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

Modular symmetry and temperature flow of conductivities in quantum Hall systems with varying Zeeman energy

The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the conductivities as a function of temperature, with the magnetic field fixed, are constructed for different Zeeman energies, for samples with particle-hole symmetry.Comment: 15 pages, 13 figure

Value encoding in the globus pallidus: fMRI reveals an interaction effect between reward and dopamine drive

The external part of the globus pallidus (GPe) is a core nucleus of the basal ganglia (BG) whose activity is disrupted under conditions of low dopamine release, as in Parkinson's disease. Current models assume decreased dopamine release in the dorsal striatum results in deactivation of dorsal GPe, which in turn affects motor expression via a regulatory effect on other nuclei of the BG. However, recent studies in healthy and pathological animal models have reported neural dynamics that do not match with this view of the GPe as a relay in the BG circuit. Thus, the computational role of the GPe in the BG is still to be determined. We previously proposed a neural model that revisits the functions of the nuclei of the BG, and this model predicts that GPe encodes values which are amplified under a condition of low striatal dopaminergic drive. To test this prediction, we used an fMRI paradigm involving a within-subject placebo-controlled design, using the dopamine antagonist risperidone, wherein healthy volunteers performed a motor selection and maintenance task under low and high reward conditions. ROI-based fMRI analysis revealed an interaction between reward and dopamine drive manipulations, with increased BOLD activity in GPe in a high compared to low reward condition, and under risperidone compared to placebo. These results confirm the core prediction of our computational model, and provide a new perspective on neural dynamics in the BG and their effects on motor selection and cognitive disorders

Physical disruption of intervertebral disc promotes cell clustering and a degenerative phenotype

© 2019, The Author(s). To test the hypothesis that physical disruption of an intervertebral disc disturbs cell-matrix binding, leading to cell clustering and increased expression of matrix degrading enzymes that contribute towards degenerative disc cell phenotype. Lumbar disc tissue was removed at surgery from 21 patients with disc herniation, 11 with disc degeneration, and 8 with adolescent scoliosis. 5 μm sections were examined with histology, and 30-µm sections by confocal microscopy. Antibodies were used against integrin α5beta1, matrix metalloproteinases (MMP) 1, MMP-3, caspase 3, and denatured collagen types I and II. Spatial associations were sought between cell clustering and various degenerative features. An additional, 11 non-herniated human discs were used to examine causality: half of each specimen was cultured in a manner that allowed free ‘unconstrained’ swelling (similar to a herniated disc in vivo), while the other half was cultured within a perspex ring that allowed ‘constrained’ swelling. Changes were monitored over 36 h using live-cell imaging. 1,9-Di-methyl methylene blue (DMMB) assay for glycosaminoglycan loss was carried out from tissue medium. Partially constrained specimens showed little swelling or cell movement in vitro. In contrast, unconstrained swelling significantly increased matrix distortion, glycosaminoglycan loss, exposure of integrin binding sites, expression of MMPs 1 and 3, and collagen denaturation. In the association studies, herniated disc specimens showed changes that resembled unconstrained swelling in vitro. In addition, they exhibited increased cell clustering, apoptosis, MMP expression, and collagen denaturation compared to ‘control’ discs. Results support our hypothesis. Further confirmation will require longitudinal animal experiments

Real and complex connections for canonical gravity

Both real and complex connections have been used for canonical gravity: the complex connection has SL(2,C) as gauge group, while the real connection has SU(2) as gauge group. We show that there is an arbitrary parameter $\beta$ which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory. A value for $\beta$ could be could be singled out in the quantum theory by the Hamiltonian constraint, or by the rotation to the complex Ashtekar connection.Comment: 8 pages, RevTeX, no figure

X-Ray and UV Orbital Phase Dependence in LMC X-3

The black-hole binary LMC X-3 is known to be variable on time scales of days to years. We investigate X-ray and ultraviolet variability in the system as a function of the 1.7 day binary phase using a 6.4 day observation with the Rossi X-ray Timing Explorer (RXTE) from December 1998. An abrupt 14% flux decrease, lasting nearly an entire orbit, is followed by a return to previous flux levels. This behavior occurs twice, at nearly the same binary phase, but it is not present in consecutive orbits. When the X-ray flux is at lower intensity, a periodic amplitude modulation of 7% is evident in data folded modulo the orbital period. The higher intensity data show weaker correlation with phase. This is the first report of X-ray variability at the orbital period of LMC X-3. Archival RXTE observations of LMC X--3 during a high flux state in December 1996 show similar phase dependence. An ultraviolet light curve obtained with the High Speed Photometer aboard the Hubble Space Telescope shows orbital modulation consistent with that in the optical, caused by the ellipsoidal variation of the spatially deformed companion. The X-ray spectrum of LMC X-3 can be acceptably represented by a phenomenological disk-black-body plus a power law. Changes in the spectrum of LMC X-3 during our observations are compatible with earlier observations during which variations in the 2-10 keV flux are tracked closely by the disk geometry spectral model parameter.Comment: 11 pages, 7 figures, ApJ in pres

A computational account of threat-related attentional bias

Visual selective attention acts as a filter on perceptual information, facilitating learning and inference about important events in an agent’s environment. A role for visual attention in reward-based decisions has previously been demonstrated, but it remains unclear how visual attention is recruited during aversive learning, particularly when learning about multiple stimuli concurrently. This question is of particular importance in psychopathology, where enhanced attention to threat is a putative feature of pathological anxiety. Using an aversive reversal learning task that required subjects to learn, and exploit, predictions about multiple stimuli, we show that the allocation of visual attention is influenced significantly by aversive value but not by uncertainty. Moreover, this relationship is bidirectional in that attention biases value updates for attended stimuli, resulting in heightened value estimates. Our findings have implications for understanding biased attention in psychopathology and support a role for learning in the expression of threat-related attentional biases in anxiety

SWIFT Observations of a Far UV Luminosity Component in SS433

SS433 is a binary system showing relativistic Doppler shifts in its two sets of emission lines. The origin of its UV continuum is not well established. We observed SS433 to determine the emission mechanism responsible for its far UV spectrum. The source was observed at several different phases of both its 13 d orbital period and 162.5 d precession period using the UVOT and XRT detector systems on Swift. The far UV spectrum down to 1880 Angstrom lies significantly above the spectral flux distribution predicted by extrapolating the reddened blackbody continuum that fits the spectrum above 3500 Angstroms. The intensity of the far UV flux varies over a period of days and the variability is correlated with the variability of the soft X-ray flux from the source. An emission mechanism in addition to those previously detected in the optical and X-ray regions must exist in the far UV spectrum of SS433

A Covariant Approach To Ashtekar's Canonical Gravity

A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the equations of motion and a symplectic functional two form is constructed which is Lorentz and general co-ordinate invariant. The subtleties and difficulties due to the complex nature of Ashtekar's variables are addressed and resolved.Comment: 18 pages, Plain Te