Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been realized in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous MI spectra recorded under quasi continuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation

Uncertainty, Fiscal, and Financial Shocks in a Nonlinear World: Empirical Investigations

Questa tesi studia gli effetti macroeconomici degli shock di incertezza, shock fiscali e shock finanziari sul ciclo economico USA. La tesi si divide in quattro capitoli indipendenti, ognuno dei quali utilizza sistemi vettoriali autoregressivi, lineari e non-lineari, e local projections, al fine di estendere la ricerca empirica e valutare l\u2019importanza dei diversi canali di trasmissione degli shock, cos\uec come proposti da modelli teorici. I risultati ottenuti dimostrano come tali shock hanno effetti non-lineari lungo il ciclo economico, e cio\ue8 la reazione delle variabili macroeconomiche \ue8 statisticamente differente se lo shock avviene durante una recessione piuttosto che durante un\u2019espansione. Dalla prospettiva teorica, questi risultati sottolineano l\u2019importanza di sviluppare modelli teorici non-lineari. Dalla prospettiva di politica economica, i risultati favoriscono l\u2019implementazione di politiche asimmetriche come risposta a instabilit\ue0 a livello macroeconomico.This thesis investigates the macroeconomic effects of uncertainty, fiscal and financial shocks on the US economy. It is set out in four self-contained chapters, which use linear and nonlinear (Smooth Transition) Vector Autoregressive models, and Local Projections techniques, to extend the literature, and evaluate the importance of different transmission channels of macroeconomic shocks suggested by theoretical models. The main results show that these shocks have nonlinear effects over the business cycle, i.e., the response of macro aggregates following the shocks are statistically different depending on whether the economy is in a recession or expansion. From a theoretical perspective, this finding highlights the importance of accounting for nonlinearities when developing macroeconomic models. From a policy perspective, the results suggest the implementation of nonlinear policy rules to properly deal with macroeconomic instability

Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis

Estimating Fiscal Multipliers: News From A Non-linear World

We estimate non-linear VARs to assess to what extent fiscal spending multipliers are countercyclical in the US. We deal with the issue of non-fundamentalness due to fiscal foresight by appealing to sums of revisions of expectations of fiscal expenditures. This measure of anticipated fiscal shocks is shown to carry valuable information about future dynamics of public spending. Results based on generalised impulse responses suggest that fiscal spending multipliers in recessions are greater than one, but not statistically larger than those in expansions. However, non-linearities arise when focusing on 'extreme' events, that is, deep recessions versus strong expansionary periods

Language re-discovered: A death education intervention in the net between kindergarten, family and territory

The article presents the positive results of a death education experience, realized owing to a collaboration between school, family and territory. The project, with the scope of reflecting on topics of death and spirituality, included 46 children of 5 from kindergarten and 50 parents, and then mobilizing the entire community. Social services and public administration had a special role in this, aiming to guarantee the necessary support for the families in the existential reflections. The experience was monitored with participatory observation, via interviews and questionnaires. The children answered questions regarding death and spirituality during an open and sincere conversation with the teachers. The parents, who at home talked about certain pre-defined teams with the children, were asked to give their informed consent and were given a questionnaire with open questions ex-ante/ ex-post. All data were processed via qualitative analysis of the texts. The results are truly positive, showing that children are capable of facing the problem of death and are able to acquire a certain representation of the spiritual dimension. The parents, who in the beginning demonstrated some anxiety, eventually were greatly satisfied and expressed their willingness to continue to search for the connection between death and transcendence

Home range dynamics of mountain hares (Lepus timidus) in the Swiss Alps.

Little is known on the ecology and behaviour of the alpine mountain hare (Lepus timidus). Between 1996 and 1997, we analysed by radiotracking the pattern of space use of 8 mountain hares from the Swiss Alps. We estimated home range size using both the kernel density estimator and the minimum convex polygon. We found smaller ranges (38 ha) compared to those reported for the species in boreal or arctic habitats, but similar to ranges in Scotland. Hares did not use a centre of major activity (core area) and showed high home range overlap, confirming their non-territorial behaviour. Smaller ranges were used during winter compared to the other seasons, whilst no difference in size was found between sexes