The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes

In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

An initial comparative map of copy number variations in the goat (Capra hircus) genome

<p>Abstract</p> <p>Background</p> <p>The goat (<it>Capra hircus</it>) represents one of the most important farm animal species. It is reared in all continents with an estimated world population of about 800 million of animals. Despite its importance, studies on the goat genome are still in their infancy compared to those in other farm animal species. Comparative mapping between cattle and goat showed only a few rearrangements in agreement with the similarity of chromosome banding. We carried out a cross species cattle-goat array comparative genome hybridization (aCGH) experiment in order to identify copy number variations (CNVs) in the goat genome analysing animals of different breeds (Saanen, Camosciata delle Alpi, Girgentana, and Murciano-Granadina) using a tiling oligonucleotide array with ~385,000 probes designed on the bovine genome.</p> <p>Results</p> <p>We identified a total of 161 CNVs (an average of 17.9 CNVs per goat), with the largest number in the Saanen breed and the lowest in the Camosciata delle Alpi goat. By aggregating overlapping CNVs identified in different animals we determined CNV regions (CNVRs): on the whole, we identified 127 CNVRs covering about 11.47 Mb of the virtual goat genome referred to the bovine genome (0.435% of the latter genome). These 127 CNVRs included 86 loss and 41 gain and ranged from about 24 kb to about 1.07 Mb with a mean and median equal to 90,292 bp and 49,530 bp, respectively. To evaluate whether the identified goat CNVRs overlap with those reported in the cattle genome, we compared our results with those obtained in four independent cattle experiments. Overlapping between goat and cattle CNVRs was highly significant (P < 0.0001) suggesting that several chromosome regions might contain recurrent interspecies CNVRs. Genes with environmental functions were over-represented in goat CNVRs as reported in other mammals.</p> <p>Conclusions</p> <p>We describe a first map of goat CNVRs. This provides information on a comparative basis with the cattle genome by identifying putative recurrent interspecies CNVs between these two ruminant species. Several goat CNVs affect genes with important biological functions. Further studies are needed to evaluate the functional relevance of these CNVs and their effects on behavior, production, and disease resistance traits in goats.</p

Why do we treat adolescent idiopathic scoliosis? What we want to obtain and to avoid for our patients. SOSORT 2005 Consensus paper

BACKGROUND: Medicine is a scientific art: once science is not clear, choices are made according to individual and collective beliefs that should be better understood. This is particularly true in a field like adolescent idiopathic scoliosis, where currently does not exist definitive scientific evidence on the efficacy either of conservative or of surgical treatments. AIM OF THE STUDY: To verify the philosophical choices on the final outcome of a group of people believing and engaged in a conservative treatment of idiopathic scoliosis. METHODS: We performed a multifaceted study that included a bibliometric analysis, a questionnaire, and a careful Consensus reaching procedure between experts in the conservative treatment of scoliosis (SOSORT members). RESULTS: The Consensus reaching procedure has shown to be useful: answers changed in a statistically significant way, and 9 new outcome criteria were included. The most important final outcomes were considered Aesthetics (100%), Quality of life and Disability (more than 90%), while more than 80% of preferences went to Back Pain, Psychological well-being, Progression in adulthood, Breathing function, Scoliosis Cobb degrees (radiographic lateral flexion), Needs of further treatments in adulthood. DISCUSSION: In the literature prevail outcome criteria driven by the contingent treatment needs or the possibility to have measurement systems (even if it seems that usual clinical and radiographic methods are given much more importance than more complex Disability or Quality of Life instruments). SOSORT members give importance to a wide range of outcome criteria, in which clinical and radiographic issues have the lowest importance. CONCLUSION: We treat our patients for what they need for their future (Breathing function, Needs of further treatments in adulthood, Progression in adulthood), and their present too (Aesthetics, Disability, Quality of life). Technical matters, such as rib hump or radiographic lateral alignment and rotation, but not lateral flexion, are secondary outcomes and only instrumental to previously reported primary outcomes. We advocate a multidimensional, comprehensive evaluation of scoliosis patients, to gather all necessary data for a complete therapeutic approach, that goes beyond x-rays to reach the person and the family

Andy Warhol and His Influence on American Cultural Life

Hlavním cílem bakalářské práce bylo představit postavu Andyho Warhola jako umělce a představitele Pop Artu, malíře a filmového producenta a prokázat jeho vliv na kulturní život ve Spojených Státech Amerických. Bakalářská práce byla rozdělena do několika kapitol. V první kapitole jsou poskytnuty informace týkající se původu a života Andy Warhola. Ve druhé kapitole je Andy Warhol představen jako zakladatel a hlavní představitel uměleckého směru Pop Art. Důraz je kladen na fakt, že se stal komerčním umělcem a přeměnil umění na byznys. Třetí kapitola obsahuje fakta týkající se the Factory - uměleckého studia Andy Warhola a jeho filmovou tvorbu. Čtvrtá kapitola je věnována uměleckému směru Pop Art jako takovému a je v ní popsán jeho vývoj jeho charakteristické znaky. Poslední kapitola se zabývá vlivem Andy Warhola na americký kulturní život. Bakalářská práce je dále doplněna o několik příloh. První přílohou je anglicko-český slovník specifických termínů, které souvisejí s Andy Warholem. Ostatní přílohy jsou přílohy obrazové, kde jsou zobrazeny vybrané příklady děl Andy Warhola a také fotografie tohoto umělce.Katedra anglického jazyka a literaturyObhájenoThe main aim of the Bachelor thesis was to introduce a Pop Art artist Andy Warhol and to prove his influence on cultural life in the United States of America. The Bachelor thesis is divided into several chapters and subchapters. The first chapter deals with Andy Warhol´s roots and his life. In the second chapter, Andy Warhol is introduced as a founder and main representative of Pop Art movement. There was emphasized the fact that Andy Warhol became a commercial artist and transformed art into business. The third chapter contains information about the Factory - Andy Warhol´s artistic studio and introduces him as a filmmaker. The fourth chapter of the thesis briefly introduces Pop Art movement, its development and basic features. Last chapter is a study and analysis proving Andy Warhol´s influence on American cultural life. The thesis is complemented with several appendices. The first appendix is in form of an English-Czech glossary of specific terms connected to Andy Warhol. Next appendices contain pictures of Andy Warhol´s works and his photographs

C1,αC^{1,\alpha } C 1 , α -regularity for surfaces with H∈LpH\in L^p H ∈ L p

In this paper, we prove several results on the geometry of surfaces immersed in with small or bounded norm of . For instance, we prove that if the norm of and the norm of , , are sufficiently small, then such a surface is graphical away from its boundary. We also prove that given an embedded disk with bounded norm of , not necessarily small, then such a disk is graphical away from its boundary, provided that the norm of is sufficiently small, . These results are related to previous work of Schoen-Simon (Surfaces with quasiconformal Gauss map. Princeton University Press, Princeton, vol 103, pp 127-146, 1983) and Colding-Minicozzi (Ann Math 160:69-92, 2004).</p