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On the -Lemma and Bott-Chern cohomology
No full textOn a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the ∂∂− -Lemma
Controlling the nonlinear intracavity dynamics of large He-Ne laser gyroscopes
No full textA model based on Lamb's theory of gas lasers is applied to a He-Ne ring laser
gyroscope in order to estimate and remove the laser dynamics contribution from
the rotation measurements. The intensities of the counter-propagating laser
beams exiting one cavity mirror are continuously observed together with a
monitor of the laser population inversion. These observables, once properly
calibrated with a dedicated procedure, allow us to estimate cold cavity and
active medium parameters driving the main part of the nonlinearities of the
system. The parameters identification and noise subtraction procedure has been
verified by means of a Monte Carlo study of the system, and experimentally
tested on the G-Pisa ring laser oriented with the normal to the ring plane
almost parallel to the Earth rotation axis. In this configuration the Earth
rotation-rate provides the maximum Sagnac effect while the contribution of the
orientation error is reduced at minimum. After the subtraction of laser
dynamics by a Kalman filter, the relative systematic errors of G-PISA reduce
from 50 to 5 part in 10^3 and can be attributed to the residual uncertainties
on geometrical scale factor and orientation of the ring
Un laboratoire pour les pratiques plébiscitaires contemporaines: les libres votes constitutionnels et les «appels au silence» dans l’Italie révolutionnaire et napoléonienne (1797-1805)
Full text linkEntre la fin du XVIIIe siècle et le début du XIXe siècle, la péninsule italienne est un laboratoire des pratiques plébiscitaires modernes en parallèle avec la France. Partant de l’analyse des «libres votes» constitutionnels qui ont lieu dans les républiques sœurs italiennes et des appels au peuple qui se tiennent à Gênes et Lucques en 1805, cette contribution focalise l’attention sur trois points. D’abord, le rôle pivot de la figure de Bonaparte constituant et père des nouvelles patries par lui-même inventées dans les discourses ainsi que dans les pratiques de vote en 1797. En second lieu, la symmétrie entre l’impératif de l’elargissement, le plus grand possible, du corps électoral (qui dessine une «citoyenneté exceptionnelle de ratification») et la raréfation progressive de l’espace déliberatif qui caractérise les libres votes constitutionnels de 1797-98 tout en gardant le suffrage en assemblée. Enfin, la médiatisation et la correction des résultats électoraux en 1797-98 jusqu’à l’introduction officielle en 1805 du principe du «silence assentiment».
SUMMARY Between the late eighteenth century and early nineteenth century , the Italian peninsula is a laboratory of modern plebiscitary practices in parallel with France. Based on the analysis of "free votes " constitutional taking place in the Italian republi
Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
No full textWe investigate the dependence of four-dimensional SU(N) gauge theories on the
topological theta term at finite temperature and, in particular, across the
deconfinement transition. For this purpose, we exploit the lattice formulation
of the theory and present numerical results for the expansion of the free
energy up to O(theta^6), for N=3 and N=6.
Our numerical analysis shows that the theta dependence of 4D SU(N) gauge
theory experiences a drastic change across the deconfinement transition: the
low-temperature phase is characterized by a large-N scaling with theta/N as
relevant variable, while in the high-temperature phase the scaling variable is
just theta and the free energy is essentially determined by the instanton-gas
approximation. The crossover between the two different behaviours gets sharper
with increasing N, suggesting that the instanton-gas regime sets in just above
Tc at large N
Critical parameters from trap-size scaling in trapped particle systems
No full textWe investigate the critical behavior of trapped particle systems at the
low-temperature superfluid transition. In particular, we consider the
three-dimensional Bose-Hubbard model in the presence of a trapping harmonic
potential coupled with the particle density, which is a realistic model of cold
bosonic atoms in optical lattices. We present a numerical study based on
quantum Monte Carlo simulations, analyzed in the framework of the trap-size
scaling (TSS).
