Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Time-reversal ultrawideband breast imaging: pulse design criteria considering multiple tumors with unknown tissue properties

Pulse design is investigated for time-reversal (TR) imaging as applied to ultrawideband (UWB) breast cancer detection. Earlier it has been shown that a suitably-designed UWB pulse may help to improve imaging performance for a single-tumor breast phantom with predetermined lesion properties. The current work considers the following more general and practical situations: presence of multiple malignancies with unknown tumor size and dielectric properties. Four pulse selection criteria are proposed with each focusing on one of the following aspects: eliminating signal clutter generated by tissue inhomogeneities, canceling mutual interference among tumors, improving image resolution, and suppressing artifacts created by sidelobe of the target response. By applying the proposed criteria, the shape parameters of UWB waveforms with desirable characteristics are identified through search of all the possible pulses. Simulation example using a numerical breast phantom, comprised of two tumors and structured clutter distribution, demonstrates the effectiveness of the proposed approach. Specifically, a tradeoff between the image resolution and signal-to-clutter contrast (SCC) is observed in terms of selection of the excitation waveforms.