Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Flow measurement inside a zinc-nickel flow cell battery using FBG based sensor system

Downloading of the abstract is permitted for personal use only. A detailed knowledge of the internal flow distribution inside a zinc-nickel flow battery is of critical importance to ensure smooth flow of the electrolyte through the battery cell and better operation of the device. Information of this type can be used as a useful means of early detection of zinc deposition and dendrite formation inside the cell, negative factors which affect the flow and thus which can lead to internal short circuiting, this being a primary failure mode of these types of batteries. This deposition occurs at low pH levels when zinc reacts with the electrolyte to form solid zinc oxide hydroxides. Traditionally, manual inspection is conducted, but this is time consuming and costly, only providing what are often inaccurate results-overall it is an impractical solution especially with the wider use of batteries in the very near future. Fibre Bragg grating (FBG) sensors integrated inside the flow cell offer the advantage of measuring flow changes at multiple locations using a single fibre and that then can be used as an indicator of the correlation between the internal flow distribution and the deposition characteristics. This work presents an initial study, where two networks of FBGs have been installed and used for flow change detection in an active zinc-nickel flow battery. Data have been obtained from the sensor networks and information of battery performance completed and summarized in this paper. The approach shows promising results and thus scope for the future research into the development of this type of sensor system

Using LIP to Gloss Over Faces in Single-Stage Face Detection Networks

This work shows that it is possible to fool/attack recent state-of-the-art face detectors which are based on the single-stage networks. Successfully attacking face detectors could be a serious malware vulnerability when deploying a smart surveillance system utilizing face detectors. We show that existing adversarial perturbation methods are not effective to perform such an attack, especially when there are multiple faces in the input image. This is because the adversarial perturbation specifically generated for one face may disrupt the adversarial perturbation for another face. In this paper, we call this problem the Instance Perturbation Interference (IPI) problem. This IPI problem is addressed by studying the relationship between the deep neural network receptive field and the adversarial perturbation. As such, we propose the Localized Instance Perturbation (LIP) that uses adversarial perturbation constrained to the Effective Receptive Field (ERF) of a target to perform the attack. Experiment results show the LIP method massively outperforms existing adversarial perturbation generation methods -- often by a factor of 2 to 10.Comment: to appear ECCV 2018 (accepted version

Fast computation of MadGraph amplitudes on graphics processing unit (GPU)

Continuing our previous studies on QED and QCD processes, we use the graphics processing unit (GPU) for fast calculations of helicity amplitudes for general Standard Model (SM) processes. Additional HEGET codes to handle all SM interactions are introduced, as well assthe program MG2CUDA that converts arbitrary MadGraph generated HELAS amplitudess(FORTRAN) into HEGET codes in CUDA. We test all the codes by comparing amplitudes and cross sections for multi-jet srocesses at the LHC associated with production of single and double weak bosonss a top-quark pair, Higgs boson plus a weak boson or a top-quark pair, and multisle Higgs bosons via weak-boson fusion, where all the heavy particles are allowes to decay into light quarks and leptons with full spin correlations. All the helicity amplitudes computed by HEGET are found to agree with those comsuted by HELAS within the expected numerical accuracy, and the cross sections obsained by gBASES, a GPU version of the Monte Carlo integration program, agree wish those obtained by BASES (FORTRAN), as well as those obtained by MadGraph. The performance of GPU was over a factor of 10 faster than CPU for all processes except those with the highest number of jets.Comment: 37 pages, 12 figure

Effect of the Fermi surface destruction on transport properties in underdoped cuprates

Motivated by recent experimental measurements on the Fermi surface(FS) destruction in underdoped high-$T_{c}$ cuprates, we examine its effect on the transport properties based on the Boltzmann equation approach. The effect is modeled by simply taking the density of states for electrons in the gapped regions to be zero. Within the nearly antiferromagnetic Fermi liquid model, we calculate the temperature dependences of the dc resistivity, the inverse Hall angle and the Hall coefficient. It is shown that the effect of the FS destruction on transport properties is sensitive to the existance and the range of the flat band near $(0,\pm\pi)$ in the dispersion of electrons, and the anistropy of the relaxation rate along the Fermi surface. We find that the experimental data are better described by the cold spot model, i.e., the transports are determined mainly by the contribution of the electrons near the Brillouin-zone diagonals.Comment: 8 pages, 7 figure

Macroscopic Black Holes, Microscopic Black Holes and Noncommutative Membrane

We study the stretched membrane of a black hole as consisting of a perfect fluid. We find that the pressure of this fluid is negative and the specific heat is negative too. A surprising result is that if we are to assume the fluid be composed of some quanta, then the dispersion relation of the fundamental quantum is $E=m^2/k$, with $m$ at the scale of the Planck mass. There are two possible interpretation of this dispersion relation, one is the noncommutative spacetime on the stretched membrane, another is that the fundamental quantum is microscopic black holes.Comment: 10 pages, harvmac; v2: refs. adde

The Exchange Rate and Interest Rate Differential Relationship: Evidence from Two Financial Crises

This paper examines the contemporaneous and inter-temporal interaction between real exchange rate and real interest rate differential in the two financial crises of 1997 and 2008 by using data from thirteen countries from different world regions. The empirical result shows that negative contemporaneous relationship exists in most countries. In addition, there is little evidence on a systematic inter-temporal relationship between the real interest rate differential and the real exchange rate, and an absence of consistent result in supporting a negative relationship among the thirteen economies. An extremely low change in the conditional correlation between real interest rate differential and real exchange rates can be found in small countries.Contemporaneous, inter-temporal relationship, exchange rate, interest rate differential, financial crisis