Nonlinear stability and ergodicity of ensemble based Kalman filters

The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and oil reservoir simulation, very little is known about the long-time behavior of these methods and why they are effective when applied with modest ensemble sizes in large dimensional turbulent dynamical systems. By following the basic principles of energy dissipation and controllability of filters, this paper establishes a simple, systematic and rigorous framework for the nonlinear analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the dynamical properties of boundedness and geometric ergodicity. The time uniform boundedness guarantees that the filter estimate will not diverge to machine infinity in finite time, which is a potential threat for EnKF and ESQF known as the catastrophic filter divergence. Geometric ergodicity ensures in addition that the filter has a unique invariant measure and that initialization errors will dissipate exponentially in time. We establish these results by introducing a natural notion of observable energy dissipation. The time uniform bound is achieved through a simple Lyapunov function argument, this result applies to systems with complete observations and strong kinetic energy dissipation, but also to concrete examples with incomplete observations. With the Lyapunov function argument established, the geometric ergodicity is obtained by verifying the controllability of the filter processes; in particular, such analysis for ESQF relies on a careful multivariate perturbation analysis of the covariance eigen-structure.Comment: 38 page

Berry phase in a composite system

The Berry phase in a composite system with only one subsystem being driven has been studied in this Letter. We choose two spin-$\frac 1 2$ systems with spin-spin couplings as the composite system, one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and what is the relation between these Berry phases of the whole system and those of the subsystems.Comment: 4 pages, 6 figure

Nitric oxide stress and activation of AMP-activated protein kinase impair β-cell sarcoendoplasmic reticulum calcium ATPase 2b activity and protein stability

The sarcoendoplasmic reticulum Ca(2+) ATPase 2b (SERCA2b) pump maintains a steep Ca(2+) concentration gradient between the cytosol and ER lumen in the pancreatic β-cell, and the integrity of this gradient has a central role in regulated insulin production and secretion, maintenance of ER function and β-cell survival. We have previously demonstrated loss of β-cell SERCA2b expression under diabetic conditions. To define the mechanisms underlying this, INS-1 cells and rat islets were treated with the proinflammatory cytokine interleukin-1β (IL-1β) combined with or without cycloheximide or actinomycin D. IL-1β treatment led to increased inducible nitric oxide synthase (iNOS) gene and protein expression, which occurred concurrently with the activation of AMP-activated protein kinase (AMPK). IL-1β led to decreased SERCA2b mRNA and protein expression, whereas time-course experiments revealed a reduction in protein half-life with no change in mRNA stability. Moreover, SERCA2b protein but not mRNA levels were rescued by treatment with the NOS inhibitor l-NMMA (NG-monomethyl L-arginine), whereas the NO donor SNAP (S-nitroso-N-acetyl-D,L-penicillamine) and the AMPK activator AICAR (5-aminoimidazole-4-carboxamide ribonucleotide) recapitulated the effects of IL-1β on SERCA2b protein stability. Similarly, IL-1β-induced reductions in SERCA2b expression were rescued by pharmacological inhibition of AMPK with compound C or by transduction of a dominant-negative form of AMPK, whereas β-cell death was prevented in parallel. Finally, to determine a functional relationship between NO and AMPK signaling and SERCA2b activity, fura-2/AM (fura-2-acetoxymethylester) Ca(2+) imaging experiments were performed in INS-1 cells. Consistent with observed changes in SERCA2b expression, IL-1β, SNAP and AICAR increased cytosolic Ca(2+) and decreased ER Ca(2+) levels, suggesting congruent modulation of SERCA activity under these conditions. In aggregate, these results show that SERCA2b protein stability is decreased under inflammatory conditions through NO- and AMPK-dependent pathways and provide novel insight into pathways leading to altered β-cell calcium homeostasis and reduced β-cell survival in diabetes

SGXIO: Generic Trusted I/O Path for Intel SGX

Application security traditionally strongly relies upon security of the underlying operating system. However, operating systems often fall victim to software attacks, compromising security of applications as well. To overcome this dependency, Intel introduced SGX, which allows to protect application code against a subverted or malicious OS by running it in a hardware-protected enclave. However, SGX lacks support for generic trusted I/O paths to protect user input and output between enclaves and I/O devices. This work presents SGXIO, a generic trusted path architecture for SGX, allowing user applications to run securely on top of an untrusted OS, while at the same time supporting trusted paths to generic I/O devices. To achieve this, SGXIO combines the benefits of SGX's easy programming model with traditional hypervisor-based trusted path architectures. Moreover, SGXIO can tweak insecure debug enclaves to behave like secure production enclaves. SGXIO surpasses traditional use cases in cloud computing and makes SGX technology usable for protecting user-centric, local applications against kernel-level keyloggers and likewise. It is compatible to unmodified operating systems and works on a modern commodity notebook out of the box. Hence, SGXIO is particularly promising for the broad x86 community to which SGX is readily available.Comment: To appear in CODASPY'1

COMPARISON OF DEEP CRUSTAL COMPOSITIONS BETWEEN THE QINLING-DABIE OROGEN (CHINA) AND CENTRAL ASIAN OROGENIC BELT AND IMPLICATIONS FOR UNDERSTANDING ACCRETIONARY AND COLLISIONAL OROGENIC PROCESSES

It is generally considered that there are different continental compositions between a subductional– collisional and an accretionary orogen, however, what are the differences and how to identify them has not been well understood. This study attempts to discuss this problem by comparing Nd isotopic compositions of granitoids in the Qinling-Dabie orogen, a typical subductional-collisional orogen, with those in southwestern segment of the Central Asian Orogenic Belt (CAOB), the world's largest phanerozoic accretionary orogenic belt.It is generally considered that there are different continental compositions between a subductional– collisional and an accretionary orogen, however, what are the differences and how to identify them has not been well understood. This study attempts to discuss this problem by comparing Nd isotopic compositions of granitoids in the Qinling-Dabie orogen, a typical subductional-collisional orogen, with those in southwestern segment of the Central Asian Orogenic Belt (CAOB), the world's largest phanerozoic accretionary orogenic belt

Ion-beam-assisted fabrication and manipulation of metallic nanowires

Metallic nanowires (NWs) are the key performers for future micro/nanodevices. The controlled manoeuvring and integration of such nanoscale entities are essential requirements. Presented is a discussion of a fabrication approach that combines chemical etching and ion beam milling to fabricate metallic NWs. The shape modification of the metallic NWs using ion beam irradiation (bending towards the ion beam side) is investigated. The bending effect of the NWs is observed to be instantaneous and permanent. The ion beam-assisted shape manoeuvre of the metallic structures is studied in the light of ion-induced vacancy formation and reconfiguration of the damaged layers. The manipulation method can be used for fabricating structures of desired shapes and aligning structures at a large scale. The controlled bending method of the metallic NWs also provides an understanding of the strain formation process in nanoscale metals

Correlation dynamics between electrons and ions in the fragmentation of D2_2 molecules by short laser pulses

We studied the recollision dynamics between the electrons and D$_2^+$ ions following the tunneling ionization of D$_2$ molecules in an intense short pulse laser field. The returning electron collisionally excites the D$_2^+$ ion to excited electronic states from there D$_2^+$ can dissociate or be further ionized by the laser field, resulting in D$^+$ + D or D$^+$ + D$^+$, respectively. We modeled the fragmentation dynamics and calculated the resulting kinetic energy spectrum of D$^+$ to compare with recent experiments. Since the recollision time is locked to the tunneling ionization time which occurs only within fraction of an optical cycle, the peaks in the D$^+$ kinetic energy spectra provides a measure of the time when the recollision occurs. This collision dynamics forms the basis of the molecular clock where the clock can be read with attosecond precision, as first proposed by Corkum and coworkers. By analyzing each of the elementary processes leading to the fragmentation quantitatively, we identified how the molecular clock is to be read from the measured kinetic energy spectra of D$^+$ and what laser parameters be used in order to measure the clock more accurately.Comment: 13 pages with 14 figure

Comparison of chemical profiles and effectiveness between Erxian decoction and mixtures of decoctions of its individual herbs : a novel approach for identification of the standard chemicals

Acknowledgements This study was partially supported by grants from the Seed Funding Programme for Basic Research (Project Number 201211159146 and 201411159213), the University of Hong Kong. We thank Mr Keith Wong and Ms Cindy Lee for their technical assistances.Peer reviewedPublisher PD