Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Strain Modulated Electronic Properties of Ge Nanowires - A First Principles Study

We used density-functional theory based first principles simulations to study the effects of uniaxial strain and quantum confinement on the electronic properties of germanium nanowires along the [110] direction, such as the energy gap and the effective masses of the electron and hole. The diameters of the nanowires being studied are up to 50 {\AA}. As shown in our calculations, the Ge [110] nanowires possess a direct band gap, in contrast to the nature of an indirect band gap in bulk. We discovered that the band gap and the effective masses of charge carries can be modulated by applying uniaxial strain to the nanowires. These strain modulations are size-dependent. For a smaller wire (~ 12 {\AA}), the band gap is almost a linear function of strain; compressive strain increases the gap while tensile strain reduces the gap. For a larger wire (20 {\AA} - 50 {\AA}), the variation of the band gap with respect to strain shows nearly parabolic behavior: compressive strain beyond -1% also reduces the gap. In addition, our studies showed that strain affects effective masses of the electron and hole very differently. The effective mass of the hole increases with a tensile strain while the effective mass of the electron increases with a compressive strain. Our results suggested both strain and size can be used to tune the band structures of nanowires, which may help in design of future nano-electronic devices. We also discussed our results by applying the tight-binding model.Comment: 1 table, 8 figure

Ballistic transport at room temperature in micrometer size multigraphene

The intrinsic values of the carriers mobility and density of the graphene layers inside graphite, the well known structure built on these layers in the Bernal stacking configuration, are not well known mainly because most of the research was done in rather bulk samples where lattice defects hide their intrinsic values. By measuring the electrical resistance through microfabricated constrictions in micrometer small graphite flakes of a few tens of nanometers thickness we studied the ballistic behavior of the carriers. We found that the carriers' mean free path is micrometer large with a mobility $\mu \simeq 6 \times 10^6$cm$^2$/Vs and a carrier density $n \simeq 7 \times 10^8$cm$^{-2}$ per graphene layer at room temperature. These distinctive transport and ballistic properties have important implications for understanding the values obtained in single graphene and in graphite as well as for implementing this last in nanoelectronic devices.Comment: 6 pages, 6 figure

Detection of Minimum-Ionizing Particles and Nuclear Counter Effect with Pure BGO and BSO Crystals with Photodiode Read-out

Long BGO (Bismuth Germanate) and BSO (Bismuth Silicate) crystals coupled with silicon photodiodes have been used to detect minimum-ionizing particles(MIP). With a low noise amplifier customized for this purpose, the crystals can detect MIPs with an excellent signal-to-noise ratio. The NCE(Nuclear Counter Effect} is also clearly observed and measured. Effect of full and partial wrapping of a reflector around the crystal on light collection is also studied.Comment: 18 pages, including 5 figures; LaTeX and EP

Probing High Redshift Radiation Fields with Gamma-Ray Absorption

The next generation of gamma-ray telescopes may be able to observe gamma-ray blazars at high redshift, possibly out to the epoch of reionization. The spectrum of such sources should exhibit an absorption edge due to pair-production against UV photons along the line of sight. One expects a sharp drop in the number density of UV photons at the Lyman edge E_{L}. This implies that the universe becomes transparent after gamma-ray photons redshift below E (m_{e}c^2)^{2}/E_{L} 18 GeV. Thus, there is only a limited redshift interval over which GeV photons can pair produce. This implies that any observed absorption will probe radiation fields in the very early universe, regardless of the subsequent star formation history of the universe. Furthermore, measurements of differential absorption between blazars at different redshifts can cleanly isolate the opacity due to UV emissivity at high redshift. An observable absorption edge should be present for most reasonable radiation fields with sufficient energy to reionize the universe. Ly-alpha photons may provide an important component of the pair-production opacity. Observations of a number of blazars at different redshifts will thus allow us to probe the rise in comoving UV emissivity with time.Comment: ApJ accepted version, minor changes. 19 pages, 5 figure

Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications

In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve large-scale problems. However, general nonsubmodular problems are significantly more challenging to solve. Finding a solution when the problem is of large size to be of practical interest, however, typically requires relaxation. Two standard relaxation methods are widely used for solving general BQPs--spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high, especially for large scale problems. In this work, we present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interior-point methods. In practice, the smoothing Newton solver is faster than the quasi-Newton solver for dense or medium-sized problems, while the quasi-Newton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, co-segmentation and registration show the potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc