On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Chemical characterization of the stained glass window from the rose window, Siena Duomo (Italy, 1288-1289)

[EN] The chemical composition of nine medieval coloured stained glasses from Duomo (Catedral) of Siena, Italy, has been characterized. They come from the rose window elaborated under the drawing of Duccio di Buoninsegna masterwork (1288- 89 AD). This note explains the results obtained by EMPA, representative of bulk chemistry of several coloured glasses (deep green, olive green, yellow, purple, pink, deep blue, light blue, red plaqué and also uncoloured), as well as the associated trace elements (obtained by Induced Coupled Plasma Mass Spectrometry) that represent the chemical fingerprint of these glasses. The studied samples are sodium-calcium glass (chemical compositions in the range 13-14 wt% Na2O, 56-64 wt% SiO2, 4 wt% MgO, 9-10 wt% CaO, 2,5-4 wt% K2O); thus of Mediterranean tradition.This fact has been found by our team in previous studies (stained glasses from the church of Monestir de Pedralbes, Barcelona) for XIV century glass made at least 40 years later. As a general rule, the conservation state of these sodium glasses is good, except for the cohesion of grisaille to glass mesostase. This study allowed to identify three glass groups developed from different raw material formulations: a first group is constituted by deep green, olive green, light blue and yellow glass; a second one comprises by uncoloured, deep purple, deep blue and pink glass; and finally, the plaqué red glass that shows deeply different composition. Pink and yellow glass was produced following the traditional recipe compiled by Theophilus, a monk who lived at the beginning of XII century. This implies a separate process of raw material purification and a careful control of the redox kiln conditions; thus, these glasses can be considered as traditional or technologically not evolved. The deep blue, light blue and deep purple were obtained after the artisan dosed addition of a cobalt salt. Olive green and deep green glasses were produced with addition of copper (together with manganese and iron), previously prepared as a pigment that has as excipient a potassium glass. The use of potassium glass instead of the sodium glass locally produced strongly suggests that the pigment could be bought directly from Middle or Northern Europe markets and/or could be a sub-product of copper ore melting. On the other hand, the production of sodium red ruby plaqué glass, technologically more evolved and comparable to the coeval potassium glass coming from the Central Europe glass factories, would be outstanding in the XIV century; but we interpret (taking into account its chemical composition) that was produced later and introduced during the restoration conducted at the end of XVII century. We can also note the use of well-dosed lead additions in order to increase the lightness and transparency of coloured glass. Manganese has been a very important element in the Siena workshop glassmaker colour palette achievements. On the other hand, the trace-element chemical fingerprint of the glass allows arguing what kind of mineral salts were used as pigments, as well as the way to introduce it in the uncoloured original glass.[ES] Se han caracterizado químicamente una colección de vidrios arquitectónicos coloreados originales del rosetón del Duomo (catedral) de Siena, Italia, realizados bajo diseño del artista Duccio di Buoninsegna en 1288-89. Esta comunicación expone los resultados obtenidos mediante el empleo de microsonda electrónica de Castaing (mayoritarios) y espectrometría de masas con fuente de plasma acoplado inductivamente (ICP-MS, elementos en traza) en vidrios de varios colores (incoloro, verde oscuro, verde oliva, amarillo, violeta, rosa, azul oscuro, azul celeste, rojo plaqué). Se trata de vidrios sódico-cálcicos (valores en peso alrededor del 13-14 % de Na2O, 56-64 % SiO2, 4% MgO, 9-10 % CaO, 2,5-4 K2O) de tradición por tanto mediterránea. Un resultado semejante se encontró precedentemente para vidrios realizados a lo largo del siglo XIV, cuanto menos unos 40 años después (vidriera de la iglesia del Monestir de Pedralbes, Barcelona). En general, el estado de conservación de estos vidrios es bueno, excepto por lo que se refiere a la adherencia de las grisallas al vidrio base. El estudio desarrollado ha permitido identificar tres grupos de vidrios desarrollados a partir de formulaciones de diferentes composiciones: un primer grupo constituido por los vidrios de color verde claro, verde oscuro, azul celeste y amarillo; un segundo grupo constituido por los vidrios incoloro, violeta, azul oscuro, y malva; y finalmente el vidrio rojo plaqué, de composición netamente diferente a todos los demás. Desde el punto de vista de la obtención de los colores, cabe destacar que los datos químicos permiten deducir que el malva y el amarillo han sido elaborados siguiendo la receta tradicional del monje Theophilus de inicios del siglo XII, utilizando un proceso de purificación especial de las materias primas, y controlando artesanalmente las condiciones redox del horno; en este sentido, estos vidrios se pueden calificar como tradicionales o tecnológicamente poco evolucionados. Los colores azul oscuro, violeta y azul celeste se han obtenido mediante la adición de una misma sal de cobalto en diferentes dosis, y los colores verde oliva y verde oscuro mediante la adición de cobre (junto con manganeso y hierro), previamente preparados en un colorante que tiene como excipiente un vidrio potásico. Este último hecho (el empleo de vidrio potásico no usual en los centros productores del área mediterránea) permite suponer que el color puede haber sido comprado directamente a un fabricante centroeuropeo o que se tratara de un subproducto de fundición de minerales de cobre. Por su parte, la fabricación del vidrio plaqué, tecnológicamente más complejo y comparable al vidrio rojo plaqué potásico centroeuropeo contemporáneo indicaría, si fuera original, la incorporación de este proceso tecnológico al taller local. En opinión de los autores se trata de un vidrio de producción local mucho más tardia, incorporado en la restauración documentada a finales del siglo XVII. Destaca también, como en Pedralbes, el empleo del plomo para aumentar la luminosidad y transparencia del vidrio, en dosis variables atendiendo al color del vidrio. Por otro lado hay que señalar que en Siena el manganeso es un elemento muy importante con el que el fabricante del vidrio jugó intensamente para obtener la paleta de colores. El análisis de los metales presentes como elementos traza, y de las tierras raras, permite establecer sólidas hipótesis sobre el tipo de sales minerales empleadas como colorantes y como fueron incorporados al vidrio incoloro original.Este trabajo se ha podido realizar en el marco de diferentes proyectos financiados (proyecto 3338 de la Fundació Bosch i Gimpera, UB; acción integrada hispano-italiana HI2006-0190: La producción y el comercio del vidrio plano en Europa y en el Mediterráneo Occidental, entre los siglos XI y XV: un estudio arqueométrico) . La caracterización geoquímica de los vidrios mediante MSE e ICP-MS se ha llevado a cabo en los Serveis Científico-Tècnics de la Universitat de Barcelona (SCT-UB);Peer reviewe

