Classical and Quantum Ensembles via Multiresolution. II. Wigner Ensembles

We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions of Wigner-like equations via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications.Comment: 5 pages, 2 figures, espcrc2.sty, Presented at IX International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT 2003, December, 2003, KEK, Tsukub

The Affine Structure of Gravitational Theories: Symplectic Groups and Geometry

We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between $CA\left( 3,1\right)$ and the centrally extended $Sp\left( 8\right)$, we perform a nonlinear realization of the centrally extended (CE)$Sp\left( 8\right)$ in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the non-linear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constraints. Finally we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.Comment: 21 pages. arXiv admin note: text overlap with arXiv:0910.2881, arXiv:0705.460

"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

Resolving vertical and east-west horizontal motion from differential interferometric synthetic aperture radar : The L&apos;Aquila earthquake

Analysis of surface coseismic displacement has already been obtained for the 6 April 2009 L'Aquila (central Italy) earthquake from differential interferometric synthetic aperture radar (DInSAR) data. Working jointly on ascending and descending DInSAR data makes for a step forward with respect to published preliminary estimates: we process data in order to retrieve a continuous displacement pattern, both in the vertical and horizontal directions, the latter being limited to the eastward component because of the low sensibility of the SAR images used to resolve northward motion. Our analysis provides new insights on the horizontal component of displacement, obtaining a clear picture of eastward displacement patterns over the epicentral area. This result is noteworthy, as until now little information has been available on horizontal displacement following normal-fault events in the central Apennines (Umbria-Marche, 1997, and L'Aquila, 2009), given the lack of dense GPS networks, the only available source of horizontal displacement data in this area. Inverted fault characteristics from such data also show noteworthy differences compared to previous studies, localizing the Paganica fault as the causative fault for the earthquake

The nature and evolution of Nova Cygni 2006

AIMS: Nova Cyg 2006 has been intensively observed throughout its full outburst. We investigate the energetics and evolution of the central source and of the expanding ejecta, their chemical abundances and ionization structure, and the formation of dust. METHOD: We recorded low, medium, and/or high-resolution spectra (calibrated into accurate absolute fluxes) on 39 nights, along with 2353 photometric UBVRcIc measures on 313 nights, and complemented them with IR data from the literature. RESULTS: The nova displayed initially the normal photometric and spectroscopic evolution of a fast nova of the FeII-type. Pre-maximum, principal, diffuse-enhanced, and Orion absorption systems developed in a normal way. After the initial outburst, the nova progressively slowed its fading pace until the decline reversed and a second maximum was reached (eight months later), accompanied by large spectroscopic changes. Following the rapid decline from second maximum, the nova finally entered the nebular phase and formed optically thin dust. We computed the amount of formed dust and performed a photo-ionization analysis of the emission-line spectrum during the nebular phase, which showed a strong enrichment of the ejecta in nitrogen and oxygen, and none in neon, in agreement with theoretical predictions for the estimated 1.0 Msun white dwarf in Nova Cyg 2006. The similarities with the poorly investigated V1493 Nova Aql 1999a are discussed.Comment: in press in Astronomy and Astrophysic

A novel structure-based encoding for machine-learning applied to the inference of SH3 domain specificity

MOTIVATION: Unravelling the rules underlying protein-protein and protein-ligand interactions is a crucial step in understanding cell machinery. Peptide recognition modules (PRMs) are globular protein domains which focus their binding targets on short protein sequences and play a key role in the frame of protein-protein interactions. High-throughput techniques permit the whole proteome scanning of each domain, but they are characterized by a high incidence of false positives. In this context, there is a pressing need for the development of in silico experiments to validate experimental results and of computational tools for the inference of domain-peptide interactions. RESULTS: We focused on the SH3 domain family and developed a machine-learning approach for inferring interaction specificity. SH3 domains are well-studied PRMs which typically bind proline-rich short sequences characterized by the PxxP consensus. The binding information is known to be held in the conformation of the domain surface and in the short sequence of the peptide. Our method relies on interaction data from high-throughput techniques and benefits from the integration of sequence and structure data of the interacting partners. Here, we propose a novel encoding technique aimed at representing binding information on the basis of the domain-peptide contact residues in complexes of known structure. Remarkably, the new encoding requires few variables to represent an interaction, thus avoiding the 'curse of dimension'. Our results display an accuracy >90% in detecting new binders of known SH3 domains, thus outperforming neural models on standard binary encodings, profile methods and recent statistical predictors. The method, moreover, shows a generalization capability, inferring specificity of unknown SH3 domains displaying some degree of similarity with the known data

A neural strategy for the inference of SH3 domain-peptide interaction specificity

The SH3 domain family is one of the most representative and widely studied cases of so-called Peptide Recognition Modules (PRM). The polyproline II motif PxxP that generally characterizes its ligands does not reflect the complex interaction spectrum of the over 1500 different SH3 domains, and the requirement of a more refined knowledge of their specificity implies the setting up of appropriate experimental and theoretical strategies. Due to the limitations of the current technology for peptide synthesis, several experimental high-throughput approaches have been devised to elucidate protein-protein interaction mechanisms. Such approaches can rely on and take advantage of computational techniques, such as regular expressions or position specific scoring matrices (PSSMs) to pre-process entire proteomes in the search for putative SH3 targets. In this regard, a reliable inference methodology to be used for reducing the sequence space of putative binding peptides represents a valuable support for molecular and cellular biologists

DYNAMICAL CONTROL OF THE HALO IN PARTICLE BEAMS: A STOCHASTIC–HYDRODYNAMIC APPROACH

In this paper we describe the beam distribution in particle accelerators in the framework of a stochastic–hydrodynamic scheme. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution. The relaxation time toward the halo is estimated, and a few examples of controlled transitions toward a permanent halo elimination are discussed