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The eyes of suckermouth armoured catfish (Loricariidae, subfamily Hypostomus): pupil response, lenticular longitudinal spherical aberration and retinal topography
The dilated, round pupils of a species of suckermouth armoured catfish (Liposarcus pardalis) constrict slowly on illumination (over 35-40 min) to form crescent-shaped apertures. Ray tracing of He-Ne laser beams shows that the lenses of a related species (Pterygoplichthys etentaculus), which also has a crescent-shaped pupil, are well corrected for longitudinal spherical aberration, suggesting that the primary purpose of the irregular pupil in armoured catfish is not to correct such aberration. It is suggested that the iris operculum may serve to camouflage the pupil of these substrate-dwelling species. An examination of the catfish retina shows the photoreceptors to be exclusively single cones interspersed with elongate rods and demonstrates the presence of multiple optic nerve head papillae. Two areas of high ganglion cell density, each side of a vertically oriented falciform process, provide increased spatial resolving power along the axes examining the substrate in front of and behind the animal
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
Optimal integral force feedback and structured PI tracking control : application for objective lens positioner
Peer reviewedPostprin
Attractor Modulation and Proliferation in 1+ Dimensional Neural Networks
We extend a recently introduced class of exactly solvable models for
recurrent neural networks with competition between 1D nearest neighbour and
infinite range information processing. We increase the potential for further
frustration and competition in these models, as well as their biological
relevance, by adding next-nearest neighbour couplings, and we allow for
modulation of the attractors so that we can interpolate continuously between
situations with different numbers of stored patterns. Our models are solved by
combining mean field and random field techniques. They exhibit increasingly
complex phase diagrams with novel phases, separated by multiple first- and
second order transitions (dynamical and thermodynamic ones), and, upon
modulating the attractor strengths, non-trivial scenarios of phase diagram
deformation. Our predictions are in excellent agreement with numerical
simulations.Comment: 16 pages, 15 postscript figures, Late
Direct determination of absolute stereochemistry of α-methylselenocysteine using the Mosher method
Mosher amides of α-methylselenocysteine were synthesized to determine the absolute stereochemistry of the sterically hindered α-carbon utilizing 1H, 13C, 19F, and 77Se NMR spectroscopies. After analysis of these spectra using the established Mosher method, the stereochemistry of the α-carbon was determined to be (R), which was subsequently confirmed using x-ray crystallography
IgM-producing tumors in the BALB/c mouse: a model for B-cell maturation
Five adjuvant induced BALB/c tumors producing IgM—McPc 1748, W 3469, TEPC 183, McPc 774, and Y 5781—were characterized morphologically by electron microscopy, analysis of the distribution of surface-bound and intracytoplasmic IgM using immunofluorescence, and by biochemical study of IgM synthesis, turnover, and secretion. The cells of different tumors appear to represent different stages in B-cell maturation when compared to normal, lipopolysaccharide-stimulated B cells. Thus, McPc 1748 tumor cells resemble 10–25-h stimulated normal B cells, 3469 cells resemble 20–35-h stimulated B cells, TEPC 183 cells resemble 45–65-h stimulated B cells, Y 5781 cells resemble 80–110-h stimulated B cells, and McPc 774 cells resemble 100–130-h stimulated B cells
The Evolution of the Cosmic Microwave Background
We discuss the time dependence and future of the Cosmic Microwave Background
(CMB) in the context of the standard cosmological model, in which we are now
entering a state of endless accelerated expansion. The mean temperature will
simply decrease until it reaches the effective temperature of the de Sitter
vacuum, while the dipole will oscillate as the Sun orbits the Galaxy. However,
the higher CMB multipoles have a richer phenomenology. The CMB anisotropy power
spectrum will for the most part simply project to smaller scales, as the
comoving distance to last scattering increases, and we derive a scaling
relation that describes this behaviour. However, there will also be a dramatic
increase in the integrated Sachs-Wolfe contribution at low multipoles. We also
discuss the effects of tensor modes and optical depth due to Thomson
scattering. We introduce a correlation function relating the sky maps at two
times and the closely related power spectrum of the difference map. We compute
the evolution both analytically and numerically, and present simulated future
sky maps.Comment: 23 pages, 11 figures; references added; one figure dropped and minor
changes to match published version. For high-resolution versions of figures
and animations, see http://www.astro.ubc.ca/people/scott/future.htm
The Value of the Cosmological Constant
We make the cosmological constant, {\Lambda}, into a field and restrict the
variations of the action with respect to it by causality. This creates an
additional Einstein constraint equation. It restricts the solutions of the
standard Einstein equations and is the requirement that the cosmological wave
function possess a classical limit. When applied to the Friedmann metric it
requires that the cosmological constant measured today, t_{U}, be {\Lambda} ~
t_{U}^(-2) ~ 10^(-122), as observed. This is the classical value of {\Lambda}
that dominates the wave function of the universe. Our new field equation
determines {\Lambda} in terms of other astronomically measurable quantities.
Specifically, it predicts that the spatial curvature parameter of the universe
is {\Omega}_{k0} \equiv -k/a_(0)^(2)H^2= -0.0055, which will be tested by
Planck Satellite data. Our theory also creates a new picture of self-consistent
quantum cosmological history.Comment: 6 pages. This article received Third Prize in the 2011 Gravity
Research Foundation Awards for Essays on Gravitatio
The effect of crystal orientation on the cryogenic strength of hydroxide catalysis bonded sapphire
Hydroxide catalysis bonding has been used in gravitational wave detectors to precisely and securely join components of quasi-monolithic silica suspensions. Plans to operate future detectors at cryogenic temperatures has created the
need for a change in the test mass and suspension material. Mono-crystalline sapphire is one candidate material for use at cryogenic temperatures and is being investigated for use in the KAGRA detector. The crystalline structure of sapphire may influence the properties of the hydroxide catalysis bond formed. Here, results are presented of studies of the potential influence of the crystal orientation of sapphire on the shear strength of the hydroxide catalysis bonds formed between sapphire samples. The strength was tested at approximately 8 K; this is the first measurement of the strength of such bonds between
sapphire at such reduced temperatures. Our results suggest that all orientation combinations investigated produce bonds of sufficient strength for use in typical mirror suspension designs, with average strengths >23 MPa
Grand Unification as a Bridge Between String Theory and Phenomenology
In the first part of the talk, I explain what empirical evidence points to
the need for having an effective grand unification-like symmetry possessing the
symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive
theory including gravity--be it string/M theory or a reincarnation--this
evidence then suggests that such a theory should lead to an effective grand
unification-like symmetry as above in 4D, near the string-GUT-scale, rather
than the standard model symmetry. Advantages of an effective supersymmetric
G(224) = SU(2) SU(2) SU(4) or SO(10) symmetry in 4D
in explaining (i) observed neutrino oscillations, (ii) baryogenesis via
leptogenesis, and (iii) certain fermion mass-relations are noted. And certain
distinguishing tests of a SUSY G(224) or SO(10)-framework involving CP and
flavor violations (as in , , edm's of the
neutron and the electron) as well as proton decay are briefly mentioned.
Recalling some of the successes we have had in our understanding of nature so
far, and the current difficulties of string/M theory as regards the large
multiplicity of string vacua, some comments are made on the traditional goal of
understanding {\em vis a vis} the recently evolved view of landscape and
anthropism.Comment: A chart showing some insights gained in the world of the very small
and that of the very large is included. A few relevant references are added.
Some clarification is made in the last section as regards the question of
understanding versus landscape and anthropis
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