Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.Comment: To appear in Journal of Statistical Physic

Knowledge transmission patterns at the border: ethnobotany of Hutsuls living in the Carpathian Mountains of Bukovina (SW Ukraine and NE Romania)

Background Cross-border research is a novel and important tool for detecting variability of ecological knowledge. This is especially evident in regions recently divided and annexed to different political regimes. Therefore, we conducted a study among Hutsuls, a cultural and linguistic minority group living in Northern and Southern Bukovina (Ukraine and Romania, respectively). Indeed, in the 1940s, a border was created: Northern Bukovina was annexed by the USSR while Southern Bukovina remained part of the Kingdom of Romania. In this research, we aim to document uses of plants for food and medicinal preparations, discussing the different dynamics of Local Ecological Knowledge (LEK) transmission among Hutsuls living in Ukraine and Romania. Methods Field research was conducted using convenience and snowball sampling techniques to recruit 31 Hutsuls in Ukraine and 30 in Romania for participation in semi-structured interviews regarding the use of plants for medicinal and food preparation purposes and the sources of such knowledge. Results The interviews revealed that, despite a common cultural and linguistic background, ethnobotanical knowledge transmission occurs in different ways on each side of the border. Family is a primary source of ethnobotanical knowledge transmission on both sides of the border; however, in Romania, knowledge from other sources is very limited, whereas in Ukraine interviewees reported several other sources including books, magazines, newspapers, the Internet and television. This is especially evident when analysing the wild plants used for medicinal purposes as we found 53 taxa that were common to both, 47 used only in Ukraine and 11 used only in Romania. While Romanian Hutsuls used almost exclusively locally available plants, Ukrainian Hutsuls often reported novel plants such as Aloe vera, Aronia melanocarpa and Elaeagnus rhamnoides. Knowledge related to these plants was transferred by sources of knowledge other than oral transmission among members of the same family. Therefore, this may imply hybridization of the local body of knowledge with foreign elements originating in the Soviet context which has enriched the corpus of ethnobotanical knowledge held by Ukrainian Hutsuls. Conclusions While ethnobotanical knowledge among Romanian Hutsuls is mainly traditional and vertically transmitted, among Ukrainian Hutsuls there is a considerable proportion of LEK that is transmitted from other (written and visual) sources of knowledge. This cross-border research reveals that despite a common cultural background, socio-political scenarios have impacted Hutsul ethnobotanical knowledge and its transmission patterns

Non-uniformly hyperbolic endomorphisms

We show the existence of large $\mathcal C^1$ open sets of area preserving endomorphisms of the two-torus which have no dominated splitting and are non-uniformly hyperbolic, meaning that Lebesgue almost every point has a positive and a negative Lyapunov exponent. The integrated Lyapunov exponents vary continuously with the dynamics in the $\mathcal C^1$ topology and can be taken as far away from zero as desired. Explicit real analytic examples are obtained by deforming linear endomorphisms, including expanding ones. The technique works in nearly every homotopy class and the examples are stably ergodic (in fact Bernoulli), provided that the linear map has no eigenvalue of modulus one.Comment: Some typos corrected, 1 figure added (Section 3.5). The abstract was re-written for clarit

GUIDANCE REPORT. Teaching integrated planning and design for coastal landscapes in Europe by exploring digital dimensions of transnational collaboration in higher education

This guidance report aims at supporting teachers and other interested parties in developing and innovating programmes for integrated spatial planning. The focus is on coastal landscapes, but the methods and techniques are also applicable to other subject areas. This report has been developed within the framework of the CO-LAND Erasmus+ Strategic Partnership. The CO-LAND Toolbox, added as an online supplement, is intended to enhance the use of e-learning and to support the practical implementation of an online course. It compares different platforms and instruments, provides online tools, links, video clips etc. and is freely available as open access at the CO-LAND wiki. This report divides into three major parts; the why, the what and the how of the CO-LAND project Part A describes the innovative teaching approach and methodology applied and further developed during the project. Chapter 2 contains the six dimensions of curriculum innovation, such as bridging the scales of planning, integrating academic disciplines, and including community and stakeholder perspectives. Chapter 3 highlights the underlying theories and teaching methods for integrated planning and design; the concept of landscape, educational constructivism, competences for sustainable development, the integrated planning and design framework and the principles of blended learning. Part B explains the relevance of coastal areas for current global developments related to the UN Sustainable Development Goals (Chapter 4) and their suitability as a study and research issue for planning and design disciplines, illustrated by the examples of the Sand Motor and the BlueHealth project (Chapter 5). Moreover, it shows the subject-specific, methodical, (inter)personal and generic competences and learning outcomes that form the basis of the curriculum. It presents the topics, exercises and references to the main lectures of the online course. It concludes with the outline of the integrated CO-LAND Case Study Assignment that students carry out through all phases of the online course (Chapter 6). Part C focuses on the implementation and dissemination process. Showing the practical steps based on the CO-LAND experiences, it describes how to set-up a blended learning project, presenting the elements of the online area and modes of student participation and the assessment strategy (Chapter 7). Chapter 8 presents the organisation of on-site workshops, with the selection of stakeholders, a preparatory visit, and schedule of the intensive programme. The fourth workshop presents a blended form that was able to deal with the challenges of the COVID-19 pandemic. The process of monitoring and evaluation for quality management is explained in a process chart and an overview of the quality objectives and indicators. Examples of the results of the survey of students give an impression of the outcomes (Chapter 9). Chapter 10 presents the dissemination of the project: the objectives, target groups, methodology and actions for communication and sharing the results. An online multiplier event forms part of it. The report concludes with the findings of the project and summarises recommendations for university teaching. The main recommendations are to improve the interactive learning platforms to allow for increased possibilities of participatory or collaborative design and more frequent iterative feedback to learners. In addition, one should be prepared to organise Intensive Student Programmes and workshops in a way that a blended form of on-site and online work can create a productive learning and working environment