Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence

We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding $L_1$ and $L_2$ statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal strength and sparsity. The two alternative tests can attain the same detection boundary of the Higher Criticism test in [Ann. Statist. 32 (2004) 962-994] which was established for uncorrelated Gaussian data. It is demonstrated that the maximal $L_2$-thresholding test is at least as powerful as the maximal $L_1$-thresholding test, and both the maximal $L_2$ and $L_1$-thresholding tests are at least as powerful as the Higher Criticism test.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1168 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Self-organization and phase transition in financial markets with multiple choices

Market confidence is essential for successful investing. By incorporating multi-market into the evolutionary minority game, we investigate the effects of investor beliefs on the evolution of collective behaviors and asset prices. When there exists another investment opportunity, market confidence, including overconfidence and under-confidence, is not always good or bad for investment. The roles of market confidence is closely related to market impact. For low market impact, overconfidence in a particular asset makes an investor become insensitive to losses and a delayed strategy adjustment leads to a decline in wealth, and thereafter, one's runaway from the market. For high market impact, under-confidence in a particular asset makes an investor over-sensitive to losses and one's too frequent strategy adjustment leads to a large fluctuation in asset prices, and thereafter, a decrease in the number of agents. At an intermediate market impact, the phase transition occurs. No matter what the market impact is, an equilibrium between different markets exists, which is reflected in the occurrence of similar price fluctuations in different markets. A theoretical analysis indicates that such an equilibrium results from the coupled effects of strategy updating and shift in investment. The runaway of the agents trading a specific asset will lead to a decline in the asset price volatility and such a decline will be inhibited by the clustering of the strategies. A uniform strategy distribution will lead to a large fluctuation in asset prices and such a fluctuation will be suppressed by the decrease in the number of agents in the market. A functional relationship between the price fluctuations and the numbers of agents is found

Is the late near-infrared bump in short-hard GRB 130603B due to the Li-Paczynski kilonova?

Short-hard gamma-ray bursts (GRBs) are widely believed to be produced by the merger of two binary compact objects, specifically by two neutron stars or by a neutron star orbiting a black hole. According to the Li-Paczynski kilonova model, the merger would launch sub-relativistic ejecta and a near-infrared/optical transient would then occur, lasting up to days, which is powered by the radioactive decay of heavy elements synthesized in the ejecta. The detection of a late bump using the {\em Hubble Space Telescope} ({\em HST}) in the near-infrared afterglow light curve of the short-hard GRB 130603B is indeed consistent with such a model. However, as shown in this Letter, the limited {\em HST} near-infrared lightcurve behavior can also be interpreted as the synchrotron radiation of the external shock driven by a wide mildly relativistic outflow. In such a scenario, the radio emission is expected to peak with a flux of $\sim 100 \mu$Jy, which is detectable for current radio arrays. Hence, the radio afterglow data can provide complementary evidence on the nature of the bump in GRB 130603B. It is worth noting that good spectroscopy during the bump phase in short-hard bursts can test validity of either model above, analogous to spectroscopy of broad-lined Type Ic supernova in long-soft GRBs.Comment: 4 pages, 2 figures, published in ApJ Lette

2-n-Butyl-1,2-benzisothia­zol-3(2H)-one 1,1-dioxide

The crystal packing of the title compound, C11H13NO3S, exhibits weak inter­molecular C—H⋯O hydrogen bonding, which links mol­ecules related by translation along the b axis into chains, and π–π inter­actions [centroid–centroid distance of 3.778 (2) Å between benzene rings]

