On the Shape of Pulse Spectra in Gamma-Ray Bursts

The discovery (Liang & Kargatis 1996), that the peak energy of time-resolved spectra of gamma-ray burst (GRB) pulses decays exponentially with fluence, is analytically shown to imply that the time-integrated photon number spectrum of a pulse should have a unique shape, given by an underlying E^-1 behavior. We also show that the asymptotic low energy normalization of the time-integrated spectrum is equal to the exponential decay constant. We study analytically how this general behavior is modified in more realistic situations and show that diversity is then introduced in the properties of time-integrated GRB pulse spectra. We argue that further diversity will occur in time-integrated multi-pulse (complex) GRB spectra. The total energy received per cm^2 is approximately the decay constant times the maximum peak energy of the pulse. Our analytical results connect the properties of the time-integrated pulse spectrum with those of the time-resolved spectra, and can thus be used when studying observed GRB pulse spectra. We illustrate with the bright burst GRB 910807 and comment on GRB 910525 and GRB 921207.Comment: 7 pages, 6 postscript figures, accepted by the Astrophysical Journa

On the Time Evolution of Gamma-Ray Burst Pulses: A Self-Consistent Description

For the first time, the consequences of combining two well-established empirical relations, describing different aspects of the spectral evolution of observed gamma-ray burst (GRB) pulses, are explored. These empirical relations are: i) the hardness-intensity correlation, and ii) the hardness-photon fluence correlation. From these we find a self-consistent, quantitative, and compact description for the temporal evolution of pulse decay phases within a GRB light curve. In particular, we show that in the case of the two empirical relations both being valid, the instantaneous photon flux (intensity) must behave as 1/(1+ t/\tau) where \tau is a time constant that can be expressed in terms of the parameters of the two empirical relations. The time evolution is fully defined by two initial constants, and two parameters. We study a complete sample of 83 bright GRB pulses observed by the Compton Gamma-Ray Observatory and identify a major subgroup of GRB pulses (~45 %), which satisfy the spectral-temporal behavior described above. In particular, the decay phase follows a reciprocal law in time. It is unclear what physics causes such a decay phase.Comment: 4 pages, 1 figure, 2 tables, to appear in ApJ

Testing the predictability and efficiency of securitized real estate markets

This paper conducts tests of the random walk hypothesis and market efficiency for 14 national public real estate markets. Random walk properties of equity prices influence the return dynamics and determine the trading strategies of investors. To examine the stochastic properties of local real estate index returns and to test the hypothesis that public real estate stock prices follow a random walk, the single variance ratio tests of Lo and MacKinlay (1988) as well as the multiple variance ratio test of Chow and Denning (1993) are employed. Weak-form market efficiency is tested directly using non-parametric runs tests. Empirical evidence shows that weekly stock prices in major securitized real estate markets do not follow a random walk. The empirical findings of return predictability suggest that investors might be able to develop trading strategies allowing them to earn excess returns compared to a buy-and-hold strategy. --Securitized real estate,weak-form market efficiency,random walk hypothesis,variance ratio tests,runs test,trading strategies

Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems

We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ionization rates and quality factors.Comment: 6 pages, 2 figure

Stochastic Database Cracking: Towards Robust Adaptive Indexing in Main-Memory Column-Stores

Modern business applications and scientific databases call for inherently dynamic data storage environments. Such environments are characterized by two challenging features: (a) they have little idle system time to devote on physical design; and (b) there is little, if any, a priori workload knowledge, while the query and data workload keeps changing dynamically. In such environments, traditional approaches to index building and maintenance cannot apply. Database cracking has been proposed as a solution that allows on-the-fly physical data reorganization, as a collateral effect of query processing. Cracking aims to continuously and automatically adapt indexes to the workload at hand, without human intervention. Indexes are built incrementally, adaptively, and on demand. Nevertheless, as we show, existing adaptive indexing methods fail to deliver workload-robustness; they perform much better with random workloads than with others. This frailty derives from the inelasticity with which these approaches interpret each query as a hint on how data should be stored. Current cracking schemes blindly reorganize the data within each query's range, even if that results into successive expensive operations with minimal indexing benefit. In this paper, we introduce stochastic cracking, a significantly more resilient approach to adaptive indexing. Stochastic cracking also uses each query as a hint on how to reorganize data, but not blindly so; it gains resilience and avoids performance bottlenecks by deliberately applying certain arbitrary choices in its decision-making. Thereby, we bring adaptive indexing forward to a mature formulation that confers the workload-robustness previous approaches lacked. Our extensive experimental study verifies that stochastic cracking maintains the desired properties of original database cracking while at the same time it performs well with diverse realistic workloads.Comment: VLDB201