BUSCADOR RECOLECTA

[EN] This paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyze the numerical stability and convergence rate., This work was partially supported by the Spanish Ministry of Economy and Competitiveness MINECO through the project PID2019-107685RB-I00 and by the Spanish State Research Agency
(AEI) through the project PDC2022-133115-I00.

[EN] A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random free boundary partial differential problem and it is addressed numerically combining the finite difference method with two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical examples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties of the schemes and show the numerical convergence., This work has been partially supported by the Spanish Ministry of Economy and Competitiveness MINECO through the project
PID2019-107685RB-I00 and by the Spanish State Research Agency (AEI) through the project PDC2022-133115-I00.

We show that the probability density function (PDF) of an area enclosed by a random perimeter is driven by the PDF of the integration bounds and the mean value of the perimeter function. With reference to wildfires, if the integration interval is aligned with the main direction of propagation, the PDF of the burned area is driven by the PDF of the position of the head of the fire times the mean value of the fire front. We show that if the random fire front perimeter is modelled as an ellipse-like curve with stochastic noise, the relation between the probability distribution of the burned area and the one of the head of the fire is linear, with the constant mean value of the perimeter as a factor. Different random noise models have been developed and implemented for this purpose. Different behaviours of the stochastic position of the head of the fire have been studied, including Viegas’ rate of spread model.
We show that for the realistic propagation model given by the operational wildfire cellular automata simulator Propagator [46], the PDF of the burned area is still driven by the position of the head of the fire and the mean value of the fire front perimeter, and the shape of the perimeter is not relevant. This has been shown for 5 case studies, ranging from easy ones to realistic complicated cases.

This 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.

This dissertation is in the mathematical physics area, more specifically, applications
in the statistics field. The thesis, under the supervision of Dr. Gianni Pagnini, was carried out at
the BCAM - Basque Centre for Applied Mathematics in Bilbao, Spain. It is
the result of the continuous interaction with the team of Statistical Physics,
characterised by an international, stimulating and constantly growing environment.
The subject of this thesis is PROPAGATOR: a stochastic cellular automaton
model for forest fire spread simulation, conceived as a rapid method
for fire risk assessment.
The reason behind the popularity of cellular automata can be traced to their
simplicity, and to the enormous potential they hold in modeling complex systems,
in spite of their simplicity. Cellular automata can be viewed as a simple
model of a spatially extended decentralized system made up of a number of
individual components: cells. The communication between constituent cells
is limited to local interaction.
PROPAGATOR is a cellular automata model which simulates wildfire
spread through empirical laws that guarantee probabilistic outputs. This
algorithm, whose first version was released in 2009, is currently in use, along
with other software, although it is constantly being updated.
In fact, the first version was requested by the Italian Civil Protection, but
later it became part of the ANYWHERE project. This project, active from
June 2016 to December 2019, was funded under the EU’s research and innovation
funding program Horizon 2020 (H2020), which aimed to improve
emergency management and response to high-impact weather and climate
events such as floods, landslides, swells, snowfalls, forest fires, heat waves
and droughts.
As part of the ANYWHERE project, Propagator was rewritten in Python.
The version we worked with is the 2020 version, but an updated 2022 version is already available.
The main aim of this work was to understand the distribution of the
wildfire propagation. As can be seen from Propagator input parameters,
the propagation depends on different factors: ignition point, wind speed and
direction, as well as fuel moisture content and firebreaks-fire fighting strategies.
Wind is recognized to be by far the most important factor in the entire
problem of forest fire propagation. In this paper, we analyzed four different
situations varying initial conditions, in particular we changed wind speed:
0 km/h, 10 km/h, 20 km/h, 30 km/h. However, the phenomenon of fire
spotting and firebreaks-fire fighting strategies were not taken into consideration.
By modifying the code, it was possible to obtain the output required to
achieve the desired result. The conclusion we came to is that the distribution
of a wildfire spreading is described by the beta distribution.
This allows us, for the first time, to attribute a new application of the beta
function: describing the propagation of a process studied using a cellular
automaton algorithm.

The thesis is organised as follows:

In the first chapter, there is an introduction to special functions. In
particular, their role in applied mathematics is analyzed, followed by
a discussion of the two most commonly used special functions: the
Gamma function and the Beta function.

