Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$, the relative frequencies of sets $C\in\mathcal{C}$ converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of $\mathcal{C}$. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOP511 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The photoperiodic control of ovarian diapause in the cabbage whitefly, Aleurodes proletella L.

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Development, distribution and properties of purine phosphoribosyltransferases in mammals

The object of the work described in this thesis has been to determine the tissue distribution, development, and properties of the purine phosphoribosyltransferases (PRTases), especially in man but also in some other animals.A major part of the work was directed to the study of hypoxanthine guanine phosphoribosyl- transferase EC 2.4.2.8 (HGPRTase) in man in view of its importance in human metabolism as shown by pathological abnormalities resulting from its deficiency.As existing assay methods would tend to give falsely low results, an assay method was developed for the purine PRTases from tissues, which incorporated thymidine triphosphate as a selective inhibitor of 5'- nucleotidase EC 3.1.3.5, to prevent the hydrolysis of the PRTase reaction products.The specific activity of HGPRTase and adenine phosphoribosyltransferase EC 2.4.2.7 (APRTase) was determined in tissues from foetuses, children and adults. In the central nervous system and, unexpectedly, in the testis, HGPRTase activity increased during childhood to reach adult levels which were several times higher than those found in the foetus and in other tissues in the adult. The activity of HGPRTase in the other tissues studied remained constant or increased only slightly during development. In central nervous system, APRTase activity decreased during the period between foetal and neonatal life, while liver APRTase activity increased during childhood. In the adult, liver activity was about three times that found in foetal liver.Since it was difficult to obtain human tissues between the ages of 2 years and 60 years, a study was carried out on the developmental changes in rat tissue HGPRTase activity. Complex changes in activity were detected, being most marked in testis, liver, and cerebral cortex. However, some evidence was obtained for a rise in testicular HGPRTase occurring during sexual maturation. Low activities of HGPRTase were detected in the testis, liver, and cerebral cortex of rats at 16 months of age which, for the P.V.G. strain of rats used, was very old age.The electrophoretic properties of the purine PRTases were investigated using a newly developed detection technique and four isoenzyme bands were detected for both HGPRTase and APRTase.HGPRTase from several human tissues was studied by determining the thermal denaturation rate constants and the results suggested the possible presence of a tissue specific testicular HGPRTase.Autoradiographic localisation of testicular HGPRTase showed that the majority of the activity was in the basal layers of the epithelium of the seminiferous tubule.As hypoxanthine is the major purine released by erythrocytes, and the uptake of hypoxanthine into erythrocytes is dependent on HGPRTase, the possible effect of differing tissue enzyme activities on the uptake of purines by tissues from erythrocytes, was investigated in the rabbit using prelabelled rabbit erythrocytes. The results demonstrated that erythrocyte purines were transported to tissues and incorporated into cellular nucleic acids. The uptake of purines by tissues from the erythrocytes did not bear a simple direct relationship to the tissue HGPRTase activity.In conclusion, the developmental changes detected in HGPRTase activity in the central nervous system may provide an explanation for the delayed onset of the neurological symptoms found in children with the Lesch -Nyhan syndrome and would appear to be broadly related to the development of function of some parts of the central nervous system. The unexpectedly high HGPRTase activity located in the seminiferous tubule of the testis, and the developmental changes in activity found to occur in this tissue, suggest a role for HGPRTase in spermatogenesis which may be important

AMENITIES IN AN URBAN EQUILIBRIUM MODEL: RESIDENTIAL DEVELOPMENT IN PORTLAND, OREGON

This paper analyzes the effect of open space and other amenities on housing prices and development density within the framework of an urban equilibrium model. The model is estimated as a system of equations that includes households' residential choice decisions and developers' development decisions and emphasizes the importance of amenities in the formation of development patterns and property values. The model is applied to Portland, Oregon, where ambitious open space programs have been implemented. The results suggest that amenities are important: households are willing to pay more for newer houses located in areas of less dense development, with more open space, better views, less traffic congestion, and near amenity locations. For the developer, increases in housing prices result in an attempt to provide more and larger houses. The attempt to provide more houses, however, results in higher density, which will ultimately reduce prices. A simulation analysis evaluates the policy implications of the model results and indicates substantial benefits from alterations in housing patternsCommunity/Rural/Urban Development, R11, R21, R31,

REIT Stock Repurchases: Completion Rates, Long - Run Returns, and the Straddle Hypothesis

This study of real estate investment trusts (REITs) analyzes three possible explanations for the stock price reaction to a repurchase announcement and the subsequent repurchase behavior of managers under each hypothesis. Two of the hypotheses, the signaling hypothesis and the exchange option hypothesis, are established in the existing literature; the third hypothesis is a modification of the exchange option hypothesis. The exchange option hypothesis is extended to allow for additional flexibility in management decisions. This extended exchange option hypothesis is termed the ‘‘straddle’’ hypothesis because it provides management with both a call and put option. The empirical analyses show the straddle hypothesis is a more robust explanation of changes in shares outstanding in the postannouncement period than the alternative explanations.