The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Understanding the Random Displacement Model: From Ground-State Properties to Localization

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

MONITORIZACIÓN DE LA PRESIÓN TISULAR DE OXÍGENO (PtiO2) EN LA UVI DEL HOSPITAL DE LA RIBERA Y HOJA DE REGISTRO DE ENFERMERÍA

Tissue pressure of oxygen (PtiO2) monitoring allows knowing the tissue injuries implications, and the diagnosis of secondary lesions in the patient with craneoencephalic traumatism. This monitoring method detects physiopathologic changes brought about by neurotraumatic injuries. The objective of our contribution is to describe and analyze this specific type of monitoring and the nurse cares with relationship to the cases taken care of in our unit, according to our experience. A Nurse’s Record Card has been developed, containing the patient's name, diagnosis, medical history number, catheter type, schedules, etc. In this way, the possible complications derived from the catheter and from the patient's own development will be avoided, and nursing quality care will be improved.La monitorización de la presión tisular de oxigeno (PtiO2) permite el conocimiento de las repercusiones de las lesiones tisulares y el diagnóstico de lesiones secundarias en el paciente con traumatismo craneoencefálico grave (TCEG). Este método de monitorización detecta cambios fisiopatológicos que conllevan las lesiones neurotraumáticas. El objetivo de nuestro artículo es describir y analizar este tipo de monitorización, así como los cuidados de enfermería con relación a los casos que hemos atendido en nuestra unidad y según nuestra experiencia. Se ha confeccionado una hoja de “registro de enfermería” que contiene los datos del paciente, diagnóstico, tipo de catéter, constantes horarias, etc. Con estos controles, pretendemos recoger las posibles complicaciones derivadas del catéter y del propio proceso del paciente, mejorando de esta manera la calidad asistencial

Towards Safer Robot Motion: Using a Qualitative Motion Model to Classify Human-Robot Spatial Interaction

For adoption of Autonomous Mobile Robots (AMR) across a breadth of industries, they must navigate around humans in a way which is safe and which humans perceive as safe, but without greatly compromising efficiency. This work aims to classify the Human-Robot Spatial Interaction (HRSI) situation of an interacting human and robot, to be applied in Human-Aware Navigation (HAN) to account for situational context. We develop qualitative probabilistic models of relative human and robot movements in various HRSI situations to classify situations, and explain our plan to develop per-situation probabilistic models of socially legible HRSI to predict human and robot movement. In future work we aim to use these predictions to generate qualitative constraints in the form of metric cost-maps for local robot motion planners, enforcing more efficient and socially legible trajectories which are both physically safe and perceived as safe

Study of radiactivity on Arctic marine seaweed from Kongsfjorden (Svalbard)

Levels of natural and anthropogenic radionuclides have been determined in six brown and red seaweed species from Arctic coasts (Kongsfjorden, Spitsbergen, Svalbard Islands) in order to characterize the radioactivity in this ecosystem. Samples were collected in September 2014, August 2017 and July 2019. Levels of 7Be, 40K, 208Tl, 210Pb, 226Ra and 228Ra were measured by high-resolution gamma spectrometry. While anthropogenic radionuclides (1 4 C and 1 2 9 I) were determined by low-energy accelerator mass spectrometry (LEAMS). The activities of 129I are two orders of magnitude higher than those found in algae collected on the Spanish Atlantic Coast and presents more variability than the 14C results, indicating their different affinity to this element depending on the species. Radionuclide tracers discharged from Sellafield and La Hague are transported into the Arctic Ocean where they circulate at different depth levels, marking water of Atlantic origin (Karcher et al., 2012).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Proyecto CGL2015/67014

Evaluación clínica y hoja de registro de cuidados de enfermería del sistema de control fecal en pacientes críticos

