Stochastic Weighted Fractal Networks

In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both classes can be completely analytically characterized in terms of the involved parameters. The proposed algorithms improve and extend the framework of weighted fractal networks recently proposed in (T. Carletti & S. Righi, in press Physica A, 2010

Uniqueness of limit cycles for a class of planar vector fields

In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.Comment: 8 pages, 2 figure

The 1/2--Complex Bruno function and the Yoccoz function. A numerical study of the Marmi--Moussa--Yoccoz Conjecture

We study the 1/2--Complex Bruno function and we produce an algorithm to evaluate it numerically, giving a characterization of the monoid $\hat{\mathcal{M}}=\mathcal{M}_T\cup \mathcal{M}_S$. We use this algorithm to test the Marmi--Moussa--Yoccoz Conjecture about the H\"older continuity of the function $z\mapsto -i\mathbf{B}(z)+ \log U(e^{2\pi i z})$ on $\{z\in \mathbb{C}: \Im z \geq 0 \}$, where $\mathbf{B}$ is the 1/2--complex Bruno function and $U$ is the Yoccoz function. We give a positive answer to an explicit question of S. Marmi et al [MMY2001].Comment: 21 pages, 11 figures, 2 table

The Lagrange inversion formula on non-Archimedean fields. Non-Analytical Form of Differential and Finite Difference Equations

The classical Lagrange inversion formula is extended to analytic and non--analytic inversion problems on non--Archimedean fields. We give some applications to the field of formal Laurent series in $n$ variables, where the non--analytic inversion formula gives explicit formal solutions of general semilinear differential and $q$--difference equations. We will be interested in linearization problems for germs of diffeomorphisms (Siegel center problem) and vector fields. In addition to analytic results, we give sufficient condition for the linearization to belong to some Classes of ultradifferentiable germs, closed under composition and derivation, including Gevrey Classes. We prove that Bruno's condition is sufficient for the linearization to belong to the same Class of the germ, whereas new conditions weaker than Bruno's one are introduced if one allows the linearization to be less regular than the germ. This generalizes to dimension $n> 1$ some results of [CarlettiMarmi]. Our formulation of the Lagrange inversion formula by mean of trees, allows us to point out the strong similarities existing between the two linearization problems, formulated (essentially) with the same functional equation. For analytic vector fields of \C^2 we prove a quantitative estimate of a previous qualitative result of [MatteiMoussu] and we compare it with a result of [YoccozPerezMarco].Comment: This is the final version in press on DCDS Series A. Some minor changes have been made, in particular the relation w.r.t. the results of Perez Marco and Yocco

Exponentially long time stability near an equilibrium point for non--linearizable analytic vector fields

We study the orbit behavior of a germ of an analytic vector field of $(C^n,0)$, $n \geq 2$. We prove that if its linear part is semisimple, non--resonant and verifies a Bruno--like condition, then the origin is effectively stable: stable for finite but exponentially long times

Topological resilience in non-normal networked systems

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species

Driving forces in researchers mobility

Starting from the dataset of the publication corpus of the APS during the period 1955-2009, we reconstruct the individual researchers trajectories, namely the list of the consecutive affiliations for each scholar. Crossing this information with different geographic datasets we embed these trajectories in a spatial framework. Using methods from network theory and complex systems analysis we characterise these patterns in terms of topological network properties and we analyse the dependence of an academic path across different dimensions: the distance between two subsequent positions, the relative importance of the institutions (in terms of number of publications) and some socio-cultural traits. We show that distance is not always a good predictor for the next affiliation while other factors like "the previous steps" of the career of the researchers (in particular the first position) or the linguistic and historical similarity between two countries can have an important impact. Finally we show that the dataset exhibit a memory effect, hence the fate of a career strongly depends from the first two affiliations

Topological resilience in non-normal networked systems

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species