Approximate Fitting of a Circular Arc When Two Points Are Known

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting requires an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.Comment: 15 pages, 4 figures, extended abstract published at the conferenc

Holographic Pomeron: Saturation and DIS

We briefly review the approach to dipole-dipole scattering in holographic QCD developed in ARXIV:1202.0831. The Pomeron is modeled by exchanging closed strings between the dipoles and yields Regge behavior for the elastic amplitude. We calculate curvature corrections to this amplitude in both a conformal and confining background, identifying the holographic direction with the virtuality of the dipoles. The it wee-dipole density is related to the string tachyon diffusion in both virtuality and the transverse directions. We give an explicit derivation of the dipole saturation momentum both in the conformal and confining metric. Our holographic result for the dipole-dipole cross section and the it wee-dipole density in the conformal limit are shown to be identical in form to the BFKL pomeron result when the non-critical string transverse dimension is $D_\perp=3$. The total dipole-dipole cross section is compared to DIS data from HERA

Coherence Phenomena in Charmonium Production off Nuclei at the Energies of RHIC and LHC

In the energy range of RHIC and LHC the mechanisms of nuclear suppression of charmonia are expected to be strikingly different from what is known for the energy of the SPS. One cannot think any more of charmonium produced on a bound nucleon which then attenuates as it passes through the rest of the nucleus. The coherence length of charmonium production substantially exceeds the nuclear radius in the new energy range. Therefore the production amplitudes on different nucleons, rather than the cross sections, add up and interfere, i.e. shadowing is at work. So far no theoretical tool has been available to calculate nuclear effects for charmonium production in this energy regime. We develop a light-cone Green function formalism which incorporates the effects of the coherence of the production amplitudes and of charmonium wave function formation, and is the central result of this paper. We found a substantial deviation from QCD factorization, namely, gluon shadowing is much stronger for charmonium production than it is in DIS. We predict for nuclear effects $x_2$ scaling which is violated at lower energies by initial state energy loss which must be also included in order to compare with available data. In this paper only the indirect J/Psi originating from decay of P-wave charmonia are considered. The calculated x_F-dependence of J/Psi nuclear suppression is in a good accord with data. We predict a dramatic variation of nuclear suppression with x_F in pA and a peculiar peak at x_F=0 in AA collisions at RHIC.Comment: 51 pages including 12 figures. Two references and comments are added at the en

Independent components in spectroscopic analysis of complex mixtures

We applied two methods of "blind" spectral decomposition (MILCA and SNICA) to quantitative and qualitative analysis of UV absorption spectra of several non-trivial mixture types. Both methods use the concept of statistical independence and aim at the reconstruction of minimally dependent components from a linear mixture. We examined mixtures of major ecotoxicants (aromatic and polyaromatic hydrocarbons), amino acids and complex mixtures of vitamins in a veterinary drug. Both MICLA and SNICA were able to recover concentrations and individual spectra with minimal errors comparable with instrumental noise. In most cases their performance was similar to or better than that of other chemometric methods such as MCR-ALS, SIMPLISMA, RADICAL, JADE and FastICA. These results suggest that the ICA methods used in this study are suitable for real life applications. Data used in this paper along with simple matlab codes to reproduce paper figures can be found at http://www.klab.caltech.edu/~kraskov/MILCA/spectraComment: 22 pages, 4 tables, 6 figure

Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation

We study the role of bosonic zero modes in light-cone quantisation on the invariant mass spectrum for the simplified setting of two-dimensional SU(2) Yang-Mills theory coupled to massive scalar adjoint matter. Specifically, we use discretised light-cone quantisation where the momentum modes become discrete. Two types of zero momentum mode appear -- constrained and dynamical zero modes. In fact only the latter type of modes turn out to mix with the Fock vacuum. Omission of the constrained modes leads to the dynamical zero modes being controlled by an infinite square-well potential. We find that taking into account the wavefunctions for these modes in the computation of the full bound state spectrum of the two dimensional theory leads to 21% shifts in the masses of the lowest lying states.Comment: LaTeX with 5 postscript file

Topological Aspects of Gauge Fixing Yang-Mills Theory on S4

For an $S_4$ space-time manifold global aspects of gauge-fixing are investigated using the relation to Topological Quantum Field Theory on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solutions to a covariant gauge conditon on the orbit of a particular instanton are found using the $SO(5)$ isometry group of the $S_4$ base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that an orbit with Pontryagin number \k=\pm1 in covariant gauges on $S_4$ contributes to physical correlation functions with a different multiplicity factor due to the Gribov copies, than an orbit in the trivial \k=0 sector. Similar topological arguments show that there is no contribution from the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discuss possible physical implications of the global gauge dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure