Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs has increased. This is a model where edges are streamed-in in an adversarial order and we are allowed a space proportional to the number of vertices in a graph. In recent years, there has been several new results in this semi-streaming model. However broad techniques such as linear programming have not been adapted to this model. We present several techniques to adapt and optimize linear programming based approaches in the semi-streaming model with an application to the maximum matching problem. As a consequence, we improve (almost) all previous results on this problem, and also prove new results on interesting variants

Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

Globally-Linked Vortex Clusters in Trapped Wave Fields

We put forward the existence of a rich variety of fully stationary vortex structures, termed H-clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as Bose-Einstein condensates. Clusters with multipolar global wave fronts are non-stationary or at best flipping.Comment: 4 pages, 5 PostScript figure

FRW Cosmology From Five Dimensional Vacuum Brans-Dicke Theory

We follow approach of induced matter theory for 5D vacuum BD, introduce induced matter and potential in 4D hypersurfaces, and employ generalized FRW type solution. We confine ourselves to scalar field and scale factors be functions of the time. This makes the induced potential, by its definition, vanishes. When the scale factor of fifth dimension and scalar field are not constants, 5D eqs for any geometry admit a power law relation between scalar field and scale factor of fifth dimension. Hence the procedure exhibits that 5D vacuum FRW like eqs are equivalent, in general, to corresponding 4D vacuum ones with the same spatial scale factor but new scalar field and coupling constant. We show that 5D vacuum FRW like eqs or its equivalent 4D vacuum ones admit accelerated solutions. For constant scalar field, eqs reduce to usual FRW eqs with typical radiation dominated universe. For this situation we obtain dynamics of scale factors for any geometry without any priori assumption. For nonconstant scalar fields and spatially flat geometries, solutions are found to be power law and exponential ones. We also employ weak energy condition for induced matter, that allows negative/positive pressures. All types of solutions fulfill WEC in different ranges. The power law solutions with negative/positive pressures admit both decelerating and accelerating ones. Some solutions accept shrinking extra dimension. By considering nonghost scalar fields and recent observational measurements, solutions are more restricted. We illustrate that accelerating power law solutions, which satisfy WEC and have nonghost fields, are compatible with recent observations in ranges -4/3 < \omega </- -1.3151 and 1.5208 </- n < 1.9583 for dependence of fifth dimension scale factor with usual scale factor. These ranges also fulfill condition nonghost fields in the equivalent 4D vacuum BD eqs.Comment: 18 pages, 16 figures, 11 table

Neutrino hierarchy from CP-blind observables with high density magnetized detectors

High density magnetized detectors are well suited to exploit the outstanding purity and intensities of novel neutrino sources like Neutrino Factories and Beta Beams. They can also provide independent measurements of leptonic mixing parameters through the observation of atmospheric muon-neutrinos. In this paper, we discuss the combination of these observables from a multi-kton iron detector and a high energy Beta Beam; in particular, we demonstrate that even with moderate detector granularities the neutrino mass hierarchy can be determined for $\theta_{13}$ values greater than 4$^\circ$.Comment: 16 pages, 7 figures. Added a new section discussing systematic errors (sec 5.2); sec.5.1 and 4 have been extended. Version to appear in EPJ

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201

A Diffractive Study of Parametric Process in Nonlinear Photonic Crystals

We report a general description of quasi-phase-matched parametric process in nonlinear photonic crystals (NLPC) by extending the conventional X-ray diffraction theory in solids. Under the virtual wave approximation, phase-matching resonance is equivalent to the diffraction of the scattered virtual wave. Hence a modified NLPC Ewald construction can be built up, which illustrates the nature of the accident for the diffraction of the virtual wave in NLPC and further reveals the complete set of diffractions of the virtual wave for both of the air-dielectric and dielectric-dielectric contacts. We show the two basic linear sequences, the anti-stacking and para-stacking linear sequences, in one-dimension (1D) NLPC and present a general rule for multiple phase-matching resonances in 1D NLPC. The parameters affecting the NLPC structure factor are investigated, which indicate that not only the Ewald construction but also the relative NLPC atom size together determine whether a diffraction of the virtual wave can occur in 2D NLPC. The results also show that 1D NLPC is a better choice than 2D NLPC for a single parametric process

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe