High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Effects of flanking band proximity, number, and modulation pattern on comodulation masking release

Comodulation masking release for a 700-Hz pure-tone signal was investigated as a function of the number and spectral positions of 20-Hz-wide comodulated flanking bands. In the first experiment, all stimuli were presented diotically. CMR was examined as a function of the number of flanking bands present, in conditions where the bands were arranged symmetrically around the signal frequency, were below the signal frequency, or were above the signal frequency. The number of flanking bands ranged from one to eight, and the magnitude of the diotic CMR ranged from approximately 5-16 dB. The results indicated: (1) bands closer to the signal resulted in larger masking release, and (2) more bands gave rise to larger CMR (but with diminishing returns above two flanking bands). Two additional sets of diotic conditions were examined and compared to the condition where all eight comodulated flanking bands were present: In one set of conditions, two of the eight flanking bands were removed; in the other set of conditions, two of the eight flanking bands were replaced with bands (termed "deviant" bands) that were not comodulated with respect to the other bands. There was very little effect of reducing eight bands to six, even when the removed bands were relatively near the signal frequency; however, CMR was substantially reduced when deviant bands were introduced, particularly when the deviant bands were placed relatively near the signal frequency. These reductions in CMR were slightly greater when each of the deviant bands had a unique modulation pattern (bideviant bands) than when the two deviant bands themselves shared the same modulation pattern (codeviant bands). In the second experiment, dichotic conditions were examined where the number and spectral positions of the flanking bands in the nonsignal ear were varied (the signal ear received only a 20-Hz-wide noise band centered on the signal frequency). The magnitude of the dichotic CMR ranged from approximately 2-10 dB, depending on condition. Effects of proximity and the number of flanking bands were similar to the effects obtained in diotic conditions. For both the diotic and the dichotic data, the effects of proximity were more consistent with an interpretation based upon across-channel processing than upon a within-channel interaction. The results obtained using deviant bands indicate that it is difficult for the auditory system to disregard the modulation pattern of flanking bands that differ from the modulation pattern of the on-signal band, particularly if such bands are proximal to the signal frequency.     

Comodulation masking release and auditory grouping

The detectability of a pure-tone signal masked by a band of noise centered on the signal can be improved by the addition of flanking noise bands, provided that the temporal envelopes of the flanking bands are correlated with that of the on-signal band. This phenomenon is referred to as comodulation masking release (CMR). The present study examined CMR in conditions in which some flanking noise bands were comodulated with the on-signal band, but other flanking bands (termed "deviant" bands) were not. Past research has indicated that CMR is often substantially reduced when deviant bands are present at spectral locations close to the signal frequency. An investigation was undertaken to determine whether the disruptive effects of such bands could be reduced by factors related to auditory grouping. The signal frequency was 100 Hz. In one condition, only 20-Hz-wide comodulated bands, centered on 400, 600, 800, 1000, 1200, 1400, and 1600 Hz, were present. The CMR for this condition, referenced to threshold for the on-signal band only, was approximately 15 dB. In a second condition, two deviant bands were added at 900 and 1100 Hz; their presence reduced the CMR to only 3-4 dB. The number of deviant bands was then increased progressively, from two to eight bands. Deviant bands either shared a common envelope (codeviant), or had unique envelopes (multideviant). The number of bands that were comodulated with the on-signal band was held constant at six.(ABSTRACT TRUNCATED AT 250 WORDS)     

Special conformal symmetries in general relativity

A geometrical discussion of special conformal vector fields in space-time is given. In particular, it is shown that if such a vector field is admitted, it is unique up to a constant scaling and the addition of a homothetic or a Killing vector field. In the case when the gradient of the conformal scalar associated with is non-null it is shown that other homothetic and affine symmetries are necessarily admitted by the space-time, that an intrinsic family of 2-dimensional flat submanifolds is determined in the space-time, that is, in general, hypersurface orthogonal and that the space-time, if non-flat, is necessarily (geodesically) incomplete. Other geometrical features of such space-times are also considered.     

Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality

Linear fractional composition operators on H2

If ? is an analytic function mapping the unit diskD into itself, the composition operatorC _? is the operator onH ² given byC _?f=fo?. The structure of the composition operatorC _? is usually complex, even if the function ? is fairly simple. In this paper, we consider composition operators whose symbol ? is a linear fractional transformation mapping the disk into itself. That is, we will assume throughout that $$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$ for some complex numbersa, b, c, d such that ? maps the unit diskD into itself. For this restricted class of examples, we address some of the basic questions of interest to operator theorists, including the computation of the adjoint.