The presentation will be based on a recent joint work with G. Carinci, C. Giberti and F. Redig.
DNA encodes multiple independent levels of functional information. For instance, one level encodes proteins and sequence targets for DNA-binding factors, another one is contained in the physical and structural properties of the DNA molecule itself, others are the signals that guide higher degrees of genome organization. In this sense DNA can be considered as a four-symbol language text, endowed with semantic meaning and a precise syntax. In order to crack these codes, lots of methods have been used, including the ones that derive from probability theory, specific entropy indicators, measurements of long- and short-range correlations and various signal-processing models.
In our talk we are going to deal with gene promoters, regulatory regions belonging to the vast noncoding portion of the genome, where the chemo-physical properties of the sequence of nucleotides are crucial to determine the double helix dynamics and, accordingly, the transmission of the genetic message. First, we are going to show our entropic analyses of base composition, periodicity and information content which point out the relation between specific motifs along the sequence and their role in determining regulatory functions. Then, we are going to present the results obtained by combining two spectral methods: one clustering algorithm, based on an alignment procedure, the other one based on a standard spectral analysis of the eigenmodes of the nonlinear chains representing promoters according to the Peyrard-Bishop DNA model. Through these methods, it is possible to recover the regular sequences that characterize different functional classes of promoters and to find out elements with important biological meanings.
Modi di vibrazione periodici con inviluppo localizzato nello spazio sono ben noti nell'ambito dei sistemi dinamici Hamiltoniani non lineari a molti corpi. Nelle ultime due decadi abbiamo assistito alla scoperta di molte interessanti e talvolta curiose proprietà di tali modi, detti breather discreti. Ma certo la cosa più stupefacente è che essi continuino a interessare studiosi in varie discipline senza che sia stata mai rinvenuta une traccia veramente convincente della loro rilevanza in fisica.
Nella mia relazione illustrerò una personalissima panoramica sulle proprietà più interessanti e curiose dei breather discreti, che hanno impegnato una buona parte della mia attività di ricerca per alcuni anni. Per finire, discuterò di certe evidenze sperimentali che rivelerebbero la presenza di breather discreti in cristalli fortemente anarmonici, con particolare riferimento a delle ulteriori recentissime misure dello stesso tipo effettuate in collaborazione con dei colleghi dell'ISC di Firenze.
Economic Complexity is a new line of research which portrays economic growth as an evolutive process of ecosystems of technologies and industrial capabilities. Complex systems analysis, simulation, systems science methods, and big data capabilities offer new opportunities to empirically map technology and capability ecosystems of countries and industrial sectors, analyse their structure, understand their dynamics and measure economic complexity. This approach provides a new perspective for data-driven fundamental economics in a strongly connected, globalised world.
In particular here we discuss how it is possible to assess the competitiveness of country and complexity of products starting from the archival data on export flows that is the COMTRADE dataset which provides the matrix of countries and their exported products. According to the standard economic theory the specialization of countries towards certain specific products should be optimal. The observed data show that this is not the case and that diversification is actually more important. Specialization may be the leading effect in a static situation but the strongly dynamic and globalized world market suggests instead that flexibility and adaptability are essential elements of competitiveness as in bio-systems.
The crucial challenge is therefore how these qualitative observations can be turned into quantitative variables. We have introduced a new metrics for the Fitness of countries and the Complexity of products which corresponds to the fixed point of the iteration of two nonlinear coupled equations. The nonlinearity is a key feature because it translates in mathematical terms the fact that the upper bound on the Complexity of a product must be mainly given by the less developed country able to produce it. The information provided by the new metrics can be used in several ways. As an example, the direct comparison of the Fitness with the country GDP per capita (Fitness-Income Plane) gives an assessment of the non-expressed potential of growth of a country. This can be used as a predictor of GDP evolution or stock index and sectors perfomances.
The global dynamic in the Fitness-Income Plane reveals, however, a large degree of heterogeneity which implies that countries can evolve with different level of predictability according to the specific zone of the Fitness-Income plane they belong to. This heterogeneous dynamics is often disregarded in usual economic analysis. When dealing with heterogeneous systems, in fact, the usual tools of linear regressions become inappropriate. Making reliable predictions of growth in the context of economic complexity will then require a paradigm shift in order to catch the information contained in the complex dynamic patterns observed.
These methods and concepts can give concrete contributions, as other possible applications, to risk analysis, investment opportunities analysis, policy-modelling of country growth and industrial planning.
After many years elapsed since the first experimental evidences of negative temperatures in quantum nuclear-spin systems, recent experiments have realized a negative temperature state in a system of ultracold bosons trapped in optical lattice, modeled by a Bose-Hubbard Hamiltonian.
I will discuss the statistical behavior of a semi-classical limit of the Bose-Hubbard model, namely the Discrete Nonlinear Schroedinger Equation. By monitoring the microcanonical temperature, it is possible to show that there exists a parameter region where the system evolves towards a state characterized by a finite density of spatially localized nonlinear excitations (discrete breathers) and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. I will also discuss possible mechanisms for the generation of negative-temperature states in experimental setups.