Multiplicative Lidskii's inequalities and optimal perturbations of frames

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame \cF for \hil\cong\C^d we compute those dual frames \cG of \cF that are optimal perturbations of the canonical dual frame for \cF under certain restrictions on the norms of the elements of \cG. On the other hand, for a fixed finite frame \cF=\{f_j\}_{j\in\In} for \hil we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame V\cdot \cF=\{V\,f_j\}_{j\in\In} - which is equivalent to \cF - is optimal among such perturbations of \cF. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.Comment: 22 page

Optimal dual frames and frame completions for majorization

In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $\mathcal F$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F$ by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Bendetto-Fickus' frame potential. On the other hand, given a fixed frame $\mathcal F$ we describe explicitly the spectral and geometrical structure of optimal frames $\mathcal G$ that are in duality with $\mathcal F$ and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.Comment: 29 pages, with modifications related with the exposition of the materia

The skewness of science in 219 sub-fields and a number of aggregates

This paper studies evidence from Thomson Scientific about the citation process of 3.7 million articles published in the period 1998-2002 in 219 Web of Science categories, or sub-fields. Reference and citation distributions have very different characteristics across sub-fields. However, when analyzed with the Characteristic Scores and Scales technique, which is replication and scale invariant, the shape of these distributions over three broad categories of articles appears strikingly similar. Reference distributions are mildly skewed, but citation distributions with a five-year citation window are highly skewed: the mean is twenty points above the median, while 9-10% of all articles in the upper tail account for about 44% of all citations. The aggregation of sub-fields into disciplines and fields according to several aggregation schemes preserve this feature of citation distributions. It should be noted that when we look into subsets of articles within the lower and upper tails of citation distributions the universality partially breaks down. On the other hand, for 140 of the 219 sub-fields the existence of a power law cannot be rejected. However, contrary to what is generally believed, at the sub-field level the scaling parameter is above 3.5 most of the time, and power laws are relatively small: on average, they represent 2% of all articles and account for 13.5% of all citations. The results of the aggregation into disciplines and fields reveal that power law algebra is a subtle phenomenon.

A comparison of the scientific performance of the U.S. and the European Union at the turn of the 21st century.

In this paper, scientific performance is identified with the impact that journal articles have through the citations they receive. In 15 disciplines, as well as in all sciences as a whole, the EU share of total publications is greater than that of the U.S. However, as soon as the citations received by these publications are taken into account the picture is completely reversed. Firstly, the EU share of total citations is still greater than the U.S. in only seven fields. Secondly, the mean citation rate in the U.S. is greater than in the EU in every one of the 22 fields studied. Thirdly, since standard indicators—such as normalized mean citation ratios—are silent about what takes place in different parts of the citation distribution, this paper compares the publication shares of the U.S. and the EU at every percentile of the world citation distribution in each field. It is found that in seven fields the initial gap between the U.S. and the EU widens as we advance towards the more cited articles, while in the remaining 15 fields—except for Agricultural Sciences—the U.S. always surpasses the EU when it counts, namely, at the upper tail of citation distributions. Finally, for all sciences as a whole the U.S. publication share becomes greater than that of the EU for the top 50% of the most highly cited articles. The data used refers to 3.6 million articles published in 1998–2002, and the more than 47 million citations they received in 1998–2007Research performance; Citation analysis; Scientific ranking; European paradox;

A comparison of the scientific performance of the U. S. and the European Union at the turn of the XXI century.

In this paper, scientific performance is identified with the impact journal articles achieve through the citations they receive. The empirical exercise refers to 3.6 million articles published in 1998-2002 in 22 scientific fields, and the more than 47 million citations they receive in 1998-2007. The first finding is that a failure to exclude co-authorship among member countries within the EU (European Union) may lead to a serious upward bias in the assignment of articles to this geographical area. In the second place, standard indicators, such as normalized mean citation ratios, are silent about what takes place in different parts of the citation distribution. Consequently, this paper compares the publication shares of the U.S. and the EU at every percentile of the world citation distribution in each field. In 15 disciplines, as well as in all sciences as a whole, the EU share of total publications is greater than that of the U.S. one. But as soon as the citations received by these publications are taken into account the picture is completely reversed. The mean citation rate in the U.S. is greater than in the EU in every one of the 22 fields. In seven fields, the initial gap between the U.S. and the EU widens up as we advance towards the more cited articles, while in the remaining 15 fields –except for Agricultural Sciences– the U.S. always surpasses the EU when it counts, namely, at the upper tail of citation distributions. For all sciences as a whole, the U.S publication share becomes greater than that of the EU one for the top 50% of the most highly cited articles.

The skewness of science in 219 sub-fields and a number of aggregates

This paper studies evidence from Thomson Scientific about the citation process of 3.7 million articles published in the period 1998-2002 in 219 Web of Science categories, or sub-fields. Reference and citation distributions have very different characteristics across sub-fields. However, when analyzed with the Characteristic Scores and Scales technique, which is size and scale independent, the shape of these distributions appear extraordinarily similar. Reference distributions are mildly skewed, but citation distributions with a five-year citation window are highly skewed: the mean is twenty points above the median, while 9-10% of all articles in the upper tail account for about 44% of all citations. The aggregation of sub-fields into disciplines and fields according to several aggregation schemes preserve this feature of citation distributions. On the other hand, for 140 of the 219 sub-fields the existence of a power law cannot be rejected. However, contrary to what is generally believed, at the sub-field level the scaling parameter is above 3.5 most of the time, and power laws are relatively small: on average, they represent 2% of all articles and account for 13.5% of all citations. The results of the aggregation into disciplines and fields reveal that power law algebra is a subtle phenomenon.

