Classical Lie symmetries and reductions of a nonisospectral Lax pair

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries provides a set of reductions that give rise to different nontrivial spectral problems in 1+1 dimensions. The form in which the spectral parameter of the 1+1 Lax pair is introduced is carefully described.Comment: 11 pages (v2: A typo corrected in the authors' names

Miura Transformation between two Non-Linear Equations in 2+1 dimensions

A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painleve Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the GLDW Equation. Through this Miura Transformation we shall also present the Lax pair of the 2LDW Equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear

Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

When Forests Take Over After Land Abandonment: Dissolved Organic Matter Response in Headwater Mountain Streams

ABSTRACT: Dissolved organic matter (DOM) represents the largest pool of organic carbon in fluvial ecosystems. The majority of DOM in rivers is of terrigenous origin?making DOM composition highly dependent on vegetation cover and soil properties. While deforestation is still a worldwide anthropogenic phenomenon, current land cover change in temperate regions is often characterized by secondary succession processes following the abandonment of agricultural activities including grazing on pasturelands. This results in (secondary) forest expansion with a consequent, time-lagged transformation of soil properties. Predicting the time scale and spatial scale (i.e., location in the catchment: riparian vs. upslope areas) at which such land cover changes affect the terrestrial-aquatic carbon linkage and concomitantly alter properties of fluvial DOM as drivers of carbon cycling in freshwater ecosystems represents a new scientific challenge. In an attempt to identify potential legacy effects of land cover, i.e., reaction delays of fluvial DOM to changes in land cover, we here investigate the influence of specific current and historic (2 decade-old) land cover types on molecularly resolved fluvial DOM composition in headwater mountain streams. Our analysis is based on a scale-sensitive approach weighing in the distance of land cover (changes) to the stream and ultrahigh-resolution mass spectrometric analyses. Results identified the dominance of terrigenous DOM, with phenolic and polyphenolic sum formulae commonly associated to lignins and tannins, in all the studied streams. DOM properties mostly reflected present-day gradients of forest cover in the riparian area. In more forested catchments, DOM had on average higher molecular weight and a greater abundance of O-rich phenols and polyphenols but less aliphatics. Besides the modulation of the DOM source, our results also point to an important influence of photodegradation associated to variation in light exposition with riparian land cover in defining fluvial DOM properties. Despite expectations, we were unable to detect an effect of historic land cover on present-day DOM composition, at least at the investigated baseflow conditions, probably because of an overriding effect of current riparian vegetation.This study was funded by the Spanish Ministry of Economy and Competitiveness as part of the RIVERLANDS (Ref: BIA2012-33572) and HYDRA (Ref: BIA2015-71197) projects

1+1 spectral problems arising from the Manakov-Santini system

This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from these symmetries. An important benefit of our procedure is that the study of the Lax pair instead of the partial differential equations yields the reductions of the eigenfunctions and also the spectral parameter. Therefore, we have obtained five interesting spectral problems in 1+1 dimensions

Inter-database validation of a deep learning approach for automatic sleep scoring

[Abstract] Study objectives Development of inter-database generalizable sleep staging algorithms represents a challenge due to increased data variability across different datasets. Sharing data between different centers is also a problem due to potential restrictions due to patient privacy protection. In this work, we describe a new deep learning approach for automatic sleep staging, and address its generalization capabilities on a wide range of public sleep staging databases. We also examine the suitability of a novel approach that uses an ensemble of individual local models and evaluate its impact on the resulting inter-database generalization performance. Methods A general deep learning network architecture for automatic sleep staging is presented. Different preprocessing and architectural variant options are tested. The resulting prediction capabilities are evaluated and compared on a heterogeneous collection of six public sleep staging datasets. Validation is carried out in the context of independent local and external dataset generalization scenarios. Results Best results were achieved using the CNN_LSTM_5 neural network variant. Average prediction capabilities on independent local testing sets achieved 0.80 kappa score. When individual local models predict data from external datasets, average kappa score decreases to 0.54. Using the proposed ensemble-based approach, average kappa performance on the external dataset prediction scenario increases to 0.62. To our knowledge this is the largest study by the number of datasets so far on validating the generalization capabilities of an automatic sleep staging algorithm using external databases. Conclusions Validation results show good general performance of our method, as compared with the expected levels of human agreement, as well as to state-of-the-art automatic sleep staging methods. The proposed ensemble-based approach enables flexible and scalable design, allowing dynamic integration of local models into the final ensemble, preserving data locality, and increasing generalization capabilities of the resulting system at the same time

Ácaros Fitoseidos de las islas Canarias (Acari, Phytoseiidae). II. Tenerife y La Gomera

Phytoseiid mites (Acari, Phytoseiidae) inhabiting plants in natural ecosystems from Tenerife and La Gomera islands (Canary Islands) have been studied. Surveys were conducted from 1997 to 2002. Eleven species were collected, one of them being reported for the first time from the Canary Islands and six of them reported for the first time from Tenerife and La Gomera islands. Euseius machadoi n. sp. collected from woody plants in the Canarian laurisilva is proposed as a new species.En muestreos realizados desde 1997 hasta 2002 se ha estudiado la fauna de ácaros fitoseidos (Acari, Phytoseiidae) asociada a plantas de ecosistemas naturales de las islas de Tenerife y La Gomera (Islas Canarias). Se han recolectado un total de 11 especies, siendo una de ellas citada por vez primera en las islas Canarias y seis de ellas citadas por primera vez en las islas de Tenerife y La Gomera. Euseius machadoi n. sp., recolectado en plantas leñosas de la laurisilva canaria, se propone como una nueva especie

O conjunto de gravuras rupestres de Santo Adrião (Caminha, Portugal): embarcações, armas, cavalos e ex-votos

Este artigo pretende dar a conhecer os primeiros resultados dos trabalhos de limpeza, decalque, levantamento fotogramétrico e escavação desenvolvidos no caos de blocos graníticos de Santo Adrião, no concelho de Caminha. Os ditos trabalhos permitiram identificar 11 afloramentos com gravuras rupestres, alguns deles com motivos pouco frequentes na arte rupestre do Norte de Portugal. Os motivos registados correspondem a composições circulares, armas, quadrúpedes, um reticulado, motivos em U e três barquiformes. Também foram exumados 24 artefactos líticos possivelmente depositados intencionalmente entre as fendas do caos de blocos onde se encontram as gravurasThe aim of this paper is to show the first results of archaeological works of cleaning, recording, photogrammetric survey and excavation developed in Santo Adrião site situated in Caminha council in North-western Portugal. During the archaeological works were found 11 new rock art outcrops, some of them with unusual designs in Portuguese rock art. These motifs are cup and rings, weapons, quadrupeds, a grid pattern, u-shaped figures and three boats. There were also collected 24 lithic artefacts probably deposited intentionally into the cracks situated in between the recorded outcrops.Manuel Santos-Estévez agradece à FCT a bolsa de pós-doutoramento com a referência SFRH/BPD/93700/2013 no âmbito da qual se insere este trabalho. Ana M. S. Bettencourt agradece à FCT a bolsa de licença sabática com a referência SFRH/BSAB/114296/2016 - Rock Art of the Northwest Iberia. Liminality and Heterothopy, no contexto da qual realiza este texto. Ambos os autores agradecem à Junta de Freguesia de Âncora e à Câmara Municipal de Caminha todo o apoio prestado durante a realização dos trabalhos de campo.info:eu-repo/semantics/acceptedVersio