Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Scalars from Top-condensation Models at Hadron Colliders

We study the production and decay of neutral scalars and pseudo-scalars at hadron colliders, in theories where the top-quark mass is the result of a $t\bar t$ condensate. We show that the dominant decay channel for masses below the $t\bar t$ threshold is the flavor changing mode $tc$. This is a consequence of the non-universal nature of the underlying interactions in all top-condensation models and provides a model-independent signature of these scenarios. We show that an upgraded Tevatron is sensitive to a sizeable region of the interesting parameter space and that the LHC will highly constrain these models through this flavor violating channel.Comment: 4 pages, 4 figures. Minor changes in figures for readibility. final version to appear in PR

Two Neuronal G Proteins are Involved in Chemosensation of the Caenorhabditis elegans Dauer-Inducing Pheromone

Caenorhabditis elegans uses chemosensation to determine its course of development. Young larvae can arrest as dauer larvae in response to increasing population density, which they measure by a nematode-excreted pheromone, and decreasing food supply. Dauer larvae can resume development in response to a decrease in pheromone and increase in food concentration. We show here that two novel G protein alpha subunits (GPA-2 and GPA-3) show promoter activity in subsets of chemosensory neurons and are involved in the decision to form dauer larvae primarily through the response to dauer pheromone. Dominant activating mutations in these G proteins result in constitutive, pheromone-independent dauer formation, whereas inactivation results in reduced sensitivity to pheromone, and, under certain conditions, an alteration in the response to food. Interactions between gpa-2, gpa-3 and other genes controlling dauer formation suggest that these G proteins may act in parallel to regulate the neuronal decision making that precedes dauer formation

The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende

Decay constants and mixing parameters in a relativistic model for q\barQ system

We extend our recent work, in which the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar $\gamma_0\sigma r$) linear '' potential is used to obtain the light quark wavefunction for $q\bar Q$ mesons in the limit $m_Q\to \infty$, to estimate the decay constant $f_P$ and the mixing parameter $B$ of the pseudoscalar mesons. We compare our results for the evolution of $f_P$ and $B$ with the meson mass $M_P$ to the non-relativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For $\sigma =0.14{{\rm ~GeV}}^{-2}$ and \lms =0.240{\rm ~GeV} we obtain: $f_D =0.371\; ,\; f_{D_s}=0.442\; ,\; f_B=0.301\; ,\; f_{B_s}=0.368 {\rm ~GeV}$ and $B_D=0.88\; ,\; B_{D_s}=0.89\; ,\; B_B=0.95\; ,\; B_{B_s}=0.96\; ,\;$ and $B_K=0.60$.Comment: 13 pages, Latex, 3 figures (included

Large Tree Level CP Violation in e+e−→ttˉH0e^+e^-\to t\bar{t}H^0 in The Two Higgs Doublet Model

We find a large CP violation effect within the Two-Higgs-Doublet-Model for the reaction $e^+e^-\to t\bar{t}H^0$ at future linear colliders. The CP-asymmetry arises already at the tree level as a result of interference between diagrams with $H^0$ emission from $t$ (and $\bar{t}$) and its emission from a $Z^0$ and can be about 10--20\%. In the best case one needs a few hundred $t\bar{t}H^0$ events to observe CP violation at the 3$\sigma$ level.Comment: UU encoded tar compressed tex file with postscript figure