9,108 research outputs found
Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials
The spectrum and coherency are useful quantities for characterizing the
temporal correlations and functional relations within and between point
processes. This paper begins with a review of these quantities, their
interpretation and how they may be estimated. A discussion of how to assess the
statistical significance of features in these measures is included. In
addition, new work is presented which builds on the framework established in
the review section. This work investigates how the estimates and their error
bars are modified by finite sample sizes. Finite sample corrections are derived
based on a doubly stochastic inhomogeneous Poisson process model in which the
rate functions are drawn from a low variance Gaussian process. It is found
that, in contrast to continuous processes, the variance of the estimators
cannot be reduced by smoothing beyond a scale which is set by the number of
point events in the interval. Alternatively, the degrees of freedom of the
estimators can be thought of as bounded from above by the expected number of
point events in the interval. Further new work describing and illustrating a
method for detecting the presence of a line in a point process spectrum is also
presented, corresponding to the detection of a periodic modulation of the
underlying rate. This work demonstrates that a known statistical test,
applicable to continuous processes, applies, with little modification, to point
process spectra, and is of utility in studying a point process driven by a
continuous stimulus. While the material discussed is of general applicability
to point processes attention will be confined to sequences of neuronal action
potentials (spike trains) which were the motivation for this work.Comment: 33 pages, 9 figure
Possible High-Redshift, Low-Luminosity AGN Activity in the Hubble Deep Field
In the Hubble Deep Field (HDF), twelve candidate sources of high-redshift (z
> 3.5) AGN activity have been identified. The color selection criteria were
established by passing spectra of selected quasars and Seyfert galaxies
(appropriately redshifted and modified for "Lyman forest" absorption), as well
as stars, observed normal and starburst galaxies, and galaxy models for various
redshifts through the filters used for the HDF observations. The actual
identification of AGN candidates also involved convolving a
Laplacian-of-Gaussian filter with the HDF images, thereby removing relatively
flat galactic backgrounds and leaving only the point-like components in the
centers. Along with positions and colors, estimated redshifts and absolute
magnitudes are reported, with the candidates falling toward the faint end of
the AGN luminosity function. One candidate has been previously observed
spectroscopically, with a measured redshift of 4.02. The number of sources
reported here is consistent with a simple extrapolation of the observed quasar
luminosity function to magnitude 30 in B_Johnson. Implications for ionization
of the intergalactic medium and for gravitational lensing are discussed.Comment: 10 pages LaTex plus 2 separate files (Table 1 which is a two-page
landscape LaTex file; and Figure 6 which is a large (0.7 MB) non-encapsulated
postscript file). Accepted for publication in the Astronomical Journa
Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics
Symmetries in quantum mechanics are realized by the projective
representations of the Lie group as physical states are defined only up to a
phase. A cornerstone theorem shows that these representations are equivalent to
the unitary representations of the central extension of the group. The
formulation of the inertial states of special relativistic quantum mechanics as
the projective representations of the inhomogeneous Lorentz group, and its
nonrelativistic limit in terms of the Galilei group, are fundamental examples.
Interestingly, neither of these symmetries includes the Weyl-Heisenberg group;
the hermitian representations of its algebra are the Heisenberg commutation
relations that are a foundation of quantum mechanics. The Weyl-Heisenberg group
is a one dimensional central extension of the abelian group and its unitary
representations are therefore a particular projective representation of the
abelian group of translations on phase space. A theorem involving the
automorphism group shows that the maximal symmetry that leaves invariant the
Heisenberg commutation relations are essentially projective representations of
the inhomogeneous symplectic group. In the nonrelativistic domain, we must also
have invariance of Newtonian time. This reduces the symmetry group to the
inhomogeneous Hamilton group that is a local noninertial symmetry of Hamilton's
equations. The projective representations of these groups are calculated using
the Mackey theorems for the general case of a nonabelian normal subgroup
A Selected Ion Flow Tube Study of the Reactions of Several Cations with the Group 6B Hexafluorides SF6, SeF6, and TeF6
