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Understanding COVID-19 Epidemics: A Multi-Scale Modeling Approach
Get PDFCOVID-19 was declared a pandemic by the World Health Organization in March 2020 and, since then, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading and control under different scenarios. In this chapter, two different approaches to model the spread of COVID-19 are presented. The model frameworks are described and results are presented in connection with the current epidemiological situation of vaccination roll-out. This chapter is structured as follows. Section 2 presents the stochastic SHARUCD modeling framework developed within a modeling task force created to support public health managers during the COVID-19 crisis. As an extension of the basic SHAR (Susceptible-Hospitalized-Asymptomatic-Recovered) model, the SHARUCD models were parameterized and validated with empirical data for the Basque Country, Spain, and have been used (up until now) to monitor COVID-19 spreading and control over the course of the pandemic. Section 3 introduces the kinetic theory of active particles (KTAP) model for the spread of a disease. With an exploratory analysis, we present a possible way to deal with heterogeneity and multiscale features. Section 4 concludes this work, with a discussion on both models and further research perspectives description
Desarrollo de sistema de Machine Learning para la prediccion de vía aérea a partir de imagen facial con dispositivo movil
Get PDFEl manejo de una vía aérea difícil (VAD) representa aún una causa importante de lesiones relacionadas con la anestesia, cuyas complicaciones son potencialmente mortales. El notable interés en la predicción de VAD ha provocado el desarrollo de modelos de
predicción, algunos de los cuales ya incluyen algoritmos de Inteligencia Artificial a partir de imágenes.
Se realizó un estudio observacional, de cohortes prospectivo, en el que se tomaron imágenes de los pacientes sometidos a una anestesia general, recogiendo la información pre-anestésica así como la información post-intubación. Nuestro equipo desarrolló un
algoritmo automático de detección de puntos faciales de cara a la toma de medidas de variables ya validadas de predicción de VAD, que se integraron con el modelo predictivo de Naguib.
La incidencia estimada de VAD en nuestra muestra de 503 pacientes fue de un 6,36%. La valoración subjetiva (pre-intervención) de los clínicos obtuvo una sensibilidad de 25.00%, con una especificidad de 93.63%. En comparación, nuestra herramienta alcanzó una sensibilidad del 53.12% y una especificidad del 79.83%. El AUC obtenida, o área bajo la curva ROC, fue de 0.680.
Integrando nuestro sistema de medición IA-ML con el modelo de Naguib, los resultados muestran que estamos cerca de igualar la capacidad predictiva del clínico. El potencial del análisis facial en la predicción de VAD nos anima a seguir investigando y a desarrollar modelos propios. Creemos que proporcionará al anestesiólogo una herramienta de ayuda en la toma de decisiones automática, objetiva y accesible
Weak* Hypertopologies with Application to Genericity of Convex Sets
Get PDFWe propose a new class of hypertopologies, called here weak
hypertopologies, on the dual space of a real or
complex topological vector space . The most well-studied and
well-known hypertopology is the one associated with the Hausdorff metric for
closed sets in a complete metric space. Therefore, we study in detail its
corresponding weak hypertopology, constructed from the Hausdorff
distance on the field (i.e. or ) of the vector
space and named here the weak-Hausdorff
hypertopology. It has not been considered so far and we show that it can
have very interesting mathematical connections with other mathematical
fields, in particular with mathematical logics. We explicitly demonstrate
that weak hypertopologies are very useful and natural structures\
by using again the weak-Hausdorff hypertopology in order to study
generic convex weak-compact sets in great generality. We show that
convex weak-compact sets have generically weak-dense set
of extreme points in infinite dimensions. An extension of the well-known
Straszewicz theorem to Gateaux-differentiability (non necessarily Banach)
spaces is also proven in the scope of this application.FAPESP (2017/22340-9)
CNPq (309723/2020-5)
by the Basque Government through the grant IT641-13
MTM2017-82160-C2-2-P
Beta Distribution in Wildfire Spreading
Get PDFThis paper is the result of research work carried out in collaboration with the Statistical Physics team of the Basque Center for Applied Mathematics in Bilbao, supervised by Dr. Gianni Pagnini.
