Characterizing mixing and measurement in quantum mechanics

What fundamental constraints characterize the relationship between a mixture rho = Sigma (i)p(i)rho (i) of quantum states, the states rho (i) being mixed, and the probabilities p(i)? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that then are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

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.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Lanczos subspace time-independent wave packet calculations of S(D-1)+H-2 reactive scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

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.

Making decisions about treatment for localized prostate cancer

Objective To describe the decision-making processes used by men diagnosed with localized prostate cancer who were considering treatment. Patients and methods Men newly diagnosed with localized prostate cancer from outpatient urology clinics and urologist's private practices were approached before treatment. Their decision-making processes and information-seeking behaviour was assessed; demographic information was also obtained. Results Of 119 men approached, 108 (90%) were interviewed; 91% reported non-systematic decision processes, with deferral to the doctor, positive and negative recollections of others' cancer experiences, and the pre-existing belief that surgery is a better cancer treatment being most common. For systematic information processing the mean (SD, range) number of items considered was 4.19 (2.28, 0-11), with 57% of men considering four or fewer treatment/medical aspects of prostate cancer. Men most commonly considered cancer stage (59%), urinary incontinence (55%) and impotence (51%) after surgery, and low overall mortality (45%). Uncertainty about probabilities for cure was reported by 43% of men and fear of cancer spread by 37%. Men also described uncertainty about the probabilities of side-effects (27%), decisional uncertainty (25%) and anticipated decisional regret (18%). Overall, 73% of men sought information about prostate cancer from external sources, most commonly the Internet, followed by family and friends. Conclusions In general, men did not use information about medical treatments comprehensively or systematically when making treatment decisions, and their processing of medical information was biased by their previous beliefs about cancer and health. These findings have implications for the provision of informational and decisional support to men considering prostate cancer treatment.

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. III. Broad-scale patterns of habitat use

To date there have been few quantitative studies of the distribution of, and relative habitat utilisation by, koalas in the mulgalands of Queensland. To examine these parameters we applied habitat-accessibility and relative habitat-utilisation indices to estimates of faecal pellet density sampled at 149 sites across the region. Modelling the presence of pellets using logistic regression showed that the potential range of accessible habitats and relative habitat use varied greatly across the region, with rainfall being probably the most important determinant of distribution. Within that distribution, landform and rainfall were both important factors affecting habitat preference. Modelling revealed vastly different probabilities of finding a pellet under trees depending on the tree species, canopy size, and location within the region.

Quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Future directions in this field are also discussed.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Dietary influences on survival after ovarian cancer

We evaluated the effects of various food groups and micronutrients in the diet on survival among women who originally participated in a population-based case-control study of ovarian cancer conducted across 3 Australian states between 1990 and 1993. This analysis included 609 women with invasive epithelial ovarian cancer, primarily because there was negligible mortality in women with borderline tumors. The women's usual diet was assessed using a validated food frequency questionnaire. Deaths in the cohort were identified using state-based cancer registries and the Australian National Death Index (NDI). Crude 5-year survival probabilities were estimated using the Kaplan-Meier technique, and adjusted hazard ratios (HRs) and 95% confidence intervals (CIs) were obtained from Cox regression models. After adjusting for important confounding factors, a survival advantage was observed for those who reported higher intake of vegetables in general (HR = 0.75, 95% CI = 0.57-0.99, p-value trend 0.01 for the highest third, compared to the lowest third), and cruciferous vegetables in particular (HR = 0.75, 95% CI = 0.57-0.98, p-value trend 0.03), and among women in the upper third of intake of vitamin E (HR = 0.76, 95% CI = 0.58-1.01, p-value trend 0.04). Inverse associations were also seen with protein (p-value trend 0.09), red meat (p-value trend 0.06) and white meat (p-value trend 0.07), and modest positive trends (maximum 30% excess) with lactose (p-value trend 0.04), calcium and dairy products. Although much remains to be learned about the influence of nutritional factors after a diagnosis of ovarian cancer, our study suggests the possibility that a diet high in vegetable intake may help improve survival. (C) 2003 Wiley-Liss, Inc.

Irreversibilidade, incerteza e teoria econômica reflexões a respeito do indeterminismo metodológico e de suas aplicações na ciência econômica

Este trabalho consiste em aplicar o princípio do indeterminismo metodológico na Ciência Econômica. Isto implica definir dois tipos de universo econômico: um que se caracteriza pela ergodicidade e pela reversibilidade do tempo e dos processos econômicos, e o outro pelas características contrárias. Uma primeira parte tratará da construção do objeto de estudo e da natureza da análise relativa a cada um desses universos. Em razão desta dicotomia, uma segunda parte estudará suas implicações no que diz respeito à natureza das probabilidades e dos processos que guiam as decisões dos agentes.

Assessment and prediction of asthma and its severity in the pediatric community

Seventy four asthmatic children aged 7 to 11 years were examined along with controls matched by age and sex. Clinical and laboratory investigations preceded a 28-day follow-up where data about morning and evening peak expiratory flow rate (PEF), symptoms and treatment were recorded. The coefficient of variation of PEF was found to be an objective measurement of asthma severity that has statistically significant correlation with both symptoms (r s= .36) and treatment (r s= .60). Moreover, it separates mild and severe asthmatics, as confirmed by statistically significant differences (p= .008 or less) in symptoms, treatment, skin allergy and airways response to exercise. Skin allergy and airways responsiveness to exercise were found to be predictors of both disease and severity. By means of logistic regression analysis it was possible to establish the probabilities for both asthma and severe asthma when children presenting and not presenting these characteristics are compared. One single positive skin test represent a probability of 88% for the development of asthma and a probability of 70% for severe disease. A PEF reduction of 10% after an exercise test implies a probability of 73% for disease and a probability of 64% for severe disease. Increases in these variables imply geometrically increased risks and their presence together have a multiplicative effect in the final risk.