Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

COMPENDIUM: A text summarization system for generating abstracts of research papers

This article analyzes the appropriateness of a text summarization system, COMPENDIUM, for generating abstracts of biomedical papers. Two approaches are suggested: an extractive (COMPENDIUM E), which only selects and extracts the most relevant sentences of the documents, and an abstractive-oriented one (COMPENDIUM E–A), thus facing also the challenge of abstractive summarization. This novel strategy combines extractive information, with some pieces of information of the article that have been previously compressed or fused. Specifically, in this article, we want to study: i) whether COMPENDIUM produces good summaries in the biomedical domain; ii) which summarization approach is more suitable; and iii) the opinion of real users towards automatic summaries. Therefore, two types of evaluation were performed: quantitative and qualitative, for evaluating both the information contained in the summaries, as well as the user satisfaction. Results show that extractive and abstractive-oriented summaries perform similarly as far as the information they contain, so both approaches are able to keep the relevant information of the source documents, but the latter is more appropriate from a human perspective, when a user satisfaction assessment is carried out. This also confirms the suitability of our suggested approach for generating summaries following an abstractive-oriented paradigm.

Accreting magnetars: a new type of high-mass X-ray binaries?

The discovery of very slow pulsations (Pspin =5560 s) has solved the long-standing question of the nature of the compact object in the high-mass X-ray binary 4U 2206+54 but has posed new ones. According to spin evolutionary models in close binary systems, such slow pulsations require a neutron star magnetic field strength larger than the quantum critical value of 4.4 × 1013 G, suggesting the presence of a magnetar. We present the first XMM–Newton observations of 4U 2206+54 and investigate its spin evolution. We find that the observed spin-down rate agrees with the magnetar scenario. We analyse Integral Spacecraft Gamma-Ray Imager (ISGRI)/INTErnational Gamma-RAy Laboratory (INTEGRAL) observations of 4U 2206+54 to search for the previously suggested cyclotron resonance scattering feature at ∼30 keV. We do not find a clear indication of the presence of the line, although certain spectra display shallow dips, not always at 30 keV. The association of these dips with a cyclotron line is very dubious because of its apparent transient nature. We also investigate the energy spectrum of 4U 2206+54 in the energy range 0.3–10 keV with unprecedented detail and report for the first time the detection of very weak 6.5 keV fluorescence iron lines. The photoelectric absorption is consistent with the interstellar value, indicating very small amount of local matter, which would explain the weakness of the florescence lines. The lack of matter locally to the source may be the consequence of the relatively large orbital separation of the two components of the binary. The wind would be too tenuous in the vicinity of the neutron star.

Central compact objects and the hidden magnetic field scenario

Central compact objects (CCOs) are X-ray sources lying close to the centre of supernova remnants, with inferred values of the surface magnetic fields significantly lower (≲1011 G) than those of standard pulsars. In this paper, we revise the hidden magnetic field scenario, presenting the first 2D simulations of the submergence and re-emergence of the magnetic field in the crust of a neutron star. A post-supernova accretion stage of about 10−4–10−3 M⊙ over a vast region of the surface is required to bury the magnetic field into the inner crust. When accretion stops, the field re-emerges on a typical time-scale of 1–100 kyr, depending on the submergence conditions. After this stage, the surface magnetic field is restored close to its birth values. A possible observable consequence of the hidden magnetic field is the anisotropy of the surface temperature distribution, in agreement with observations of several of these sources. We conclude that the hidden magnetic field model is viable as an alternative to the antimagnetar scenario, and it could provide the missing link between CCOs and the other classes of isolated neutron stars.

