Space-Based Gravity Detector for a Space Laboratory

A space-based superconducting gravitational low-frequency wave detector is considered. Sensitivity of the detector is sufficient to use the detector as a partner of other contemporary low-frequency detectors like LIGO and LISA. This device can also be very useful for experimental study of other effects predicted by theories of gravitation.Comment: 4 pages, 4 figures

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

Goodness-of-fit tests for a heavy tailed distribution

For testing whether a distribution function is heavy tailed, we study theKolmogorov test, Berk-Jones test, score test and their integratedversions. A comparison is conducted via Bahadur efficiency and simulations.The score test and the integrated score test show the best performance.Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnovtest, this does not hold true for their integrated versions; this differsfrom results in \\citet{EinmahlMckeague2003}, which shows the difference ofBerk-Jones test in testing distributions and tails.Bahadur efficiency;heavy tail;tail index

Field-effect mobility enhanced by tuning the Fermi level into the band gap of Bi2Se3

By eliminating normal fabrication processes, we preserve the bulk insulating state of calcium-doped Bi2Se3 single crystals in suspended nanodevices, as indicated by the activated temperature dependence of the resistivity at low temperatures. We perform low-energy electron beam irradiation (<16 keV) and electrostatic gating to control the carrier density and therefore the Fermi level position in the nanodevices. In slightly p-doped Bi2-xCaxSe3 devices, continuous tuning of the Fermi level from the bulk valence band to the band-gap reveals dramatic enhancement (> a factor of 10) in the field-effect mobility, which suggests suppressed backscattering expected for the Dirac fermion surface states in the gap of topological insulators

Iterative Row Sampling

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which allows one to solve a poly(d) sized problem instead. In practice, the best performances are often obtained by invoking these routines in an iterative fashion. We show these iterative methods can be adapted to give theoretical guarantees comparable and better than the current state of the art. Our approaches are based on computing the importances of the rows, known as leverage scores, in an iterative manner. We show that alternating between computing a short matrix estimate and finding more accurate approximate leverage scores leads to a series of geometrically smaller instances. This gives an algorithm that runs in $O(nnz(A) + d^{\omega + \theta} \epsilon^{-2})$ time for any $\theta > 0$, where the $d^{\omega + \theta}$ term is comparable to the cost of solving a regression problem on the small approximation. Our results are built upon the close connection between randomized matrix algorithms, iterative methods, and graph sparsification.Comment: 26 pages, 2 figure

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page