Feasibility of Imaging Tissue Electrical Conductivity by Switching Field Gradients with MRI.

Tissue conductivity is a biophysical marker of tissue structure and physiology. Present methods of measuring tissue conductivity are limited. Electrical impedance tomography, and magnetic resonance electrical impedance tomography rely on passing external current through the object being imaged, which prevents its use in most human imaging. Recently, the RF field used for MR excitation has been used to non-invasively measure tissue conductivity. This technique is promising, but conductivity at higher frequencies is less sensitive to tissue structure. Measuring tissue conductivity non-invasively at low frequencies remains elusive. It has been proposed that eddy currents generated during the rise and decay of gradient pulses could act as a current source to map low-frequency conductivity. This work centers on a gradient echo pulse sequence that uses large gradients prior to excitation to create eddy currents. The electric and magnetic fields during a gradient pulse are simulated by a finite-difference time-domain simulation. The sequence is also tested with a phantom and an animal MRI scanner equipped with gradients of high gradient strengths and slew rate. The simulation demonstrates that eddy currents in materials with conductivity similar to biological tissue decay with a half-life on the order of nanoseconds and any eddy currents generated prior to excitation decay completely before influencing the RF signal. Gradient-induced eddy currents can influence phase accumulation after excitation but the effect is too small to image. The animal scanner images show no measurable phase accumulation. Measuring low-frequency conductivity by gradient-induced eddy currents is presently unfeasible

Etalon Array Reconstructive Spectrometry.

Compact spectrometers are crucial in areas where size and weight may need to be minimized. These types of spectrometers often contain no moving parts, which makes for an instrument that can be highly durable. With the recent proliferation in low-cost and high-resolution cameras, camera-based spectrometry methods have the potential to make portable spectrometers small, ubiquitous, and cheap. Here, we demonstrate a novel method for compact spectrometry that uses an array of etalons to perform spectral encoding, and uses a reconstruction algorithm to recover the incident spectrum. This spectrometer has the unique capability for both high resolution and a large working bandwidth without sacrificing sensitivity, and we anticipate that its simplicity makes it an excellent candidate whenever a compact, robust, and flexible spectrometry solution is needed

The financial integration of China: New evidence on temporally aggregated data for the A-share market

In spite of high trade openness, existing empirical work, using daily data, has not found any evidence of international financial integration of China. In this paper we examine to what extent the Chinese A-share market, de jure protected from foreign influences by capital controls, is actually integrated with global or regional markets. We study a long sample (October 1992 through March 2005) of active trading, within the framework of a regime-switching error correction model. We confirm the role of temporal aggregation in cointegration tests. With daily or mid-week closing prices, we do not find any long run relationship with either the New York or the Hong Kong market, thus replicating previous findings. However, the use of weekly averaged prices implies that, up to late 1996, the Shanghai A-share market index was cointegrated with the S&P500. Subsequently, this relationship broke down and a long run relationship with the Hang Seng index gradually arose. Information flows, as well as the prospects of de jure financial opening, and the growing awareness of valuation concepts among Chinese domestic investors, in the presence of multiple listing of Mainland firms, help explain the evidence of financial integration in spite of capital controlsChina's A-share market, Markov-switching ECM, temporal aggregation, international financial integration

Berry-Esseen's bound and Cram\'er's large deviation expansion for a supercritical branching process in a random environment

Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve some earlier results about the harmonic moments of the limit variable $W=lim_{n\to \infty} W_n$, where $W_n =Z_n/ \mathbb{E}_{\xi} Z_n$ is the normalized population size

Asymptotic of the distribution and harmonic moments for a supercritical branching process in a random environment

Let $(Z_n)$ be a supercritical branching process in an independent and identically distributed random environment $\xi$. We show the exact decay rate of the probability $\mathbb{P}(Z_n=j | Z_0 = k)$ as $n \to \infty$, for each $j \geq k,$ assuming that $\mathbb{P} (Z_1 = 0) =0$. We also determine the critical value for the existence of harmonic moments of the random variable $W=\lim_{n\to\infty}\frac{Z_n}{\mathbb E (Z_n|\xi)}$ under a simple moment condition