Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Lamproites from Gaussberg, Antarctica: Possible transition zone melts of Archaean subducted sediments

Petrogenetic models for the origin of lamproites are evaluated using new major element, trace element, and Sr, Nd, and Pb isotope data for Holocene lamproites from the Gaussberg volcano in the East Antarctic Shield. Gaussberg lamproites exhibit very unusual Pb isotope compositions (Pb-206/Pb-204 = 17.44-17.55 and Pb-207/Pb-204 = 15.56-15.63), which in common Pb isotope space plot above mantle evolution lines and to the left of the meteorite isochron. Combined with very unradiogenic Nd, such compositions are shown to be inconsistent with an origin by melting of sub-continental lithospheric mantle. Instead, a model is proposed in which late Archaean continent-derived sediment is subducted as K-hollandite and other ultra-high-pressure phases and sequestered in the Transition Zone (or lower mantle) where it is effectively isolated for 2-3 Gyr. The high Pb-207/Pb-204 ratio is thus inherited from ancient continent-derived sediment, and the relatively low Pb-206/Pb-204 ratio is the result of a single stage of U/Pb fractionation by subduction-related U loss during slab dehydration. Sr and Nd isotope ratios, and trace element characteristics (e.g. Nb/Ta ratios) are consistent with sediment subduction and dehydration-related fractionation. Similar models that use variable time of isolation of subducted sediment can be derived for all lamproites. Our interpretation of lamproite sources has important implications for ocean island basalt petrogenesis as well as the preservation of geochemically anomalous reservoirs in the mantle.

Ductile fabrics in the zone of active oblique convergence near the Alpine Fault, New Zealand: identifying the neotectonic overprint

The mid-crustal Alpine Schist in central Southern Alps, New Zealand has been exhumed during the past similar to3 m.y. on the hanging wall of the oblique-slip Alpine Fault. These rocks underwent ductile deformation during their passage through the similar to 150-km-wide Pacific-Australia plate boundary zone. Likely to be Cretaceous in age, peak metamorphism predates the largely Pliocene and younger oblique convergence that continues to uplift the Southern Alps today. Late Cenozoic ductile deformation constructively reinforced a pre-existing fabric that was well oriented to accommodate a dextral-transpressive overprint. Quartz microstructures below a recently exhumed brittle-ductile transition zone reflect a late Cenozoic increment of ductile strain that was distributed across deeper levels of the Pacific Plate. Deformation was transpressive, including a dextral-normal shear component that bends and rotates a delaminated panel of Pacific Plate crust onto the oblique footwall ramp of the Alpine Fault. Progressive ductile shear in mylonites at the base of the Pacific Plate overprints earlier fabrics in a dextral-reverse sense, a deformation that accompanies translation of the schists up the Alpine Fault. Ductile shear along that structure affects not only the 12-km-thick section of Alpine mylonites, but is distributed across several kilometres of overlying nonmylonitic rocks. (C) 2001 Elsevier Science Ltd. All rights reserved.

Tide-induced water table fluctuations in coastal aquifers bounded by rhythmic shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer's properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.

Tillering in grain sorghum over a wide range of population densities: Modelling dynamics of tiller fertility

The prediction of tillering is poor or absent in existing sorghum crop models even though fertile tillers contribute significantly to grain yield. The objective of this study was to identify general quantitative relationships underpinning tiller dynamics of sorghum for a broad range of assimilate availabilities. Emergence, phenology, leaf area development and fertility of individual main calms and tillers were quantified weekly in plants grown at one of four plant densities ranging from two to 16 plants m(-2). On any given day, a tiller was considered potentially fertile (a posteriori) if its number of leaves continued to increase thereafter. The dynamics of potentially fertile tiller number per plant varied greatly with plant density, but could generally be described by three determinants, stable across plant densities: tiller emergence rate aligned with leaf ligule appearance rate; cessation of tiller emergence occurred at a stable leaf area index; and rate of decrease in potentially fertile tillers was linearly related to the ratio of realized to potential leaf area growth. Realized leaf area growth is the measured increase in leaf area, whereas potential leaf area growth is the estimated increase in leaf area if all potentially fertile tillers were to continue to develop. Procedures to predict this ratio, by estimating realized leaf area per plant from intercepted radiation and potential leaf area per plant from the number and type of developing axes, are presented. While it is suitable for modelling tiller dynamics in grain sorghum, this general framework needs to be validated by testing it in different environments and for other cultivars. (C) 2002 Annals of Botany Company.

A quantitative state and transition model for the Mitchell grasslands of central western Queensland

Concerns of reduced productivity and land degradation in the Mitchell grasslands of central western Queensland were addressed through a range monitoring program to interpret condition and trend. Botanical and eclaphic parameters were recorded along piosphere and grazing gradients, and across fenceline impact areas, to maximise changes resulting from grazing. The Degradation Gradient Method was used in conjunction with State and Transition Models to develop models of rangeland dynamics and condition. States were found to be ordered along a degradation gradient, indicator species developed according to rainfall trends and transitions determined from field data and available literature. Astrebla spp. abundance declined with declining range condition and increasing grazing pressure, while annual grasses and forbs increased in dominance under poor range condition. Soil erosion increased and litter decreased with decreasing range condition. An approach to quantitatively define states within a variable rainfall environment based upon a time-series ordination analysis is described. The derived model could provide the interpretive framework necessary to integrate on-ground monitoring, remote sensing and geographic information systems to trace states and transitions at the paddock scale. However, further work is needed to determine the full catalogue of states and transitions and to refine the model for application at the paddock scale.

Koala mortality on roads in south-east Queensland: the koala speed-zone trial

In 1995, the Queensland Parks and Wildlife Service, the Queensland Department of Main Roads and Redland Shire Council initiated the Koala Speed Zone Trial in the Koala Coast, south-east Queensland. The aim of the trial was to assess the effect of differential speed signs on the number of koalas ( Phascolarctos cinereus) hit by vehicles in the Koala Coast from 1995 to 1999. On the basis of information collected by the Queensland Parks and Wildlife Service 1407 koalas were hit by vehicles in the Koala Coast during the five-year study ( mean 281 koalas per year, range 251 - 315). Monitoring of vehicle speeds by the Queensland Department of Main Roads suggested that there was no significant reduction in vehicle speed during the trial period from August to December. Consequently, there was no evidence to suggest that a reduction in the number of koalas hit by vehicles occurred during the trial. Approximately 70% of koalas were hit on arterial and sub-arterial roads and approximately 83% did not survive. The location of each koala hit was recorded and the signed speed limit of the road was noted. Most koalas that were hit by vehicles were young healthy males. Pooling of data on koala collisions and road speed limits suggested that the proportion of koalas that survived being hit by vehicles was slightly higher on roads with lower speed limits. However, vehicle speed was not the only factor that affected the number of koalas hit by vehicles. It is suggested that habitat destruction, koala density and traffic volume also contribute to road-associated koala mortality in the Koala Coast.

Modelling the size of the crushed zone around a blasthole

A new model to predict the extent of crushing around a blasthole is presented. The model is based on the back-analysis of a comprehensive experimental program that included the direct measurement of the zone of crushing from 92 blasting tests on concrete blocks using two commercial explosives. The concrete blocks varied from low, medium to high strength and measured 1.5 in in length, 1.0 m in width and 1.1 m in height. A dimensionless parameter called the crushing zone index (CZI) is introduced. This index measures the crushing potential of a charged blasthole and is a function of the borehole pressure, the unconfined compressive strength of the rock material, dynamic Young's modulus and Poisson's ratio. It is shown that the radius of crushing is a function of the CZI and the blasthole radius. A good correlation between the new model and measured results was obtained. A number of previously proposed models could not approximate the conditions measured in the experimental work and there are noted discrepancies between the different approaches reviewed, particularly for smaller diameter holes and low strength rock conditions. The new model has been verified with full scale tests reported in the literature. Results from this validation and model evaluations show its applicability to production blasting. (C) 2003 Elsevier Science Ltd. All rights reserved.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.

Classical approach to interpretation of the charge-dependence of peptide mobilities obtained by capillary zone electrophoresis

Published mobility measurements obtained by capillary zone electrophoresis of human growth hormone peptides are described reasonably well by the classical theoretical relationships for electrophoretic migration. This conformity between theory and experiment has rendered possible a more critical assessment of a commonly employed empirical relationship between mobility (u), net charge (z) and molecular mass (M) of peptides in capillary electrophoresis. The assumed linear dependence between u and z/M-2/3 is shown to be an approximate description of a shallow curvilinear dependence convex to the abscissa. An improved procedure for the calculation of peptide charge (valence) is also described. (C) 2003 Elsevier B.V. All rights reserved.

Dynamics of Gray Matter Loss in Alzheimer's Disease

We detected and mapped a dynamically spreading wave of gray matter loss in the brains of patients with Alzheimer's disease (AD). The loss pattern was visualized in four dimensions as it spread over time from temporal and limbic cortices into frontal and occipital brain regions, sparing sensorimotor cortices. The shifting deficits were asymmetric (left hemisphere >right hemisphere) and correlated with progressively declining cognitive status ( p 15% loss). The maps distinguished different phases of AD and differentiated AD from normal aging. Local gray matter loss rates (5.3 +/- 2.3% per year in AD v 0.9 +/- 0.9% per year in controls) were faster in the left hemisphere ( p < 0.029) than the right. Transient barriers to disease progression appeared at limbic/frontal boundaries. This degenerative sequence, observed in vivo as it developed, provides the first quantitative, dynamic visualization of cortical atrophic rates in normal elderly populations and in those with dementia.

The trans-membrane protein p25 forms highly specialized domains that regulate membrane composition and dynamics

Trans-membrane proteins of the p24 family are abundant, oligomeric proteins predominantly found in cis-Golgi membranes. They are not easily studied in vivo and their functions are controversial. We found that p25 can be targeted to the plasma membrane after inactivation of its canonical KKXX motif (KK to SS, p25SS), and that p25SS causes the co-transport of other p24 proteins beyond the Golgi complex, indicating that wild-type p25 plays a crucial role in retaining p24 proteins in cis-Golgi membranes. We then made use of these observations to study the intrinsic properties of these proteins, when present in a different membrane context. At the cell surface, the p25SS mutant segregates away from both the transferrin receptor and markers of lipid rafts, which are enriched in cholesterol and glycosphingolipids. This suggests that p25SS localizes to, or contributes to form, specialized membrane domains, presumably corresponding to oligomers of p25SS and other p24 proteins. Once at the cell surface, p25SS is endocytosed, together with other p24 proteins, and eventually accumulates in late endosomes, where it remains confined to well-defined membrane regions visible by electron microscopy. We find that this p25SS accumulation causes a concomitant accumulation of cholesterol in late endosomes, and an inhibition of their motility - two processes that are functionally linked. Yet, the p25SS-rich regions themselves seem to-exclude not only Lamp1 but also accumulated cholesterol. One may envision that p25SS accumulation, by excluding cholesterol from oligomers, eventually overloads neighboring late endosomal membranes with cholesterol beyond their capacity (see Discussion). In any case, our data show that p25 and presumably other p24 proteins are endowed with the intrinsic capacity to form highly specialized domains that control membrane composition and dynamics. We propose that p25 and other p24 proteins control the fidelity of membrane transport by maintaining cholesterol-poor membranes in the Golgi complex.

Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.