• In the second chapter, the PROPAGATOR model was introduced following
the article "PROPAGATOR: An Operational Cellular-Automata
Based Wildfire Simulator" by A. Trucchia.

• The third chapter contains the analysis carried out on the output data.
A discussion of the obtained results and suitable observations can be
found in the conclusions.

• There are three appendixes containing:

– Appendix A: the lines of code we wrote to carry out the analysis.

– Appendix B: explanation of the software, apps and routines used,
with particular reference to the Hypathia server.

– Appendix C: discussion on stochastic processes carried out as an
approach and preparation for the subsequent work with Propagator.

We study the mean first-passage time (MFPT) for asymmetric continuous-time random walks in continuous-space characterised by waiting-times with finite mean and by jump-sizes with both finite mean and finite variance. In the asymptotic limit, this well-controlled process is governed by an advection-diffusion equation and the MFPT results to be finite when the advecting velocity is in the direction of the boundary. We derive a nonhomogeneous Wiener–Hopf integral equation that allows for the exact calculation of the MFPT by avoiding asymptotic limits and it emerges to depend on the whole distribution of the jump-sizes and on the
mean-value only of the waiting-times, thus it holds for general non-Markovian random walks. Through the case study of a quite general family of asymmetric distributions of the jump-sizes that is exponential towards the boundary and arbitrary in the opposite
direction, we show that the MFPT is indeed independent of the jump-sizes distribution in the opposite direction to the boundary. Moreover, we show also that there exists a length-scale, which depends only on the features of the distribution of jumps in the direction of the boundary, such that for starting points near the boundary the MFPT depends on the specific whole distribution of jump-sizes, in opposition to the universality emerging for starting points far-away from the boundary., PRE2018-084427.

We study the mean first-passage time (MFPT) for asymmetric continuous time random walks in continuous space characterised by finite mean waiting times and jump amplitudes with both finite average and finite variance. We derive an inhomogeneous Wiener-Hopf integral equation that allows the exact estimation of the MFPT, which depends on the whole distribution of the jump amplitudes, but on the average of the waiting times only. Thus, our findings hold for general non-Markovian processes, since Markovianity emerges solely with an exponential distribution of the waiting times. Through the paradigmatic case study of a
general class of asymmetric distributions of the jump-amplitudes that is exponential towards the boundary and arbitrary in the opposite direction, we show, that only the average of the jump amplitudes in the opposite direction of the boundary contributes to the MFPT. Moreover, we determine a length-scale, which depends only of the distribution of jumps in the direction of the boundary, such that for initial positions close to the boundary the MFPT depends on the specific whole distribution of jump amplitudes, in opposition to the appearing universality for initial positions far away from the boundary., PRE2018-084427

Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets $G^1$ (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve $G^1$ continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the $G^1$ connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness.

A discrete map for modelling wildfire propagation is derived from a prototypical reaction-diffusion equation for the temperature field. We show that, for a constant fuel concentration at the fire-front, the heat transfer coefficient from fuel to surroundings and as well as an effective heat of reaction are two independent mechanisms that can cause the transition to chaos, when they may depend on temperature as a consequence of the fire-atmosphere coupling and of the fuel inhomogeneity, respectively. In particular, chaos can enter when the coefficient for the heat transfer from the fuel to the surrounding depends linearly on the temperature and when the effective heat of reaction depends quadratically. Moreover, when the fuel concentration field at the fire-front fluctuates, this embodies a third mechanism that may cause the transition to chaos even without any fire-atmosphere coupling or fuel inhomogeneity. Surprisingly, when the effective heat of reaction depends linearly on the temperature, the chaos generated by the non-constant fuel concentration is ceased. This suppression is not observed when the chaos is due to the fire-atmosphere coupling with constant fuel concentration. In all cases, the onset of chaos is related to the logistic map. The application of this approach for setting an alternative method for real-time risk assessment is discussed in the conclusions., This research is supported by the Basque Government through the BERC 2022–2025 program, by the Ministry of Science and Innovation: BCAM Severo Ochoa accreditation CEX2021-001142-S / MICIN / AEI / 10.13039/501100011033 and the project PID2019-107685RB-I00, and by the Spanish State Research Agency (AEI) through the project PDC2022-133115-I00 entitled ”B 2 F 2: Be a Better digital Fire-Fighter” and funded by the European Union Next Generation EU; by the European Regional Development Fund (ERDF) and the Department of Education of the regional government, the Junta of Castilla y Le ́on (Grant contract SA089P20).

