Economic and accounting rates of return

The rate of return on invested capital is a central concept in financial analysis. The purpose of calculating the rate of return on investment in general is to measure the financial performance, to assess the desirability of a project and to make decisions on the valuation of firms. Financial statement users make regular use of the accounting rate of return (ARR) rather than the economic rate of return (IRR) to assess the performance of corporations and public-sector enterprises, to evaluate capital investment projects, and to price financial claims such as shares. Since ARR measures are based on published accounting statements, there has been a long and sometimes heated debate as to whether such measures have any economic significance. This paper aims to provide a summary of the economic and accounting rates of return discussions in the literature. We analyze the concepts of ARR and IRR and explore possible relationships between them. We extend the previous studies in this line to provide more specific relations of IRR and ARR.

Adaptive Quantum Measurements of a Continuously Varying Phase

We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is \delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/\hbar\omega\kappa, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance \simeq N^{-1/2}/2. This is \sqrt{2} times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N^{-1/2}. It offers a significant improvement over nonadaptive interferometry only for N of order unity.Comment: 11 pages, 6 figures, journal versio

Asteroidal differentiation processes deduced from ultramafic achondrite ureilite meteorites

Ureilite meteorites are partial melt residues of an asteroid-sized object. They record the differentiation process that transformed many asteroids during the earliest stages of solar system formation

An investigation of the relationship between BOLD and perfusion signal changes during epileptic generalised spike wave activity

In pathological conditions interpretation of functional magnetic resonance imaging (fMRI) results can be difficult. This is due to a reliance on the assumed coupling between neuronal activity and changes in cerebral blood flow (CBF) and oxygenation. We wanted to investigate the coupling between blood oxygen level dependant contrast (BOLD) and CBF time courses in epilepsy patients with generalised spike wave activity (GSW) to better understand the underlying mechanisms behind the EEG-fMRI signal changes observed, especially in regions of negative BOLD response (NBR). Four patients with frequent GSW were scanned with simultaneous electroencephalographic (EEG)-fMRI with BOLD and arterial spin labeling (ASL) sequences. We examined the relationship between simultaneous CBF and BOLD measurements by looking at the correlation of the two signals in terms of percentage signal change on a voxel-by-voxel basis. This method is not reliant on coincident activation. BOLD and CBF were positively correlated in patients with epilepsy during background EEG activity and GSW. The subject average value of the ΔCBF/ΔBOLD slope lay between +19 and +36 and also showed spatial variation which could indicate areas with altered vascular response. There was not a significant difference between ΔCBF/ΔBOLD during GSW, suggesting that neurovascular coupling to BOLD signal is generally maintained between states and, in particular, within areas of NBR

BOLD and perfusion changes during epileptic generalised spike wave activity

It is unclear whether neurovascular coupling is maintained during epileptic discharges. Knowing this is important to allow appropriate inferences from functional imaging studies of epileptic activity. Recent blood oxygen level-dependent (BOLD) functional MRI (fMRI) studies have demonstrated negative BOLD responses (NBR) in frontal, parietal and posterior cingulate cortices during generalised spike wave activity (GSW). We hypothesized that GSW-related NBR commonly reflect decreased cerebral blood flow (CBF). We measured BOLD and cerebral blood flow responses using simultaneous EEG with BOLD and arterial spin label (ASL) fMRI at 3 T. Four patients with epilepsy were studied; two with idiopathic generalized epilepsy (IGE) and two with secondary generalized epilepsy (SGE). We found GSW-related NBR in frontal, parietal and posterior cingulate cortices. We measured the coupling between BOLD and CBF changes during GSW and normal background EEG and found a positive correlation between the simultaneously measured BOLD and CBF throughout the imaged volume. Frontal and thalamic activation were seen in two patients with SGE, concordant with the electro-clinical features of their epilepsy. There was striking reproducibility of the GSW-associated BOLD response in subjects previously studied at 1.5 T. Our results show a preserved relationship between BOLD and CBF changes during rest and GSW activity consistent with normal neurovascular coupling in patients with generalized epilepsy and in particular during GSW activity. Cortical activations appear to reflect areas of discharge generation whilst deactivations reflect changes in conscious resting state activity

Optimal Sizes of Dielectric Microspheres for Cavity QED with Strong Coupling

The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number, n, and critical atom number, N, cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean, (n x N)^(1/2), is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is minimized occurs at a=7.83microns. On an experimental front, we have fabricated fused-silica microspheres with radii a=10microns and consistently observed quality factors Q=0.8x10^(7). These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.Comment: 12 pages, 14 figure

Anti de Sitter quantum field theory and a new class of hypergeometric identities

We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the K\"all\'en-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical structure emerges. We apply our results to study the decay of unstable Anti-de Sitter particles. The total amplitude is in this case finite and Anti-de Sitter invariant