Alessandro Giuliani

Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification

Abstract The demonstrated ability of recurrence quantification analysis to detect very subtle patterns in time series was exploited to devise a filter able to recognize and extract signals buried in large amounts of noise. The proposed technique, cross-recurrence quantification, demonstrates the ability to extract signals up to a very low signal-to-noise-ratio and to allow an immediate appreciation of their degree of periodicity. The lack of any stationarity dependence of the proposed method opens the way to many possible applications, including encryption.

Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals

Abstract Recurrence plots were introduced to aid in the detection of signals in complicated data series. This effort was taken a step further by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation of the presence of deterministic signals in relatively short data lengths.

The Ground State Energy of the Weakly Interacting Bose Gas at High Density

We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.

Ising models with long-range antiferromagnetic and short-range ferromagnetic interactions

We study the ground state of a

The Two-Dimensional Hubbard Model on the Honeycomb Lattice

d

Striped phases in two-dimensional dipole systems

-dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The long-range interaction is equal to

Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

{r}^{\ensuremath{-}p}

Fractional Lindstedt series

,

Absolute Stability Limit for Relativistic Charged Spheres

pgd

Absence of interaction corrections in the optical conductivity of graphene

, while the FM interaction has strength