We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $tau$ between volume volatilities above a given threshold q. For different thresholds q, the pr
obability density function P_q(tau) scales with mean interval <tau> as P_q(tau)=<tau>^{-1}f(tau/<tau>) and the tails of the scaling function can be well approximated by a power-law f(x)~x^{-gamma}. We also study the relation between the form of the distribution function P_q(tau) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P_q(tau) associated with these factors, suggesting a multi-scaling feature in the volume return intervals. We analyze the conditional probability P_q(tau|tau_0) for $tau$ following a certain interval tau_0, and find that P_q(tau|tau_0) depends on tau_0 such that immediately following a short/long return interval a second short/long return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.
We present results on two-particle angular correlations in Cu+Cu and Au+Au collisions at a center of mass energy per nucleon pair of 200 GeV over a broad range of pseudorapidity ($eta$) and azimuthal angle ($phi$) as a function of collision centralit
y. The PHOBOS detector at RHIC has a uniquely-large angular coverage for inclusive charged particles, which allows for the study of correlations on both long- and short-range scales. A complex two-dimensional correlation structure in $Delta eta$ and $Delta phi$ emerges, which is interpreted in the context of a cluster model. The effective cluster size and decay width are extracted from the two-particle pseudorapidity correlation functions. The effective cluster size found in semi-central Cu+Cu and Au+Au collisions is comparable to that found in proton-proton collisions but a non-trivial decrease of the size with increasing centrality is observed. Moreover, a comparison between results from Cu+Cu and Au+Au collisions shows an interesting scaling of the effective cluster size with the measured fraction of total cross section (which is related to the ratio of the impact parameter to the nuclear radius, $b/2R$), suggesting a geometric origin. Further analysis for pairs from restricted azimuthal regions shows that the effective cluster size at $Deltaphi sim 180^{circ}$ drops more rapidly toward central collisions than the size at $Deltaphi sim 0^{circ}$. The effect of limited $eta$ acceptance on the cluster parameters is also addressed, and a correction is applied to present cluster parameters for full $eta$ coverage, leading to much larger effective cluster sizes and widths than previously noted in the literature. These results should provide insight into the hot and dense medium created in heavy ion collisions.
