Formal recursion operators of integrable PDEs of the form Utt = F(U,Ux,Ut,...)

We will explain how the symmetry approach to integrability applies to partial differential equations of the form qtt=F(q,qx,…,qn,qt,qtx,…,qtm). Any such equation is integrable if it admits a formal recursion operator, i.e. a pseudodifferential operator R of the form R:=L+MDt where L and M are pseudodifferential operators in the derivation Dx satisfying the symmetry condition F(L+MDt)=(L+MDt)F... We are confronted with solving an equation over pseudodifferential operators in two derivations, a rather nontrivial problem. The equation happens to have a somewhat triangular structure, making its resolution possible. But in the solving process there appear obstructions, written as conditions over the rhs F of the PDE, that are interpreted as integrability conditions. The algebra of formal recursion operators has an interesting structure, and it has important relationships to algebras of commuting (pseudo)-differential operators in two derivations

The shaping of gut immunity in cirrhosis

Cirrhosis is the common end-stage of chronic liver diseases of different etiology. The altered bile acids metabolism in the cirrhotic liver and the increase in the blood-brain barrier permeability, along with the progressive dysbiosis of intestinal microbiota, contribute to gut immunity changes, from compromised antimicrobial host defense to pro-inflammatory adaptive responses. In turn, these changes elicit a disruption in the epithelial and gut vascular barriers, promoting the increased access of potential pathogenic microbial antigens to portal circulation, further aggravating liver disease. After summarizing the key aspects of gut immunity during homeostasis, this review is intended to update the contribution of liver and brain metabolites in shaping the intestinal immune status and, in turn, to understand how the loss of homeostasis in the gut-associated lymphoid tissue, as present in cirrhosis, cooperates in the advanced chronic liver disease progression. Finally, several therapeutic approaches targeting the intestinal homeostasis in cirrhosis are discussed

Performance isolation for network slices in Industry 4.0: The 5Growth approach

Network slicing plays a key role in the 5G ecosystem for verticals to introduce new use cases in the industrial sector, i.e., Industry 4.0. However, a widely recognized challenge of network slicing is to provide traffic isolation and concurrently satisfy diverse performance requirements, e.g., bandwidth and latency. Such challenge becomes even more important when serving a large number of network traffic flows under a resource-limited condition between distributed sites, e.g., factory floor and remote office. In this work, we present the capability to retain these two goals at the same time, by applying the virtual queue notion over a priority queuing based pipeline in P4 switch over software-defined networks. To examine the effectiveness of our approach, a proof-of-concept is setup to serve different requests of Industry 4.0 use cases over a mixed data path, including P4 switch and Open vSwitch, for a large number of network flows.This work was supported in part by the EU H2020 5GROWTH Project under Grant 856709

Metabolic-associated fatty liver disease: from simple steatosis towards liver cirrhosis and potential complications. Proceedings of the Third Translational Hepatology Meeting, endorsed by the Spanish Association for the Study of the Liver (AEEH)

This is a meeting report of the 3rd Translational Hepatology Meeting held in Alicante, Spain, in October 2021. The meeting, which was organized by the Spanish Association for the Study of the Liver (AEEH), provided an update on the recent advances in the field of basic and translational hepatology, with a particular focus on the molecular and cellular mechanisms and therapeutic targets involved in metabolic-associated fatty liver disease (MAFLD), metabolic-associated steatohepatitis (MASH), cirrhosis and end-stage hepatocellular carcinoma (HCC).S

