Abstract:
the marsupial and placental mammals originated at a time when the pattern of geographical barriers (oceans, shallow seas and mountains) was very different from that of today, and climates were warmer. the sequence of changes in these barriers, and their effects on the dispersal of the mammal families and on the faunas of mammals in the different continents, are reviewed. the mammal fauna of south america changed greatly in the pliocene/pleistocene, when the newly-complete panama isthmus allowed the north american fauna to enter the continent and replace most of the former south american mammal families. marsupial, but not placental, mammals reached australia via antarctica before australia became isolated, while rats and bats are the only placentals that dispersed naturally from asia to australia in the late cenozoic. little is known of the early history of the mammal fauna of india. a few mammal families reached madagascar from africa in the early cenozoic over a chain of islands. africa was isolated for much of the early cenozoic, though some groups did succeed in entering from europe. before the climate cooled in the mid-cenozoic, the mammal faunas of the northern hemisphere were much richer than those of today.

Abstract:
The marsupial and placental mammals originated at a time when the pattern of geographical barriers (oceans, shallow seas and mountains) was very different from that of today, and climates were warmer. The sequence of changes in these barriers, and their effects on the dispersal of the mammal families and on the faunas of mammals in the different continents, are reviewed. The mammal fauna of South America changed greatly in the Pliocene/Pleistocene, when the newly-complete Panama Isthmus allowed the North American fauna to enter the continent and replace most of the former South American mammal families. Marsupial, but not placental, mammals reached Australia via Antarctica before Australia became isolated, while rats and bats are the only placentals that dispersed naturally from Asia to Australia in the late Cenozoic. Little is known of the early history of the mammal fauna of India. A few mammal families reached Madagascar from Africa in the early Cenozoic over a chain of islands. Africa was isolated for much of the early Cenozoic, though some groups did succeed in entering from Europe. Before the climate cooled in the mid-Cenozoic, the mammal faunas of the Northern Hemisphere were much richer than those of today.

Abstract:
Gravitational wave emission is expected to arise from a variety of astrophysical phenomena. A new generation of detectors with sensitivity consistent with expectation from such sources is being developed. The Laser Interferometer Gravitational-Wave Observatory (LIGO), one of these ambitious undertakings, is being developed by a Caltech-MIT collaboration. It consists of two widely separated interferometers, which will be used in coincidence to search for sources from compact binary systems, spinning neutron stars, supernovae and other astrophysical or cosmological phenomena that emit gravitational waves. The construction of LIGO is well underway and preparations are being made for the commissioning phase. In this lecture, I review the underlying physics of gravitational waves, review possible astrophysical and cosmological sources and discuss the LIGO interferometer status and plans.

Abstract:
The appearance of Marshall and Olkin's 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years this continues to be the case. The present article presents a sampling of the diverse areas in which majorization has been found to be useful in the past 25 years.

Abstract:
Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.

Abstract:
Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, \sigma(x,x'), the square root of the Van Vleck determinant, \Delta^{1/2}(x,x'), and the tail-term, V(x,x'), appearing in the Hadamard form of the Green function. These bi-tensors are central to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity. Their transport equations may be used either in a semi-recursive approach to determining their covariant Taylor series expansions, or as the basis of numerical calculations. To illustrate the power of the semi-recursive approach, we present an implementation in \textsl{Mathematica} which computes very high order covariant series expansions of these objects. Using this code, a moderate laptop can, for example, calculate the coincidence limit a_7(x,x) and V(x,x') to order (\sigma^a)^{20} in a matter of minutes. Results may be output in either a compact notation or in xTensor form. In a second application of the approach, we present a scheme for numerically integrating the transport equations as a system of coupled ordinary differential equations. As an example application of the scheme, we integrate along null geodesics to solve for V(x,x') in Nariai and Schwarzschild spacetimes.

Abstract:
We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an arbitrary sequence of single-qubit measurements are independent of how many unmeasured qubits have been lost prior to the measurement. Our results are valuable for quantum information processing of indistinguishable particles by post-selection, e.g. in cases where the results of an experiment are discarded conditioned upon the occurrence of a given event such as particle loss. Furthermore, our results are important for the design of adaptive-measurement strategies, e.g. a series of measurements where for each measurement instance, the measurement basis is chosen depending on prior measurement results.

Abstract:
We consider a scalar charge travelling in a curved background spacetime. We calculate the quasi-local contribution to the scalar self-force experienced by such a particle following a geodesic in a general spacetime. We also show that if we assume a massless field and a vacuum background spacetime, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analog are of immediate physical interest for the calculation of radiation reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.

Abstract:
In a recent work, we presented the first application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function which are respectively valid in the `quasilocal' and `distant past' regimes, and which may be matched together within the normal neighbourhood. In this article, we introduce the method of matched expansions and discuss transport equation methods for the calculation of the Green function in the quasilocal region. These methods allow the Green function to be evaluated throughout the normal neighborhood and are also relevant to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity.