7,156 research outputs found
Non-commutative Complex Projective Spaces and the Standard Model
The standard model fermion spectrum, including a right handed neutrino, can
be obtained as a zero-mode of the Dirac operator on a space which is the
product of complex projective spaces of complex dimension two and three. The
construction requires the introduction of topologically non-trivial background
gauge fields. By borrowing from ideas in Connes' non-commutative geometry and
making the complex spaces `fuzzy' a matrix approximation to the fuzzy space
allows for three generations to emerge. The generations are associated with
three copies of space-time. Higgs' fields and Yukawa couplings can be
accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th
birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri
sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe
Compressibility of rotating black holes
Interpreting the cosmological constant as a pressure, whose thermodynamically
conjugate variable is a volume, modifies the first law of black hole
thermodynamics. Properties of the resulting thermodynamic volume are
investigated: the compressibility and the speed of sound of the black hole are
derived in the case of non-positive cosmological constant. The adiabatic
compressibility vanishes for a non-rotating black hole and is maximal in the
extremal case --- comparable with, but still less than, that of a cold neutron
star. A speed of sound is associated with the adiabatic compressibility,
which is is equal to for a non-rotating black hole and decreases as the
angular momentum is increased. An extremal black hole has
when the cosmological constant vanishes, and more generally is bounded
below by .Comment: 8 pages, 1 figure, uses revtex4, references added in v
The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law
Low-energy transport measurements in Quantum Hall systems have been argued to
be governed by emergent modular symmetries whose predictions are robust against
many of the detailed microscopic dynamics. We propose the recently-observed
quantum Hall effect in graphene as a test of these ideas, and identify to this
end a class of predictions for graphene which would follow from the same
modular arguments. We are led to a suite of predictions for high mobility
samples that differs from those obtained for the conventional quantum Hall
effect in semiconductors, including: predictions for the locations of the
quantum Hall plateaux; predictions for the positions of critical points on
transitions between plateaux; a selection rule for which plateaux can be
connected by low-temperature transitions; and a semi-circle law for
conductivities traversed during these transitions. Many of these predictions
appear to provide a good description of graphene measurements performed with
intermediate-strength magnetic fields.Comment: 4 pages, 2 figure
Neural activity associated with the passive prediction of ambiguity and risk for aversive events
In economic decision making, outcomes are described in terms of risk (uncertain outcomes with certain probabilities) and ambiguity
(uncertain outcomes with uncertain probabilities). Humans are more averse to ambiguity than to risk, with a distinct neural system
suggested as mediating this effect. However, there has been no clear disambiguation of activity related to decisions themselves from
perceptual processing of ambiguity. In a functional magnetic resonance imaging (fMRI) experiment, we contrasted ambiguity, defined as
a lack of information about outcome probabilities, to risk, where outcome probabilities are known, or ignorance, where outcomes are
completely unknown and unknowable.Wemodified previously learned pavlovian CSstimuli such that they became an ambiguous cue
and contrasted evoked brain activity both with an unmodified predictive CS(risky cue), and a cue that conveyed no information about
outcome probabilities (ignorance cue). Compared with risk, ambiguous cues elicited activity in posterior inferior frontal gyrus and
posterior parietal cortex during outcome anticipation. Furthermore, a similar set of regions was activated when ambiguous cues were
compared with ignorance cues. Thus, regions previously shown to be engaged by decisions about ambiguous rewarding outcomes are
also engaged by ambiguous outcome prediction in the context of aversive outcomes. Moreover, activation in these regions was seen even
when no actual decision is made. Our findings suggest that these regions subserve a general function of contextual analysis when search
for hidden information during outcome anticipation is both necessary and meaningful
Stress concentration at fillets, holes, and keyways as found by the plaster-model method
Bibliography: p. 31-32
The Information Geometry of the One-Dimensional Potts Model
In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, , and the
external field variable, , in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, , of this metric can be calculated explicitly in
the thermodynamic limit and is found to be . This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
In this note we calculate for the one-dimensional -state Potts
model, finding an expression of the form , where is the Potts
analogue of . This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.Comment: 9 pages + 4 eps figure
LANDSAT application of remote sensing to shoreline-form analysis
There are no author-identified significant results in this report
Noncommutative BTZ Black Hole and Discrete Time
We search for all Poisson brackets for the BTZ black hole which are
consistent with the geometry of the commutative solution and are of lowest
order in the embedding coordinates. For arbitrary values for the angular
momentum we obtain two two-parameter families of contact structures. We obtain
the symplectic leaves, which characterize the irreducible representations of
the noncommutative theory. The requirement that they be invariant under the
action of the isometry group restricts to symplectic leaves,
where is associated with the Schwarzschild time. Quantization may then lead
to a discrete spectrum for the time operator.Comment: 10 page
Neural signals encoding shifts in beliefs
Dopamine is implicated in a diverse range of cognitive functions including cognitive flexibility, task switching, signalling novel or unexpected stimuli as well as advance information. There is also longstanding line of thought that links dopamine with belief formation and, crucially, aberrant belief formation in psychosis. Integrating these strands of evidence would suggest that dopamine plays a central role in belief updating and more specifically in encoding of meaningful information content in observations. The precise nature of this relationship has remained unclear. To directly address this question we developed a paradigm that allowed us to decompose two distinct types of information content, information-theoretic surprise that reflects the unexpectedness of an observation, and epistemic value that induces shifts in beliefs or, more formally, Bayesian surprise. Using functional magnetic-resonance imaging in humans we show that dopamine-rich midbrain regions encode shifts in beliefs whereas surprise is encoded in prefrontal regions, including the pre-supplementary motor area and dorsal cingulate cortex. By linking putative dopaminergic activity to belief updating these data provide a link to false belief formation that characterises hyperdopaminergic states associated with idiopathic and drug induced psychosis
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