A functional equation related to the product in a quadratic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Tropical cyclones as a critical phenomenon

It has been proposed that the number of tropical cyclones as a function of the energy they release is a decreasing power-law function, up to a characteristic energy cutoff determined by the spatial size of the ocean basin in which the storm occurs. This means that no characteristic scale exists for the energy of tropical cyclones, except for the finite-size effects induced by the boundaries of the basins. This has important implications for the physics of tropical cyclones. We discuss up to what point tropical cyclones are related to critical phenomena (in the same way as earthquakes, rainfall, etc.), providing a consistent picture of the energy balance in the system. Moreover, this perspective allows one to visualize more clearly the effects of global warming on tropical-cyclone occurrence.

Variability of North Atlantic hurricanes: seasonal versus individual-event features

Tropical cyclones are affected by a large number of climatic factors, which translates into complex patterns of occurrence. The variability of annual metrics of tropical-cyclone activity has been intensively studied, in particular since the sudden activation of the North Atlantic in the mid 1990’s. We provide first a swift overview on previous work by diverse authors about these annual metrics for the North-Atlantic basin, where the natural variability of the phenomenon, the existence of trends, the drawbacks of the records, and the influence of global warming have been the subject of interesting debates. Next, we present an alternative approach that does not focus on seasonal features but on the characteristics of single events [Corral et al., Nature Phys. 6, 693 (2010)]. It is argued that the individual-storm power dissipation index (PDI) constitutes a natural way to describe each event, and further, that the PDI statistics yields a robust law for the occurrence of tropical cyclones in terms of a power law. In this context, methods of fitting these distributions are discussed. As an important extension to this work we introduce a distribution function that models the whole range of the PDI density (excluding incompleteness effects at the smallest values), the gamma distribution, consisting in a powerlaw with an exponential decay at the tail. The characteristic scale of this decay, represented by the cutoff parameter, provides very valuable information on the finiteness size of the basin, via the largest values of the PDIs that the basin can sustain. We use the gamma fit to evaluate the influence of sea surface temperature (SST) on the occurrence of extreme PDI values, for which we find an increase around 50 % in the values of these basin-wide events for a 0.49 C SST average difference. Similar findings are observed for the effects of the positive phase of the Atlantic multidecadal oscillation and the number of hurricanes in a season on the PDI distribution. In the case of the El Niño Southern oscillation (ENSO), positive and negative values of the multivariate ENSO index do not have a significant effect on the PDI distribution; however, when only extreme values of the index are used, it is found that the presence of El Niño decreases the PDI of the most extreme hurricanes.

Social capital and the equilibrium number of entrepreneurs

Social capital is viewed either as a proprietary asset that serves private interests, including those of entrepreneurs, or as a collective asset that supports trust-based transactions saving on transaction costs both in markets and within the boundaries of firms, and benefiting society as a whole. This paper explains the relative specialization between entrepreneurs and market-governed exchanges as a result of the interaction between social capital that lowers transaction costs, and the scale economies of ability in managerial jobs (Lucas 1978). The main hypothesis formulated in the paper is that higher social capital will benefit the hierarchy relatively more than the market as a governance mechanism, and therefore in economies with higher social capital, the equilibrium number of entrepreneurs will be lower and their average span of control larger than in economies with lower social capital. The empirical evidence, with data from the Spanish Autonomous Communities, is consistent with this prediction.

Prominent use of distal 5’ transcription start sites and discovery of a large number of additional exons in ENCODE regions

This report presents systematic empirical annotation of transcript products from 399 annotated protein-coding loci across the 1% of the human genome targeted by the Encyclopedia of DNA elements (ENCODE) pilot project using a combination of 5' rapid amplification of cDNA ends (RACE) and high-density resolution tiling arrays. We identified previously unannotated and often tissue- or cell-line-specific transcribed fragments (RACEfrags), both 5' distal to the annotated 5' terminus and internal to the annotated gene bounds for the vast majority (81.5%) of the tested genes. Half of the distal RACEfrags span large segments of genomic sequences away from the main portion of the coding transcript and often overlap with the upstream-annotated gene(s). Notably, at least 20% of the resultant novel transcripts have changes in their open reading frames (ORFs), most of them fusing ORFs of adjacent transcripts. A significant fraction of distal RACEfrags show expression levels comparable to those of known exons of the same locus, suggesting that they are not part of very minority splice forms. These results have significant implications concerning (1) our current understanding of the architecture of protein-coding genes; (2) our views on locations of regulatory regions in the genome; and (3) the interpretation of sequence polymorphisms mapping to regions hitherto considered to be "noncoding," ultimately relating to the identification of disease-related sequence alterations.

X-chromosome tiling path array detection of copy number variants in patients with chromosome X-linked mental retardation

Background: Aproximately 5–10% of cases of mental retardation in males are due to copy number variations (CNV) on the X chromosome. Novel technologies, such as array comparative genomic hybridization (aCGH), may help to uncover cryptic rearrangements in X-linked mental retardation (XLMR) patients. We have constructed an X-chromosome tiling path array using bacterial artificial chromosomes (BACs) and validated it using samples with cytogenetically defined copy number changes. We have studied 54 patients with idiopathic mental retardation and 20 controls subjects. Results: Known genomic aberrations were reliably detected on the array and eight novel submicroscopic imbalances, likely causative for the mental retardation (MR) phenotype, were detected. Putatively pathogenic rearrangements included three deletions and five duplications (ranging between 82 kb to one Mb), all but two affecting genes previously known to be responsible for XLMR. Additionally, we describe different CNV regions with significant different frequencies in XLMR and control subjects (44% vs. 20%). Conclusion:This tiling path array of the human X chromosome has proven successful for the detection and characterization of known rearrangements and novel CNVs in XLMR patients.

Analysis of the multi-copy gene family FAM90A as a copy number variant in different ethnic backgrounds

Copy number variants contribute extensively to inter-individual genomic differences, but little is known about their inter-population variability and diversity. In a previous study (Bosch et al., 2007; 16:2572-2582), we reported that the primate-specific gene family FAM90A, which accounts for as many as 25 members in the human reference assembly, has expanded the number of FAM90A clusters across the hominoid lineage. Here we examined the copy number variability of FAM90A genes in 260 HapMap samples of European, African, and Asian ancestry, and showed significant inter-population differences (p<0.0001). Based on the recent study of Stranger et al. (2007; 315:848-853), we also explored the correlation between copy number variability and expression levels of the FAM90A gene family. Despite the high genomic variability, we found a low correlation between FAM90A copy number and expression levels, which could be due to the action of independent trans-acting factors. Our results show that FAM90A is highly variable in copy number between individuals and between populations. However, this variability has little impact on gene expression levels, thus highlighting the importance of genomic variability for genes located in regions containing segmental duplications.

Multiuser detection with an unknown number of active users: receiver design

In multiuser detection, the set of users active at any time may be unknown to the receiver. In these conditions, optimum reception consists of detecting simultaneously the set of activeusers and their data, problem that can be solved exactly by applying random-set theory (RST) and Bayesian recursions (BR). However, implementation of optimum receivers may be limited by their complexity, which grows exponentially with the number of potential users. In this paper we examine three strategies leading to reduced-complexity receivers.In particular, we show how a simple approximation of BRs enables the use of Sphere Detection (SD) algorithm, whichexhibits satisfactory performance with limited complexity.

Asymptotic capacity of static multiuser channels with an unknown number of users

We examine a multiple-access communication system in which multiuser detection is performed without knowledge of the number of active interferers. Using a statistical-physics approach, we compute the single-user channel capacity and spectral efficiency in the large-system limit.