Estimating hyperbolicity of chaotic bidimensional maps

We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so called covariant Lyapunov vectors (CLV) and corresponding to the Lyapunov spectrum. These subspaces are the analog of linearized invariant manifolds for non-periodic points, so the angles between them can be used to quantify the degree of hyperbolicity of generic orbits; however, being such splitting non invariant under smooth transformations of phase space, it is interesting to investigate the properties of transversality when coordinates change, e.g. to study it in distinct dynamical systems. To illustrate this issue on the Chirikov-Taylor standard map we compare the probability densities of transversality for two different coordinate systems; these are connected by a linear transformation that deforms splitting angles through phase space, changing also the probability density of almost-zero angles although complete tangencies are in fact invariant. This is completely due to the PDF transformation law and strongly suggests that any statistical inference from such distributions must be generally taken with care.Comment: 14 pages, 23 figures (This paper is for the IJBC Special Issue edited by Prof. Gregoire Nicolis, Prof. Marko Robnik, Dr. Vassilis Rothos and Dr. Haris Skokos

Correlation decay and large deviations for mixed systems

We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.Comment: 6 pages, 2 figures, submitted to publicatio

Flow-induced torsion.

missin

Flow-induced torsion.

missin

Nuova stazione di Utricularia sp. (Lentibulariaceae) per il Modenese

The presence of Utricularia sp. was observed in a pond during a survey in some small water bodies in the Modena Apennines (Italy). This ecosystem was sampled and observed in order to apply the IBEM index, which allows judging the quality of these habitats on the basis of their biodiversity. A specific taxonomic determination was not possible because of the lack of the flower on the individuals; nevertheless, some features led to U. australis. However, it was decided to report the new finding since all species of the genus Utricularia have become quite rare in Italy

Extensive numerical investigations on the ergodic properties of two coupled Pomeau-Manneville maps

We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but with strong deviations from the single intermittent map: Such differences are characterized by numerical experiments with densities which {\it do not} have singularities in the marginal fixed point, escape and Poincar\'e recurrence time statistics that share a power-law decay exponent modified by a clear {\it dimensional} scaling, while the rate of phase-space filling and the convergence of ensembles of Lyapunov exponents show a {\it stretched} instead of pure exponential behaviour. In spite of the lack of rigorous results about this system, the dependence on both the intermittency and the coupling parameters appears to be smooth, paving the way for further analytical development. We remark that dynamical exponents appear to be independent of the (nonzero) coupling strength.Comment: 9 pages, 7 figure

Invasive alien species of European Union concern: the use of a faunistic database for the knowledge and future management at a local scale

A research group of the Department of Life Sciences, University of Modena and Reggio Emilia, with the contribution of the Province of Modena and the Emilia-Romagna Region, implemented a faunistic database named Darwin. The database gathers information chiefly on the vertebrate fauna of the province of Modena (Northern Italy). To date, over 20,000 historical and recent records have been collected, regarding 535 vertebrate species and 7 invertebrates (Bivalvia and Crustacea) of high managing interest. Darwin allows to register the modification of the local fauna, with regards to the most problematic taxa and especially to the allochthonous species, which are mainly organisms living in the lowlands that became invasive at different levels. Some of these assumed the role of key species in a variety of ecosystems (e.g., Pseudorasbora parva), some threaten certain autochthonous species already at risk (e.g., Trachemys scripta and Procambarus clarkii), others give rise to economic issues (e.g., Myocastor coypus), whilst the remaining ones have progressively lost their invasivity, becoming rare or sporadic (e.g., Ameiurus melas and Lepomis gibbosus). The database represents a strongly effective tool for the basic knowledge functional to the actions deriving from the European Regulation 2014/1143, regarding the recent “List of invasive alien species of Union concern” (EU 2016/1141). Overall, Darwin collects information on the local distribution of 32 invasive allochthonous species, 7 of which of Union concern, namely: Lithobates catesbeianus, Myocastor coypus, Procambarus clarkii, Pseudorasbora parva, Trachemys scripta, Threskiornis aethiopicus, and Oxyura jamaicensis. The first four species are established within the province, while T. scripta is diffused but not definitively confirmed as breeding, T. aethiopicus is present but not breeding, and O. jamaicensis is observed only occasionally. Thanks to the database the autochthonous species of EU interest comprised in the national IUCN Red list and their competitors could be brought into focus. For instance, we revealed the presence of merely 8 local populations of Emys orbicularis, threatened by the wide distribution of T. scripta, which is reported from over 20 sites within Modena’s territory. Furthermore, we found Austropotamobius pallipes at 122 mid-elevation sites (100-1100 m a.s.l.), whilst its direct competitor P. clarkii, currently expanding to the foothills, was recorded from 101 locations from 10 to 100 m a.s.l. These preliminary results highlight the necessity of control plans towards the two alien species, which could be developed on the basis of the already available distribution patterns. Our research group aims at the constant implementation of the database by adding information from ongoing and forthcoming studies on species of major interest. The existing data, presently used in various control plans, will pave the way to more specific investigations on the invasive alien fauna and increase the effectiveness of future managing actions

Discovering Evolving Temporal Information: Theory and Application to Clinical Databases

Functional dependencies (FDs) allow us to represent database constraints, corresponding to requirements as \u201cpatients having the same symptoms undergo the same medical tests.\u201d Some research eforts have focused on extending such dependencies to consider also temporal constraints such as \u201cpatients having the same symptoms undergo in the next period the same medical tests.\u201d Temporal functional dependencies are able to represent such kind of temporal constraints in relational databases. Another extension for FDs allows one to represent approximate functional dependencies (AFDs), as \u201cpatients with the same symptoms generally undergo the same medical tests.\u201d It enables data to deviate from the defned constraints according to a user-defned percentage. Approximate temporal functional dependencies (ATFDs) merge the concepts of temporal functional dependency and of approximate functional dependency. Among the diferent kinds of ATFD, the Approximate Pure Temporally Evolving Functional Dependencies (APE-FDs for short) allow one to detect patterns on the evolution of data in the database and to discover dependencies as \u201cFor most patients with the same initial diagnosis, the same medical test is prescribed after the occurrence of same symptom.\u201d Mining ATFDs from large databases may be computationally expensive. In this paper, we focus on APE-FDs and prove that, unfortunately, verifying a single APE-FD over a given database instance is in general NP-complete. In order to cope with this problem, we propose a framework for mining complex APE-FDs in real-world data collections. In the framework, we designed and applied sound and advanced model-checking techniques. To prove the feasibility of our proposal, we used real-world databases from two medical domains (namely, psychiatry and pharmacovigilance) and tested the running prototype we developed on such databases