COMPENDIUM: a text summarisation tool for generating summaries of multiple purposes, domains, and genres

In this paper, we present a Text Summarisation tool, compendium, capable of generating the most common types of summaries. Regarding the input, single- and multi-document summaries can be produced; as the output, the summaries can be extractive or abstractive-oriented; and finally, concerning their purpose, the summaries can be generic, query-focused, or sentiment-based. The proposed architecture for compendium is divided in various stages, making a distinction between core and additional stages. The former constitute the backbone of the tool and are common for the generation of any type of summary, whereas the latter are used for enhancing the capabilities of the tool. The main contributions of compendium with respect to the state-of-the-art summarisation systems are that (i) it specifically deals with the problem of redundancy, by means of textual entailment; (ii) it combines statistical and cognitive-based techniques for determining relevant content; and (iii) it proposes an abstractive-oriented approach for facing the challenge of abstractive summarisation. The evaluation performed in different domains and textual genres, comprising traditional texts, as well as texts extracted from the Web 2.0, shows that compendium is very competitive and appropriate to be used as a tool for generating summaries.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Conformational changes of dissolved humic and fulvic superstructures with progressive iron complexation

Conformational changes of a humic acid (HA) and a fulvic acid (FA) induced by iron complexation were followed by high-performance size exclusion chromatography (HPSEC) with both UV–vis and refractive index (RI) detectors. Molecular size distribution was reduced for HA and increased for FA with progressive iron complexation. Since interactions of Fe with humic components are electrostatic, it is likely that the triple-charged Fe ions formed stronger complexes with the more acidic hydrophilic and hydrated FA than with the less acidic and more hydrophobic HA. The large content of ionized carboxyl groups in FA, thus favored the formation of intra- or intermolecular bridges between the negatively charged fulvic acid molecules, and led to more compact and larger size network than for HA. Conversely, iron complexation with HA disrupted the humic conformational arrangements stabilized by only weak hydrophobic bonds into smaller-size aggregates of greater conformational stability due to formation of strong metal complexes. These results confirmed that humic molecules in solution were organized in supramolecular associations of relatively small molecules loosely bound together by dispersive interactions and hydrogen bonds, and they specifically responded to chemical changes brought about by metal additions. The present study revealed the molecular changes occurring in superstructures of natural organic matter when in metal complexes and contributed to understand and predict the environmental behavior in waters and soil of metal complexes with natural organic matter.

Improving classification using a Confidence Matrix based on weak classifiers applied to OCR

This paper proposes a new feature representation method based on the construction of a Confidence Matrix (CM). This representation consists of posterior probability values provided by several weak classifiers, each one trained and used in different sets of features from the original sample. The CM allows the final classifier to abstract itself from discovering underlying groups of features. In this work the CM is applied to isolated character image recognition, for which several set of features can be extracted from each sample. Experimentation has shown that the use of CM permits a significant improvement in accuracy in most cases, while the others remain the same. The results were obtained after experimenting with four well-known corpora, using evolved meta-classifiers with the k-Nearest Neighbor rule as a weak classifier and by applying statistical significance tests.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Are pulsars born with a hidden magnetic field?

The observation of several neutron stars in the centre of supernova remnants and with significantly lower values of the dipolar magnetic field than the average radio-pulsar population has motivated a lively debate about their formation and origin, with controversial interpretations. A possible explanation requires the slow rotation of the protoneutron star at birth, which is unable to amplify its magnetic field to typical pulsar levels. An alternative possibility, the hidden magnetic field scenario, considers the accretion of the fallback of the supernova debris on to the neutron star as responsible for the submergence (or screening) of the field and its apparently low value. In this paper, we study under which conditions the magnetic field of a neutron star can be buried into the crust due to an accreting, conducting fluid. For this purpose, we consider a spherically symmetric calculation in general relativity to estimate the balance between the incoming accretion flow and the magnetosphere. Our study analyses several models with different specific entropy, composition, and neutron star masses. The main conclusion of our work is that typical magnetic fields of a few times 1012 G can be buried by accreting only 10−3–10−2 M⊙, a relatively modest amount of mass. In view of this result, the central compact object scenario should not be considered unusual, and we predict that anomalously weak magnetic fields should be common in very young (< few kyr) neutron stars.