Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Rotor interaction in the annulus billiard

Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity

The demographic consequences of growing older and bigger in oyster populations

Structured population models, particularly size-or age-structured, have a long history of informing conservation and natural resource management. While size is often easier to measure than age and is the focus of many management strategies, age-structure can have important effects on population dynamics that are not captured in size-only models. However, relatively few studies have included the simultaneous effects of both age-and size-structure. To better understand how population structure, particularly that of age and size, impacts restoration and management decisions, we developed and compared a size-structured integral projection model (IPM) and an age-and size-structured IPM, using a population of Crassostrea gigas oysters in the northeastern Pacific Ocean. We analyzed sensitivity of model results across values of local retention that give populations decreasing in size to populations increasing in size. We found that age-and size-structured models yielded the best fit to the demographic data and provided more reliable results about long-term demography. Elasticity analysis showed that population growth rate was most sensitive to changes in the survival of both large (\u3e175 mm shell length) and small (length) oysters, indicating that a maximum size limit, in addition to a minimum size limit, could be an effective strategy for maintaining a sustainable population. In contrast, the purely size-structured model did not detect the importance of large individuals. Finally, patterns in stable age and stable size distributions differed between populations decreasing in size due to limited local retention and populations increasing in size due to high local retention. These patterns can be used to determine population status and restoration success. The methodology described here provides general insight into the necessity of including both age-and size-structure into modeling frameworks when using population models to inform restoration and management decisions

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Low-loss criterion and effective area considerations for photonic crystal fibers

We study the class of endlessly single-mode all-silica photonic crystal fibers with a triangular air-hole cladding. We consider the sensibility to longitudinal nonuniformities and the consequences and limitations for realizing low-loss large-mode area photonic crystal fibers. We also discuss the dominating scattering mechanism and experimentally we confirm that both macro and micro-bending can be the limiting factor.Comment: Accepted for Journal of Optics A - Pure and Applied Optic

An integrated Pan-European perspective on coastal Lagoons management through a mosaic-DPSIR approach

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Scientific Reports 6 (2016): 19400, doi:10.1038/srep19400.A decision support framework for the management of lagoon ecosystems was tested using four European Lagoons: Ria de Aveiro (Portugal), Mar Menor (Spain), Tyligulskyi Liman (Ukraine) and Vistula Lagoon (Poland/Russia). Our aim was to formulate integrated management recommendations for European lagoons. To achieve this we followed a DPSIR (Drivers-Pressures-State Change-Impacts-Responses) approach, with focus on integrating aspects of human wellbeing, welfare and ecosystem sustainability. The most important drivers in each lagoon were identified, based on information gathered from the lagoons’ stakeholders, complemented by scientific knowledge on each lagoon as seen from a land-sea perspective. The DPSIR cycles for each driver were combined into a mosaic-DPSIR conceptual model to examine the interdependency between the multiple and interacting uses of the lagoon. This framework emphasizes the common links, but also the specificities of responses to drivers and the ecosystem services provided. The information collected was used to formulate recommendations for the sustainable management of lagoons within a Pan-European context. Several common management recommendations were proposed, but specificities were also identified. The study synthesizes the present conditions for the management of lagoons, thus analysing and examining the activities that might be developed in different scenarios, scenarios which facilitate ecosystem protection without compromising future generations.This study was supported by the European Commission, under the 7th Framework Programme, through the collaborative research project LAGOONS (contract n° 283157); by European funds through COMPETE and by Portuguese funds through the national Foundation for Science and Technology – FCT (PEst-C/MAR/LA0017/2013). The post-Doc grant SFRH/BPD/41117/2007 (M Dolbeth) and the PhD grant SFRH/BD/79170/2011 (LP Sousa) supported by FCT are also acknowledged

Galaxies with unusually high abundances of molecular hydrogen

A sample of 66 galaxies from the catalog of Bettoni et al. (CISM) with anomalously high molecular-to-atomic hydrogen mass ratios (M_{mol}/M_{HI}>2) is considered. The sample galaxies do not differ systematically from other galaxies in the catalog with the same morphological types, in terms of their photometric parameters, rotational velocities, dust contents, or the total mass of gas in comparison with galaxies of similar linear sizes and disk angular momentum. This suggests that the overabundance of $H_2$ is due to transition of HI to H_2. Galaxies with bars and active nuclei are found more frequently among galaxies which have M_{mol} estimates in CISM. In a small fraction of galaxies, high M_{mol}/M_{HI} ratios are caused by the overestimation of M_{mol} due to a low conversion factor for the translation of CO-line intensities into the number of H_2 molecules along the line of sight. It is argued that the "molecularization" of the bulk of the gas mass could be due 1) to the concentration of gas in the inner regions of the galactic disks, resulting to a high gas pressure and 2) to relatively low star-formation rate per unit mass of molecular gas which indeed takes place in galaxies with high M_{mol}/M_{HI} ratios.Comment: 11 pages,7 figures, published in Astronomy Report

The population burden of heart failure attributable to modifiable risk factors: The ARIC (atherosclerosis risk in communities) study

OBJECTIVES: The goal of this study was to estimate the population burden of heart failure and the influence of modifiable risk factors. BACKGROUND: Heart failure is a common, costly, and fatal disorder, yet few studies have evaluated the population-level influence of modifiable risk factors. METHODS: From 14,709 ARIC (Atherosclerosis Risk in Communities) study participants, we estimated incidence rate differences (IRD) for the association between 5 modifiable risk factors (cigarette smoking, diabetes, elevated low-density lipoproteins, hypertension, and obesity) and heart failure. Potential impact fractions were used to measure expected changes in the heart failure incidence assuming achievement of a 5% proportional decrement in the prevalence of each risk factor. RESULTS: Over an average of 17.6 years of follow-up, 1 in 3 African American and 1 in 4 Caucasian participants were hospitalized with heart failure, defined as the first hospitalization with International Classification of Diseases, Ninth Revision discharge codes of 428.x. Of the 5 modifiable risk factors, the largest IRD was observed for diabetes, which was associated with 1,058 (95% confidence interval [CI]: 787 to 1,329) and 660 (95% CI: 514 to 805) incident hospitalizations of heart failure/100,000 person-years among African-American and Caucasian participants, respectively. A 5% proportional reduction in the prevalence of diabetes would result in approximately 53 and 33 fewer incident heart failure hospitalizations per 100,000 person-years in African-American and Caucasian ARIC participants, respectively. When applied to U.S. populations, this reduction may prevent approximately 30,000 incident cases of heart failure annually. CONCLUSIONS: Modest decrements in the prevalence of modifiable heart failure risk factors such as diabetes may substantially decrease the incidence of this major disease

Elliptical Galaxies and Bulges of Disk Galaxies: Summary of Progress and Outstanding Issues

This is the summary chapter of a review book on galaxy bulges. Bulge properties and formation histories are more varied than those of ellipticals. I emphasize two advances: 1 - "Classical bulges" are observationally indistinguishable from ellipticals, and like them, are thought to form by major galaxy mergers. "Disky pseudobulges" are diskier and more actively star-forming (except in S0s) than are ellipticals. Theys are products of the slow ("secular") evolution of galaxy disks: bars and other nonaxisymmetries move disk gas toward the center, where it starbursts and builds relatively flat, rapidly rotating components. This secular evolution is a new area of galaxy evolution work that complements hierarchical clustering. 2 - Disks of high-redshift galaxies are unstable to the formation of mass clumps that sink to the center and merge - an alternative channel for the formation of classical bulges. I review successes and unsolved problems in the formation of bulges+ellipticals and their coevolution (or not) with supermassive black holes. I present an observer's perspective on simulations of dark matter galaxy formation including baryons. I review how our picture of the quenching of star formation is becoming general and secure at redshifts z < 1. The biggest challenge is to produce realistic bulges+ellipticals and disks that overlap over a factor of 10**3 in mass but that differ from each other as observed over that whole range. Second, how does hierarchical clustering make so many giant, bulgeless galaxies in field but not cluster environments? I argue that we rely too much on AGN and star-formation feedback to solve these challenges.Comment: 46 pages, 10 postscript figures, accepted for publication in Galactic Bulges, ed. E. Laurikainen, R. F. Peletier, & D. A. Gadotti (New York: Springer), in press (2015