An improved Ant Colony System for the Sequential Ordering Problem

It is not rare that the performance of one metaheuristic algorithm can be improved by incorporating ideas taken from another. In this article we present how Simulated Annealing (SA) can be used to improve the efficiency of the Ant Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering Problem (SOP). Moreover, we show how the very same ideas can be applied to improve the convergence of a dedicated local search, i.e. the SOP-3-exchange algorithm. A statistical analysis of the proposed algorithms both in terms of finding suitable parameter values and the quality of the generated solutions is presented based on a series of computational experiments conducted on SOP instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed ACS-SA and EACS-SA algorithms often generate solutions of better quality than the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with the proposed SOP-3-exchange-SA local search was able to find 10 new best solutions for the SOP instances from the SOPLIB2006 repository, thus improving the state-of-the-art results as known from the literature. Overall, the best known or improved solutions were found in 41 out of 48 cases.Comment: 30 pages, 8 tables, 11 figure

Is Strong Gravitational Radiation predicted by TeV-Gravity?

In TeV-gravity models the gravitational coupling to particles with energies E\sim m_{Pl} \sim 10 TeV is not suppressed by powers of ultra-small ratio E/M_{Pl} with M_{Pl} \sim 10^{19} GeV. Therefore one could imagine strong synchrotron radiation of gravitons by the accelerating particles to become the most pronounced manifestation of TeV-gravity at LHC. However, this turns out to be not true: considerable damping continues to exist, only the place of E/M_{Pl} it taken by a power of a ratio \theta\omega/E, where the typical frequency \omega of emitted radiation, while increased by a number of \gamma-factors, can not reach E/\vartheta unless particles are accelerated by nearly critical fields. Moreover, for currently available magnetic fields B \sim 10 Tesla, multi-dimensionality does not enhance gravitational radiation at all even if TeV-gravity is correct.Comment: 7 pages, LaTe

Differential expansion for link polynomials

The differential expansion is one of the key structures reflecting group theory properties of colored knot polynomials, which also becomes an important tool for evaluation of non-trivial Racah matrices. This makes highly desirable its extension from knots to links, which, however, requires knowledge of the $6j$-symbols, at least, for the simplest triples of non-coincident representations. Based on the recent achievements in this direction, we conjecture a shape of the differential expansion for symmetrically-colored links and provide a set of examples. Within this study, we use a special framing that is an unusual extension of the topological framing from knots to links. In the particular cases of Whitehead and Borromean rings links, the differential expansions are different from the previously discovered.Comment: 11 page

Generalized matrix models and AGT correspondence at all genera

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE

Energy loss rates of two-dimensional hole gases in inverted Si/Si0.8Ge0.2 heterostructures

We have investigated the energy loss rate of hot holes as a function of carrier temperature TC in p-type inverted modulation-doped (MD) Si/SiGe heterostructures over the carrier sheet density range (3.5–13)×1011 cm–2, at lattice temperatures of 0.34 and 1.8 K. It is found that the energy loss rate (ELR) depends significantly upon the carrier sheet density, n2D. Such an n2D dependence of ELR has not been observed previously in p-type SiGe MD structures. The extracted effective mass decreases as n2D increases, which is in agreement with recent measurements on a gated inverted sample. It is shown that the energy relaxation of the two-dimensional hole gases is dominated by unscreened acoustic phonon scattering and a deformation potential of 3.0±0.4 eV is deduced

Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals

The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev matrix model (beta-ensemble) representations the latter being polylinear combinations of Selberg integrals. The "pure gauge" limit of these matrix models is, however, a non-trivial multiscaling large-N limit, which requires a separate investigation. We show that in this pure gauge limit the Selberg integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the Nekrasov function for pure SU(2) theory acquires a form very much reminiscent of the AMM decomposition formula for some model X into a pair of the BGW models. At the same time, X, which still has to be found, is the pure gauge limit of the elliptic Selberg integral. Presumably, it is again a BGW model, only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

Wave function-dependent mobility and suppression of interface roughness scattering in a strained SiGe p-channel field-effect structure

The 4 K Hall mobility has been measured in a top-gated, inverted, modulation-doped Si/Si0.8Ge0.2 structure having a Si:B doping layer beneath the alloy. From comparisons with theoretical calculations, we argue that, unlike an ordinary enhancement-mode SiGe p-channel metal–oxide–semiconductor structure, this configuration leads to a decrease of interface roughness scattering with increasing sheet carrier density. We also speculate on the nature of the interface charge observed in these structures at low temperature