the capability profile. It is shown how empirical evidence of exercise specificity can be formulated mathematically and integrated in this framework. A detailed description of the proposed model is followed by examples of its application—new insights into the effects of accommodating loading for powerlifting are demonstrated. This is followed by a discussion of the limitations of the proposed model and an overview of avenues for future work.

Dynamics of childhood growth and obesity: development and validation of a quantitative mathematical model

Background
Clinicians and policy makers need the ability to predict quantitatively how childhood bodyweight will respond to obesity interventions.

Methods
We developed and validated a mathematical model of childhood energy balance that accounts for healthy growth and development of obesity, and that makes quantitative predictions about weight-management interventions. The model was calibrated to reference body composition data in healthy children and validated by comparing model predictions with data other than those used to build the model.

Findings
The model accurately simulated the changes in body composition and energy expenditure reported in reference data during healthy growth, and predicted increases in energy intake from ages 5—18 years of roughly 1200 kcal per day in boys and 900 kcal per day in girls. Development of childhood obesity necessitated a substantially greater excess energy intake than for development of adult obesity. Furthermore, excess energy intake in overweight and obese children calculated by the model greatly exceeded the typical energy balance calculated on the basis of growth charts. At the population level, the excess weight of US children in 2003—06 was associated with a mean increase in energy intake of roughly 200 kcal per day per child compared with similar children in 1971—74. The model also suggests that therapeutic windows when children can outgrow obesity without losing weight might exist, especially during periods of high growth potential in boys who are not severely obese.

Interpretation
This model quantifies the energy excess underlying obesity and calculates the necessary intervention magnitude to achieve bodyweight change in children. Policy makers and clinicians now have a quantitative technique for understanding the childhood obesity epidemic and planning interventions to control it.

Funding
Intramural Research Program of the National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases.

A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype

We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R e. For R e ≤ 1,  there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R e > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium.

A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type

This paper discusses a simple mathematical model to describe the spread of Streptococcus pneumoniae. We suppose that the transmission of the bacterium is determined by multi-locus sequence type. The model includes vaccination and is designed to examine what happens in a vaccinated population if MLSTs can exist as both vaccine and non vaccine serotypes with capsular switching possible from the former to the latter. We start off with a discussion of Streptococcus pneumoniae and a review of previous work. We propose a simple mathematical model with two sequence types and then perform an equilibrium and (global) stability analysis on the model. We show that in general there are only three equilibria, the carriage-free equilibrium and two carriage equilibria. If the effective reproduction number Re is less than or equal to one, then the carriage will die out. If Re > 1, then the carriage will tend to the carriage equilibrium corresponding to the multi-locus sequence type with the largest transmission parameter. In the case where both multi-locus sequence types have the same transmission parameter then there is a line of carriage equilibria. Provided that carriage is initially present then as time progresses the carriage will approach a point on this line. The results generalize to many competing sequence types. Simulations with realistic parameter values confirm the analytical results.

A universal optimization strategy for ant colony optimization algorithms based on the Physarum-inspired mathematical model

Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP.

A multi-objective ant colony optimization algorithm based on the physarum-inspired mathematical model

Multi-objective traveling salesman problem (MOTSP) is an important field in operations research, which has wide applications in the real world. Multi-objective ant colony optimization (MOACO) as one of the most effective algorithms has gained popularity for solving a MOTSP. However, there exists the problem of premature convergence in most of MOACO algorithms. With this observation in mind, an improved multiobjective network ant colony optimization, denoted as PMMONACO, is proposed, which employs the unique feature of critical tubes reserved in the network evolution process of the Physarum-inspired mathematical model (PMM). By considering both pheromones deposited by ants and flowing in the Physarum network, PM-MONACO uses an optimized pheromone matrix updating strategy. Experimental results in benchmark networks show that PM-MONACO can achieve a better compromise solution than the original MOACO algorithm for solving MOTSPs.

GPS Satellite Kinematic Relative Positioning: Analyzing and Improving the Functional Mathematical Model Using Wavelets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effectiveness-ntu computation with a mathematical model for cross-flow heat exchangers

Due to the wide range of design possibilities, simple manufactured, low maintenance and low cost, cross-flow heat exchangers are extensively used in the petroleum, petrochemical, air conditioning, food storage, and others industries. In this paper a mathematical model for cross-flow heat exchangers with complex flow arrangements for determining epsilon -NTU relations is presented. The model is based on the tube element approach, according to which the heat exchanger outlet temperatures are obtained by discretizing the coil along the tube fluid path. In each cross section of the element, tube-side fluid temperature is assumed to be constant because the heat capacity rate ratio C*=Cmin/Cmax tends toward zero in the element. Thus temperature is controlled by effectiveness of a local element corresponding to an evaporator or a condenser-type element. The model is validated through comparison with theoretical algebraic relations for single-pass cross-flow arrangements with one or more rows. Very small relative errors are obtained showing the accuracy of the present model. epsilon -NTU curves for several complex circuit arrangements are presented. The model developed represents a useful research tool for theoretical and experimental studies on heat exchangers performance.