Computability and Beltrami fields in Euclidean space

In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami type, that can simulate a universal Turing machine. In particular, these solutions possess undecidable trajectories. Heretofore, the known Turing complete constructions of steady Euler flows in dimension 3 or higher were not associated to a prescribed metric. Our solutions do not have finite energy, and their construction makes crucial use of the non-compactness of R³ , however they can be employed to show that an arbitrary tape-bounded Turing machine can be robustly simulated by a Beltrami flow on T³ (with the standard flat metric). This shows that there exist steady solutions to the Euler equations on the flat torus exhibiting dynamical phenomena of (robust) computational complexity as high as desired. We also quantify the energetic cost for a Beltrami field on T³ to simulate a tape-bounded Turing machine, thus providing additional support for the space-bounded ChurchTuring thesis. Another implication of our construction is that a Gaussian random Beltrami field on Euclidean space exhibits arbitrarily high computational complexity with probability 1. Finally, our proof also yields Turing complete flows and diffeomorphisms on S² with zero topological entropy, thus disclosing a certain degree of independence within different hierarchies of complexityPostprint (author's final draft

Turing universality of the incompressible Euler equations and a conjecture of Moore

In this article, we construct a compact Riemannian manifold of high dimension on which the time-dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain global solution of the Euler equations entering a certain open set in the space of divergence-free vector fields. In particular, this implies the undecidability of whether a solution to the Euler equations with an initial datum will reach a certain open set or not in the space of divergence-free fields. This result goes one step further in Tao’s programme to study the blow-up problem for the Euler and Navier–Stokes equations using fluid computers. As a remarkable spin-off, our method of proof allows us to give a counterexample to a conjecture of Moore dating back to 1998 on the non-existence of analytic maps on compact manifolds that are Turing complete.María de Maeztu Programme (MDM-2014-0445) AGAUR grant 2017SGR932 ICMAT–Severo Ochoa grant CEX2019-000904-SRobert Cardona acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Mar´ıa de Maeztu Programme for Units of Excellence in R& D (MDM-2014-0445) via an FPI grant. Robert Cardona and Eva Miranda are partially supported by the grants MTM2015-69135- P/FEDER and PID2019-103849GB-I00 / AEI / 10.13039/501100011033, and AGAUR grant 2017SGR932. Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2016. Daniel Peralta-Salas is supported by the grants MTM PID2019-106715GB-C21 (MICINN) and Europa Excelencia EUR2019-103821 (MCIU). This work was partially supported by the ICMAT– Severo Ochoa grant CEX2019-000904-S.Postprint (author's final draft

Looking at Euler flows through a contact mirror: universality and undecidability

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers by Cardona, Miranda, and Peralta- Salas, several unknown facets of the Euler flows have been discovered, including universality properties of the stationary solutions to the Euler equations. The study of these universality features was suggested by Tao (2019) as a novel way to address the problem of global existence for Euler and Navier–Stokes. Universality of the Euler equations was proved by Cardona et al. (2019) for stationary solutions using a contact mirror which reflects a Beltrami flow as a Reeb vector field. This contact mirror permits the use of advanced geometric techniques in fluid dynamics. On the other hand, motivated by Tao’s approach relating Turing machines to Navier– Stokes equations, a Turing complete stationary Euler solution on a Riemannian 3-dimensional sphere was constructed by Cardona et al. (2021). Since the Turing completeness of a vector field can be characterized in terms of the halting problem, which is known to be undecidable (as shown by Turing (1936)), a striking consequence of this fact is that a Turing complete Euler flow exhibits undecidable particle paths (as shown by Cardona et al. (2021)). In this article, we give a panoramic overview of this fascinating subject, and go one step further in investigating the undecidability of different dynamical properties of Turing complete flows. In particular, we show that variations of the work of Cardona et al. (2021) allow us to construct a stationary Euler flow of Beltrami type (and, via the contact mirror, a Reeb vector field) for which it is undecidable to determine whether its orbits through an explicit set of points are periodic.Peer ReviewedPostprint (author's final draft

Reeb embeddings and universality of Euler flows

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021We use a new geometrical approach to the universality of Euler flows. By proving flexibility results on embeddings for Reeb flows in contact topology, we deduce some new universal properties for Euler flows. As a byproduct, we deduce the Turing completeness of stationary Euler flows, answering an open question for steady solutions. The results contained in this article are an announcement and short version of [2], where the complete list of results and proofs can be found.This work was partially supported by the ICMAT–Severo Ochoa grant SEV-2015-0554Peer ReviewedPostprint (author's final draft

