Two-batch liar games on a general bounded channel

We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies are governed by a channel $C$, a set of allowable lie strings of maximum length $k$. Carole selects $x\in[n]$, and Paul makes $t$-ary queries to uniquely determine $x$. In each of $q$ rounds, Paul weakly partitions $[n]=A_0\cup >... \cup A_{t-1}$ and asks for $a$ such that $x\in A_a$. Carole responds with some $b$, and if $a\neq b$, then $x$ accumulates a lie $(a,b)$. Carole's string of lies for $x$ must be in the channel $C$. Paul wins if he determines $x$ within $q$ rounds. We further restrict Paul to ask his questions in two off-line batches. We show that for a range of sizes of the second batch, the maximum size of the search space $[n]$ for which Paul can guarantee finding the distinguished element is $\sim t^{q+k}/(E_k(C)\binom{q}{k})$ as $q\to\infty$, where $E_k(C)$ is the number of lie strings in $C$ of maximum length $k$. This generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese, and Deppe. We extend Paul's strategy to solve also the pathological liar variant, in a unified manner which gives the existence of asymptotically perfect two-batch adaptive codes for the channel $C$.Comment: 26 page

M Theory from World-Sheet Defects in Liouville String

We have argued previously that black holes may be represented in a D-brane approach by monopole and vortex defects in a sine-Gordon field theory model of Liouville dynamics on the world sheet. Supersymmetrizing this sine-Gordon system, we find critical behaviour in 11 dimensions, due to defect condensation that is the world-sheet analogue of D-brane condensation around an extra space-time dimension in M theory. This supersymmetric description of Liouville dynamics has a natural embedding within a 12-dimensional framework suggestive of F theory.Comment: 17 pages LATEX, 1 epsf figure include

Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the "size" of the constituent quark, rho ~ 0.3 fm. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power (1/Q^2-) corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, f_2^{u - d}, has a sizable negative value of the order rho^{-2}, due to the presence of sea quarks with virtualities ~ rho^{-2} in the proton wave function. The twist-3 matrix element, d_2, is not related to the scale rho^{-2}. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on g_1^p and g_1^n, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale rho for quark-hadron duality and the x-dependence of higher-twist contributions.Comment: 8 pages, 4 figure

The ESO Spectroscopic facility

We present the concept of a novel facility dedicated to massively-multiplexed spectroscopy. The telescope has a very wide field Cassegrain focus optimised for fibre feeding. With a Field of View (FoV) of 2.5 degrees diameter and a 11.4m pupil, it will be the largest etendue telescope. The large focal plane can easily host up to 16.000 fibres. In addition, a gravity invariant focus for the central 10 arc-minutes is available to host a giant integral field unit (IFU). The 3 lenses corrector includes an ADC, and has good performance in the 360-1300 nm wavelength range. The top level science requirements were developed by a dedicated ESO working group, and one of the primary cases is high resolution spectroscopy of GAIA stars and, in general, how our Galaxy formed and evolves. The facility will therefore be equipped with both, high and low resolution spectrographs. We stress the importance of developing the telescope and instrument designs simultaneously. The most relevant R\&D aspect is also briefly discussed.Comment: 6 pages 4 figures , presented at IAU Symposium 334 "rediscovering our galaxy

Severe New Limits on the Host Galaxies of Gamma Ray Bursts

The nature of Gamma Ray Bursts (GRBs) remains a complete mystery, despite the recent breakthrough discovery of low energy counterparts, although it is now generally believed that at least most GRBs are at cosmological distances. Virtually all proposed cosmological models require bursters to reside in ordinary galaxies. This can be tested by looking inside the smallest GRB error boxes to see if ordinary galaxies appear at the expected brightness levels. This letter reports on an analysis of the contents of 26 of the smallest regions, many from the brightest bursts. These events will have $z < 0.4$ and small uncertainties about luminosity functions, K corrections and galaxy evolutions; whereas the recent events with optical transients are much fainter and hence have high redshifts and grave difficulties in interpretation. This analysis strongly rejects the many models with peak luminosities of $10^{57} photons \cdot s^{-1}$ as deduced from the $LogN-LogP$ curve with no evolution. Indeed, the lower limit on acceptable luminosities is $6 \times 10^{58} photons \cdot s^{-1}$. The only possible solution is to either place GRBs at unexpectedly large distances (with $z > 5.9$ for the faint BATSE bursts) or to require bursters to be far outside any normal host galaxy.Comment: 17 pages, to be published by ApJ