Evaluation of a Bayesian Algorithm to Detect Burned Areas in the Canary Islands’ Dry Woodlands and Forests Ecoregion Using MODIS Data

Burned Area (BA) is deemed as a primary variable to understand the Earth’s climate system. Satellite remote sensing data have allowed for the development of various burned area detection algorithms that have been globally applied to and assessed in diverse ecosystems, ranging from tropical to boreal. In this paper, we present a Bayesian algorithm (BY-MODIS) that detects burned areas in a time series of Moderate Resolution Imaging Spectroradiometer (MODIS) images from 2002 to 2012 of the Canary Islands’ dry woodlands and forests ecoregion (Spain). Based on daily image products MODIS, MOD09GQ (250 m), and MOD11A1 (1 km), the surface spectral reflectance and the land surface temperature, respectively, 10 day composites were built using the maximum temperature criterion. Variables used in BY-MODIS were the Global Environment Monitoring Index (GEMI) and Burn Boreal Forest Index (BBFI), alongside the NIR spectral band, all of which refer to the previous year and the year the fire took place in. Reference polygons for the 14 fires exceeding 100 hectares and identified within the period under analysis were developed using both post-fire LANDSAT images and official information from the forest fires national database by the Ministry of Agriculture and Fisheries, Food and Environment of Spain (MAPAMA). The results obtained by BY-MODIS can be compared to those by official burned area products, MCD45A1 and MCD64A1. Despite that the best overall results correspond to MCD64A1, BY-MODIS proved to be an alternative for burned area mapping in the Canary Islands, a region with a great topographic complexity and diverse types of ecosystems. The total burned area detected by the BY-MODIS classifier was 64.9% of the MAPAMA reference data, and 78.6% according to data obtained from the LANDSAT images, with the lowest average commission error (11%) out of the three products and a correlation (R2) of 0.82. The Bayesian algorithm—originally developed to detect burned areas in North American boreal forests using AVHRR archival data Long-Term Data Record—can be successfully applied to a lower latitude forest ecosystem totally different from the boreal ecosystem and using daily time series of satellite images from MODIS with a 250 m spatial resolution, as long as a set of training areas adequately characterising the dynamics of the forest canopy affected by the fire is defined

Landscape Assessment via Regression Analysis

This paper presents a methodology for assessing the visual quality of agricultural landscapes through direct and indirect techniques of landscape valuation. The first technique enables us to rank agricultural landscapes on the basis of a survey of public preferences. The latter weighs the contribution of the elements and attributes contained in the picture to its overall scenic beauty via regression analysis. The photos used in the survey included man-made elements, positive and negative, agricultural fields, mainly of cereals and olive trees, and a natural park. The results show that perceived visual quality increases, in decreasing order of importance, with the degree of wilderness of the landscape, the presence of well-preserved man-made elements, the percentage of plant cover, the amount of water, the presence of mountains and the colour contrast.landscape assessment, visual quality, landscape elements, landscape value, Land Economics/Use, H41, Q21, Q26,

Revisiting the dynamics of catastrophic late Pleistocene glacial-lake drainage, Altai Mountains, central Asia

In this work, we present a whole system model of megafloods from catastrophic ice-dam failure in the late Pleistocene that comprises the study of the dynamics of the glacial lake, the propagation of the flood wave downstream of the dam, and an approximation to the ice breach process. The ice-dam incision rate was simply considered an unknown constant, which was varied systematically to best fit the maximum altitude of the simulated water surface and the paleostage indicators in the downstream valley during the transient megaflood. Hence, the hydrograph resulting from the breach of the ice dam was not prescribed but was an output of the paleohydraulic reconstruction. By considering two possible configurations of the breach in the ice dam, i.e. full or partial removal of the ice, we constrained the incision rate in the narrow range of 28 − 42 m ⋅ h−1. Two connected glacial lakes, Kuray and Chuja, released 95% of the stored water volume (i.e., 564 km3) in 33.8 hours. A peak discharge of 10.5 M m3 ⋅ s−1 was required to form numerous giant bars and run-up deposits in the Chuja and Katun valleys. The peak streamflow occurred after 11 h when 45% of the available lake volume had been evacuated from the Kuray and Chuja basins. Further verification of the reconstructed megaflood was achieved by studying the computed hydraulic conditions during the lake draining that justify the existence and orientation of several fields of subaqueous gravel-dunes in the glacial lake. Complex spatiotemporal patterns during the recession stage of the flood built most of the fields of bedforms. In terms of nondimensional parameters, the Froude and Shields numbers that formed the dune fields were similar to those observed in large sandy rivers, but the flow was undoubtedly unsteady and two-dimensional. We conclude by noting that the extensions of the simulated area cannot be cropped or analysed by independent parts in order to predict the formation of the most relevant geological records due to the unsteady, two-dimensional nature of the flow motion and the development of backwater effects in the drainage network. Lastly, the paleohydrological reconstruction of a megaflood has helped not only to infer the dynamics of the event but also to retrodict the mean parameters of the ice-dam failure mechanism.This work was supported by the Spanish Ministry of Science, Innovation and Universities (MICINN/FEDER, UE) under Grant SEDRETOCGL2015-70736-R. P.R.J. was supported by the European Social Fund and the University of Jaén