Fecal incontinence in critical patients predisposes them to several complications as: tissue viability problems, infections, or patients well-being effects. This kind of problems could increase average stay hospital, with economic and health system repercussions.The evidence shows that traditional managements of fecal incontinence have adverse outcomes which are unresolved.The Flexi-seal® management system (FMS), reduces these complications, and its effectiveness is based on different studies (Martínez Estadella G et al, 2006), (Ares Sánchez M et al, 2006) (Bordes J et all, 2007), (Pelleschi ME, 2008).It is necessary to describe the insertion technique, and Nursing interventions orientated to patients who need Flexi-seal® management system (FMS), in order to improve Nursing Cares.La incontinencia fecal en los Pacientes Críticos produce una serie de complicaciones como son: el deterioro de la integridad cutánea de la piel, infecciones, alteración en la autoestima del paciente, etc. Esta serie de problemas puede ocasionar un aumento en la media de estancia de los pacientes ingresados con repercusiones sanitarias y económicas.La evidencia científica nos indica que los sistemas tradicionales utilizados para la incontinencia fecal producen diferentes problemas potenciales aún sin solucionar.El sistema de control de la incontinencia fecal Flexi-Seal® FMS (Fig. nº1) produce una reducción de estos problemas y su efectividad está basada en diferentes estudios recientes que así lo demuestran (Martínez Estadella, G. et al, 2006), (Ares Sánchez, M. et al, 2006) (Bordes, J. et al, 2007), (Pelleschi, ME, 2008).Es necesario describir tanto la técnica de inserción como los Cuidados de Enfermería de este nuevo dispositivo de incontinencia fecal

Database of multiparametric geophysical data from the TOMO-DEC experiment on Deception Island, Antarctica

We are grateful to the officers and crew of the Spanish vessels 'R/V Hesperides' and 'R/V Las Palmas', the personnel of the Marine Technology Unit (UTM), the military personnel of the 'Gabriel de Castilla' Spanish base, and the members of the TOMODEC Working Group. This manuscript has been partially funded by the following research projects: the Spanish project TEC2015-68752-R (MINECO/FEDER); KNOWAVES; the Spanish Education and Research Ministry grants REN 2001-3833, CGL2005-05789-C02-02/ANT, POL2006-08663, and CGL2008-01660; the U.S. National Science Foundation grant ANT-0230094; the European project MED-SUV funded by the European Union's Seventh Framework Program for research, technological development and demonstration under grant agreement No 308665; the European project EPOS; the European Union's Horizon 2020 research and innovation programme under grant agreement No 676564; and the U.S. National Science Foundation grant NSF-1521855 Hazard SEES project. Ocean bottom seismometers were provided by the U.S National Oceanographic Instrument Pool. This publication reflects only the authors' views. The European Commission is not responsible for any use that may be made of the information it contains.Deception Island volcano (Antarctica) is one of the most closely monitored and studied volcanoes on the region. In January 2005, a multi-parametric international experiment was conducted that encompassed both Deception Island and its surrounding waters. We performed this experiment from aboard the Spanish oceanographic vessel 'Hesperides', and from five land-based locations on Deception Island (the Spanish scientific Antarctic base 'Gabriel de Castilla' and four temporary camps). This experiment allowed us to record active seismic signals using a large network of seismic stations that were deployed both on land and on the seafloor. In addition, other geophysical data were acquired, including bathymetric high precision multi-beam data, and gravimetric and magnetic profiles. To date, the seismic and bathymetric data have been analysed but the magnetic and gravimetric data have not. We provide P-wave arrival-time picks and seismic tomography results in velocity and attenuation. In this manuscript, we describe the main characteristics of the experiment, the instruments, the data, and the repositories from which data and information can be obtained.MINECO/FEDER TEC2015-68752-RKNOWAVESSpanish Education and Research Ministry REN 2001-3833 CGL2005-05789-C02-02/ANT POL2006-08663 CGL2008-01660National Science Foundation (NSF) ANT-0230094 NSF-1521855European project MED-SUV - European Union's Seventh Framework Program 308665European project EPOSEuropean Union (EU) 67656

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

The risk of menstrual abnormalities after tubal sterilization: a case control study

BACKGROUND: Tubal sterilization is the method of family planning most commonly used. The existence of the post-tubal-ligation syndrome of menstrual abnormalities has been the subject of debate for decades. METHODS: In a cross-sectional study, 112 women with the history of Pomeroy type of tubal ligation achieved by minilaparatomy as the case group and 288 women with no previous tubal ligation as the control group were assessed for menstrual abnormalities. RESULTS: Menstrual abnormalities were not significantly different between the case and control groups (p = 0.824). The abnormal uterine bleeding frequency differences in two different age groups (30–39 and 40–45 years old) were statistically significant (p = 0.0176). CONCLUSION: Tubal sterilization does not cause menstrual irregularities