Dynamic programming in sport: a survey of applications

This paper surveys applications of dynamic programming to decisionproblems faced by active participants in sports.     

A MOLECULAR MODEL FOR A PHOSPHOLIPID-RETINALDEHYDE COMPLEX ABSORBING AT 500 nm

Abstract— –The structure of a complex formed from retinaldehyde and ethanolamine phosphoglyceride has been proposed as a Schiff's base stabilized byπ–πinteraction between the double bond of an oleic acid group (Δ9) and the 9–10 double bond of the retinaldehyde chain. Considerations of stereochemistry and simple MO theory indicate the proposed structure to be energetically favored, and its absorption maximum is predicted by free electron theory.     

A METAPHYSIOLOGICAL POPULATION MODEL OF STORAGE IN VARIABLE ENVIRONMENTS

ABSTRACT. We use mechanistic arguments to generalize a hierarchical metaphysiological approach developed by one of us to modeling biological populations (Getz, [1991, 1993]) and extend the approach to include a storage component in the population. We model the growth of single species and consumer-resource interactions, both with and without storage. Our approach unifies modeling storage across trophic levels and is much simpler and more efficient to implement numerically than individual based approaches or population approaches that include integral, delay, or partial differential equation components in the model. Using intake functions (i.e., functional responses) that include the effects of interference competition, we apply the model to a hypothetical herbivore feeding on a resource that fluctuates seasonally and demonstrate the importance of a flow from storage that buffers the population against periods when resources are scarce or absent. We also apply the model to a hypothetical plant population that is driven by fluctuating resources and demonstrate the importance of a translocation flow from storage at the end of a dormant season, corresponding to periods when resources are most scarce. Finally, we couple these two populations for the case where the herbivore feeds exclusively on non-storage biomass, and demonstrate how the population dynamics can be affected by the rates at which buffering and translocation flows transfer from storage to active tissue in the herbivore and plant populations. In particular, for certain buffering and translocation flow rates, 1-year unimodal, 2-year bimodal, and 2-year unimodal cycles can emerge in the same herbivore population.     

Annihilation rates of ortho—positronium in organic liquids: correlation with liquid compressibility and polarization ratio

The bubble model of ortho—positronium annihilation rates customarily employs the value of the planar-surface tension in the estimation of the (surface) energy required to expand a normal interstitial cavity to form the bubble. However, bubble radii are estimated to be only about 0.4 nm; the surface of such a small bubble is expected to have a tension different from that of the planar surface. We have replaced the surface tension parameter by the isothermal compressibility, which is thought not to have a nanostructure limitation. The model has been further improved by introducing the polarization ratio (n ² _D ? 1)/(n ² _D + 2) as a parameter, n _D being the refractive index of the organic liquid. Calculations are presented for 20 liquids.     

MODELING THE POPULATION DYNAMICS OF A SUBTROPICAL UNGULATE IN A VARIABLE ENVIRONMENT: RAIN,COLD AND PREDATORS

ABSTRACT. A structured population model was developed for a large ungulate, the kudu (Tragelaphus strepsiceros). From a ten-year study in South Africa's Kruger National Park, relationships were established between annual survival rates of particular age classes and resource availability indexed by the ratio between annual rainfall and population biomass density. The projected population dynamics resembled that from a simple logistic model, but with the convexity of density dependence and intrinsic growth rate dependent upon assumptions about how age-specific mortality changed at low density levels. Moreover, rather than being a preset constant, the effective carrying capacity K wasa dynamic variable dependent upon rainfall. The model closely replicated the observed dynamicsof the kudu population over the study period, but failed to predict the observed kudu density at the start of the study from prior rainfall alone. Episodic cold weather extremeswere identified ashaving an additional influence on kudu dynamics. The model was also unsuccessful in predicting the changesin kudu abundance that occurred in Kruger Park subsequent to the study. Here changes in predation perhaps due to predator switching were a possible influence. These additional factorsinfluencing population dynamicswould not have been recognized without first establishing the effects of changing resource availability in response to rainfall fluctu-ationsbetween years. The elaborated model incorporating the effects of resource supply as influenced by rainfall, density dependence, background predation pressure and episodic severe weather hasbroader reliability than simpler modelsfor conservation applications, while still having a firm empirical foundation.     

PHOTOCHEMICAL OXIDATIONS—IV. THE PHOTOOXIDATION OF CYCLOHEXANE WITH OXYGEN

Abstract— –For the photooxidation of cyclohexane, data on the rates of formation of cyclohexanol (I), cyclohexanone (II), and cyclohexylhydroperoxide (III) are presented. There are induction periods for the formation of I and II but not for III. The alcohol (I) is not the precursor of II in this reaction. The photooxidation does not occur when optical filters eliminate wavelengths of 260 nm or less from the incident light, and therefore the contact charge transfer absorption is responsible for the initiation of the reaction. Ozone is not involved to any significant extent in this reaction. The photodecomposition of III produces I and II, and this decomposition is first order during the initial stages. An overall 11 step mechanism is suggested for the photooxidation.     

STUDIES ON THE PROTECTIVE FUNCTION OF THE CAROTENOID PIGMENTS OF SARCINA LUTEA

Abstract— An investigation was made of both the composition of and mechanism of photo-protection by the carotenoid pigments of Sarcina lutea ATCC 9341a and three induced mutants.
The wild-type and mutants 2a and 4b were each found to contain three major pigment fractions, each fraction consisting of a single pigment having identical absorption maxima but differing from each other in chromatographic mobility. Although the mutants contain the same kinds of pigments as does the wild-type, the mutant cells contain less pigment per cell than does the wild-type. The third mutant, 93a, contains no colored carotenoids.
It was found that there were changes in both the absolute and relative amounts of the various pigment fractions when cultures of wild-type, mutants 2a and 4b, grown in nutrient broth in the dark, were examined during the logarithmic and stationary phases of the growth curve. In addition, changes were observed in the pigments when the cells were exposed to light in buffer. These changes were similar in the wild-type and in mutant 2a, but were quite different in mutant 4b. Studies of photokilling curves suggested that these changes in amounts of the various pigment fractions were not related to photoprotection, but that the important factor may be the total amount of pigment per cell.