Gravitational Wave Burst Source Direction Estimation using Time and Amplitude Information

In this article we study two problems that arise when using timing and amplitude estimates from a network of interferometers (IFOs) to evaluate the direction of an incident gravitational wave burst (GWB). First, we discuss an angular bias in the least squares timing-based approach that becomes increasingly relevant for moderate to low signal-to-noise ratios. We show how estimates of the arrival time uncertainties in each detector can be used to correct this bias. We also introduce a stand alone parameter estimation algorithm that can improve the arrival time estimation and provide root-sum-squared strain amplitude (hrss) values for each site. In the second part of the paper we discuss how to resolve the directional ambiguity that arises from observations in three non co-located interferometers between the true source location and its mirror image across the plane containing the detectors. We introduce a new, exact relationship among the hrss values at the three sites that, for sufficiently large signal amplitudes, determines the true source direction regardless of whether or not the signal is linearly polarized. Both the algorithm estimating arrival times, arrival time uncertainties, and hrss values and the directional follow-up can be applied to any set of gravitational wave candidates observed in a network of three non co-located interferometers. As a case study we test the methods on simulated waveforms embedded in simulations of the noise of the LIGO and Virgo detectors at design sensitivity.Comment: 10 pages, 14 figures, submitted to PR

Portfolio Optimization and the Random Magnet Problem

Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movement of assets are are mutually correlated and therefore knowledge of cross--correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this ``random magnet problem'' are given by the cross-correlation matrix {\bf \sf C} of stock returns. We find that random matrix theory allows us to make an estimate for {\bf \sf C} which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.Comment: 12 pages, 4 figures, revte

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj

Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Managing Risk of Bidding in Display Advertising

In this paper, we deal with the uncertainty of bidding for display advertising. Similar to the financial market trading, real-time bidding (RTB) based display advertising employs an auction mechanism to automate the impression level media buying; and running a campaign is no different than an investment of acquiring new customers in return for obtaining additional converted sales. Thus, how to optimally bid on an ad impression to drive the profit and return-on-investment becomes essential. However, the large randomness of the user behaviors and the cost uncertainty caused by the auction competition may result in a significant risk from the campaign performance estimation. In this paper, we explicitly model the uncertainty of user click-through rate estimation and auction competition to capture the risk. We borrow an idea from finance and derive the value at risk for each ad display opportunity. Our formulation results in two risk-aware bidding strategies that penalize risky ad impressions and focus more on the ones with higher expected return and lower risk. The empirical study on real-world data demonstrates the effectiveness of our proposed risk-aware bidding strategies: yielding profit gains of 15.4% in offline experiments and up to 17.5% in an online A/B test on a commercial RTB platform over the widely applied bidding strategies