A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.Comment: 21 pages, 11 figures. v2 matches published version: improved presentation (including title, abstract and references), results and conclusions unchange

In-situ CO measurements at Izaña global GAW station: GC-RGA system, data processing, and 2008-2011 time series

Comunicación presentada en: 16th WMO/IAEA Meeting on Carbon Dioxide, Other Greenhouse Gases, and Related Measurement Techniques celebrado del 25 al 28 de octubre de 2011 en Wellington, Nueva Zelanda

Stability of the Faber-Krahn inequality for the Short-time Fourier Transform

We prove a sharp quantitative version of the Faber--Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit $\delta(f;\Omega)$ which measures by how much the STFT of a function $f\in L^2(\mathbb R)$ fails to be optimally concentrated on an arbitrary set $\Omega\subset \mathbb R^2$ of positive, finite measure. We then show that an optimal power of the deficit $\delta(f;\Omega)$ controls both the $L^2$-distance of $f$ to an appropriate class of Gaussians and the distance of $\Omega$ to a ball, through the Fraenkel asymmetry of $\Omega$. Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context.Comment: 46 page

Regulatory estimates for defaulted exposures: A case study of Spanish mortgages

The capital requirements derived from the Basel Accord were issued with the purpose of deploying a transnational regulatory framework. Further regulatory developments on risk measurement is included across several documents published both by the European Banking Authority and the European Central Bank. Among others, the referred additional documentation focused on the models’ estimation and calibration for credit risk measurement purposes, especially the Advanced Internal-Ratings Based models, which may be estimated both for non-defaulted and defaulted assets. A concrete proposal of the referred defaulted exposures models, namely the Expected Loss Best Estimate (ELBE) and the Loss Given Default (LGD) in-default, is presented. The proposed methodology is eventually calibrated on the basis of data from the mortgage’s portfolios of the six largest financial institutions in Spain. The outcome allows for a comparison of the risk profile particularities attached to each of the referred portfolios. Eventually, the economic sense of the results is analyzed.Regional Government of Andalusia, Spain (Research Group SEJ-555)

Forecasting for regulatory credit loss derived from the COVID-19 pandemic: A machine learning approach

The economic onslaught of the COVID-19 pandemic has compromised the risk management of financial institutions. The consequences related to such an unprecedented situation are difficult to foresee with certainty using traditional methods. The regulatory credit loss attached to defaulted mortgages, so-called expected loss best estimate (ELBE), is forecasted using a machine learning technique. The projection of two ELBEs for 2022 and their comparison are presented. One accounts for the outbreak’s impact, and the other presumes the nonexistence of the pandemic. Then, it is concluded that the referred crisis surely adversely affects said high-risk portfolios. The proposed method has excellent performance and may serve to estimate future expected and unexpected losses amidst any event of extraordinary magnitud

A statistical approach to quantify uncertainty in carbon monoxide measurements at the Izaña global GAW station: 2008–2011

Atmospheric CO in situ measurements are carried out at the Izaña (Tenerife) global GAW (Global Atmosphere Watch Programme of the World Meteorological Organization – WMO) mountain station using a Reduction Gas Analyser (RGA). In situ measurements at Izaña are representative of the subtropical Northeast Atlantic free troposphere, especially during nighttime. We present the measurement system configuration, the response function, the calibration scheme, the data processing, the Izaña 2008–2011 CO nocturnal time series, and the mean diurnal cycle by months

Galactoseismology in cosmological simulations: Vertical perturbations by dark matter, satellite galaxies and gas

Only recently, complex models that include the global dynamics from dwarf satellite galaxies, dark matter halo structure, gas infalls, and stellar disk in a cosmological context became available to study the dynamics of disk galaxies such as the Milky Way (MW). We use a MW model from a high-resolution hydrodynamical cosmological simulation named GARROTXA to establish the relationship between the vertical disturbances seen in its galactic disk and multiple perturbations, from the dark matter halo, satellites and gas. We calculate the bending modes in the galactic disk in the last 6 Gyr of evolution. To quantify the impact of dark matter and gas we compute the vertical acceleration exerted by these components onto the disk and compare them with the bending behavior with Fourier analysis. We find complex bending patterns at different radii and times, such as an inner retrograde mode with high frequency, as well as an outer slower retrograde mode excited at different times. The amplitudes of these bending modes are highest during the early stages of the thin disk formation and reach up to 8.5 km s-1 in the late disk evolution. We find that the infall of satellite galaxies leads to a tilt of the disk, and produces anisotropic gas accretion with subsequent star formation events, and supernovae, creating significant vertical accelerations onto the disk plane. The misalignment between the disk and the inner stellar/dark matter triaxial structure, formed during the ancient assembly of the galaxy, creates a strong vertical acceleration on the stars. We conclude that several agents trigger the bending of the stellar disk and its phase spirals in this simulation, including satellite galaxies, dark sub-halos, misaligned gaseous structures, and the inner dark matter profile, which coexist and influence each other, making it challenging to establish direct causality