Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

The modeling of turbulent reactive flows based on multiple mapping conditioning

A new modeling approach-multiple mapping conditioning (MMC)-is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem. (C) 2003 American Institute of Physics.

Promiscuous CTL recognition of viral epitopes on multiple human leukocyte antigens: Biological validation of the proposed HLA A24 supertype

Multiple HLA class I alleles can bind peptides with common sequence motifs due to structural similarities in the peptide binding cleft, and these groups of alleles have been classified into supertypes. Nine major HLA supertypes have been proposed, including an A24 supertype that includes A*2301, A*2402, and A*3001. Evidence for this A24 supertype is limited to HLA sequence homology and/or similarity in peptide binding motifs for the alleles. To investigate the immunological relevance of this proposed supertype, we have examined two viral epitopes (from EBV and CMV) initially defined as HLA-A*2301-binding peptides. The data clearly demonstrate that each peptide could be recognized by CTL clones in the context of A*2301 or A*2402; thus validating the inclusion of these three alleles within an A24 supertype. Furthermore, CTL responses to the EBV epitope were detectable in both A*2301(+) and A*2402(+) individuals who had been previously exposed to this virus. These data substantiate the biological relevance of the A24 supertype, and the identification of viral epitopes with the capacity to bind promiscuously across this supertype could aid efforts to develop CTL-based vaccines or immunotherapy. The degeneracy in HLA restriction displayed by some T cells in this study also suggests that the dogma of self-MHC restriction needs some refinement to accommodate foreign peptide recognition in the context of multiple supertype alleles.

Ex vivo profiling of CD8(+)-T-cell responses to human cytomegalovirus reveals broad and multispecific reactivities in healthy virus carriers

Human cytomegalovirus (HCMV) can establish both nonproductive (latent) and productive (lytic) infections. Many of the proteins expressed during these phases of infection could be expected to be targets of the immune response; however, much of our understanding of the CD8(+)-T-cell response to HCMV is mainly based on the pp65 antigen. Very little is known about T-cell control over other antigens expressed during the different stages of virus infection; this imbalance in our understanding undermines the importance of these antigens in several aspects of HCMV disease pathogenesis. In the present study, an efficient and rapid strategy based on predictive bioinformatics and ex vivo functional T-cell assays was adopted to profile CD8(+)-T-cell responses to a large panel of HCMV antigens expressed during different phases of replication. These studies revealed that CD8(+)-T-cell responses to HCMV often contained multiple antigen-specific reactivities, which were not just constrained to the previously identified pp65 or IE-1 antigens. Unexpectedly, a number of viral proteins including structural, early/late antigens and HCMV-encoded immunomodulators (pp28, pp50, gH, gB, US2, US3, US6, and UL18) were also identified as potential targets for HCMV-specific CD8(+)-T-cell immunity. Based on this extensive analysis, numerous novel HCMV peptide epitopes and their HLA-restricting determinants recognized by these T cells have been defined. These observations contrast with previous findings that viral interference with the antigen-processing pathway during lytic infection would render immediate-early and early/late proteins less immunogenic. This work strongly suggests that successful HCMV-specific immune control in healthy virus carriers is dependent on a strong T-cell response towards a broad repertoire of antigens.

Estimates of global and regional potential health gains from reducing multiple major risk factors

Background Estimates of the disease burden due to multiple risk factors can show the potential gain from combined preventive measures. But few such investigations have been attempted, and none on a global scale. Our aim was to estimate the potential health benefits from removal of multiple major risk factors. Methods We assessed the burden of disease and injury attributable to the joint effects of 20 selected leading risk factors in 14 epidemiological subregions of the world. We estimated population attributable fractions, defined as the proportional reduction in disease or mortality that would occur if exposure to a risk factor were reduced to an alternative level, from data for risk factor prevalence and hazard size. For every disease, we estimated joint population attributable fractions, for multiple risk factors, by age and sex, from the direct contributions of individual risk factors. To obtain the direct hazards, we reviewed publications and re-analysed cohort data to account for that part of hazard that is mediated through other risks. Results Globally, an estimated 47% of premature deaths and 39% of total disease burden in 2000 resulted from the joint effects of the risk factors considered. These risks caused a substantial proportion of important diseases, including diarrhoea (92%-94%), lower respiratory infections (55-62%), lung cancer (72%), chronic obstructive pulmonary disease (60%), ischaemic heart disease (83-89%), and stroke (70-76%). Removal of these risks would have increased global healthy life expectancy by 9.3 years (17%) ranging from 4.4 years (6%) in the developed countries of the western Pacific to 16.1 years (43%) in parts of sub-Saharan Africa. Interpretation Removal of major risk factors would not only increase healthy life expectancy in every region, but also reduce some of the differences between regions, The potential for disease prevention and health gain from tackling major known risks simultaneously would be substantial.

Epitope-blocking enzyme-linked immunosorbent assays for the detection of serum antibodies to West Nile virus in multiple avian species

We report the development of epitope-blocking enzyme-linked immunosorbent assays (ELISAs) for the rapid detection of serum antibodies to West Nile virus (WNV) in taxonomically diverse North American avian species. A panel of flavivirus-specific monoclonal antibodies (MAbs) was tested in blocking assays with serum samples from WNV-infected chickens and crows. Selected MAbs were further tested against serum samples from birds that represented 16 species and 10 families. Serum samples were collected from birds infected with WW or Saint Louis encephalitis virus (SLEV) and from noninfected control birds. Serum samples from SLEV-infected birds were included in these experiments because WNV and SLEV are closely related antigenically, are maintained in similar transmission cycles, and have overlapping geographic distributions. The ELISA that utilized MAb 3.11126 potentially discriminated between WW and SLEV infections, as all serum samples from WNV-infected birds and none from SLEV-infected birds were positive in this assay. Assays with MAbs 2132 and 6B6C-1 readily detected serum antibodies in all birds infected with WNV and SLEV, respectively, and in most birds infected with the other virus. Two other MAbs partially discriminated between infections with these two viruses. Serum samples from most WNV-infected birds but no SLEV-infected birds were positive with MAb 3.676, while almost all serum samples from SLEV-infected birds but few from WNV-infected birds were positive with MAb 6B5A-5. The blocking assays reported here provide a rapid, reliable, and inexpensive diagnostic and surveillance technique to monitor WNV activity in multiple avian species.

