Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Evaluación de la competencia clínica de tutores de residentes de medicina familiar y comunitaria

ObjetivoDescribir la primera experiencia de una evaluación clínica objetiva y estructurada (ECOE) a tutores de residentes realizada en la comunidad autónoma de AndalucíaDiseñoObservacional descriptivoEmplazamientoUnidad Docente de Medicina Familiar y Comunitaria de HuelvaParticipantesTutores de residentes de medicina familiar y comunitariaMediciones principalesLos componentes competenciales que se consensuaron y ponderaron fueron los siguientes: anamnesis, exploración física, comunicación,habilidades técnicas, manejo, atención a la familia y actividades preventivas. La selección de las 10 situaciones clínicas de las que constaba la prueba se realizó utilizando unos criterios de priorización según la prevalencia, gravedad clínica, importancia de la prevención y del diagnóstico precoz, complejidad del caso, evaluación de la capacidad resolutiva del médico y simplicidad evaluativaResultadosRealizaron la ECOE 13 tutores. La edad media ± desviación estándar de los participantes fue de 42,8 ± 3,64 años. La prueba tuvo un coeficiente de fiabilidad (alfa de Cronbach) de 0,73. Por lo que se refiere a los resultados por participantes, la media global fue de 73 ± 6,2. Al analizar los resultados para los diferentes componentes competenciales, los mejores resultados se obtuvieron en la atención a la familia, la comunicación y las habilidades técnicasConclusionesLas pruebas de evaluación clínica objetiva y estructurada pueden ser útiles para la valoración de los tutores, con el objetivo de orientar su formación en los puntos débiles e incluso para, en un futuro no muy lejano, servir como instrumento para acreditar y reacreditar a los tutores de residentes de medicina familiar y comunitariaObjectivesWe show the first experience of the application of an objetive and structured clinical evaluation (OSCE) procedure to family medicine trainers, that has been carried out in Andalucia. The objective is to use a competence evaluation instrument that, in the short term, will be used not only for trainer accreditation but also for other public sanitary professionalsParticipantsTutors of family and commnity medicine residentsDesignObservational descriptiveSettingEducational unity of family medicinePrincipal measurementsThe competencial components to be assessed are the following: anamnesis, physical exploration, communication, technical skill, management, family attention y preventive activities. The clinical situations were selected using the following priority criteria: prevalence, clinical gravity, prevention and early diagnosis importance, case complexity, doctor's capacity of evaluation and simplicityResultsThirteen family medicine trainers took part in the OSCE. Their average age was 42.8±3.6 years. The test had an overall reliability coefficient (Cronbach's alpha) of 0.73. The overall mean score of the participants was 73±6.2. The best results about the competencial components were family attention, communication and technical skillConclusionsThe OSCE can be a convenient tool for family medical trainer evaluation, helping to orientate their education in the weak points and, in the near future, it can also be used as an instrument do accredit family medicine trainer

Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Optimal lower exponent for the higher gradient integrability of solutions to two-phase elliptic equations in two dimensions

We study the higher gradient integrability of distributional solutions u to the equation div(σ∇u) = 0 in dimension two, in the case when the essential range of σ consists of only two elliptic matrices, i.e., σ ∈ {σ1,σ2} a.e. in Ω. In [9], for every pair of elliptic matrices σ1 and σ2 exponents pσ1,σ2 ∈ (2,+∞) and qσ1,σ2 ∈ (1,2) have been found so that if u ∈ W1,qσ1,σ2(Ω) is solution to the elliptic equation then ∇u ∈ Lpσ1,σ2(Ω) and the optimality of the upper exponent pσ1,σ2 has been proved. In this paper we complement the above result by proving the optimality of the lower exponent qσ1,σ2. Precisely, we show that for every arbitrarily small δ, one can find a particular microgeometry, i.e. an arrangement of the sets σ-1(σ1) and σ-1(σ2), for which there exists a solution u to the corresponding elliptic equation such that ∇u ∈ Lqσ1,σ2-δ, but ∇u Ɇ Lqσ1,σ2-δ. The existence of such optimal microgeometries is achieved by convex integration methods, adapting to the present setting the geometric constructions provided in [2] for the isotropic case

A Novel Role For Nanog As An Early Cancer Risk Marker In Patients With Laryngeal Precancerous Lesions

NANOG is a master regulator of embryonic stem cell pluripotency, found to be frequently aberrantly expressed in a variety of cancers, including laryngeal carcinomas. This study investigates for the first time the role of NANOG expression in early stages of laryngeal tumourigenesis and its potential utility as cancer risk marker. NANOG protein expression was evaluated by immunohistochemistry using two large independent cohorts of patients with laryngeal precancerous lesions, and correlated with clinicopathological parameters and laryngeal cancer risk. NANOG expression was detected by immunohistochemistry in 49 (60%) of 82 laryngeal dysplasias, whereas expression was negligible in patient-matched normal epithelia. Strong NANOG expression was found in 22 (27%) lesions and was established as cut-off point, showing the most robust association with laryngeal cancer risk (P = 0.003) superior to the histological classification (P = 0.320) the current gold standard in the clinical practice. Similar trends were obtained using a multicenter validation cohort of 86 patients with laryngeal dysplasia. Our findings uncover a novel role for NANOG expression in laryngeal tumourigenesis, and its unprecedented application as biomarker for cancer risk assessment

Integrated Ugi-Based Assembly of Functionally, Skeletally, and Stereochemically Diverse 1,4-Benzodiazepin-2-ones

A practical, integrated and versatile U-4CR-based assembly of 1,4-benzodiazepin-2-ones exhibiting functionally, skeletally, and stereochemically diverse substitution patterns is described. By virtue of its convergence, atom economy, and bond-forming efficiency, the methodology documented herein exemplifies the reconciliation of structural complexity and experimental simplicity in the context of medicinal chemistry projects.This work was financially supported by the Galician Government (Spain), Projects: 09CSA016234PR and GPC-2014-PG037. J.A. thanks FUNDAYACUCHO (Venezuela) for a predoctoral grant and Deputación da Coruña (Spain) for a postdoctoral research grant. A.N.-V. thanks the Spanish government for a Ramón y Cajal research contract

Forecasting: theory and practice

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

On the automatic identification of unobserved components models

Automatic identi cation of time series models is a necessity once the big data era has come and is staying among us. This has become obvious for many companies and public entities that has passed from a crafted analysis of each individual problem to handle a tsunami of information that has to be processed e ciently, online and in record time. Automatic identi cation tools has never been tried out on Unobserved Components models (UC). This chapter shows how information criteria, such as Akaike's or Schwarz's, are rather useful for model selection within the UC family. The di culty lies, however, on choosing an appropriate and as general as possible set of models to search in. A set too narrow would render poor forecast accuracy, while a set too wide would be highly time consuming. The forecasting results suggest that UC models are powerful potential forecasting competitors to other well-known methods. Though there are several pieces of software available for UC modeling, this is the rst implementation of an automatic algorithm for this class of models, to the best of the authors knowledge