One-Step Recurrences for Stationary Random Fields on the Sphere

Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

A Cloud-Based Framework for Machine Learning Workloads and Applications

[EN] In this paper we propose a distributed architecture to provide machine learning practitioners with a set of tools and cloud services that cover the whole machine learning development cycle: ranging from the models creation, training, validation and testing to the models serving as a service, sharing and publication. In such respect, the DEEP-Hybrid-DataCloud framework allows transparent access to existing e-Infrastructures, effectively exploiting distributed resources for the most compute-intensive tasks coming from the machine learning development cycle. Moreover, it provides scientists with a set of Cloud-oriented services to make their models publicly available, by adopting a serverless architecture and a DevOps approach, allowing an easy share, publish and deploy of the developed models.This work was supported by the project DEEP-Hybrid-DataCloud ``Designing and Enabling E-infrastructures for intensive Processing in a Hybrid DataCloud'' that has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant 777435Lopez Garcia, A.; Marco De Lucas, J.; Antonacci, M.; Zu Castell, W.; David, M.; Hardt, M.; Lloret Iglesias, L.... (2020). A Cloud-Based Framework for Machine Learning Workloads and Applications. IEEE Access. 8:18681-18692. https://doi.org/10.1109/ACCESS.2020.2964386S1868118692

Evaluating the Impact of Nature-Based Solutions: A Handbook for Practitioners

The Handbook aims to provide decision-makers with a comprehensive NBS impact assessment framework, and a robust set of indicators and methodologies to assess impacts of nature-based solutions across 12 societal challenge areas: Climate Resilience; Water Management; Natural and Climate Hazards; Green Space Management; Biodiversity; Air Quality; Place Regeneration; Knowledge and Social Capacity Building for Sustainable Urban Transformation; Participatory Planning and Governance; Social Justice and Social Cohesion; Health and Well-being; New Economic Opportunities and Green Jobs. Indicators have been developed collaboratively by representatives of 17 individual EU-funded NBS projects and collaborating institutions such as the EEA and JRC, as part of the European Taskforce for NBS Impact Assessment, with the four-fold objective of: serving as a reference for relevant EU policies and activities; orient urban practitioners in developing robust impact evaluation frameworks for nature-based solutions at different scales; expand upon the pioneering work of the EKLIPSE framework by providing a comprehensive set of indicators and methodologies; and build the European evidence base regarding NBS impacts. They reflect the state of the art in current scientific research on impacts of nature-based solutions and valid and standardized methods of assessment, as well as the state of play in urban implementation of evaluation frameworks

Complex systems: Chances and risks for experimental data analysis.

Die Beiträge eines internationalen Symposiums greifen den Konflikt auf, unterschiedliche ökophysiologische Anforderungen an Pflanzen im Prozessgeschehen der Ressourcenallokation auszubalancieren. Der Schwerpunkt liegt dabei auf dem Trade-off zwischen Wachstum und Stressabwehr mit jeweiligen Kosten-/Nutzen-Bewertungen. Wachstum stellt die Voraussetzung dar, um kompetitive Ressourcenakquirierung sicherzustellen, und Abwehr die Voraussetzung, um die Ressourcen nach Inkorporation für die Pflanze zu erhalten. Diese integrierte Betrachtungsweise erfordert in der Erkenntnis des intensiven Ressourcenaustausches der Pflanze mit ihrer abiotischen und biotischen Umwelt eine räumlich-zeitliche Prozessskalierung. Dies wird hinsichtlich des mechanistischen und zugleich ökologisch relevanten Klärungspotenzials geprüft. Die Analyse der Prozessvernetzung zwischen funktionalen und strukturellen pflanzen- und ökosysteminhärenten biologischen Organisationsebenen (Skalen) wird dabei als Voraussetzung für räumlich-zeitliche Musteraufdeckung im Allokationsgeschehen identifiziert. Die Beiträge erreichen so eine neue Qualität eines umfassenden, prozessbasiert integrierenden Verständnisses von „Systembiologie“

Interpolation with reflection invariant positive definite functions.

Concepts of abstract harmonic analysis can be used to provide a unifying framework for basis function methods, like radial basis functions in Euclidean spaces or zonal basis functions on the sphere. To illustrate how these concepts can be applied reflection invariant functions are considered. A specialization of the Bochner-Godement Theorem leads to a characterization of suitable basis functions