Main subject is PROPAGATOR, an algorithm for fires simulation based on a cellular automata model (CA).
The choice of such a modelling approach is not random, the cellular automata, in fact, thanks to their modular nature, are able to simplify the physical processes that influence the propagation of fires, while retaining the ability to achieve whatever you want level of complexity and accuracy. They are also one of the most widely known examples of stochastic lattice models.
The PROPAGATOR model, in fact, is based on raster implementation, which discretizes the space in a grid composed of rectangular cells of arbitrary length, and the propagation is modeled as a contamination process between adjacent cells of the considered domain.
The aim is to identify how the burned area is distributed in a limited observation interval.
For this purpose, a simplified case of fire propagation is considered. In fact, fuels and possible intervention of fire-fighting helicopters, which can affect fire size, intensity and duration, are not being studied.
In addition, the fire-spotting phenomenon is excluded. It consists in the propagation of fires outside the perimeter of the main fire caused by burning particles that, raised in the air by convective currents and driven by the wind, generate secondary fires with distances of the order of tens meters.
The focus is therefore on the following parameters: observation interval; propagation perimeter; vegetation type; wind intensity and direction; inclination of the territory.
In this thesis, in particular, we report the results obtained by studying the phenomenon of propagation as the slope of the territory changes and fixing the remaining parameters. To obtain these results, a modification to the PROPAGATOR algorithm was made, in that the latter is programmed to return in output, for each instant of time, the arithmetic mean over the number of realizations of the burned area values, whereas for the analysis these values were needed for each realization, since they were interested, not only in the mean, but also in the variance, skewness, kurtosis and more generally in their distribution. This accuracy has cost in terms of computational effort. For a large number of realizations, in fact, it was necessary to use the Hypatia server.
The work is organized as follow:
* In the first chapter, after a first introduction to the special functions and their history, with references to those most known and used, are defined, starting from the Beta function and the Gamma function, the Beta Distribution and the General Logistics Distribution.
* The second chapter introduces the PROPAGATOR model, the story of the algorithm development, and then arrive at the role of the territory inclination in the fires propagation.
* The third chapter describes in detail the data analysis carried out and gives the graphic results for each case studied: slope 10º, slope 15º, slope 20º, slope 30º, slope 40º e slope 50º.
* In Appendix A some preliminary work on the simulation of known stochastic processes, to develop a kind of critical sense for the results, in order to get prepared for the use of PROPAGATOR.
* Appendix B shows the codes developed for the analysis.
* Appendix C lists the software, apps and routines used.
Finally, we inform that the PROPAGATOR algorithm is currently in use by the Department of National Civil Protection and that the version used in the following is of 2020, even if an update to 2022 is already available
Offsets and front tire tracks to projective hedgehogs
Get PDFThere are some known properties on curves of constant width and Zindler curves and their relationship with offsets and front tire-track curves in convex geometry. In this work, a generalization of all these concepts and results to hedgehogs is presented. Discontinuity issues coming from the common parametric definition of offsets and front track curves are solved with parameterizations by a support function. Finally, it is seen that there is a one-to-one correspondence between constant width hedgehogs of constant width and generalized Zindler curves
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
Get PDFThe periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 under these transformations for any [Formula presented]. This extends previous achievements by Nahmod, Ray-Bellet, Sheffield and Staffilani (2011) and Genovese, Lucà and Valeri (2018), who proved the result for integer values of the regularity parameter s
On the BBM-Phenomenon in Fractional Poincaré–Sobolev Inequalities with Weights
Get PDFIn this paper, we unify and improve some of the results of Bourgain, Brezis, and Mironescu and the weighted Poincaré–Sobolev estimate by Fabes, Kenig, and Serapioni. More precisely, we get weighted counterparts of the Poincaré–Sobolev-type inequality and also of the Hardy type inequality in the fractional case under some mild natural restrictions. A main feature of the results we obtain is the fact that we keep track of the behavior of the constants involved when the fractional parameter approaches to 1. Our main method is based on techniques coming from harmonic analysis related to the self-improving property of generalized Poincaré inequalities
Impact of Glucose on the Nanostructure and Mechanical Properties of Calcium-Alginate Hydrogels
Get PDFAlginate is a polysaccharide obtained from brown seaweed that is widely used in food, pharmaceutical, and biotechnological applications due to its versatility as a viscosifier and gelling agent. Here, we investigated the influence of the addition of glucose on the structure and mechanical properties of alginate solutions and calcium-alginate hydrogels produced by internal gelation through crosslinking with Ca2+ . Using1H low-field nuclear magnetic resonance (NMR) and small angle neutron scattering (SANS), we showed that alginate solutions at 1 wt % present structural hetero-geneities at local scale whose size increases with glucose concentration (15–45 wt %). Remarkably, the molecular conformation of alginate in the gels obtained from internal gelation by Ca2+ crosslinking is similar to that found in solution. The mechanical properties of the gels evidence an increase in gel strength and elasticity upon the addition of glucose. The fitting of mechanical properties to a poroelastic model shows that structural changes within solutions prior to gelation and the increase in solvent viscosity contribute to the gel strength. The nanostructure of the gels (at local scale, i.e., up to few hundreds of Å) remains unaltered by the presence of glucose up to 30 wt %. At 45 wt %, the permeability obtained by the poroelastic model decreases, and the Young’s modulus increases. We suggest that macro (rather than micro) structural changes lead to this behavior due to the creation of a network of denser zones of chains at 45 wt % glucose. Our study paves the way for the design of calcium-alginate hydrogels with controlled structure for food and pharmaceutical applications in which interactions with glucose are of relevance
Approximating the quantum approximate optimization algorithm with digital-analog interactions
Get PDFThe quantum approximate optimization algorithm was proposed as a heuristic method for solving combinatorial optimization problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the postsupremacy, noisy, intermediate-scale era of quantum computing. In this work we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the quantum approximate optimization algorithm due to the algorithm's variational resilience against the coherent errors introduced by the scheme. By performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation time we observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over nonvariational counterparts in the digital-analog scheme.Basque Government QUANTEK project from the ELKARTEK program (KK-2021/00070)
Basque Government IT1470-22
Spanish Ramón y Cajal Grant RYC-2020-030503-I
Spanish project grant PID2021-125823NA-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and “ERDF Invest in your Future”
OpenSuperQ (820363) and QMiCS (820505) of the EU Flagship on Quantum Technologies
EU FET-Open projects Quromorphic (828826) and EPIQUS (899368
Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air
Get PDFOpen-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a cryostat, where they are created, to an environment dominated by thermal noise. Indeed, the states carrying such quantum resources are generated in a cryostat characterized by a temperature Tin ' 50 mK and an intrinsic impedance Zin = 50 Ω. Then, an antenna-like device is required to transfer them with minimal losses into open air, characterized by an intrinsic impedance of Zout = 377 Ω and a temperature Tout ' 300 K. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure, we find the optimal shape of the impedance, and we propose a functional ansatz to qualitatively describe this shape. Additionally, this study reveals that the reflectivity of the antenna is very sensitive to this shape, so that small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work is relevant in the fields of microwave quantum sensing and quantum metrology with special application to the development of the quantum radar, as well as any open-air microwave quantum communication protocol.Basque Government QUANTEK project from ELKARTEK program (KK-2021/00070)
Spanish Ramón y Cajal Grant RYC-2020-030503-I
Spanish project grant PID2021-125823NA-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and “ERDF Invest in your Future”
QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies
EU FET-Open projects Quromorphic (828826) and EPIQUS (899368)