The first investigation of the ion chemistry of SeF and TeF is presented. Using a selected ion flow tube, the thermal rate coefficients and ion product distributions have been determined at 300 K for the reactions of fourteen atomic and molecular cations, namely HO, CF, CF, CF, HO, NO, O, CO, CO, N, N, Ar, F and Ne (in order of increasing recombination energy), with SeF and TeF. The results are compared with those from the reactions of these ions with SF, for which the reactions with CF, CF, NO and F are reported for the first time. Several distinct processes are observed amongst the large number of reactions studied, including dissociative charge transfer, and F, F, F and F abstraction from the neutral reactant molecule to the reagent ion. The dissociative charge transfer channels are discussed in relation to vacuum ultraviolet photoelectron and threshold photoelectron-photoion coincidence spectra of XF (X = S, Se, and Te). For reagent ions whose recombination energies lie between the first dissociative ionisation limit, XF XF + F + e, and the onset of ionisation of the XF molecule, the results suggest that if dissociative charge transfer occurs, it proceeds via an intimate encounter. For those reagent ions whose recombination energies are greater than the onset of ionisation, long-range electron transfer may occur depending on whether certain physical factors apply, for example non-zero Franck-Condon overlap. From the reaction kinetics, limits for the heats of formation of SeF, SeF, TeF and TeF at 298 K have been obtained; H(SeF) < -369 kJ mol, H(SeF) < -621 kJ mol, H(TeF) > -570 kJ mol, and H(TeF) < -822 kJ mol
Weak Lensing Determination of the Mass in Galaxy Halos
We detect the weak gravitational lensing distortion of 450,000 background
galaxies (20<R<23) by 790 foreground galaxies (R<18) selected from the Las
Campanas Redshift Survey (LCRS). This is the first detection of weak lensing by
field galaxies of known redshift, and as such permits us to reconstruct the
shear profile of the typical field galaxy halo in absolute physical units
(modulo H_0), and to investigate the dependence of halo mass upon galaxy
luminosity. This is also the first galaxy-galaxy lensing study for which the
calibration errors are negligible. Within a projected radius of 200 \hkpc, the
shear profile is consistent with an isothermal profile with circular velocity
164+-20 km/s for an L* galaxy, consistent with typical disk rotation at this
luminosity. This halo mass normalization, combined with the halo profile
derived by Fischer et al (2000) from lensing analysis SDSS data, places a lower
limit of (2.7+-0.6) x 10^{12}h^{-1} solar masses on the mass of an L* galaxy
halo, in good agreement with satellite galaxy studies. Given the known
luminosity function of LCRS galaxies, and the assumption that for galaxies, we determine that the mass within 260\hkpc of normal
galaxies contributes to the density of the Universe (for
) or for . These lensing data suggest
that (95% CL), only marginally in agreement with the usual
Faber-Jackson or Tully-Fisher scaling. This is the most
complete direct inventory of the matter content of the Universe to date.Comment: 18 pages, incl. 3 figures. Submitted to ApJ 6/7/00, still no response
from the referee after four months
The environment and host haloes of the brightest z~6 Lyman-break galaxies
By studying the large-scale structure of the bright high-redshift Lyman-break
galaxy (LBG) population it is possible to gain an insight into the role of
environment in galaxy formation physics in the early Universe. We measure the
clustering of a sample of bright (-22.7<M_UV<-21.125) LBGs at z~6 and use a
halo occupation distribution (HOD) model to measure their typical halo masses.
We find that the clustering amplitude and corresponding HOD fits suggests that
these sources are highly biased (b~8) objects in the densest regions of the
high-redshift Universe. Coupled with the observed rapid evolution of the number
density of these objects, our results suggest that the shape of high luminosity
end of the luminosity function is related to feedback processes or dust
obscuration in the early Universe - as opposed to a scenario where these
sources are predominantly rare instances of the much more numerous M_UV ~ -19
population of galaxies caught in a particularly vigorous period of star
formation. There is a slight tension between the number densities and
clustering measurements, which we interpret this as a signal that a refinement
of the model halo bias relation at high redshifts or the incorporation of
quasi-linear effects may be needed for future attempts at modelling the
clustering and number counts. Finally, the difference in number density between
the fields (UltraVISTA has a surface density ~1.8 times greater than UDS) is
shown to be consistent with the cosmic variance implied by the clustering
measurements.Comment: 19 pages, 8 figures, accepted MNRAS 23rd March 201
On Combining Lensing Shear Information from Multiple Filters
We consider the possible gain in the measurement of lensing shear from
imaging data in multiple filters. Galaxy shapes may differ significantly across
filters, so that the same galaxy offers multiple samples of the shear. On the
other extreme, if galaxy shapes are identical in different filters, one can
combine them to improve the signal-to-noise and thus increase the effective
number density of faint, high redshift galaxies. We use the GOODS dataset to
test these scenarios by calculating the covariance matrix of galaxy
ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are
highly correlated, and estimate the gain in galaxy number density by combining
their shapes.Comment: 8 pages, no figures, submitted to JCA
A note on monopole moduli spaces
We discuss the structure of the framed moduli space of Bogomolny monopoles
for arbitrary symmetry breaking and extend the definition of its stratification
to the case of arbitrary compact Lie groups. We show that each stratum is a
union of submanifolds for which we conjecture that the natural metric is
hyperKahler. The dimensions of the strata and of these submanifolds are
calculated, and it is found that for the latter, the dimension is always a
multiple of four.Comment: 17 pages, LaTe
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