Remarks on the geometry of coordinate projections in R^n

We study geometric properties of coordinate projections. Among other results, we show that if a body K in R^n has an "almost extremal" volume ratio, then it has a projection of proportional dimension which is close to the cube. We compare type 2 and infratype 2 constant of a Banach space. This follows from a comparison lemma for Rademacher and Gaussian averages. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.Comment: Israel Journal of Mathematics, to appea

Bufo cavifrons

Number of Pages: 3Integrative BiologyGeological Science

Entropy, dimension and the Elton-Pajor Theorem

The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case

Welded transition joints of 9 Cr-1 Mo alloy steel/316SS for short life /100 hours maximum/ application

Welding parameters and elevated temperature aging and strength characteristics of transition joints between chromium molybdenum alloy steel and stainless stee

Geographic Variation in Bufo valliceps (Anura: Bufonidae), a Widespread Toad in the United States and Middle America

The common lowland toad Bufo valliceps has a large distribution in the southern United States, Mexico, and most of Central America; this ample distribution across diverse temperate and tropical habitats is unusual among frogs. Geographic variation in size, shape, skin texture, and color pattern among populations of this species was reviewed. Although there are great differences between extreme northern and southern populations, I did not find smooth clinal variation for any character examined. Nor is there a discrete break among these continuous morphological variables that separate the the northern and southern morphs. Variation in Biifo valliceps is characterized by a high degree of inter- and intrapopulational variation that cannot be attributed to simple trends associated with latitude, elevation, or climate. An analysis the relationship between body size and aridity, along a precipiation gradient on the Yucatan Peninsula, found no consistent covariation. Previous claims for a positive relationship between elevation and degree of development of the cranial crests were found not to be accurate. Although the several relatively distinct populations are referable to the taxa Bufo nebulifer and Bnfo valliceps wilsoni, 1 do not propose recognition of these taxa, pending further research

Systematics of the Bufo Valliceps Group (Anura: Bufonidae) of Middle America

The University of Kansas has long historical connections with Central America and the many Central Americans who have earned graduate degrees at KU. This work is part of the Central American Theses and Dissertations collection in KU ScholarWorks and is being made freely available with permission of the author through the efforts of Professor Emeritus Charles Stansifer of the History department and the staff of the Scholarly Communications program at the University of Kansas Libraries’ Center for Digital Scholarship.A phylogenetic analysis of morphological characters revealed that the species content of the Bufo valliceps group is limited to eight species (two of them new) occurring between the southern United States and Costa Rica. Several Middle American species usually associated with this group are shown to be closely related, but outside of the Bufo valliceps group. The monotypic genus Crepidophryne is placed in the synonymy of Bufo. The taxon Bufo valliceps macrocristatus is recognized as a species distinct from Bufo valliceps. Seven species in the Bufo valliceps group appear to be allopatric with respect to one another and are restricted to humid primary forest habitat on the lower slopes of the major mountain ranges of southern Mexico, Guatemala, Honduras, and Costa Rica. The species Bufo valliceps is widespread in humid lowland habitats from the southern United States to Costa Rica that are either naturally more open (e.g., savanna) or disturbed secondary growth. There are great differences in size, shape, skin texture, and color pattern between northern and southern populations of this species; however, these differences do not vary along a smooth cline among populations from intermediate areas. Nor is there a discrete break among these continuous variables that separate the northern and southern morphs. Variation in Bufo valliceps is characterized by a high degree of. inter- and intrapopulational variation that cannot be attributed to simple trends associated with latitude, altitude, or climate. Bufo ibarrai, long assumed to be in the Bufo valliceps group but here shown to lie outside of the group, is reviewed and rediagnosed with respect to other similar Central American toads. The taxon Bufo valliceps microtis is placed in the synonymy of Bufo coccifer. Diagnostic accounts for all species in the Bufo valliceps group and a key to the species are provided