Integrable Lagrangian systems and symmetries

Esta tesis ha sido escrita por Agustín Caparrós Quintero para optar al grado de Doctor por la Universidad Complutense de Madrid y la Universidad Politécnica de Madrid, tras la finalización de todas las actividades académicas comprendidas el programa doctoral IMEIO (http://www.mat.ucm.es/imeio/). Está basada en la investigación, bajo la supervisión del Dr. Rafael Hernández Heredero, en integrabilidad de sistemas Lagrangianos, un tópico de la Física Matemática. Tras presentar el método de las simetrías formales para la clasificación de ecuaciones integrables, utilizamos su extensión a ecuaciones no evolutivas para obtener nuevos resultados en el campo de los sistemas lagrangianos integrables. Como aplicación, se realiza una clasificación de dichos sistemas de segundo orden y se describe todo el proceso hasta la obtención de las expresiones funcionales exactas para los representantes de las clases encontradas. En esta tesis nos centramos en la extensión a ordenes superiores del método de las simetrías formales para la integrabilidad de ecuaciones diferenciales en derivadas parciales. El método extendido se aplica a ecuaciones no evolutivas de orden (2, 4) que aparecen como ecuaciones de Euler-Lagrange de sistemas lagrangianos, cuyas condiciones de integrabilidad son calculadas explícitamente y aplicadas a la clasificación de densidades lagrangianas de segundo orden. Los fundamentos teóricos del método de simetrías formales y de sus extensiones, tal y como se describen en la primera parte, son las provenientes de la teoría de grupos de Lie, invariantes diferenciales y simetrías aplicados a sistemas de ecuaciones diferenciales. Aunque existe un marco teórico más especifico para la determinación de simetrías de problemas variacionales, para los objetivos de esta tesis es suficiente el uso de la teoría general para ecuaciones diferenciales, sin tener en cuenta la estructura variacional. En la segunda parte detallamos las técnicas de cálculo empleadas para la clasificación de sistemas lagrangianos integrables de segundo orden. En el capítulo 5, se presentan los resultados de la clasificación y para algunos de ellos se comprueban contra los fundamentos teóricos del método extendido de simetrías formales para ecuaciones de orden genérico (n,m). Para ello se calculan algunos operadores de recursión en forma explícita para sistemas de tipos bien conocidos como Bussinesq o NLS. ----------ABSTRACT---------- This thesis has been written by Agustín Caparrós Quintero to acquire the PhD degree Doctor por la Universidad Complutense de Madrid y la Universidad Politécnica de Madrid, after completion of all academic activities under IMEIO doctoral program (http://www.mat.ucm.es/ imeio/). It is based on the personal research of the student under guidance of supervisor Rafael Hernández Heredero on the subject of Lagrangian systems integrability, a topic in Mathematical Physics. After introducing the symmetry approach to integrability, an extended formal symmetry approach is used to obtain new results in second order integrable Lagrangian systems. As an application, the classification of such systems is done and described in full detail. All the computational techniques used are detailed as well as the exact functional expressions of the integrable classes representatives. This thesis focuses on the extension to higher orders of the symmetry approach for the integrability of Partial Differential Equation (PDE)s. The extended symmetry approach is applied to non-evolutionary equations of order (2, 4) arising as Euler-Lagrange equations of Lagrangian systems, whose integrability conditions are explicitly computed and applied to the classification of integrable second order Lagrangian densities. The theory underlying the symmetry approach and its extension, as described in part I, is that becoming from Lie groups, differential invariance and symmetries applied to systems of differential equations. Although a more specific theoretical framework exists for the determination of symmetries of variational problems, for the purposes of this Thesis it is enough to use the general theory for differential equations, disregarding the variational structure. In the second part of this thesis we detail the computational techniques employed to derive all cases and expressions in the integrable Lagrangian systems classification. In chapter 5, the classification results are presented and some of them are checked to comply with the theoretical formulation of the extended symmetry approach for equations of generic order (n,m). In order to achieve this, some explicit, non-formal recursion operators are computed and tables of explicit canonical densities are provided. For instance, special cases of second order Lagrangian systems associated with the well-known Boussinesq equation or Non Linear Schrodinger (NLS) equations are studied in detail

Formal recursion operators of integrable PDEs of the form Utt = F(U,Ux,Ut,...)

