Total Space in Resolution Is at Least Width Squared

Given an unsatisfiable k-CNF formula phi we consider two complexity measures in Resolution: width and total space. The width is the minimal W such that there exists a Resolution refutation of phi with clauses of at most W literals. The total space is the minimal size T of a memory used to write down a Resolution refutation of phi where the size of the memory is measured as the total number of literals it can contain. We prove that T = Omega((W - k)^2)

Detecting and Studying Higgs Bosons

I review the ability of the LHC (large hadron collider), NLC (next linear lepton collider) and FMC (first muon collider) to detect and study Higgs bosons, with emphasis on the Higgs bosons of extended Higgs sectors, especially those of the minimal supersymmetric standard model (MSSM). Particular attention is given to means for distinguishing the lightest neutral CP-even Higgs boson of the MSSM from the single Higgs boson of the minimal Standard Model (SM).Comment: 65 pages, to appear in ``Perspectives on Higgs Physics'', ed. G. Kane, 2nd edition (World Scientific Publishing). Full postscript file is available via anonymous ftp at ftp://ucdhep.ucdavis.edu/gunion/perspectives97.p

Higgs Boson Discovery and Properties

We outline issues examined and progress made by the Light Higgs Snowmass 1996 working group regarding discovering Higgs bosons and measuring their detailed properties. We focused primarily on what could be learned at LEP2, the Tevatron (after upgrade), the LHC, a next linear \epem collider and a \mupmum collider.Comment: 47 pages, full postscript file also available via anonymous ftp at ftp://ucdhep.ucdavis.edu/gunion/summary_snowmass96.ps To appear in ``Proceedings of the 1996 DPF/DPB Summer Study on New Directions for High Energy Physics''. Minor revisions of references and wording have been made in a few place

Theoretical analysis of neutron scattering results for quasi-two dimensional ferromagnets

A theoretical study has been carried out to analyse the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1/2 ferromagnetic material $K_2CuF_4$. Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1/2, show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems.Comment: 16 pages, 6 figures, 1 Table Submitted for publicatio

Optimal neuronal tuning for finite stimulus spaces

The efficiency of neuronal encoding in sensory and motor systems has been proposed as a first principle governing response properties within the central nervous system. We present a continuation of a theoretical study presented by Zhang and Sejnowski, where the influence of neuronal tuning properties on encoding accuracy is analyzed using information theory. When a finite stimulus space is considered, we show that the encoding accuracy improves with narrow tuning for one- and two-dimensional stimuli. For three dimensions and higher, there is an optimal tuning width

Ground-based detection of sodium in the transmission spectrum of exoplanet HD209458b

[Context] The first detection of an atmosphere around an extrasolar planet was presented by Charbonneau and collaborators in 2002. In the optical transmission spectrum of the transiting exoplanet HD209458b, an absorption signal from sodium was measured at a level of 0.023+-0.006%, using the STIS spectrograph on the Hubble Space Telescope. Despite several attempts, so far only upper limits to the Na D absorption have been obtained using telescopes from the ground, and the HST result has yet to be confirmed. [Aims] The aims of this paper are to re-analyse data taken with the High Dispersion Spectrograph on the Subaru telescope, to correct for systematic effects dominating the data quality, and to improve on previous results presented in the literature. [Methods] The data reduction process was altered in several places, most importantly allowing for small shifts in the wavelength solution. The relative depth of all lines in the spectra, including the two sodium D lines, are found to correlate strongly with the continuum count level in the spectra. These variations are attributed to non-linearity effects in the CCDs. After removal of this empirical relation the uncertainties in the line depths are only a fraction above that expected from photon statistics. [Results] The sodium absorption due to the planet's atmosphere is detected at >5 sigma, at a level of 0.056+-0.007% (2x3.0 Ang band), 0.070+-0.011% (2x1.5 Ang band), and 0.135+-0.017% (2x0.75 Ang band). There is no evidence that the planetary absorption signal is shifted with respect to the stellar absorption, as recently claimed for HD189733b. The measurements in the two most narrow bands indicate that some signal is being resolved.[abridged]Comment: Latex, 7 pages: accepted for publication in Astronomy & Astrophysic