Some differential systems driven by a fBm with Hurst parameter greater than 1/4

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with H\"older regularity greater than 1/4. After recalling how to treat the case of ordinary stochastic differential equations, we mainly focus on the case of delay equations. A careful analysis is then performed in order to show that a fractional Brownian motion with Hurst parameter H>1/4 fulfills the assumptions of our abstract theorems.Comment: 32 page

Probability density for a hyperbolic SPDE with time dependent coefficients

We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF 2002, to an infinite dimensional setting.Comment: 15 page

Controlled viscosity solutions of fully nonlinear rough PDEs

We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path via appropriate notions of test functions and rough jets. These objects will be defined as controlled processes with respect to the driving rough path. We show that this notion is compatible with the seminal results of Lions and Souganidis and with the recent results of Friz and coauthors on fully non-linear SPDEs with rough drivers

On the use of reproducing kernel Hilbert spaces in functional classification

The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic processes. This paper provides: (a) Explicit expressions for the optimal (Bayes) rule and the minimal classification error probability in several relevant problems of supervised binary classification of mutually absolutely continuous Gaussian processes. The approach relies on some classical results in the theory of Reproducing Kernel Hilbert Spaces (RKHS). (b) An interpretation, in terms of mutual singularity, for the "near perfect classification" phenomenon described by Delaigle and Hall (2012). We show that the asymptotically optimal rule proposed by these authors can be identified with the sequence of optimal rules for an approximating sequence of classification problems in the absolutely continuous case. (c) A new model-based method for variable selection in binary classification problems, which arises in a very natural way from the explicit knowledge of the RN-derivatives and the underlying RKHS structure. Different classifiers might be used from the selected variables. In particular, the classical, linear finite-dimensional Fisher rule turns out to be consistent under some standard conditions on the underlying functional model

Modelling for Pest Risk Analysis: Spread and Economic Impacts

The introduction of invasive pests beyond their natural range is one of the main causes of the loss of biodiversity and leads to severe costs. Bioeconomic models that integrate biological invasion spread theory, economic impacts and invasion management would be of great help to increase the transparency of pest risk analysis (PRA) and provide for more effective and efficient management of invasive pests. In this thesis, bioeconomic models of management of invasive pests are developed. The models are applied to three cases of study. The main case looks at the invasion in Europe by the western corn rootworm (WCR), Diabrotica virgifera ssp. virgifera LeConte (Coleoptera: Chrysomelidae). A range of quantitative modelling approaches was employed: (i) dispersal kernels fitted to mark-release-recapture experimental data; (ii) optimal control models combined with info-gap theory; (iii) spatially explicit stochastic simulation models; and (iv) agent-based models. As a result of the application of the models new insights on the management of invasive pests and the links between spread and economic impacts were gained: (i) current official management measures to eradicate WCR were found to be ineffective; (ii) eradication and containment programmes that are economically optimal under no uncertainty were found out to be also the most robustly immune policy to unacceptable outcomes under severe uncertainty; (iii) PRA focusing on single invasive pests might lead to management alternatives that dot not correspond to the optimal economic allocation if the rest of the invasive pests sharing the same management budget are considered; (iv) the control of satellite colonies of an invasion occurring by stratified dispersal is ineffective when a strong propagule pressure is generated from the main body of the invasion and this effect is increased by the presence of human-assisted long-distance dispersal; and (v) agent-based models were shown to be an adequate tool to integrate biological invasion spread models with economic analysis models

Competitive intelligence systems as a basis for the effective R&D management in the plastics industry in Andalusia

The main purpose of present work is to inquire the range of implementation an effective use of Competitive Intelligence Systems in the andalusian plastics industry linked to the agrifood industry of the region. This research seeks the model generalization of how CI Systems asses the generation of the competitive advantage and how they become an essential tool of new products creation, as well as the insfruments of the productive processes planning and management in the industrial organization. Through the case study of 5 big andalusian plastics companies and currently in phase of extending the analysis to whole branch with the DELPHI method, the research intends to contribute to comprehend how the internal systems of Technology Watch and Competitive Intelligence impact directly (measured short-term and long- term) on degree of competitiveness and innovating potential of the industrial companies. These systems can become tools of internal knowledge generation and means of feedback to R&D management systems, being able to provide answers to new emergent consumption trends, new product demands and any advances in technologies of materials or manufacturing.Comunicación presentada dentro del Congreso “III International Forum on Management”. Celebrado en la Universidad de Évora de Portugal, los días 1 y 2 de febrero de 2019. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Spanish Identity: Nation, Myth, and History

In the last two centuries, conservatives and liberals have offered two mutually exclusive visions of Spanish history, each with distinct myths, symbols, and heroes. The conservative image, formed in the Middle Ages, was based on the myth of the Reconquest and the need to restore (or keep) the homogeneity of a country characterized by its Christian religion and Latin culture. At the beginning of the nineteenth century, faced with Napoleon’s invasion, Spanish liberals understood the danger of associating their modern ideas with France and invented a progressive and democratic Spanish tradition. According to their interpretation, the most authentic Spain was not the one identified with the Reconquest and the Empire, but the Spain of all those who had been excluded from the nation-building process because of their religion or ideas: the tolerant al-Andalus Muslims, the freedom-fighter comuneros and the defenders of the democratic medieval fueros. The great success of the transition to democracy and the Constitution of 1978 resided in the ability of all different tendencies and parties to overcome this division, to build bridges and create a common national project. For the first time in history, Spaniards managed to build a successful society based on consensus, pluralism and democracy. However, as a reality based on agreements, its nature is fragile. What is at stake now in Spain is to strengthen the viability of this model