We will explain how the symmetry approach to integrability applies to partial differential equations of the form qtt=F(q,qx,…,qn,qt,qtx,…,qtm). Any such equation is integrable if it admits a formal recursion operator, i.e. a pseudodifferential operator R of the form R:=L+MDt where L and M are pseudodifferential operators in the derivation Dx satisfying the symmetry condition F(L+MDt)=(L+MDt)F... We are confronted with solving an equation over pseudodifferential operators in two derivations, a rather nontrivial problem. The equation happens to have a somewhat triangular structure, making its resolution possible. But in the solving process there appear obstructions, written as conditions over the rhs F of the PDE, that are interpreted as integrability conditions. The algebra of formal recursion operators has an interesting structure, and it has important relationships to algebras of commuting (pseudo)-differential operators in two derivations

¿Evalúa PISA la competencia lectora?

Los resultados del International Project Students Assesment (PISA) están removiendo los cimientos de nuestro sistema educativo, pues los medios de comunicación y diferentes sectores del ámbito educativo creen, sin más, que esos resultados revelan el nivel de desarrollo competencial alcanzado por los estudiantes en su trayectoria escolar. Sin embargo, son escasas las investigaciones realizadas para determinar la pertinencia de las pruebas de lápiz y papel utilizadas para evaluar este desarrollo. En este artículo, enmarcado en la investigación Evaluación de las competencias de segundo orden. Aprender cómo aprender, dirigida por Ángel I. Pérez Gómez, se expone el trabajo realizado en la segunda fase de dicha investigación, fase a la que se denominó «Revisión de proyectos y programas de evaluación diagnóstica del rendimiento de estudiantes apoyados en los planteamientos de “aprender cómo aprender” y otras competencias relacionadas». Concretamente, a través de los marcos teóricos y de las pruebas aplicadas liberadas, analizamos la evaluación de la Lectura en PISA (ciclos de los años 2000, 2003 y 2006), que determina el nivel de los estudiantes en competencia lectora, para descubrir las debilidades y fortalezas de PISA en lo que a la esta competencia se refiere. Se buscan respuestas, entre otras, a la cuestión: ¿mide PISA lo que dice medir? Contrastados y valorados los resultados del análisis cabe destacar que con pruebas de papel y lápiz no parece posible medir todas las dimensiones de la competencia lectora, porque se descuida y aparta lo que no tiene que ver con las capacidades cognitivas. Es necesario, pues, diseñar procesos de evaluación para aproximarse a otras dimensiones de la competencia lectora y para salvar incongruencias, como la atomización de las capacidades, que restan validez a las pruebas de PISA. --------------------------------------------------------------------------------------------------------------------------------------------------------------- The results of the Programme for International Student Assessment (PISA) are shifting the foundations of our educational system, as the media and various educational sectors simply assume that these results reveal the level of student competence. However, there is little research on the relevance of the pencil and-paper tests used to assess student development. This article, which is part of Assessment of Second-order Competences. Learning to Learn, a research project directed by Ángel I. Pérez Gómez, reports the work done in the second phase of research, entitled “Review of Projects and Programmes for the Diagnostic Assessment of Performance by Students Given Support in ‘Learning to Learn’ and Other Related Competences.” The evaluation of the PISA Reading competence, series 2000, 2003, 2006, is analyzed with the aim of discovering the weaknesses and strengths of PISA as far as reading competence is concerned. Answers are sought to the question: Is PISA measuring what it claims? The theoretical frameworks behind pisa and released test items are studied to determine students’ reading competence. The results of the analysis are compared and evaluated in the light of knowledge about assessment processes and PISA in particular. It is found that paper-and-pencil tests are unable to measure all aspects in reading competence, because PISA only pays attention to cognitive abilities. It is therefore necessary to design assessment processes that envisage other dimensions of reading competence and avert the kinds of inconsistencies that invalidate PISA tests, such as the fragmentation of abilities