On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

Continuous-time perpetuities and time reversal of diffusions

We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markov model. Two approaches are used to obtain the distribution. The first identifies a partial differential equation for the conditional cumulative distribution function of the perpetuity given the initial factor value, which under certain conditions ensures the existence of a density for the perpetuity. The second (and more general) approach, identifies the joint law as the stationary distribution of an ergodic multi-dimensional diffusion using techniques of time reversal. This later approach allows for efficient use of Monte-Carlo simulation when estimating the distribution, as the distribution is obtained by sampling a single path of the reversed process.Comment: 42 pages; added numerical exampl

Irving Fisher and Index Number Theory

There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test and economic approaches. The paper reviews the contributions of Irving Fisher to these approaches to index number theory which are still in use today. The paper also reviews Fisher’s contributions to multilateral index number theory. The main themes of the paper are developed in the context of a review of the early history of index number theory: a history that conveys a wealth of information and insight into the making and use of index numbers today.Price indexes, quantity indexes, bilateral price indexes, multilateral price indexes, the Fisher ideal index, the test approach to index number theory

Near-Infrared Light Curves of the Brown Dwarf Eclipsing Binary 2MASS J05352184-0546085: Can Spots Explain the Temperature Reversal?

We present the JHKs light curves for the double-lined eclipsing binary 2MASS J05352184-0546085, in which both components are brown dwarfs. We analyze these light curves with the published Ic-band light curve and radial velocities to provide refined measurements of the system's physical parameters. The component masses and radii are here determined with an accuracy of ~6.5% and ~1.5%, respectively. We confirm the previous surprising finding that the primary brown dwarf has a cooler effective temperature than its companion. Next, we perform a detailed study of the variations in the out-of-eclipse phases of the light curves to ascertain the properties of any inhomogeneities on the surfaces of the brown dwarfs. Our analysis reveals two low-amplitude periodic signals, one attributable to the rotation of the primary (with a period of 3.293+/-0.001 d) and the other to that of the secondary (14.05+/-0.05 d). Finally, we explore the effects on the derived physical parameters of the system when spots are included in the modeling. The observed low-amplitude rotational modulations are well fit by cool spots covering a small fraction of their surfaces. To mimic the observed ~200 K suppression of the primary's temperature, our model requires that the primary possess a very large spot coverage fraction of ~65%. Altogether, a spot configuration in which the primary is heavily spotted while the secondary is lightly spotted can explain the apparent temperature reversal and can bring the temperatures of the brown dwarfs into agreement with the predictions of theoretical models.Comment: Accepted for publication in The Astrophysical Journal; 13 pages, 8 figures, 6 tables. Updated parameter uncertaintie

Motorway Tidal Flow Lane Control

A traffic control case of particular importance occurs when inbound and outbound traffic on a motorway stretch is unbalanced throughout the day. This scenario may benefit of a lane management strategy called tidal flow (or reversible) lane control, in which case the direction of a contraflow buffer lane is reversed according to the needs of each direction. This paper proposes a simple and practical real-time strategy for efficient motorway tidal flow lane control. A switching policy based on the fundamental diagram, that requires only aggregated measurements of density (or occupancy), is adopted. A kinematic wave theory-based traffic flow analysis shows that the proposed strategy provides a Pareto-optimal solution. Simulation studies of the A38(M) Aston Expressway (Birmingham, UK), are used to demonstrate its operation. The results confirm an increase of motorway throughput and a smooth operation of the strategy