A supra-massive magnetar central engine for short GRB 130603B

We show that the peculiar early optical and in particular X-ray afterglow emission of the short duration burst GRB 130603B can be explained by continuous energy injection into the blastwave from a supra-massive magnetar central engine. The observed energetics and temporal/spectral properties of the late infrared bump (i.e., the "kilonova") are also found consistent with emission from the ejecta launched during an NS-NS merger and powered by a magnetar central engine. The isotropic-equivalent kinetic energies of both the GRB blastwave and the kilonova are about $E_{\rm k}\sim 10^{51}$ erg, consistent with being powered by a near-isotropic magnetar wind. However, this relatively small value demands that most of the initial rotational energy of the magnetar $(\sim {\rm a~ few \times 10^{52}~ erg})$ is carried away by gravitational wave radiation. Our results suggest that (i) the progenitor of GRB 130603B would be a NS-NS binary system, whose merger product would be a supra-massive neutron star that lasted for about $\sim 1000$ seconds; (ii) the equation-of-state of nuclear matter would be stiff enough to allow survival of a long-lived supra-massive neutron star, so that it is promising to detect bright electromagnetic counterparts of gravitational wave triggers without short GRB associations in the upcoming Advanced LIGO/Virgo era.Comment: Five pages including 1 Figure, to appear in ApJ

Diethyl 2,2-bis­(3,5-di-tert-butyl-4-hy­droxy­benz­yl)malonate

The title mol­ecule, C37H56O6, possesses twofold symmetry, with the twofold axis passing through the quaternary C atom. In the crystal, neighbouring mol­ecules are linked via O—H⋯O hydrogen bonds involving the phenol OH group and the carbonyl O atom, forming chains propagating in [101]. Within these chains, rings are formed with an R 2 2(20) motif. There are also C—H⋯O inter­actions present within the rings

Application of the robust estimate in SLR data preprocessing

An M-estimator, one kind of a robust estimator, has been used in satellite laser ranging (SLR) data preprocessing. It has been shown that the M-estimator has a 50 percent or more breakdown point

Separation and Recycling of Concentrated Heavy Metal Wastewater by Tube Membrane Distillation Integrated with Crystallization

Tube membrane distillation (MD) integrated with a crystallization method is used in this study for the concurrent productions of pure water and salt crystals from concentrated single and mixed system solutions. The effects of concentrated Zn 2+ and Ni 2+ on performance in terms of membrane flux, permeate conductivity, crystal recovery rates, and crystal grades are investigated. Preferred crystallization and co-crystallization determinations were performed for mixed solutions. The results revealed that membrane fluxes remained at 2.61 kg·m −2 ·h −1 and showed a sharp decline until the saturation increased to 1.38. Water yield conductivity was below 10 μs·cm −1. High concentrated zinc and nickel did not have a particular effect on the rejection of the membrane process. For the mixed solutions, membrane flux showed a sharp decrease due to the high saturation, while the conductivity of permeate remained below 10 μs·cm −1 during the whole process. Co-crystallization has been proven to be a better method due to the existence of the SO 2− common-ion effect. Membrane fouling studies have suggested that the membrane has excellent resistance to fouling from highly concentrated solutions. The MD integrated with crystallization proves to be a promising technology for treating highly concentrated heavy metal solutions

Quantum delayed-choice experiment with a beam splitter in a quantum superposition

A quantum system can behave as a wave or as a particle, depending on the experimental arrangement. When for example measuring a photon using a Mach-Zehnder interferometer, the photon acts as a wave if the second beam-splitter is inserted, but as a particle if this beam-splitter is omitted. The decision of whether or not to insert this beam-splitter can be made after the photon has entered the interferometer, as in Wheeler's famous delayed-choice thought experiment. In recent quantum versions of this experiment, this decision is controlled by a quantum ancilla, while the beam splitter is itself still a classical object. Here we propose and realize a variant of the quantum delayed-choice experiment. We configure a superconducting quantum circuit as a Ramsey interferometer, where the element that acts as the first beam-splitter can be put in a quantum superposition of its active and inactive states, as verified by the negative values of its Wigner function. We show that this enables the wave and particle aspects of the system to be observed with a single setup, without involving an ancilla that is not itself a part of the interferometer. We also study the transition of this quantum beam-splitter from a quantum to a classical object due to decoherence, as observed by monitoring the interferometer output.Comment: 9 pages, 7 figures, Accepted by Physical Review Letter