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Psychiatric morbidity in epilepsy: a case controlled study of adults receiving disability benefits
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Riccati parameter modes from Newtonian free damping motion by supersymmetry
We determine the class of damped modes \tilde{y} which are related to the
common free damping modes y by supersymmetry. They are obtained by employing
the factorization of Newton's differential equation of motion for the free
damped oscillator by means of the general solution of the corresponding Riccati
equation together with Witten's method of constructing the supersymmetric
partner operator. This procedure leads to one-parameter families of (transient)
modes for each of the three types of free damping, corresponding to a
particular type of %time-dependent angular frequency. %time-dependent,
antirestoring acceleration (adding up to the usual Hooke restoring
acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y},
where \gamma is the family parameter that has been chosen as the inverse of the
Riccati integration constant. In supersymmetric terms, they represent all those
one Riccati parameter damping modes having the same Newtonian free damping
partner modeComment: 6 pages, twocolumn, 6 figures, only first 3 publishe
Observables for spacetimes with two Killing field symmetries
The Einstein equations for spacetimes with two commuting spacelike Killing
field symmetries are studied from a Hamiltonian point of view. The complexified
Ashtekar canonical variables are used, and the symmetry reduction is performed
directly in the Hamiltonian theory. The reduced system corresponds to the field
equations of the SL(2,R) chiral model with additional constraints.
On the classical phase space, a method of obtaining an infinite number of
constants of the motion, or observables, is given. The procedure involves
writing the Hamiltonian evolution equations as a single `zero curvature'
equation, and then employing techniques used in the study of two dimensional
integrable models. Two infinite sets of observables are obtained explicitly as
functionals of the phase space variables. One set carries sl(2,R) Lie algebra
indices and forms an infinite dimensional Poisson algebra, while the other is
formed from traces of SL(2,R) holonomies that commute with one another. The
restriction of the (complex) observables to the Euclidean and Lorentzian
sectors is discussed.
It is also shown that the sl(2,R) observables can be associated with a
solution generating technique which is linked to that given by Geroch.Comment: 23 pages (LateX-RevTeX), Alberta-Thy-55-9
Einstein's equations and the chiral model
The vacuum Einstein equations for spacetimes with two commuting spacelike
Killing field symmetries are studied using the Ashtekar variables. The case of
compact spacelike hypersurfaces which are three-tori is considered, and the
determinant of the Killing two-torus metric is chosen as the time gauge. The
Hamiltonian evolution equations in this gauge may be rewritten as those of a
modified SL(2) principal chiral model with a time dependent `coupling
constant', or equivalently, with time dependent SL(2) structure constants. The
evolution equations have a generalized zero-curvature formulation. Using this
form, the explicit time dependence of an infinite number of
spatial-diffeomorphism invariant phase space functionals is extracted, and it
is shown that these are observables in the sense that they Poisson commute with
the reduced Hamiltonian. An infinite set of observables that have SL(2) indices
are also found. This determination of the explicit time dependence of an
infinite set of spatial-diffeomorphism invariant observables amounts to the
solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.