Reverse Engineering Gene Networks with ANN: Variability in Network Inference Algorithms

Motivation :Reconstructing the topology of a gene regulatory network is one of the key tasks in systems biology. Despite of the wide variety of proposed methods, very little work has been dedicated to the assessment of their stability properties. Here we present a methodical comparison of the performance of a novel method (RegnANN) for gene network inference based on multilayer perceptrons with three reference algorithms (ARACNE, CLR, KELLER), focussing our analysis on the prediction variability induced by both the network intrinsic structure and the available data. Results: The extensive evaluation on both synthetic data and a selection of gene modules of "Escherichia coli" indicates that all the algorithms suffer of instability and variability issues with regards to the reconstruction of the topology of the network. This instability makes objectively very hard the task of establishing which method performs best. Nevertheless, RegnANN shows MCC scores that compare very favorably with all the other inference methods tested. Availability: The software for the RegnANN inference algorithm is distributed under GPL3 and it is available at the corresponding author home page (http://mpba.fbk.eu/grimaldi/regnann-supmat

Algebraic Comparison of Partial Lists in Bioinformatics

The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or just within a meta-analysis comparison, instead of one list it is often the case that sets of alternative feature lists (possibly of different lengths) are obtained. Here we introduce a method, based on the algebraic theory of symmetric groups, for studying the variability between lists ("list stability") in the case of lists of unequal length. We provide algorithms evaluating stability for lists embedded in the full feature set or just limited to the features occurring in the partial lists. The method is demonstrated first on synthetic data in a gene filtering task and then for finding gene profiles on a recent prostate cancer dataset

Lifespan extension and the doctrine of double effect

Recent developments in biogerontology—the study of the biology of ageing—suggest that it may eventually be possible to intervene in the human ageing process. This, in turn, offers the prospect of significantly postponing the onset of age-related diseases. The biogerontological project, however, has met with strong resistance, especially by deontologists. They consider the act of intervening in the ageing process impermissible on the grounds that it would (most probably) bring about an extended maximum lifespan—a state of affairs that they deem intrinsically bad. In a bid to convince their deontological opponents of the permissibility of this act, proponents of biogerontology invoke an argument which is grounded in the doctrine of double effect. Surprisingly, their argument, which we refer to as the ‘double effect argument’, has gone unnoticed. This article exposes and critically evaluates this ‘double effect argument’. To this end, we first review a series of excerpts from the ethical debate on biogerontology in order to substantiate the presence of double effect reasoning. Next, we attempt to determine the role that the ‘double effect argument’ is meant to fulfil within this debate. Finally, we assess whether the act of intervening in ageing actually can be justified using double effect reasoning

Function-Based Discovery of Significant Transcriptional Temporal Patterns in Insulin Stimulated Muscle Cells

Background: Insulin action on protein synthesis (translation of transcripts) and post-translational modifications, especially of those involving the reversible modifications such as phosphorylation of various signaling proteins, are extensively studied but insulin effect on transcription of genes, especially of transcriptional temporal patterns remains to be fully defined. Methodology/Principal Findings: To identify significant transcriptional temporal patterns we utilized primary differentiated rat skeletal muscle myotubes which were treated with insulin and samples were collected every 20 min for 8 hours. Pooled samples at every hour were analyzed by gene array approach to measure transcript levels. The patterns of transcript levels were analyzed based on a novel method that integrates selection, clustering, and functional annotation to find the main temporal patterns associated to functional groups of differentially expressed genes. 326 genes were found to be differentially expressed in response to in vitro insulin administration in skeletal muscle myotubes. Approximately 20 % of the genes that were differentially expressed were identified as belonging to the insulin signaling pathway. Characteristic transcriptional temporal patterns include: (a) a slow and gradual decrease in gene expression, (b) a gradual increase in gene expression reaching a peak at about 5 hours and then reaching a plateau or an initial decrease and other different variable pattern of increase in gene expression over time. Conclusion/Significance: The new method allows identifying characteristic dynamic responses to insulin stimulus, commo