Localization and delocalization of eigenvectors for heavy-tailed random matrices

Consider an $n \times n$ Hermitian random matrix with, above the diagonal, independent entries with $\alpha $ -stable symmetric distribution and $0 < \alpha < 2$ . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as $n$ goes to infinity. When $1 < \alpha < 2$ and $ p > 2$ , we give vanishing bounds on the $L^p$ -norm of the eigenvectors normalized to have unit $L^2$ -norm. On the contrary, when $0 < \alpha < 2/3$ , we prove that these eigenvectors are localized.     

Hereditarily Optimal Realizations of Consistent Metrics

One of the main problems in phylogenetics is to find good approximations of metrics by weighted trees. As an aid to solving this problem, it could be tempting to consider optimal realizations of metrics—the guiding principle being that, the (necessarily unique) optimal realization of a tree metric is the weighted tree that realizes this metric. And, although optimal realizations of arbitrary metrics are, in general, not trees, but rather weighted networks, one could still hope to obtain a phylogenetically informative representation of a given metric, maybe even more informative than the best approximating tree. However, optimal realizations are not only difficult to compute, they may also be non-unique. Here we focus on one possible way out of this dilemma: hereditarily optimal realizations. These are essentially unique, and can be described in a rather explicit way. In this paper, we recall what a hereditarily optimal realization of a metric is and how it is related to the 1-skeleton of the tight span of that metric, and we investigate under what conditions it coincides with this 1-skeleton. As a consequence, we will show that hereditarily optimal realizations for consistent metrics, a large class of phylogentically relevant metrics, can be computed in a straight-forward fashion. Received August 26, 2004     

Densely Functionalized 2-Methylideneazetidines: Evaluation as Antibacterials

Twenty-two novel, variously substituted nitroazetidines were designed as both sulfonamide and urethane vinylogs possibly endowed with antimicrobial activity. The compounds under study were obtained following a general procedure recently developed, starting from 4-nitropentadienoates deriving from a common β-nitrothiophenic precursor. While being devoid of any activity against fungi and Gram-negative bacteria, most of the title compounds performed as potent antibacterial agents on Gram-positive bacteria (E. faecalis and three strains of S. aureus), with the most potent congener being the 1-(4-chlorobenzyl)-3-nitro-4-(p-tolyl)azetidine 22, which displayed potency close to that of norfloxacin, the reference antibiotic (minimum inhibitory concentration values 4 and 1–2 μg/mL, respectively). Since 22 combines a relatively efficient activity against Gram-positive bacteria and a cytotoxicity on eucharyotic cells only at 4-times higher concentrations (inhibiting concentration on 50% of the cultured eukaryotic cells: 36 ± 10 μM, MIC: 8.6 μM), it may be considered as a promising hit compound for the development of a new series of antibacterials selectively active on Gram-positive pathogens. The relatively concise synthetic route described herein, based on widely available starting materials, could feed further structure–activity relationship studies, thus allowing for the fine investigation and optimization of the toxico-pharmacological profile.     

FDR,an easier way to NNLO calculations: a two-loop case study

In this paper we illustrate the simplifications produced by FDR in NNLO computations. We show with an explicit example that—due to its four-dimensionality—FDR does not require an order-by-order renormalization and that, unlike the one-loop case, FDR and dimensional regularization generate intermediate two-loop results which are no longer linked by a simple subtraction of the ultraviolet (UV) poles in $\epsilon $ . Our case study is the two-loop amplitude for $H \rightarrow \gamma \gamma $ , mediated by an infinitely heavy top loop, in the presence of gluonic corrections. We use this to elucidate how gauge invariance is preserved with no need of introducing counterterms in the Lagrangian. In addition, we discuss a possible four-dimensional approach to the infrared problem compatible with the FDR treatment of the UV infinities.     

Die Elementaranalyse mittels einer Kalorimeterbombe

Ohne Zusammenfassung     

1H-pyrazolo[3,4-d]thieno[2,3-b]pyridine and its derivatives

The synthesis of the parent ring system and some of the derivatives of 1H-pyrazolo[3,4-d]thieno[2,3-b]pyridine are described.     

Acoustic analysis of voice in multiple sclerosis patients

The objective is to investigate the presence of dysphonic symptoms in multiple sclerosis (MS) patients and to compare quantitative acoustic parameters in multiple sclerosis patients and normal individuals. The method of study was an 8-month controlled cross-sectional that was carried out with 106 individuals (30 MS, 76 controls). Both groups included males and females from 20 to 55 years. Exclusion criteria were prior vocal disorder, laryngeal microsurgery, recent endotracheal intubation, tumors, laryngeal, lung or mediastinal metastases, respiratory disease, and other associated neurological diagnoses. For dysphonic symptoms (qualitative variables), associations were assessed using Mantel-Haenszel's chi2 test, with Yates correction or the Fisher exact test when necessary. Statistical significance was set at p< or =0.05. Dysphonia was observed in 70% of MS individuals versus 33% of controls (p=0.01). Association was found between MS and dysphonia (OR: 2.2, CI 95%: 1.13-4.25). Fundamental frequency was higher among MS patients (p=0.01). Fundamental frequency deviation was significantly higher in MS women (but not men) than controls (p=0.00). Jitter was higher in MS men than in all other groups (p=0.00). Results suggest that evaluation and treatment of MS patients should be revised, evaluating voice alterations in relation to other signs. MS seems to intensify gender effect on fundamental frequency deviation, noise, and jitter, with MS women presenting fewer voice variations than men.     

Antifungal copyrine alkaloids: crystal structure of 3-methylsampangine

3-Methylsampangine, C₁₆H₁₀N₂O, crystallizes in the monoclinic space group P2₁/c witha=7.260(3),b=10.697(5),c=15.342(6) Å, and =102.69(4). All nonhydrogen atoms of this potent antifungal agent are planar to within 0.082 Å. The title compound exhibits potentin vitro antifungal activity againstC. neoformans, C. albicans andA. fumigatus.