Chandra survey in the AKARI North Ecliptic Pole Deep Field. I. X-ray data, point-like source catalog, sensitivity maps, and number counts

We present data products from the 300 ks Chandra survey in the AKARI North Ecliptic Pole (NEP) deep field. This field has a unique set of 9-band infrared photometry covering 2-24 micron from the AKARI Infrared Camera, including mid-infrared (MIR) bands not covered by Spitzer. The survey is one of the deepest ever achieved at ~15 micron, and is by far the widest among those with similar depths in the MIR. This makes this field unique for the MIR-selection of AGN at z~1. We design a source detection procedure, which performs joint Maximum Likelihood PSF fits on all of our 15 mosaicked Chandra pointings covering an area of 0.34 square degree. The procedure has been highly optimized and tested by simulations. We provide a point source catalog with photometry and Bayesian-based 90 per cent confidence upper limits in the 0.5-7, 0.5-2, 2-7, 2-4, and 4-7 keV bands. The catalog contains 457 X-ray sources and the spurious fraction is estimated to be ~1.7 per cent. Sensitivity and 90 per cent confidence upper flux limits maps in all bands are provided as well. We search for optical MIR counterparts in the central 0.25 square degree, where deep Subaru Suprime-Cam multiband images exist. Among the 377 X-ray sources detected there, ~80 per cent have optical counterparts and ~60 per cent also have AKARI mid-IR counterparts. We cross-match our X-ray sources with MIR-selected AGN from Hanami et al. (2012). Around 30 per cent of all AGN that have MID-IR SEDs purely explainable by AGN activity are strong Compton-thick AGN candidates.Comment: 23 pages, 20 figures; catalogs, sensitivity maps, and upper limit flux maps are available from the VizieR Servic

Adaptive Investment Strategies For Periodic Environments

In this paper, we present an adaptive investment strategy for environments with periodic returns on investment. In our approach, we consider an investment model where the agent decides at every time step the proportion of wealth to invest in a risky asset, keeping the rest of the budget in a risk-free asset. Every investment is evaluated in the market via a stylized return on investment function (RoI), which is modeled by a stochastic process with unknown periodicities and levels of noise. For comparison reasons, we present two reference strategies which represent the case of agents with zero-knowledge and complete-knowledge of the dynamics of the returns. We consider also an investment strategy based on technical analysis to forecast the next return by fitting a trend line to previous received returns. To account for the performance of the different strategies, we perform some computer experiments to calculate the average budget that can be obtained with them over a certain number of time steps. To assure for fair comparisons, we first tune the parameters of each strategy. Afterwards, we compare the performance of these strategies for RoIs with different periodicities and levels of noise.Comment: Paper submitted to Advances in Complex Systems (November, 2007) 22 pages, 9 figure

Collective behavior of stock price movements in an emerging market

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intra-sector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.Comment: 10 pages, 10 figure

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

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

Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text

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

Learning a Factor Model via Regularized PCA

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those produced by pre-existing factor analysis approaches. We also establish theoretical results that explain how our algorithm corrects the biases induced by conventional approaches. An important feature of our algorithm is that its computational requirements are similar to those of PCA, which enjoys wide use in large part due to its efficiency