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.

Repair of three pathologic fractures in a dog with multiple myeloma

Three pathological fractures occurred secondary to osteolytic lesions of multiple myeloma. Two long bone fractures were each stabilised using interlocking nail fixation augmented with polymethyl meth acral ate bone cement. One vertebral fracture was stabilised using Steinmann pins and PMMA. Successful stabilisation, rapid return to function and improvement in quality of life occurred in all fractures. The patient survived approximately eight months on concurrent chemotherapy.

Actively shielded multi-layer gradient coil designs with improved cooling properties

In standard cylindrical gradient coils consisting of a single layer of wires, a limiting factor in achieving very large magnetic field gradients is the rapid increase in coil resistance with efficiency. This is a particular problem in small-bore scanners, such as those used for MR microscopy. By adopting a multi-layer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favourable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. Previously this approach has been applied to the design of unshielded, longitudinal, and transverse gradient coils. Here, the multi-layer approach has been extended to allow the design of actively shielded multi-layer gradient coils, and also to produce coils exhibiting enhanced cooling characteristics. An iterative approach to modelling the steady-state temperature distribution within the coil has also been developed. Results indicate that a good level of screening can be achieved in multi-layer coils, that small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers of increases. Simulations show that by optimising multi-layer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature. A four-layer coil of 8 mm inner diameter has been constructed and used to test the steady-state temperature model. (C) 2003 Elsevier Inc. All rights reserved.

Multilayer transverse gradient coil design

In small, cylindrical gradient coils consisting of a single layer of wires, the limiting factor in achieving large magnetic field gradients is the rapid increase in coil resistance with efficiency. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, mathematical expressions have been developed that allow the design of multilayer coils. These expressions have previously been applied to the design of a four-layer z-gradient coil. As a further development, the equations have now been modified to allow the design of multilayer transverse gradient coils. The variation in coil performance with the number of layers employed has been investigated for coils of a size suitable for use in NMR microscopy, and the effect of constructing the coil using wires or cuts in a continuous conducting surface has also been assessed. We find that at fixed resistance a small wire-wound two-layer coil offers an increase in efficiency of a factor of about 1.5 compared with a single-layer coil. In addition, a two-layer coil of 10-mm inner diameter has been designed and built. This coil had an efficiency of 0.41 Tm-1 A(-1), a resistance of 0.96 +/- 0.01 Omega, and an inductance of 22.3 +/- 0.2 muH. The coil produces a gradient that deviates from linearity by less than 5% over a central cylindrical region of interest of height and length 6.2 mm. (C) 2003 Wiley Periodicals, Inc.

Use of confocal scanning laser microscopy to measure the concentrations of aerial and penetrative hyphae during growth of Rhizopus oligosporus on a solid surface

In order to develop a method for use in investigations of spatial biomass distribution in solid-state fermentation systems, confocal scanning laser microscopy was used to determine the concentrations of aerial and penetrative biomass against height and depth above and below the substrate surface, during growth of Rhizopus oligosporus on potato dextrose agar. Penetrative hyphae had penetrated to a depth of 0.445 cm by 64 h and showed rhizoid morphology, in which the maximum biomass concentration, of 4.45 mg dry wt cm(-3), occurred at a depth of 0.075 cm. For aerial biomass the maximum density of 39.54 mg dry wt(-3) occurred at the substrate surface. For both aerial and penetrative biomass, there were two distinct regions in which the biomass concentration decayed exponentially with distance from the surface. For aerial biomass, the first exponential decay region was up to 0.1 cm height. The second region above the height of 0.1 cm corresponded to that in which sporangiophores dominated. This work lays the foundation for deeper studies into what controls the growth of fungal hyphae above and below the surfaces of solid substrates. (C) Wiley Periodicals, Inc.

Use of confocal microscopy to follow the development of penetrative hyphae during growth of Rhizopus oligosporus in an artificial solid-state fermentation system

Two methods were compared for determining the concentration of penetrative biomass during growth of Rhizopus oligosporus on an artificial solid substrate consisting of an inert gel and starch as the sole source of carbon and energy. The first method was based on the use of a hand microtome to make sections of approximately 0.2- to 0.4-mm thickness parallel to the substrate surface and the determination of the glucosamine content in each slice. Use of glucosamine measurements to estimate biomass concentrations was shown to be problematic due to the large variations in glucosamine content with mycelial age. The second method was a novel method based on the use of confocal scanning laser microscopy to estimate the fractional volume occupied by the biomass. Although it is not simple to translate fractional volumes into dry weights of hyphae due to the lack of experimentally determined conversion factors, measurement of the fractional volumes in themselves is useful for characterizing fungal penetration into the substrate. Growth of penetrative biomass in the artificial model substrate showed two forms of growth with an indistinct mass in the region close to the substrate surface and a few hyphae penetrating perpendicularly to the surface in regions further away from the substrate surface. The biomass profiles against depth obtained from the confocal microscopy showed two linear regions on log-linear plots, which are possibly related to different oxygen availability at different depths within the substrate. Confocal microscopy has the potential to be a powerful tool in the investigation of fungal growth mechanisms in solid-state fermentation. (C) 2003 Wiley Periodicals, Inc.