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The Neurophysiology of Functionally Meaningful Categories: Macaque Ventrolateral Prefrontal Cortex Plays a Critical Role in Spontaneous Categorization of Species-Specific Vocalizations
Neurophysiological studies in nonhuman primates have demonstrated that the prefrontal cortex (PFC) plays a critical role in the acquisition of learned categories following training. What is presently unclear is whether this cortical area also plays a role in spontaneous recognition and discrimination of natural categories. Here, we explore this possibility by recording from neurons in the PFC while rhesus listen to species-specific vocalizations that vary in terms of their social function and acoustic morphology. We found that ventral prefrontal cortex (vPFC) activity, on average, did not differentiate between food calls that were associated with the same functional category, despite having different acoustic properties. In contrast, vPFC activity differentiated between food calls associated with different functional classes and specifically, information about the quality and motivational value of the food. These results suggest that the vPFC is involved in the categorization of socially meaningful signals, thereby both extending its previously conceived role in the acquisition of learned categories and showing the significance of using natural categorical distinctions in the study of neural mechanisms.Psycholog
Composition of the Innermost Core Collapse Supernova Ejecta
With presently known input physics and computer simulations in 1D, a
self-consistent treatment of core collapse supernovae does not yet lead to
successful explosions, while 2D models show some promise. Thus, there are
strong indications that the delayed neutrino mechanism works combined with a
multi-D convection treatment for unstable layers. On the other hand there is a
need to provide correct nucleosynthesis abundances for the progressing field of
galactic evolution and observations of low metallicity stars. The innermost
ejecta is directly affected by the explosion mechanism, i.e. most strongly the
yields of Fe-group nuclei for which an induced piston or thermal bomb treatment
will not provide the correct yields because the effect of neutrino interactions
is not included. We apply parameterized variations to the neutrino scattering
cross sections and alternatively, parameterized variations are applied to the
neutrino absorption cross sections on nucleons in the ``gain region''. We find
that both measures lead to similar results, causing explosions and a Ye>0.5 in
the innermost ejected layers, due to the combined effect of a short weak
interaction time scale and a negligible electron degeneracy, unveiling the
proton-neutron mass difference. We include all weak interactions (electron and
positron capture, beta-decay, neutrino and antineutrino capture on nuclei, and
neutrino and antineutrino capture on nucleons) and present first
nucleosynthesis results for these innermost ejected layers to discuss how they
improve predictions for Fe-group nuclei. The proton-rich environment results in
enhanced abundances of 45Sc, 49Ti, and 64Zn as requested by chemical evolution
studies and observations of low metallicity stars as well as appreciable
production of nuclei in the mass range up to A=80.Comment: 13 pages, 8 figures. Final versio
How can exact and approximate solutions of Einstein's field equations be compared?
The problem of comparison of the stationary axisymmetric vacuum solutions
obtained within the framework of exact and approximate approaches for the
description of the same general relativistic systems is considered. We suggest
two ways of carrying out such comparison: (i) through the calculation of the
Ernst complex potential associated with the approximate solution whose form on
the symmetry axis is subsequently used for the identification of the exact
solution possessing the same multipole structure, and (ii) the generation of
approximate solutions from exact ones by expanding the latter in series of
powers of a small parameter. The central result of our paper is the derivation
of the correct approximate analogues of the double-Kerr solution possessing the
physically meaningful equilibrium configurations. We also show that the
interpretation of an approximate solution originally attributed to it on the
basis of some general physical suppositions may not coincide with its true
nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure
Iridium complexes of the conformationally rigid IBioxMe4Ligand : hydride complexes and dehydrogenation of cyclooctene
A method for accessing the formally 14 VE iridium(III) hydride fragment {Ir(IBioxMe4)2(H)2}+ (2), containing the conformationally rigid NHC ligand IBioxMe4, is reported. Hydrogenation of trans-[Ir(IBioxMe4)2(COE)Cl] (1) in the presence of excess Na[BArF4] leads to the formation of dimeric [{Ir(IBioxMe4)2(H)2}2Cl][BArF4] (3), which is structurally fluxional in solution and acts as a reservoir of monomeric 2 in the presence of excess halogen ion abstractor. Stable dihydride complexes trans-[Ir(IBioxMe4)2(2,2′-bipyridine)(H)2][BArF4] (4) and [Ir(IBioxMe4)3(H)2][BArF4] (5) were subsequently isolated through in situ trapping of 2 using 2,2′-bipyridine and IBioxMe4, respectively, and fully characterized. Using mixtures of 3 and Na[BArF4] as a latent source of 2, the reactive monomeric fragment’s reactivity was explored with excess ethylene and cyclooctene, and trans-[Ir(IBioxMe4)2(C2H4)2][BArF4] (6) and cis-[Ir(IBioxMe4)2(COD)][BArF4] (7) were isolated, respectively, through sacrificial hydrogenation of the alkenes. Complex 6 is notable for the adoption of a very unusual orthogonal arrangement of the trans-ethylene ligands in the solid state, which has been analyzed computationally using energy and charge decomposition (EDA-NOCV). The formation of 7 via transfer dehydrogenation of COE highlights the ability to partner IBioxMe4 with reactive metal centers capable of C–H bond activation, without intramolecular activation. Reaction of 7 with CO slowly formed trans-[Ir(IBioxMe4)2(CO)2][BArF4] (8), but the equivalent reaction with bis-ethylene 6 was an order of magnitude faster, quantifying the strong coordination of COD in 7
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