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.

CD40 and CD86 upregulation with divergent CMRF44 expression on blood dendritic cells in inflammatory bowel diseases

OBJECTIVE: Dendritic cells (DC) are the only antigen-presenting cells that can activate naive T lymphocytes and initiate a primary immune response. They are also thought to have a role in immune tolerance. DC traffic from the blood to peripheral tissue where they become activated. They then present antigen and the costimulating signals necessary to initiate an immune response. In this study, we investigated the number, subsets, and activation pattern of circulating and intestinal DC from patients with clinically mild ulcerative colitis (UC) or Crohn's disease. METHODS: Patients were recruited, if they were not taking immunosuppressive therapy, and were assessed for clinical severity of their disease using for UC, the Clinical Activity Index, and for Crohn's disease, the Crohn's Disease Activity Index. Blood CD11c(+) and CD11c(-) DC subsets, expression of costimulatory antigens, CD86 and CD40, and the early differentiation/activation antigen, CMRF44, were enumerated by multicolor flow cytometry of lineage negative (lin(-) = CD3(-), CD19(-), CD14(-), CD16(-)) HLA-DR+ DC. These data were compared with age-matched healthy and the disease control groups of chronic noninflammatory GI diseases (cGI), acute noninflammatory GI diseases (aGI), and chronic non-GI inflammation (non-GI). In addition, cryostat sections of colonoscopic biopsies from healthy control patients and inflamed versus noninflamed gut mucosa of inflammatory bowel disease (IBD) patients were examined for CD86(+) and CD40(+)lin(-) cells. RESULTS: Twenty-one Crohn's disease and 25 UC patients, with mean Crohn's Disease Activity Index of 98 and Clinical Activity Index of 3.1, and 56 healthy controls, five cGI, five aGI, and six non-GI were studied. CD11c(+) and CD11c(-) DC subsets did not differ significantly between Crohn's, UC, and healthy control groups. Expression of CD86 and CD40 on freshly isolated blood DC from Crohn's patients appeared higher (16.6%, 31%) and was significantly higher in UC (26.6%, 46.3%) versus healthy controls (5.5%, 25%) (p = 0.004, p = 0.012) and non-GI controls (10.2%, 22.8%) (p = 0.012, p = 0.008), but not versus cGI or aGI controls. CD86(+) and CD40(+) DC were also present in inflamed colonic and ileal mucosa from UC and Crohn's patients but not in noninflamed IBD mucosa or normal mucosa. Expression of the CMRF44 antigen was low on freshly isolated DC, but it was upregulated after 24-h culture on DC from all groups, although significantly less so on DC from UC versus Crohn's or healthy controls (p = 0.024). The CMRF44(+) antigen was mainly associated with CD11c(+) DC, and in UC was inversely related to the Clinical Activity Index (r = -0.69, p = 0.0002). CONCLUSIONS: There is upregulation of costimulatory molecules on blood DC even in very mild IBD but surprisingly, there is divergent expression of the differentiation/activation CMRF44 antigen. Upregulation of costimulatory molecules and divergent expression of CMRF44 in blood DC was also apparent in cGI and aGI but not in non-GI or healthy controls, whereas intestinal CD86(+) and CD40(+) DC were found only in inflamed mucosa from IBD patients. Persistent or distorted activation of blood DC or divergent regulation of costimulatory and activation antigens may have important implications for gut mucosal immunity and inflammation. (Am J Gastroenterol 2001;96:2946-2956. (C) 2001 by Am. Coll. of Gastroenterology).

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.

Investigation of electrical conductivity as a function of dopant-ion radius in the systems Zr0.75Ce0.08M0.17O1.92 (M=Nd, Sm, Gd, Dy, Ho, Y, Er, Yb, Sc)

Electrical conductivity versus dopant ionic radius studies in zirconia- and ceria-based, solid oxide fuel cell (SOFC) electrolyte systems have shown that oxygen-ion conductivity is highest when the host and dopant ions are similar in size [J. Am. Ceram. Soc. 48 (1965) 286; Solid State Ionics 37 (1989) 67; Solid State Ionics 5 (1981) 547]. Under these conditions, it is thought that the conduction paths within the crystal lattice become less distorted [Solid State Ionics 8 (1983) 201]. In this study, binary ZrO2-M2O3 unit cells were expanded, via the partial substitution of Ce+4 for Zr+4 into the lattice, in an attempt to identify new, ternary, zirconia/ceria-based electrolyte systems with enhanced electrical conductivity. The compositions Zr0.75Ce0.08M0.17O1.92 (M = Nd, Sm, Gd, Dy, Ho, Y, Yb, Sc) were prepared using traditional solid state techniques. Bulk phase characterisation and precise lattice parameter measurements were performed with X-ray diffraction techniques. Four-probe DC conductivity measurements between 400 and 900 degreesC showed that the dopant-ion radius influenced electrical conductivity. The conductivity versus dopant-ion radius trends previously observed in zirconia-based, binary systems are clearly apparent in the ternary systems investigated in this study. The addition of ceria was found to have a negative influence on the electrical conductivity over the temperature range 400-900 degreesC. It is suggested that distortion of the oxygen-ion conduction path by the presence of the larger M+3 and Ce+4 species (relative to Zr+4) is the reason for the decreasing electrical conductivity as a function of increasing dopant size and ceria addition, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.

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.

Synthesis and characterization of mono- and bis-ligand zinc(II) and cadmium(II) complexes of the di-2-pyridylketone Schiff base of S-benzyl dithiocarbazate (Hdpksbz) and the X-ray crystal structures of the [Zn(dpksbz)2] and [Cd(dpksbz)NCS]2 complexes

New mono- and bis-chelated zinc(II) and cadmium(II) complexes of formula, [M(dpksbz)NCS] (dpksbz = anionic form of the di-2-pyridylketone Schiff base of S-benzyldithiocarbazate) and [M(dpksbz)(2)] (M = Zn-II, Cd-II) have been prepared and characterized. The structure of the bis-ligand complex, [Zn(dpksbZ)(2)] has been determined by X-ray diffraction. The complex has a distorted octahedral geometry in which the ligands are coordinated to the zinc(II) ion as uninegatively charged tridentate chelates via the thiolate sulfur atoms, the azomethine nitrogen atoms and the pyridine nitrogen atoms. The distortion from a regular octahedral geometry is attributed to the restricted bite angles of the Schiff base ligands. X-ray structural analysis shows that the [Cd(dpksbz)NCS](2) complex is a centrosymmetric dimer in which each of the cadmium(II) ions adopts a five-coordinate, approximately square-pyramidal configuration with the Schiff base acting as a tetradentate chelating agent coordinating a cadmium(II) ion via one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur atom; the second pyridine nitrogen atom is coordinated to the other cadmium(II) ion of the dimer. The fifth coordination position around each cadmium(II) is occupied by an N-bonded thiocyanate ligand. (C) 2003 Elsevier Science Ltd. All rights reserved.

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.