Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems

Recently, a new finite-sample system identification algorithm, called Sign-Perturbed Sums (SPS), was introduced in [2]. SPS constructs finite-sample confidence regions that are centered around the least squares estimate, and are guaranteed to contain the true system parameters with a user-chosen exact probability for any finite number of data points. The main assumption of SPS is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. Although it is easy to determine if a particular parameter belongs to the confidence region, it is not easy to describe the boundary of the region, and hence to compactly represent the exact confidence region. In this paper we show that an ellipsoidal outer-approximation of the SPS confidence region can be found by solving a convex optimization problem, and we illustrate the properties of the SPS region and the ellipsoidal outer-approximation in simulation examples

Asymptotic properties of SPS confidence regions

Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example

Zipf's law in Multifragmentation

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition

Knowledge and valorization of historical sites through 3D documentation and modeling

The paper presents the first results of an interdisciplinary project related to the 3D documentation, dissemination, valorization and digital access of archeological sites. Beside the mere 3D documentation aim, the project has two goals: (i) to easily explore and share via web references and results of the interdisciplinary work, including the interpretative process and the final reconstruction of the remains; (ii) to promote and valorize archaeological areas using reality-based 3D data and Virtual Reality devices. This method has been verified on the ruins of the archeological site of Pausilypon, a maritime villa of Roman period (Naples, Italy). Using Unity3D, the virtual tour of the heritage site was integrated and enriched with the surveyed 3D data, text documents, CAAD reconstruction hypotheses, drawings, photos, etc. In this way, starting from the actual appearance of the ruins (panoramic images), passing through the 3D digital surveying models and several other historical information, the user is able to access virtual contents and reconstructed scenarios, all in a single virtual, interactive and immersive environment. These contents and scenarios allow to derive documentation and geometrical information, understand the site, perform analyses, see interpretative processes, communicate historical information and valorize the heritage location

Sc substitution for Mg in MgB2: effects on Tc and Kohn anomaly

Here we report synthesis and characterization of Mg_{1-x}Sc_{x}B_{2} (0.12T_{c}>6 K. We find that the Sc doping moves the chemical potential through the 2D/3D electronic topological transition (ETT) in the sigma band where the ``shape resonance" of interband pairing occurs. In the 3D regime beyond the ETT we observe a hardening of the E_{2g} Raman mode with a significant line-width narrowing due to suppression of the Kohn anomaly over the range 0<q<2k_{F}.Comment: 8 pages, 4 EPS figures, to be published in Phys. Rev.

The Multifragmentation Freeze--Out Volume in Heavy Ion Collisions

The reduced velocity correlation function for fragments from the reaction Fe + Au at 100 A~MeV bombarding energy is investigated using the dynamical--statistical approach QMD+SMM and compared to experimental data to extract the Freeze--Out volume assuming simultaneous multifragmentation.Comment: 8 pages; 3 uuencoded figures available with figures command, LateX, UCRL-J-1157

Cluster emission and phase transition behaviours in nuclear disassembly

The features of the emissions of light particles (LP), charged particles (CP), intermediate mass fragments (IMF) and the largest fragment (MAX) are investigated for $^{129}Xe$ as functions of temperature and 'freeze-out' density in the frameworks of the isospin-dependent lattice gas model and the classical molecular dynamics model. Definite turning points for the slopes of average multiplicity of LP, CP and IMF, and of the mean mass of the largest fragment ($A_{max}$) are shown around a liquid-gas phase transition temperature and while the largest variances of the distributions of LP, CP, IMF and MAX appear there. It indicates that the cluster emission rate can be taken as a probe of nuclear liquid--gas phase transition. Furthermore, the largest fluctuation is simultaneously accompanied at the point of the phase transition as can be noted by investigating both the variances of their cluster multiplicity or mass distributions and the Campi scatter plots within the lattice gas model and the molecular dynamics model, which is consistent with the result of the traditional thermodynamical theory when a phase transition occurs.Comment: replace nucl-th/0103009 due to the technique problem to access old versio

Universal Behavior of Lyapunov Exponents in Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic $^4He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda\propto |T-T_c|^{-\omega}$, where the exponent $\omega=0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition.Comment: 11 pages, RevTeX, 3 figures not included available upon reques

Spin-orbit interaction in Hartree-Fock calculations

The contribution of the spin-orbit interaction in Hartree-Fock calculations for closed shell nuclei is studied. We obtain explicit expressions for the finite range spin-orbit force. New terms with respect to the traditional spin-orbit expressions are found. The importance of the finite-range is analyzed. Results obtained with spin-orbit terms taken from realistic interactions are presented. The effect of the spin-orbit isospin dependent terms is evaluated.Comment: To be published on Nuovo Cimento

Finite size effects and the order of a phase transition in fragmenting nuclear systems

We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise the smoothed transition observed in a finite system. We show that the microcanonical ensemble may be a useful framework for the determination of the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change