Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measures. Section 2 gives the central framework in random metric theory, topological structures, important examples, the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals. Section 3 gives several important representation theorems for random conjugate spaces. Section 4 gives characterizations for a complete random normed module to be random reflexive. Section 5 gives hyperplane separation theorems currently available in random locally convex modules. Section 6 gives the theory of random duality with respect to the locally $L^{0}-$convex topology and in particular a characterization for a locally $L^{0}-$convex module to be $L^{0}-$pre$-$barreled. Section 7 gives some basic results on $L^{0}-$convex analysis together with some applications to conditional risk measures. Finally, Section 8 is devoted to extensions of conditional convex risk measures, which shows that every representable $L^{\infty}-$type of conditional convex risk measure and every continuous $L^{p}-$type of convex conditional risk measure ($1\leq p<+\infty$) can be extended to an $L^{\infty}_{\cal F}({\cal E})-$type of $\sigma_{\epsilon,\lambda}(L^{\infty}_{\cal F}({\cal E}), L^{1}_{\cal F}({\cal E}))-$lower semicontinuous conditional convex risk measure and an $L^{p}_{\cal F}({\cal E})-$type of ${\cal T}_{\epsilon,\lambda}-$continuous conditional convex risk measure ($1\leq p<+\infty$), respectively.Comment: 37 page

QCD Factorization in BB Decays into ρπ\rho \pi

Based on the QCD factorization approach we analyse the branching ratios for the channel $B \to \rho \pi$. From the comparisons with experimental data provided by CLEO, BELLE and BABAR we constrain the form factor $F^{B \to \pi}(m_{\rho}^{2})$ and propose boundaries for this form factor depending on the CKM matrix element parameters $\rho$ and $\eta$.Comment: 11 pages, 9 figures. Talk presented at Fourth Tropical Workshop, Cairns, Australia, 9--13 June 2003. Proceedings to be published by AI

A large-scale one-way quantum computer in an array of coupled cavities

We propose an efficient method to realize a large-scale one-way quantum computer in a two-dimensional (2D) array of coupled cavities, based on coherent displacements of an arbitrary state of cavity fields in a closed phase space. Due to the nontrivial geometric phase shifts accumulating only between the qubits in nearest-neighbor cavities, a large-scale 2D cluster state can be created within a short time. We discuss the feasibility of our method for scale solid-state quantum computationComment: 5 pages, 3 figure

Conditions for Nondistortion Interrogation of Quantum System

Under some physical considerations, we present a universal formulation to study the possibility of localizing a quantum object in a given region without disturbing its unknown internal state. When the interaction between the object and probe wave function takes place only once, we prove the necessary and sufficient condition that the object's presence can be detected in an initial state preserving way. Meanwhile, a conditioned optimal interrogation probability is obtained.Comment: 5 pages, Revtex, 1 figures, Presentation improved, corollary 1 added. To appear in Europhysics Letter

Discriminating invasive crested wheatgrass (Agropyron cristatum) in northern mixed grass prairie using remote sensing technology

Non-Peer ReviewedInvasive crested wheatgrass in the Grasslands National Park cause biodiversity decrease and irreparable damage to prairie ecosystems. Controlling and managing invasive species require new methods to map and monitor their presence and spread. Traditional mapping techniques based on field observation and data collection are considered time-consuming, subjective, and always very limited in spatial extent and economically for relatively large areas. Remote sensing techniques provide a potential solution to this problem. However, previous work has been limited because of low spatial and spectral resolution of some data sources. The principal challenges in using remote sensors to detect invasive species lie in the spectral similarity across species and invasive species often mixing with the native species. This paper discusses how SPOT-5 imagery with 10-m resolution can be used to detect invasive crested wheatgrass in the mixed prairie. Several vegetation indices, including Normalized Difference Vegetation Index (NDVI), Normalized Difference Moisture Index (NDMI), Soil Adjusted Vegetation Index (SAVI), Modified Soil Adjusted Vegetation Index (MSAVI), Simple Ratio (SR), and Triangulated Vegetation Index (TVI), were initially selected and their spectral separability in separating crested wheatgrass and natives was examined. A new vegetation index, ExpNDMI, was derived from NDMI by incorporating an adjustment factor (L) to enlarge the difference among classes; and, further, performing a exponential transformation upon the modified index to suppress the variations in all classes. An artificial Neural Netwok (ANN) classifier based on back propagation (BP) algorithm was employed to classify crested wheatgrass and native grasslands in this study. The results indicated that ExpNDMI could significantly increase the spectral separability between crested wheatgrass and native grasslands and improve the classification accuracy. The highest overall accuracy of 79% was obtained. Band/VI combination with ExpNDMI improved the classification accuracy by more than 4% than the combination without ExpNDMI. The result of this study suggests that single-date SPOT 5 image with 10 m resolution could be useful in discriminating crested wheatgrass from natives in the mixed grasslands, and thus may reduce the dependence on the multitemporal data

Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.Comment: 13 pages, 4 figure