Universality of Euler flows and flexibility of Reeb embeddings

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. In this article we prove that the Euler equations exhibit universality features. More precisely, we show that any non autonomous flow on a compact manifold can be extended to a smooth solution of the Euler equations on some Riemannian manifold of possibly higher dimension. The solutions we construct are stationary of Beltrami type, so they exist for all time. Using this result, we establish the Turing completeness of the Euler flows, i.e. that there exist solutions that encode a universal Turing machine. The proofs exploit the correspondence between contact topology and hydrodynamics, which allows us to import the flexibility principles from the contact realm, in the form of holonomic h-principles for isocontact embeddings.Preprin

Technical and economic feasibility of a solar-bio-powered waste utilization and treatment system in Central America

The purpose of this study was to implement and evaluate a pilot-scale and closed-loop system that synergistically combines solar thermal collector, anaerobic digester, and constructed treatment wetland to simultaneously treat and utilize organic wastes. The system utilizes 863 kg of mixed animal and food wastes to generate 263 MJ renewable energy, produced 28 kg nitrogen and phosphorus fertilizer, and reclaimed 550 kg water per day. The net revenue considering electricity and fertilizer was $2436 annually. The payback period for the system is estimated to be 17.8 years for a relatively dilute waste stream (i.e., 2% total solids). The implemented system has successfully demonstrated a self-efficient and flexible waste utilization and treatment system. It creates a win-win solution to satisfy the energy needs of the community and address environmental concerns of organic wastes disposal in the region.U.S. Department of State West Hemisphere Affairs/[S-LMAQM-11-GR-075]//Estados UnidosMichigan AgBioResearch/[]//Estados UnidosUniversity of Costa Rica: Agronomy Research Center /[]/CIA/Costa RicaUniversity of Costa Rica: Water Quality Laboratory at the Research Center of Environmental Pollution /[]/CICA-LCA/ Costa RicaUniversity of Costa Rica: Center for Research in Electrochemistry and Chemical Energy /[]/CELEQ/Costa RicaUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Agroalimentarias::Estación Experimental Agrícola Fabio Baudrit Moreno (EEAFBM

SANAA, Rolex Learning Center

En el curso 2012-2013 el Laboratorio de Crítica centró su atención en el Rolex Learning Center de l´Ecole Polytechnique Fédérale de Lausanne en Suiza, obra de indudable interés del estudio japonés SANAA que constituye en sí misma un auténtico experimento y, consecuentemente, un objeto de observación apropiado para el estudio dentro del Laboratorio. En octubre de 2012 se realizó un viaje para visitar el edificio y, posteriormente, se realizaron por parte de los alumnos, ejercicios críticos y experimentos de los que en esta publicación aparece una muestra representativa. También se recogen en este libro, publicado gracias al apoyo de la ETSAM dentro de su colección de Texto Académicos, algunas aportaciones externas como el escrito y los dibujos del arquitecto Javier Aguilera, así como otros textos de antiguos alumnos del Laboratorio como Rosa Ballester, Berta González Salinero o Daniel Sacristán que, además han contribuido decisivamente en la edición. Se incluye, asimismo, un artículo de Eider Holgado, alumna de doctorado que está realizando su tesis, dentro del G.I. ARKRIT

Programa de internacionalización de los productos de Finca La Isla

Dentro del proyecto 3J04 “Inteligencia Cultural y Comercial para los Negocios Internacionales”, se realizó el programa de internacionalización de varios productos naturales de la empresa “Finca La Isla”. Estos van desde: Miel, Jengibre, Vainilla, Cúrcuma, Canela, entre otros. El proyecto se centró en la exportación de la miel en dos destinos: Alemania y Turquía, centrándose en las ferias Internacionales de la Anuga 2023, en Colonia, y Apimondia 2022 en Estambul. El proyecto nos llevó a crear un brochure, en donde se pueden encontrar diferentes aspectos económicos, culturales, sociales, políticos, y de mercado, para que el empresario tenga en cuenta todo antes de iniciar la inversión. Nos dividimos en dos equipos de trabajo, cada uno enfocado en un país.ITESO, A.C

Clinical aspects of dementia cases diagnosed at the Memory Clinic of the National Geriatric and Gerontology Hospital

Antecedentes: la demencia es una entidad clínica cada vez más prevalente en nuestro medio, cuya incidencia aumenta con la edad. El objetivo del presente estudio es identificar los principales tipos de demencia atendidos en una unidad de trastornos de memoria. Métodos: registro consecutivo y estandarizado de pacientes diagnosticados con demencia en la Unidad de Trastornos de Memoria y Conducta, del Hospital Nacional de Geriatría y Gerontología. Resultados: se evaluó 1659 casos, de los cuales el 65,8% reunió criterios de demencia. El 42,9% correspondió a enfermedad de Alzheimer, el 28,5% a demencia secundaria a patología vascular, el 17,1% a formas mixtas, y el 11,5% a tipos varios. La edad media fue de 79,6 + 6,7 años, y el 66,2% fueron mujeres. La escolaridad promedio fue 4,95 + 4,09 años; el 41,7% estaba casado; el 47,3% tenía un hijo como cuidador; el tiempo promedio entre la aparición de los síntomas y el diagnóstico clínico fue de 3,18 + 2,6 años. La puntuación media del test Minimental fue de 18,35 + 5,9 puntos; en el test de dibujo del reloj fue de 3,4 + 2,5, y el Clinical Dementia Rating fue de 1,7 + 0,7; el 45,2% de los casos correspondió a CDR de 1. El 24% de los casos tenía antecedente familiar de demencia, y el 95,7% presentaba uno o más factores de riesgo cardiovascular, siendo la HTA el más frecuente, en un 70,2%. El 27,1% de los casos fue demencias leves; el 31,9%, moderadas; el 39,3% moderadas-severas, y el 1,7%, severas. El 90% de los casos presentó uno o más trastornos neuroconductuales. Conclusiones: la determinación de los principales tipos de demencia en la población adulta mayor y sus principales características, ha permitido registrar gran cantidad de información que se desconocía y que será de útil para la gestión y planificación de estrategias de atención en salud pública.Background: Dementia is an increasingly prevalent clinical entity in the medical field, whose incidence increases with age. The purpose of this study is to identify the main types of dementia treated in a memory-disorders unit. Methodology: A consecutive and standardized register of patients diagnosed with dementia at the Memory Disorders Unit of the National Geriatrics and Gerontology Hospital. Results: 1659 cases were evaluated, 65.8% met criteria for dementia. 42.9% of the cases were Alzheimer’s disease, 28.5% secondary vascular dementia pathology, mixed forms represented 17.1% and 11.5% were diverse types. The mean age was 79.6 + 6.7 years and 66.2% were women. Average schooling was 4.95+ 4.09 years, 41.7% were married, 47.3% had a child as a caregiver, the average time between onset of symptoms and the clinical diagnosis was 3.18 + 2.6 years. The mean Minimental test score was 18.35 + 5.9 points, in the clock drawing test it was 3.4 + 2.5 and the Clinical Dementia Rating was 1.7 + 0.7; 45.2% of cases were CDR 1. 24% of cases had a family history of dementia and 95.7% had one or more cardiovascular risk factors, with AHT being the most common in 70.2%. 27.1% of dementia cases were mild, 31.9% moderate, 39.3% moderatesevere and 1.7% were severe. 90% of patients had one or more neurobehavioral disorders.Conclusions: The determination of the main types of dementia in the elderly population and their main features has allowed the registry of abundant information that was unknown and that will be useful for the management and strategic planning of public health care.UCR::Vicerrectoría de Docencia::Ciencias Sociales::Facultad de Ciencias Económicas::Escuela de Estadístic

#DIenlínea UNIA : guía para una docencia innovadora en red

256 páginas.El presente libro, en coherencia con la filosofía que inspira el curso en formato Spoc titulado Formación para la docencia innovadora (#DIenlínea) en el que se basa y para el que es un recurso didáctico, se ofrece en abierto en línea, al igual que ésta y otras actividades que venimos trabajando para la formación del profesorado en e-learning, innovación educativa y competencias digitales conforme al marco Europeo del DigComp, desde Innovación de la Universidad Internacional de Andalucía (UNIA). En él se recogen las experiencias, prácticas y orientaciones metodológicas de los mejores expertos y expertas que trabajan en la última frontera de la innovación educativa, quienes de forma asequible y fácil muestran tecnologías y técnicas para responder a las principales hitos de transformación digital de la docencia, como son: los principios y planteamientos metodológicos de una enseñanza enfocada como innovación, la creación de contenidos digitales multimedia e interactivos, cómo, qué y cuándo emplear herramientas para la evaluación online, la tutoría y el seguimiento de los estudiantes en línea, etcétera. Todo ello de tal modo que favorezca el autoaprendizaje y una enseñanza más personalizada en todas sus modalidades (híbridas, a distancia y semipresenciales)