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 $v_s$ is associated with the adiabatic compressibility, which is is equal to $c$ for a non-rotating black hole and decreases as the angular momentum is increased. An extremal black hole has $v_s^2=0.9 \,c^2$ when the cosmological constant vanishes, and more generally $v_s$ is bounded below by $c/ {\sqrt 2}$.Comment: 8 pages, 1 figure, uses revtex4, references added in v

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, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. 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 ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. 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

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 $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.Comment: 10 page

Hardening electronic devices against very high total dose radiation environments

The possibilities and limitations of hardening silicon semiconductor devices to the high neutron and gamma radiation levels and greater than 10 to the eighth power rads required for the NERVA nuclear engine development are discussed. A comparison is made of the high dose neutron and gamma hardening potential of bipolar, metal insulator semiconductors and junction field effect transistors. Experimental data is presented on device degradation for the high neutron and gamma doses. Previous data and comparisons indicate that the JFET is much more immune to the combined neutron displacement and gamma ionizing effects than other transistor types. Experimental evidence is also presented which indicates that p channel MOS devices may be able to meet the requirements

Learning Contextual Reward Expectations for Value Adaptation

Substantial evidence indicates that subjective value is adapted to the statistics of reward expected within a given temporal context. However, how these contextual expectations are learned is poorly understood. To examine such learning, we exploited a recent observation that participants performing a gambling task adjust their preferences as a function of context. We show that, in the absence of contextual cues providing reward information, an average reward expectation was learned from recent past experience. Learning dependent on contextual cues emerged when two contexts alternated at a fast rate, whereas both cue-independent and cue-dependent forms of learning were apparent when two contexts alternated at a slower rate. Motivated by these behavioral findings, we reanalyzed a previous fMRI data set to probe the neural substrates of learning contextual reward expectations. We observed a form of reward prediction error related to average reward such that, at option presentation, activity in ventral tegmental area/substantia nigra and ventral striatum correlated positively and negatively, respectively, with the actual and predicted value of options. Moreover, an inverse correlation between activity in ventral tegmental area/substantia nigra (but not striatum) and predicted option value was greater in participants showing enhanced choice adaptation to context. The findings help understanding the mechanisms underlying learning of contextual reward expectation

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