Asymmetry and duration dependence in Australian GDP and unemployment

The per iodic structure of business cycles suggests that significant asymmetries are present over different phases of the cycle. This paper uses markov regime-switching models with fixed and duration dependent transition probabilities to directly model expansions, contractions and durations in Australian GDP growth and unemployment growth. Evidence is found of significant asymmetry in growth rates across expansions and contractions for both series. GDP contractions exhibit duration dependence implying that as output recessions age the likelihood of switching into an expansion phase increases. Unemployment growth does not exhibit duration dependence in either phase. Evidence is also presented that non-linearities in unemployment growth are well explained by the asymmetries in the GDP growth cycle. The analysis suggests that recessions are periods of rapid and intense job destruction, that Australian unemployment tends to ratchet up in recessionary periods and, in contrast to US and UK studies, that shocks to Australian unemployment growth are more persistent in recessions than expansions. [E37 C5 C41].

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

A cost-effectiveness analysis of fluvastatin in patients with diabetes after successful percutaneous coronary intervention

Background: The Lescol Intervention Prevention Study (LIPS) was a multinational randomized controlled trial that showed a 47% reduction in the relative risk of cardiac death and a 22% reduction in major adverse cardiac events (MACEs) from the routine use of fluvastatin, compared with controls, in patients undergoing percutaneous coronary intervention (PCI, defined as angioplasty with or without stents). In this study, MACEs included cardiac death, nonfatal myocardial infarction, and subsequent PCI and coronary artery bypass graft. Diabetes was the greatest risk factor for MACEs. Objective: This study estimated the cost-effectiveness of fluvastatin when used for secondary prevention of MACEs after PCI in people with diabetes. Methods: A post hoc subgroup analysis of patients with diabetes from the LIPS was used to estimate the effectiveness of fluvastatin in reducing myocardial infarction, revascularization, and cardiac death. A probabilistic Markov model was developed using United Kingdom resource and cost data to estimate the additional costs and quality-adjusted life-years (QALYs) gained over 10 years from the perspective of the British National Health Service. The model contained 6 health states, and the transition probabilities were derived from the LIPS data. Crossover from fluvastatin to other lipid-lowering drugs, withdrawal from fluvastatin, and the use of lipid-lowering drugs in the control group were included. Results: In the subgroup of 202 patients with diabetes in the LIPS trial, 18 (15.0%) of 120 fluvastatin patients and 21 (25.6%) of 82 control participants were insulin dependent (P = NS). Compared with the control group, patients treated with fluvastatin can expect to gain an additional mean (SD) of 0.196 (0.139) QALY per patient over 10 years (P < 0.001) and will cost the health service an additional mean (SD) of 10 (E448) (P = NS) (mean [SD] US $16 [$689]). The additional cost per QALY gained was;(51 (US $78). The key determinants of cost-effectiveness included the probabilities of repeat interventions, cardiac death, the cost of fluvastatin, and the time horizon used for the evaluation. Conclusion: Fluvastatin was an economically efficient treatment to prevent MACEs in these patients with diabetes undergoing PCI.

XSophe, a computer simulation software suite for the analysis of electron paramagnetic resonance spectra

The XSophe computer simulation software suite consisting of a daemon, the XSophe interface and the computational program Sophe is a state of the art package for the simulation of electron paramagnetic resonance spectra. The Sophe program performs the computer simulation and includes a number of new technologies including; the SOPHE partition and interpolation schemes, a field segmentation algorithm, homotopy, parallelisation and spectral optimisation. The SOPHE partition and interpolation scheme along with a field segmentation algorithm greatly increases the speed of simulations for most systems. Multidimensional homotopy provides an efficient method for accurately tracing energy levels and hence tracing transitions in the presence of energy level anticrossings and looping transitions and allowing computer simulations in frequency space. Recent enhancements to Sophe include the generalised treatment of distributions of orientational parameters, termed the mosaic misorientation linewidth model and a faster more efficient algorithm for the calculation of resonant field positions and transition probabilities. For complex systems the parallelisation enables the simulation of these systems on a parallel computer and the optimisation algorithms in the suite provide the experimentalist with the possibility of finding the spin Hamiltonian parameters in a systematic manner rather than a trial-and-error process. The XSophe software suite has been used to simulate multifrequency EPR spectra (200 MHz to 6 00 GHz) from isolated spin systems (S > ~½) and coupled centres (Si, Sj _> I/2). Griffin, M.; Muys, A.; Noble, C.; Wang, D.; Eldershaw, C.; Gates, K.E.; Burrage, K.; Hanson, G.R."XSophe, a Computer Simulation Software Suite for the Analysis of Electron Paramagnetic Resonance Spectra", 1999, Mol. Phys. Rep., 26, 60-84.

Spontaneous transitions in the coordination of a whole body task

This paper describes an example of spontaneous transitions between qualitatively different coordination patterns during a cyclic lifting and lowering task. Eleven participants performed 12 trials of repetitive lifting and lowering in a ramp protocol in which the height of the lower shelf was raised or lowered 1 cm per cycle between 10 and 50 cm. Two distinct patterns of coordination were evident: a squat technique in which moderate range of hip, knee and ankle movement was utilised and ankle plantar-flexion occurred simultaneously with knee and hip extension; and a stoop technique in which the range of knee movement was reduced and knee and hip extension was accompanied by simultaneous ankle dorsi-flexion. Abrupt transitions from stoop to squat techniques were observed during descending trials, and from squat to stoop during ascending trials. Indications of hysteresis was observed in that transitions were more frequently observed during descending trials, and the average shelf height at the transition was 5 cm higher during ascending trials. The transitions may be a consequence of a trade-off between the biomechanical advantages of each technique and the influence of the lift height on this trade-off.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Entanglement induced by spontaneous emission in spatially extended two-atom systems

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.

Simulating quantum interference in a three-level system with perpendicular transition dipole moments

We consider a three-level V-type atomic system with the ground state coupled by a laser field to only one of the excited states, and with the two excited states coupled together by a dc field. Although the dipole moments of the two dipole-allowed transitions are assumed perpendicular, we demonstrate that this system emulates to a large degree a three-level system with parallel dipole moments-the latter being a system that exhibits quantum interference and displays a number of interesting features. As examples, we show that the system can produce extremely large values for the intensity-intensity correlation function, and that its resonance fluorescence spectrum can display ultranarrow lines. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. We also show that this system is capable of exhibiting considerable squeezing.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Magnetic susceptibility of the normal-superconducting transition in high-purity single-crystal α-uranium

We report complex ac magnetic susceptibility measurements of a superconducting transition in very high-quality single-crystal alpha-uranium using microfabricated coplanar magnetometers. We identify an onset of superconductivity at Tapproximate to0.7 K in both the real and imaginary components of the susceptibility which is confirmed by resistivity data. A superconducting volume fraction argument, based on a comparison with a calibration YBa2Cu3O7-delta sample, indicates that superconductivity in these samples may be filamentary. Our data also demonstrate the sensitivity of the coplanar micro-magnetometers, which are ideally suited to measurements in pulsed magnetic fields exceeding 100 T.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.