Semi-classical Approach to Charged Dilatonic Black Hole in Two Dimensions

We consider exactly solvable semi-classical theory of two dimensional dilatonic gravity with electromagnetic interactions. As was done in the paper by Russo, Susskind and Thorlacius, the term which changes the kinetic term is added to the action. The theory contains massless fermions as matter fields and there appear the quantum corrections including chiral anomaly. The screening effect due to the chiral anomaly has a tendency to cloak the singularity. In a region of the parameter space, the essential behavior of the theory is similar to that of Callan, Giddings, Harvey and Strominger's dilatonic black hole theory modified in the paper by Russo, Susskind and Thorlacius and the singularity formed by the collapsing matter emerges naked. We find, however, another region of the parameter space where the singularity disappears in a finite proper time. Furthermore, in the region of the parameter space, there appears a discontinuity in the metric on the trajectory of the collapsing matter, which would be a signal of topology changeComment: 21pp, NDA-FP-5/92, OCHA-PP-2

Low Tension Strings on a Cosmological Singularity

It has recently been argued that the singularity of the Milne orbifold can be resolved in higher spin theories. In string theory scattering amplitudes, however, the Milne singularity gives rise to ultraviolet divergences that signal uncontrolled backreaction. Since string theory in the low tension limit is expected to be a higher spin theory (although precise proposals only exist in special cases), we investigate what happens to these scattering amplitudes in the low tension limit. We point out that the known problematic ultraviolet divergences disappear in this limit. In addition we systematically identify all divergences of the simplest 2-to-2 string scattering amplitude on the Milne orbifold, and argue that the divergences that survive in the low tension limit have sensible infrared interpretations.Comment: 17 pages, 3 figures. V2: Complete list of IR divergences, more refs, published version. Plus one minor correctio

Some Comments On String Dynamics

Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity at such points which may signal quantum effects that persist even at weak coupling; and the rich dynamics of the real world under compactification, which may be relevant to some attempts to explain the vanishing of the cosmological constant.Comment: 26 page

Curing black hole singularities with local scale invariance

We show that Weyl-invariant dilaton gravity provides a description of black holes without classical spacetime singularities. Singularities appear due to ill-behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are: (1) singularities signal a phase transition from broken to unbroken phase of Weyl symmetry, (2) instead of a singularity there is a "baby-universe" or a white hole inside a black hole, (3) in the baby universe scenario there is a critical mass after which reducing mass makes black hole larger as viewed by outside observers, (4) if a black hole could be connected with white hole through the "singularity", this would require breakdown of (classical) geometric description, (5) the singularity of Schwarzschild BH solution is non-generic and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information-loss puzzle. The theory we use is basically a completion of General Relativity, containing neither additional physical excitations nor higher-derivative terms, but requires physical scalar field such as Higgs field of Standard Model. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point.Comment: 13 pages, 2 figures, v2: Improved explanations, restoration of Weyl symmetry emphasized. References added. v3: Misprints corrected, improved explanations, one new figure. References added. v4: improved explanations. Discussion on regularity of observables added. v5: improved presentation, additional examples added. Main results and conclusions unchanged. Matches published versio

Coarse-to-fine partitioning of signals

An empirically acquired signal can be analyzed in a multi-scale framework. Its multi-scale structure induces a hierarchical partitioning of the signal domain into topologically meaningful segments. A method is proposed to operationalize this using elementary results from singularity theory for certain generic solutions of the one-dimensional heat equatio

Binocular contrast discrimination needs monocular multiplicative noise.

The effects of signal and noise on contrast discrimination are difficult to separate because of a singularity in the signal-detection-theory model of two-alternative forced-choice contrast discrimination (Katkov, Tsodyks, & Sagi, 2006). In this article, we show that it is possible to eliminate the singularity by combining that model with a binocular combination model to fit monocular, dichoptic, and binocular contrast discrimination. We performed three experiments using identical stimuli to measure the perceived phase, perceived contrast, and contrast discrimination of a cyclopean sine wave. In the absence of a fixation point, we found a binocular advantage in contrast discrimination both at low contrasts (<4%), consistent with previous studies, and at high contrasts (≥34%), which has not been previously reported. However, control experiments showed no binocular advantage at high contrasts in the presence of a fixation point or for observers without accommodation. We evaluated two putative contrast-discrimination mechanisms: a nonlinear contrast transducer and multiplicative noise (MN). A binocular combination model (the DSKL model; Ding, Klein, & Levi, 2013b) was first fitted to both the perceived-phase and the perceived-contrast data sets, then combined with either the nonlinear contrast transducer or the MN mechanism to fit the contrast-discrimination data. We found that the best model combined the DSKL model with early MN. Model simulations showed that, after going through interocular suppression, the uncorrelated noise in the two eyes became anticorrelated, resulting in less binocular noise and therefore a binocular advantage in the discrimination task. Combining a nonlinear contrast transducer or MN with a binocular combination model (DSKL) provides a powerful method for evaluating the two putative contrast-discrimination mechanisms

Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe