Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit

We give a unified description of tree-level multigluon amplitudes in the high-energy limit. We represent the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes in terms of color configurations that are ordered in rapidity on a two-sided plot. We show that for the helicity configurations they have in common the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes coincide.Comment: LaTeX, 24 pages (including 4 tar-compressed uuencoded figures

Efficient Feature Selection and Multiclass Classification with Integrated Instance and Model Based Learning

Multiclass classification and feature (variable) selections are commonly encountered in many biological and medical applications. However, extending binary classification approaches to multiclass problems is not trivial. Instance-based methods such as the K nearest neighbor (KNN) can naturally extend to multiclass problems and usually perform well with unbalanced data, but suffer from the curse of dimensionality. Their performance is degraded when applied to high dimensional data. On the other hand, model-based methods such as logistic regression require the decomposition of the multiclass problem into several binary problems with one-vs.-one or one-vs.-rest schemes. Even though they can be applied to high dimensional data with L1 or Lp penalized methods, such approaches can only select independent features and the features selected with different binary problems are usually different. They also produce unbalanced classification problems with one vs. the rest scheme even if the original multiclass problem is balanced

Anharmonic force fields of perchloric acid, HClO4_4, and perchloric anhydride, Cl2_2O7_7. An extreme case of inner polarization

DFT (density functional theory) anharmonic force fields with basis sets near the Kohn-Sham limit have been obtained for perchloric acid, HClO$_4$, and perchloric anhydride, Cl$_2$O$_7$. Calculated fundamental frequencies are in very good agreement with available experimental data. Some reassignments in the vibrational spectra of Cl$_2$O$_7$ are proposed based on our calculations. HClO$_4$ and Cl$_2$O$_7$ are particularly severe examples of the `inner polarization' phenomenon. The polarization consistent basis sets pc-1 and pc-2 (as well as their augmented counterparts) should be supplemented with two (preferably three) and one (preferably two) high-exponent $d$ functions, respectively, on second-row atoms. Complete anharmonic force fields are available as electronic supporting information.Comment: J. Mol. Struct., in press (special issue); Electronic Supporting Information at http://theochem.weizmann.ac.il/web/papers/Cl2O7.htm

Scattering phases in quantum dots: an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.Comment: 18 pages, 9 figures. to appear in Physical Review

Light scattering from disordered overlayers of metallic nanoparticles

We develop a theory for light scattering from a disordered layer of metal nanoparticles resting on a sample. Averaging over different disorder realizations is done by a coherent potential approximation. The calculational scheme takes into account effects of retardation, multipole excitations, and interactions with the sample. We apply the theory to a system similar to the one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663 (1998)] who used a layered Si/SiO$_2$/Si sample. The calculated results agree rather well with the experimental ones. In particular we find conspicuous maxima in the scattering intensity at long wavelengths (much longer than those corresponding to plasmon resonances in the particles). We show that these maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure

Isotopic composition of fragments in multifragmentation of very large nuclear systems: effects of the chemical equilibrium

Studies on the isospin of fragments resulting from the disassembly of highly excited large thermal-like nuclear emitting sources, formed in the ^{197}Au + ^{197}Au reaction at 35 MeV/nucleon beam energy, are presented. Two different decay systems (the quasiprojectile formed in midperipheral reactions and the unique source coming from the incomplete fusion of projectile and target in the most central collisions) were considered; these emitting sources have the same initial N/Z ratio and excitation energy (E^* ~= 5--6 MeV/nucleon), but different size. Their charge yields and isotopic content of the fragments show different distributions. It is observed that the neutron content of intermediate mass fragments increases with the size of the source. These evidences are consistent with chemical equilibrium reached in the systems. This fact is confirmed by the analysis with the statistical multifragmentation model.Comment: 9 pages, 4 ps figure

Statefinder and Om Diagnostics for Interacting New Holographic Dark Energy Model and Generalized Second Law of Thermodynamics

In this work, we have considered that the flat FRW universe is filled with the mixture of dark matter and the new holographic dark energy. If there is an interaction, we have investigated the natures of deceleration parameter, statefinder and $Om$ diagnostics. We have examined the validity of the first and generalized second laws of thermodynamics under these interactions on the event as well as apparent horizon. It has been observed that the first law is violated on the event horizon. However, the generalized second law is valid throughout the evolution of the universe enveloped by the apparent horizon. When the event horizon is considered as the enveloping horizon, the generalized second law is found to break down excepting at late stage of the universe.Comment: 9 pages, 13 figure