Approximation Algorithms for the Asymmetric Traveling Salesman Problem : Describing two recent methods

The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the previous $O(\log n)$ approximation algorithm, by improving the constant from 0.84 to 0.66 and modifying the work of Kaplan et. al\ [3] and also shows an efficient reduction from ATSPP to ATSP. Combining both the results, they finally establish an approximation ratio of $\left(\frac{4}{3}+\epsilon \right)\log n$ for ATSPP,\ considering a small $\epsilon>0$,\ improving the work of Chekuri and Pal.[4]\newline Asadpour et.al, in their seminal work\ [2], gives an $O\left(\frac{\log n}{\log \log n}\right)$ randomized algorithm for the ATSP, by symmetrizing and modifying the solution of the Held-Karp relaxation problem and then proving an exponential family distribution for probabilistically constructing a maximum entropy spanning tree from a spanning tree polytope and then finally defining the thin-ness property and transforming a thin spanning tree into an Eulerian walk.\ The optimization methods used in\ [2] are quite elegant and the approximation ratio could further be improved, by manipulating the thin-ness of the cuts.Comment: 12 page

Low Energy Dynamics of Monopoles in Supersymmetric Yang-Mills Theories with Hypermultiplets

We derive the low energy dynamics of monopoles and dyons in N=2 supersymmetric Yang-Mills theories with hypermultiplets in arbitrary representations by utilizing a collective coordinate expansion. We consider the most general case that Higgs fields both in the vector multiplet and in the hypermultiplets have nonzero vacuum expectation values. The resulting theory is a supersymmetric quantum mechanics which has been obtained by a nontrivial dimensional reduction of two-dimensional (4,0) supersymmetric sigma models with potentials.Comment: 17pages, LaTeX, minor changes, references added, version published in JHE

Generation Mixing of Sneutrinos in Heavier Chargino Decay

The heavier chargino decay could yield two charged leptons of different generations, owing to generation mixing of sneutrinos. We discuss the possibility of producing $e$ and $\mu$ through this process in near future collider experiments. The analyses are made systematically in the supersymmetric extension of the standard model without assuming a specific scenario for the mixing. Production of the heavier chargino is evaluated in $e^+e^-$ collisions. In the parameter region consistent with nonobservation of the radiative $\mu$ decay, sizable parts lead to a detectable branching ratio for the generation-changing decay of the heavier chargino.Comment: 22 pages, Revtex, 7 figures. v2: For the total width of the heavier chargino, the contribution from the decay into a charged slepton and a neutirno has been included. The figures (Figs. 2, 3, 4, 5), the equations and the related descriptions in sections II and III have been revised. Several references and equations added. v3: Several sentences of section I and V have been rewritten, conclusions unchange

Partially composite two-Higgs doublet model

In the extra dimensional scenarios with gauge fields in the bulk, the Kaluza-Klein (KK) gauge bosons can induce Nambu-Jona-Lasinio (NJL) type attractive four-fermion interactions, which can break electroweak symmetry dynamically with accompanying composite Higgs fields. We consider a possibility that electroweak symmetry breaking (EWSB) is triggered by both a fundamental Higgs and a composite Higgs arising in a dynamical symmetry breaking mechanism induced by a new strong dynamics. The resulting Higgs sector is a partially composite two-Higgs doublet model with specific boundary conditions on the coupling and mass parameters originating at a compositeness scale $\Lambda$. The phenomenology of this model is discussed including the collider phenomenology at LHC and ILC.Comment: 20 pages, 7 figure

S-particles at their naturalness limits

We draw attention on a particular configuration of supersymmetric particle masses, motivated by naturalness and flavour considerations. All its relevant phenomenological properties for the LHC are described in terms of a few physical parameters, irrespective of the underlying theoretical model. This allows a simple characterization of its main features, useful to define a strategy for its discovery.Comment: 13 pages, 8 figures, added reference

The scalars from the topcolor scenario and the spin correlations of the top pair production at the LHC

The topcolor scenario predicts the existences of some new scalars. In this paper, we consider the contributions of these new particles to the observables, which are related to the top quark pair ($t\bar{t}$) production at the LHC. It is found that these new particles can generate significant corrections to the $t\bar{t}$ production cross section and the $t\bar{t}$ spin correlations.Comment: 23 pages, 4 figures; discussions and references added; agrees with published versio

Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.Comment: 5 pages, submitted to J. Phys.

Hubbard Models as Fusion Products of Free Fermions

A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a conjugation matrix and give a new and simple proof of the corresponding decorated Yang-Baxter equation. This provides the algebraic tools required to couple in an integrable way two copies of free-fermion models. Complete integrability of the resulting Hubbard-like models is shown by exhibiting their L and R matrices. Local symmetries of the models are discussed. The diagonalization of the free-fermion models is carried out using the algebraic Bethe Ansatz.Comment: 14 pages, LaTeX. Minor modification