Searching for a preferred direction with Union2.1 data

A cosmological preferred direction was reported from the type Ia supernovae (SNe Ia) data in recent years. We use the Union2.1 data to give a simple classification of such studies for the first time. Because the maximum anisotropic direction is independent of isotropic dark energy models, we adopt two cosmological models ($\Lambda$CDM, $w$CDM) for the hemisphere comparison analysis and $\Lambda$CDM model for dipole fit approach. In hemisphere comparison method, the matter density and the equation of state of dark energy are adopted as the diagnostic qualities in the $\Lambda$CDM model and $w$CDM model, respectively. In dipole fit approach, we fit the fluctuation of distance modulus. We find that there is a null signal for the hemisphere comparison method, while a preferred direction ($b=-14.3^\circ \pm 10.1^\circ, l=307.1^\circ \pm 16.2^\circ$) for the dipole fit method. This result indicates that the dipole fit is more sensitive than the hemisphere comparison method.Comment: 8 pages, 2 figures, accepted for publication in MNRA

A class of anisotropic (Finsler-) space-time geometries

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of isometries. These turn out to be isomorphic to subgroups of the Poincar\'e (Lorentz-) group complemented by the generator of a dilatation. The arising Finsler geometries may be used for the construction of relativistic theories testing the isotropy of space. It is shown that the Finsler space with the only preferred null direction is the anisotropic space closest to isotropic Minkowski-space of the full class discussed.Comment: 12 pages, latex, no figure

A simplified orthotropic formulation of the viscoplasticity theory based on overstress

An orthotropic, small strain viscoplasticity theory based on overstress is presented. In each preferred direction the stress is composed of time (rate) independent (or plastic) and viscous (or rate dependent) contributions. Tension-compression asymmetry can depend on direction and is included in the model. Upon a proper choice of a material constant one preferred direction can exhibit linear elastic response while the other two deform in a viscoplastic manner

A Model of Movement Coordinates in Motor Cortex: Posture-Dependent Changes in the Gain and Direction of Single Cell Tuning Curves

Central to the problem of elucidating the cortical mechanisms that mediate movement behavior is an investigation of the coordinate systems by which movement variables are encoded in the firing rates of individual motor cortical neurons. In the last decade, neurophysiologists have probed how the preferred direction of an individual motor cortical cell (as determined by a center-out task) will change with posture because such changes are useful for inferring underlying cordinates. However, while the importance of shifts in preferred direction is well-known and widely accepted, posture-dependent changes in the depth of modulation of a cell's tuning curve, i.e. gain changes, have not been similarly identified as a means of coordinate inference. This paper develops a vector field framework which, by viewing the preferred direction and the gain of a cell's tuning curve as dual components of a unitary response vector, can compute how each aspect of cell response covaries with posture as a function of the coordinate system in which a given cell is hypothesized to encode its movement information. This integrated approach leads to a model of motor cortical cell activity that codifies the following four observations: 1) cell activity correlates with hand movement direction, 2) cell activity correlates with hand movement speed, 3) preferred directions vary with posture, and 4) the modulation depth of tuning curves varies with posture. Finally, the model suggests general methods for testing coordinate hypotheses at the single cell level and example protocols arc simulated for three possible coordinate systems: Cartesian spatial, shoulder-centered, and joint angle.Defense Advanced Research Projects Agency (N00014-92-J-4015); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-90-00530, IRI-97-20333); Office of Naval Research (N00014-91-J-4100, N00014-92-J-1309, N00014-94-l-0940, N00014-95-1-0657)

Imprints of a Primordial Preferred Direction on the Microwave Background

Rotational invariance is a well-established feature of low-energy physics. Violations of this symmetry must be extremely small today, but could have been larger in earlier epochs. In this paper we examine the consequences of a small breaking of rotational invariance during the inflationary era when the primordial density fluctuations were generated. Assuming that a fixed-norm vector picked out a preferred direction during the inflationary era, we explore the imprint it would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $$ of the spherical-harmonic coefficients. We suggest that it is natural to expect that the imprint on the primordial power spectrum of a preferred spatial direction is approximately scale-invariant, and examine a simple model in which this is true.Comment: 7 pages, no figures; v5: Corrections, as well as use of more standard convention, in section I

The Langevin equation for systems with a preferred spatial direction

In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients.Comment: 1 figur

Modeling Reverse-Phi Motion-Selective Neurons in Cortex: Double Synaptic-Veto Mechanism

Reverse-phi motion is the illusory reversal of perceived direction of movement when the stimulus contrast is reversed in successive frames. Livingstone, Tsao, and Conway (2000) showed that direction-selective cells in striate cortex of the alert macaque monkey showed reversed excitatory and inhibitory regions when two different contrast bars were flashed sequentially during a two-bar interaction analysis. While correlation or motion energy models predict the reverse-phi response, it is unclear how neurons can accomplish this. We carried out detailed biophysical simulations of a direction-selective cell model implementing a synaptic shunting scheme. Our results suggest that a simple synaptic-veto mechanism with strong direction selectivity for normal motion cannot account for the observed reverse-phi motion effect. Given the nature of reverse-phi motion, a direct interaction between the ON and OFF pathway, missing in the original shunting-inhibition model, it is essential to account for the reversal of response. We here propose a double synaptic-veto mechanism in which ON excitatory synapses are gated by both delayed ON inhibition at their null side and delayed OFF inhibition at their preferred side. The converse applies to OFF excitatory synapses. Mapping this scheme onto the dendrites of a direction-selective neuron permits the model to respond best to normal motion in its preferred direction and to reverse-phi motion in its null direction. Two-bar interaction maps showed reversed excitation and inhibition regions when two different contrast bars are presented

Causality and CPT violation from an Abelian Chern-Simons-like term

We study a class of generalized Abelian gauge field theories where CPT symmetry is violated by a Chern-Simons-like term which selects a preferred direction in spacetime. Such Chern-Simons-like terms may either emerge as part of the low-energy effective action of a more fundamental theory or be produced by chiral anomalies over a nonsimply connected spacetime manifold. Specifically, we investigate the issues of unitarity and causality. We find that the behaviour of these gauge field theories depends on whether the preferred direction is spacelike or timelike. For a purely spacelike preferred direction, a well-behaved Feynman propagator exists and microcausality holds, which indicates the possibility of a consistent quantization of the theory. For timelike preferred directions, unitarity or causality is violated and a consistent quantization does not seem to be possible.Comment: LaTeX, 27 pages, v4: to appear in NP