X-ray flares have routinely been observed from the supermassive black hole, Sagittarius A$^star$ (Sgr A$^star$), at our Galactic center. The nature of these flares remains largely unclear, despite of many theoretical models. In this paper, we study t
he statistical properties of the Sgr A$^star$ X-ray flares, by fitting the count rate (CR) distribution and the structure function (SF) of the light curve with a Markov Chain Monte Carlo (MCMC) method. With the 3 million second textit{Chandra} observations accumulated in the Sgr A$^star$ X-ray Visionary Project, we construct the theoretical light curves through Monte Carlo simulations. We find that the $2-8$ keV X-ray light curve can be decomposed into a quiescent component with a constant count rate of $sim6times10^{-3}~$count s$^{-1}$ and a flare component with a power-law fluence distribution $dN/dEpropto E^{-alpha_{rm E}}$ with $alpha_{rm E}=1.65pm0.17$. The duration-fluence correlation can also be modelled as a power-law $Tpropto E^{alpha_{rm ET}}$ with $alpha_{rm ET} < 0.55$ ($95%$ confidence). These statistical properties are consistent with the theoretical prediction of the self-organized criticality (SOC) system with the spatial dimension $S = 3$. We suggest that the X-ray flares represent plasmoid ejections driven by magnetic reconnection (similar to solar flares) in the accretion flow onto the black hole.
We develop the concept of ABC-Boost (Adaptive Base Class Boost) for multi-class classification and present ABC-MART, a concrete implementation of ABC-Boost. The original MART (Multiple Additive Regression Trees) algorithm has been very successful in
large-scale applications. For binary classification, ABC-MART recovers MART. For multi-class classification, ABC-MART considerably improves MART, as evaluated on several public data sets.
Compressed Counting (CC)} was recently proposed for approximating the $alpha$th frequency moments of data streams, for $0<alpha leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on symmetric stabl
e random projections}, especially as $alphato 1$. A direct application of CC is to estimate the entropy, which is an important summary statistic in Web/network measurement and often serves a crucial feature for data mining. The Renyi entropy and the Tsallis entropy are functions of the $alpha$th frequency moments; and both approach the Shannon entropy as $alphato 1$. A recent theoretical work suggested using the $alpha$th frequency moment to approximate the Shannon entropy with $alpha=1+delta$ and very small $|delta|$ (e.g., $<10^{-4}$). In this study, we experiment using CC to estimate frequency moments, Renyi entropy, Tsallis entropy, and Shannon entropy, on real Web crawl data. We demonstrate the variance-bias trade-off in estimating Shannon entropy and provide practical recommendations. In particular, our experiments enable us to draw some important conclusions: (1) As $alphato 1$, CC dramatically improves {em symmetric stable random projections} in estimating frequency moments, Renyi entropy, Tsallis entropy, and Shannon entropy. The improvements appear to approach infinity. (2) Using {em symmetric stable random projections} and $alpha = 1+delta$ with very small $|delta|$ does not provide a practical algorithm because the required sample size is enormous.
Compressed Counting (CC) was recently proposed for very efficiently computing the (approximate) $alpha$th frequency moments of data streams, where $0<alpha <= 2$. Several estimators were reported including the geometric mean estimator, the harmonic m
ean estimator, the optimal power estimator, etc. The geometric mean estimator is particularly interesting for theoretical purposes. For example, when $alpha -> 1$, the complexity of CC (using the geometric mean estimator) is $O(1/epsilon)$, breaking the well-known large-deviation bound $O(1/epsilon^2)$. The case $alphaapprox 1$ has important applications, for example, computing entropy of data streams. For practical purposes, this study proposes the optimal quantile estimator. Compared with previous estimators, this estimator is computationally more efficient and is also more accurate when $alpha> 1$.
we will present an estimation for the upper-bound of the amount of 16-bytes plaintexts for English texts, which indicates that the block ciphers with block length no more than 16-bytes will be subject to recover plaintext attacks in the occasions of plaintext -known or plaintext-chosen attacks.