One crucial mechanism in the spread of wildfires is the so-called fire-spotting: a random phenomenon which occurs when embers are transported over large distances. Fire-spotting speeds up the Rate of Spread and starts new ignitions which constitute a menace for fire fighting operations. Unfortunately, operational fire-spread simulators may not account for spotting effects, thus overlooking the harmful consequences associated with this phenomenon. In this work, several fire spotting methods are integrated in the operational wildfire simulator PROPAGATOR based on Cellular Automata (CA). Ran- domFront, a physics-based parametrization of fire-spotting, is tested for the first time in the context of CA simulators. RandomFront is compared with other two parametrizations already adopted in CA based simulators, the ones of Alexandridis et al. and Perryman et al. A wildfire occurred in the summer of 2021 in the municipality of Campomarino (Molise, Italy), and where spotting effects were clearly reported, has been used as a study case. RandomFront parametrization produced a more complex burnt probability pattern than the other models. Moreover, it predicted higher burning proba- bility in the area of the domain affected by spotting effects in the real wildfire event., This research has been supported by the Basque Government through the BERC 2022–2025 programme; by the Spanish Ministry of Economy and Competitiveness (MINECO) through the BCAM Severo Ochoa excel- lence accreditation SEV-2017-0718 and CEX2021-001142-S / MICIN / AEI / 10.13039/501100011033 and through the national projects PID2019-107685RB- I00 and PDC2022-133115-I00; by the European Regional Development Fund (ERDF) and the Department of Education of the regional government, the Junta of Castilla y Le ́on, (Grant contract SA089P20); and by the Interreg IPA CBC Italy-Albania-Montenegro programme through the project The flOod and Big firE foREst, prediction, forecAst anD emergencY management (TO BE READY). This work has been partially supported by the Horizon 2020-funded project SAFERS “Structured Approaches for Forest Fire Emer- gencies in Resilient Societies” (H2020/Innovation Action), grant agreement No. 869353.

Deep neural networks (DNNs) offer a real-time solution for the inversion of borehole resistivity measurements to approximate forward and inverse operators. Using extremely large DNNs to approximate the operators is possible, but it demands considerable training time. Moreover, evaluating the network after training also requires a significant amount of memory and processing power. In addition, we may overfit the model. In this work, we propose a scoring function that accounts for the accuracy and size of the DNNs compared to a reference DNNs that provides good approximations for the operators. Using this scoring function, we use DNN architecture search algorithms to obtain a quasi-optimal DNN smaller than the reference network; hence, it requires less computational effort during training and evaluation. The quasi-optimal DNN delivers comparable accuracy to the original large DNN., PDC2021-121093-I00
IA4TES
RYC2021-032853-I

For the correct operation of the electricity system, producers must provide an estimate of the energy they are going to discharge into the system, and they must face financial penalties if their forecasts are wrong. This is especially difficult in the case of renewable energies, and in particular wind energy because of its variability and intermittency. The tool proposed allows, in a first step, to improve the prediction of wind energy to be produced and, in a second step, to optimize the offer to be presented to the electricity market, so that the overall economic performance can be improved. This tool is based on the use of public information and automatic learning and has been evaluated on a set of 30 wind farms in Spain, using their historical production data. The results indicate improvements in both the accuracy of the energy estimation and the profit obtained from the energy sold., This work has been supported by the Ministerio de Ciencia, Innovación y Universidades, Spain, grant contract RTC-2017-6635-3; by the Ministerio de Economía y Competitividad, Spain, grant contract PID2019-107685RB-I00; by the Fundación General de la Universidad de Salamanca, Spain, grant contract PC_TCUE2-23_012; by the European Regional Development Fund (ERDF) and the Department of Education of the regional government, the Junta of Castilla y León, Spain, grant contract SA089P20; and by the European Union's Horizon 2020 - Research and Innovation Framework Program under grant agreement ID 101036926.