On the properties of level spacings for decomposable systems

In this paper we show that the quantum theory of chaos, based on the statistical theory of energy spectra, presents inconsistencies difficult to overcome. In classical mechanics a system described by an hamiltonian $H = H_1 + H_2$ (decomposable) cannot be ergodic, because there are always two dependent integrals of motion besides the constant of energy. In quantum mechanics we prove the existence of decomposable systems \linebreak $H^q = H^q_1 + H^q_2$ whose spacing distribution agrees with the Wigner law and we show that in general the spacing distribution of $H^q$ is not the Poisson law, even if it has often the same qualitative behaviour. We have found that the spacings of $H^q$ are among the solutions of a well defined class of homogeneous linear systems. We have obtained an explicit formula for the bases of the kernels of these systems, and a chain of inequalities which the coefficients of a generic linear combination of the basis vectors must satisfy so that the elements of a particular solution will be all positive, i.e. can be considered a set of spacings.Comment: LateX, 13 page

Non-linear Quantization of Integrable Classical Systems

It is demonstrated that the so-called "unavoidable quantum anomalies" can be avoided in the farmework of a special non-linear quantization scheme. A simple example is discussed in detail.Comment: LaTeX, 14 p

E7 groups from octonionic magic square

In this paper we continue our program, started in [2], of building up explicit generalized Euler angle parameterizations for all exceptional compact Lie groups. Here we solve the problem for E7, by first providing explicit matrix realizations of the Tits construction of a Magic Square product between the exceptional octonionic algebra J and the quaternionic algebra H, both in the adjoint and the 56 dimensional representations. Then, we provide the Euler parametrization of E7 starting from its maximal subgroup U=(E6 x U(1))/Z3. Next, we give the constructions for all the other maximal compact subgroups.Comment: 23 pages, added sections with new construction

Mapping the geometry of the F4 group

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.Comment: 50 pages; some typos correcte

Mapping the geometry of the E6 group

In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6, which we realize as the the sum of f4, the derivations of the exceptional Jordan algebra J3 of dimension 3 with octonionic entries, and the right multiplication by the elements of J3 with vanishing trace. Our parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F4. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E6 group manifold.Comment: 30 page

Flow network indices signal a directional change in ecosystems: Evidence from a small mountain lake (Lake Santo, northern Italy)

Empirical evidence of the theoretically expected trends of ecosystem development is scarce so far. In this research, we used long-term empirical data about the plankton community of a small mountain lake (Lake Santo, northern Apennines, Italy) to reconstruct its developmental trajectory during a period comprised between early 1970 s and 2010 s. We exploited these data to build yearly ecological networks and from their configuration of energy flows we computed network information indices. The trends of these indices enlighten about the developmental trajectory of this ecosystem during the period covered by the data set. In particular, they indicate that Lake Santo evolved in the direction of increasing stability at the expense of efficiency in energy transfer. We compared these results with current hypotheses about the directionality of ecosystem development, which are rooted in ecosystem theory, and discussed the possibility that, counter to some theoretical models of ecosystem development, Lake Santo followed an unimpeded direction of development rather than a trajectory typical of an ecosystem under stress. Finally, the long-term trends of flow network indices provided insights about the health status of the ecosystem

Understanding Social–Ecological Systems using Loop Analysis

The sustainable management of social–ecological systems (SESs) requires that we understand the complex structure of relationships and feedbacks among ecosystem components and socioeconomic entities. Therefore, the construction and analysis of models integrating ecological and human actors is crucial for describing the functioning of SESs, and qualitative modeling represents an ideal tool since it allows studying dependencies among variables of diverse types. In particular, the qualitative technique of loop analysis yields predictions about how a system’s variables respond to stress factors. Different interaction types, scarce information about functional relationships among variables, and uncertainties in the values of the parameters are the rule rather than exceptions when studying SESs. Accordingly, loop analysis seems to be perfectly suitable to investigate them. Here, we introduce the key aspects of loop analysis, discuss its applications to SESs, and suggest it enables making the first steps toward the integration of the three dimensions of sustainability

Euler angles for G2

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.Comment: 21 pages, 2 figures, some misprints correcte

The Open Data Kit suite, Mobile Data Collection technology as an opportunity for forest mensuration practices

This paper examines the potential for using Mobile Data Collection (MDC) as an effective database supported technology to substantially improve forest mensuration practices. Open source Open Data Kit (ODK) procedures and tools were used during a survey campaign that initiated a local forest monitoring process in the Marganai forest (Sardinia). The ODK suite is practical to use and its procedures allow authoring and use of digital survey forms without users needing software development expertise. Form design enables a high degree of customization to be achieved by means of specifying a wide range of data flow control mechanisms. ODK has proved to be a valid tool for data coherence and completeness improvements. As forestry’s contribution to regional Gross Domestic Product has dramatically decreased, forest mensuration practices have been reduced. Meeting the increased need to monitor environmental assets such as forests requires these practices to be re-evaluated. If regional public institutions took an active part in the process of enhancing forest mensuration, by contributing with open database systems acting as repositories and knowledge engines, support for MDC tools like ODK would potentially be a great opportunity to disseminate the use of the system and boost its development