Resonant CP Violation in Higgs Radiation at e^+e^- Linear Collider

We study resonant CP violation in the Higgsstrahlung process e^+e^- -> H_{1,2,3} (Z -> e^+e^-, \mu^+\mu^-) and subsequent decays H_{1,2,3} -> b \bar{b}, \tau^-\tau^+, in the MSSM with Higgs-sector CP violation induced by radiative corrections. At a high-energy e^+e^- linear collider, the recoil-mass method enables one to determine the invariant mass of a fermion pair produced by Higgs decays with a precision as good as 1 GeV. Assuming an integrated luminosity of 100/fb, we show that the production lineshape of a coupled system of neutral Higgs bosons decaying into b\bar{b} quarks is sensitive to the CP-violating parameters. When the Higgs bosons decay into \tau^-\tau^+, two CP asymmetries can be defined using the longitudinal and transverse polarizations of the tau leptons. Taking into account the constraints from electric dipole moments, we find that these CP asymmetries can be as large as 80 %, in a tri-mixing scenario where all three neutral Higgs states of the MSSM are nearly degenerate and mix significantly.Comment: 22 pages, 8 figures, to appear in Phys. Rev.

Geodesic Deviation Equation in Bianchi Cosmologies

We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson-Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor in the GDE.Comment: Submitted to Journal of Physics: Conference Series (JPCS), ERE200

The Origin of \lya Absorption Systems at z>1z>1---Implications from the Hubble Deep Field

The Hubble Deep Field images have provided us with a unique chance to relate statistical properties of high-redshift galaxies to statistical properties of \lya absorption systems. Combining an {\em empirical} measure of the galaxy surface density versus redshift with an {\em empirical} measure of the gaseous extent of galaxies, we predict the number density of \lya absorption systems that originate in extended gaseous envelopes of galaxies versus redshift. We show that at least 50% and as much as 100% of observed \lya absorption systems of W\apg0.32 \AA can be explained by extended gaseous envelops of galaxies. Therefore, we conclude that known galaxies of known gaseous extent must produce a significant fraction and perhaps all of \lya absorption systems over a large redshift range.Comment: 12 pages, 3 figures, accepted for publication in the Astrophysical Journal, April 10, 2000 issu

Dark Matter in SuperGUT Unification Models

After a brief update on the prospects for dark matter in the constrained version of the MSSM (CMSSM) and its differences with models based on minimal supergravity (mSUGRA), I will consider the effects of unifying the supersymmetry-breaking parameters at a scale above M_{GUT}. One of the consequences of superGUT unification, is the ability to take vanishing scalar masses at the unification scale with a neutralino LSP dark matter candidate. This allows one to resurrect no-scale supergravity as a viable phenomenological model.Comment: 12 pages, 16 figures, To be published in the Proceedings of the 6th DSU Conference, Leon, Mexico, ed. D. Delepin

A Layman's guide to SUSY GUTs

The determination of the most straightforward evidence for the existence of the Superworld requires a guide for non-experts (especially experimental physicists) for them to make their own judgement on the value of such predictions. For this purpose we review the most basic results of Super-Grand unification in a simple and clear way. We focus the attention on two specific models and their predictions. These two models represent an example of a direct comparison between a traditional unified-theory and a string-inspired approach to the solution of the many open problems of the Standard Model. We emphasize that viable models must satisfy {\em all} available experimental constraints and be as simple as theoretically possible. The two well defined supergravity models, $SU(5)$ and $SU(5)\times U(1)$, can be described in terms of only a few parameters (five and three respectively) instead of the more than twenty needed in the MSSM model, \ie, the Minimal Supersymmetric extension of the Standard Model. A case of special interest is the strict no-scale $SU(5)\times U(1)$ supergravity where all predictions depend on only one parameter (plus the top-quark mass). A general consequence of these analyses is that supersymmetric particles can be at the verge of discovery, lurking around the corner at present and near future facilities. This review should help anyone distinguish between well motivated predictions and predictions based on arbitrary choices of parameters in undefined models.Comment: 25 pages, Latex, 11 figures (not included), CERN-TH.7077/93, CTP-TAMU-65/93. A complete ps file (1.31MB) with embedded figures is available by request from [email protected]