John F. Moxnes

Stochastic conditional and unconditional warfare

Abstract This article constructs a foundation for warfare at the individual level, where agents in two groups fire and absorb shots according to a non-stationary Poisson process. We determine for generalized forms of warfare the conditional and unconditional point probabilities of a certain number of agents in each group through time, and the conditional and unconditional expected sizes and variances. Conditional variables are especially useful in modern warfare since these allow for updated intelligence. We determine the conditions for discrepancies between the stochastic version and the associated Lanchester model. Correspondence is demonstrated for square warfare for large groups where the probability that a group goes extinct is negligible. For linear warfare equivalence occurs for the conditional case, whereas for the unconditional case correspondence arises at the limit where the covariance of the group sizes approaches zero. Finally the stochastic model is tested against newly released empirics for the Ardennes Campaign during World War II.

A dynamic model of Nordic diagonal stride skiing, with a literature review of cross country skiing

The forces during the kicking phase in Nordic diagonal stride skiing are described by differential equations and the results are compared with experiments. The difference between static and dynamic friction, interacting with characteristics of the skier such as weight, velocity and the kicking forces angle with the terrain, are essential for high-velocity diagonal striding. Analytical results for relationships between glide length, friction and kicking force are shown. Aerodynamic drag and gravity are accounted for. A propulsion force based on the Hill (1970) equation for muscle contraction velocity and activation is constructed. The model shows a feasible tool for studying the effects of ski stiffness, the kicking force and the amount of waxing during diagonal stride skiing.

The kinetics of lactate production and removal during whole-body exercise

BackgroundBased on a literature review, the current study aimed to construct mathematical models of lactate production and removal in both muscles and blood during steady state and at varying intensities during whole-body exercise. In order to experimentally test the models in dynamic situations, a cross-country skier performed laboratory tests while treadmill roller skiing, from where work rate, aerobic power and blood lactate concentration were measured. A two-compartment simulation model for blood lactate production and removal was constructed.ResultsThe simulated and experimental data differed less than 0.5 mmol/L both during steady state and varying sub-maximal intensities. However, the simulation model for lactate removal after high exercise intensities seems to require further examination.ConclusionsOverall, the simulation models of lactate production and removal provide useful insight into the parameters that affect blood lactate response, and specifically how blood lactate concentration during practical training and testing in dynamical situations should be interpreted.

Methicillin-Resistant Staphylococcus aureus (MRSA) Is Increasing in Norway: A Time Series Analysis of Reported MRSA and Methicillin-Sensitive S. aureus Cases, 1997–2010

Background Accurate estimates of the incidence and prevalence of methicillin-resistant Staphylococcus aureus (MRSA) infections are needed to inform public health policies. In Norway, where both MRSA infection and carriage are notifiable conditions, the reported incidence of MRSA is slowly increasing. However, the proportion of MRSA in relation to all S. aureus isolates is unknown, making it difficult to determine if the rising incidence is real or an artifact of an increasing number of tests performed. Aim To characterize recent trends in MRSA infections and obtain a more complete understanding of the MRSA level in Norway. Methods All reported cases of MRSA and methicillin-sensitive S. aureus (MSSA) from Oslo County (1997–2010) and Health Region East (2008–2008), representing approximately 11% and 36% of the Norwegian population, respectively, were analyzed using a stochastic time series analysis to characterize trends. Results In Oslo County, the proportion of methicillin-resistant cases increased from 0.73% to 3.78% during the study period and was well modeled by an exponential growth with a doubling constant of 5.7 years (95% CI 4.5–7.4 years). In Health Region East, the proportion of MRSA cases increased from 0.4% to 2.1% from 2002 to 2008, with a best-fitting linear increase of 0.26% (95% CI 0.21–0.30%) per year. In both cases, the choice of a linear or exponential model for the time trend produced only marginally different model fits. We found no significant changes due to revised national MRSA guidelines published in June 2009. Significant variations in the increasing time trend were observed in the five hospitals within the region. The yearly reported incidence of MSSA was relatively stable in both study areas although we found seasonal patterns with peaks in August. Conclusion The level of MRSA is increasing in Norway, and the proportion of methicillin resistance in all S. aureus isolates are higher than the reported proportion of MRSA in invasive infections.

Cross-country skiing motion equations, locomotive forces and mass scaling laws

This article presents differential equations for locomotive force and velocity during cross-country skiing. A muscles work power is modelled. Thereafter, a locomotive force that depends on the skiers velocity is constructed. The external forces aerodynamic drag, friction forces and the force of gravity are incorporated in order to provide the equation of motion. Some allometric mass scaling relations are established and used to analyse the effect of a skiers mass on velocity. The model is tested by using a GPS instrument. We compare analytically and experimentally determined skiing distances and velocities as functions of time, and under different conditions. The article provides tools useful for practising athletes and coaches.

The dynamics of athletic performance, fitness and fatigue

We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the two well-known principles ‘train to failure’ and ‘use it or lose it’. The anabolic and catabolic processes are modelled with differential equations. Fitness is defined as muscle fitness. We model the work power of any muscle or set of muscles, and the muscles maximum work power. Parameters are estimated and we present analytical and numerical results. The relationships between performance, fitness and fatigue are demonstrated for various activity scenarios. For example, the model quantifies the exact manner in which the optimal rest period can be determined to maximize the performance on a given day. The model provides realistic predictions, and constitutes a powerful tool which describes the processes by which performance, fitness and fatigue can be regulated and controlled.

Using the power balance model to simulate cross-country skiing on varying terrain

The current study adapts the power balance model to simulate cross-country skiing on varying terrain. We assumed that the skier’s locomotive power at a self-chosen pace is a function of speed, which is impacted by friction, incline, air drag, and mass. An elite male skier’s position along the track during ski skating was simulated and compared with his experimental data. As input values in the model, air drag and friction were estimated from the literature based on the skier’s mass, snow conditions, and speed. We regard the fit as good, since the difference in racing time between simulations and measurements was 2 seconds of the 815 seconds racing time, with acceptable fit both in uphill and downhill terrain. Using this model, we estimated the influence of changes in various factors such as air drag, friction, and body mass on performance. In conclusion, the power balance model with locomotive power as a function of speed was found to be a valid tool for analyzing performance in cross-country skiing.

Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations

Moxnes, John Fredrik; Hausken, Kjell. Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations. Advances in Mathematical Physics 2010 s. -

A simulation of cross-country skiing on varying terrain by using a mathematical power balance model

The current study simulated cross-country skiing on varying terrain by using a power balance model. By applying the hypothetical inductive deductive method, we compared the simulated position along the track with actual skiing on snow, and calculated the theoretical effect of friction and air drag on skiing performance. As input values in the model, air drag and friction were estimated from the literature, whereas the model included relationships between heart rate, metabolic rate, and work rate based on the treadmill roller-ski testing of an elite cross-country skier. We verified this procedure by testing four models of metabolic rate against experimental data on the treadmill. The experimental data corresponded well with the simulations, with the best fit when work rate was increased on uphill and decreased on downhill terrain. The simulations predicted that skiing time increases by 3%–4% when either friction or air drag increases by 10%. In conclusion, the power balance model was found to be a useful tool for predicting how various factors influence racing performance in cross-country skiing.

THE DYNAMICS OF BILATERAL EXCHANGE AND DIVISION OF LABOR

The article presents a dynamic model of exchange, production, and consumption. In a dynamic world, complicated predictions often have to be made. Thus, in this article, the classical exchange model is expanded with a dynamic model specifying the intermediate states toward a static equilibrium, which may or may not be reached. A price mechanism was necessary to develop in order to describe these changes over time. The model is illustrated with two examples of the emergence of division of labor. The robustness of the dynamic model is tested with sensitivity analysis.