We show how the critical parameters can be derived from the trap-size
dependences of appropriate observables, matching them with TSS. This provides a
systematic scheme which is supposed to exactly converge to the critical
parameters of the transition in the large trap-size limit. Our numerical
analysis may provide a guide for experimental investigations of trapped systems
at finite-temperature and quantum transitions, showing how critical parameters
may be determined by looking at the scaling of the critical modes with respect
to the trap size, i.e. by matching the trap-size dependence of the experimental
data with the expected TSS Ansatz
Delay-Constrained Shortest Paths: Approximation Algorithms and Second-Order Cone Models
No full textReal-time traffic with stringent Quality of Service requirements is becoming more and more prevalent in contemporary telecommunication networks. When maximum packet delay has to be considered, optimal delay-constrained routing requires not only choosing a path, but also reserving resources (transmission capacity) along its arcs, as the delay is a nonlinear function of both kinds of components. So far only simple versions of the problem have been considered in the literature where all arcs are reserved the same capacity (this is referred to as ERA, i.e., Equal Rate Allocations) and have the same capacity reservation cost, because in such a restricted case polynomial time exact algorithms can be devised, whereas the general problem is \Mcnp-hard. We first extend the polynomial-time approaches for the ERA version of the problem with unit arc costs by deriving a pseudo-polynomial time algorithm for the integer arc costs case and a FPTAS for the general arc costs case. We then show that, under the main latency models proposed in the literature, the general problem can be formulated as a mixed-integer Second-Order Cone (SOCP) program, and therefore solved with off-the-shelf technology. We compare two formulations: one based on standard big-M constraints, and an improved one where Perspective Reformulation techniques are used to tighten the continuous relaxation. Extensive computational experiments on both real-world networks and randomly-generated realistic ones show that the ERA approach is extremely fast and provides a surprisingly effective heuristic for the general problem whenever it manages to find a solution at all, but it fails for a significant fraction of the instances that the SOCP models can solve. We therefore propose a three-pronged approach that combines the fast running time of the ERA algorithm and the effectiveness of the SOCP models, and show that the combined approach is capable of solving realistic-sized instances at different levels of network load in a time compatible with real-time usage in an operating environment
D-gap functions and descent techniques for solving quilibrium problems
No full textA new algorithm for solving equilibrium problems with differentiable bifunctions is provided. The algorithm is based on descent directions of a suitable family of D-gap functions. Its convergence is proved under assumptions which do not guarantee the equivalence between the stationary points of the D-gap functions and the solutions of the equilibrium problem. Moreover, the algorithm does not require to set parameters according to thresholds which depend on regularity properties of the equilibrium bifunction. Finally, the results of preliminary numerical tests on Nash equilibrium problems with quadratic payoffs are reported
Rydberg tomography of an ultra-cold atomic cloud
No full textOne of the most striking features of the strong interactions between Rydberg
atoms is the dipole blockade effect, which allows only a single excitation to
the Rydberg state within the volume of the blockade sphere. Here we present a
method that spatially visualizes this phenomenon in an inhomogeneous gas of
ultra-cold rubidium atoms. In our experiment we scan the position of one of the
excitation lasers across the cold cloud and determine the number of Rydberg
excitations detected as a function of position. Comparing this distribution to
the one obtained for the number of ions created by a two-photon ionization
process via the intermediate 5P level, we demonstrate that the blockade effect
modifies the width of the Rydberg excitation profile. Furthermore, we study the
dynamics of the Rydberg excitation and find that the timescale for the
excitation depends on the atomic density at the beam position
Equilibrium and nonequilibrium entanglement properties of 2D and 3D Fermi gases
No full textWe investigate the entanglement properties of the equilibrium and
nonequilibrium quantum dynamics of 2D and 3D Fermi gases, by computing
entanglement entropies of extended space regions, which generally show
multiplicative logarithmic corrections to the leading power-law behaviors,
corresponding to the logarithmic corrections to the area law.
We consider 2D and 3D Fermi gases of N particles constrained within a limited
space region, for example by a hard-wall trap, at equilibrium at T=0, i.e. in
their ground state, and compute the first few terms of the asymptotic large-N
behaviors of entanglement entropies and particle fluctuations of subsystems
with some convenient geometries, which allow us to significantly extend their
computation. Then, we consider their nonequilibrium dynamics after
instantaneously dropping the hard-wall trap, which allows the gas to expand
freely. We compute the time dependence of the von Neumann entanglement entropy
of space regions around the original trap. We show that at small time it is
characterized by the relation with the particle variance,
and multiplicative logarithmic corrections to the leading power law, i.e.
Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
No full textWe investigate the dependence of four-dimensional SU(N) gauge theories on the
topological theta term at finite temperature and, in particular, across the
deconfinement transition. For this purpose, we exploit the lattice formulation
of the theory and present numerical results for the expansion of the free
energy up to O(theta^6), for N=3 and N=6.
Our numerical analysis shows that the theta dependence of 4D SU(N) gauge
theory experiences a drastic change across the deconfinement transition: the
low-temperature phase is characterized by a large-N scaling with theta/N as
relevant variable, while in the high-temperature phase the scaling variable is
just theta and the free energy is essentially determined by the instanton-gas
approximation. The crossover between the two different behaviours gets sharper
with increasing N, suggesting that the instanton-gas regime sets in just above
Tc at large N