Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.Comment: 36 page

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities

A new method for experimental characterisation of scattered radiation in 64-slice CT scanner

PURPOSE: The consummate 64-slice CT scanner that spawns a new generation of non-invasive diagnostic tool, however revolutionary, brings with it the incidental by-product that is scattered radiation. The extended detector aperture capability in the 64-slcie CT scanner allows the effects of scattered radiation to be more pronounced and therefore demands that the magnitude and spatial distribution of scatter component be addressed during the imaging process. To this end, corrective algorithms need to be formulated on a basis of a precise understanding of scatter distribution. Relative to a 64-slice CT scanner, here now a unique solution is based upon dedicated blockers operative within various detector rows, calculating scatter profiles and scatter to primary ratios (SPR). MATERIALS AND METHODS: A single dimension blocker array was installed beneath the collimator, and the extrapolated shadow area on the detectors revealed the scatter radiation after exposure. The experiment was conducted using a 64-slice CT scanner manufactured by GE Healthcare Technologies. RESULTS: Variables such as tube voltage, phantom size and phantom-off centring on the scatter profile and the SPR was measured using the dedicated blocker method introduced above. When tube voltage is increased from 80kVp to 140kVp in a 21.5 cm water phantom, the SPR is found to reduce from 219.9 to 39.9 respectively. CONCLUSION: The method developed within this study is applicable to any measurement and is direct with minimal complexity

Synthetic gene design - The rationale for codon optimization and implications for molecular pharming in plants.

Degeneracy in the genetic code allows multiple codon sequences to encode the same protein. Codon usage bias in genes is the term given to the preferred use of particular synonymous codons. Synonymous codon substitutions had been regarded as "silent" as the primary structure of the protein was not affected; however, it is now accepted that synonymous substitutions can have a significant effect on heterologous protein expression. Codon optimization, the process of altering codons within the gene sequence to improve recombinant protein expression, has become widely practised. Multiple inter-linked factors affecting protein expression need to be taken into consideration when optimizing a gene sequence. Over the years, various computer programmes have been developed to aid in the gene sequence optimization process. However, as the rulebook for altering codon usage to affect protein expression is still not completely understood, it is difficult to predict which strategy, if any, will design the 'optimal' gene sequence. In this review, codon usage bias and factors affecting codon selection will be discussed and the evidence for codon optimization impact will be reviewed for recombinant protein expression using plants as a case study. These developments will be relevant to all recombinant expression systems, however, molecular pharming in plants is an area which has consistently encountered difficulties with low levels of recombinant protein expression, and should benefit from an evidence based rational approach to synthetic gene design

Growth, micro-structuring, spectroscopy, and optical gain in as-deposited Al2O3:ErAl_2O_3:Er waveguides

Deposition and micro-structuring of $Al_2O_3:Er$ layers with low background losses (0.11 dB/cm) and lifetimes up to 7 ms have been optimized for active devices. Net gain of 0.7 dB/cm at 1533 nm has been measured.\ud \u

The Added Value of Water Footprint Assessment for National Water Policy: A Case Study for Morocco

A Water Footprint Assessment is carried out for Morocco, mapping the water footprint of different activities at river basin and monthly scale, distinguishing between surface- and groundwater. The paper aims to demonstrate the added value of detailed analysis of the human water footprint within a country and thorough assessment of the virtual water flows leaving and entering a country for formulating national water policy. Green, blue and grey water footprint estimates and virtual water flows are mainly derived from a previous grid-based (5×5 arc minute) global study for the period 1996–2005. These estimates are placed in the context of monthly natural runoff and waste assimilation capacity per river basin derived from Moroccan data sources. The study finds that: (i) evaporation from storage reservoirs is the second largest form of blue water consumption in Morocco, after irrigated crop production; (ii) Morocco’s water and land resources are mainly used to produce relatively low-value (in US$/m3 and US$/ha) crops such as cereals, olives and almonds; (iii) most of the virtual water export from Morocco relates to the export of products with a relatively low economic water productivity (in US$/m3); (iv) blue water scarcity on a monthly scale is severe in all river basins and pressure on groundwater resources by abstractions and nitrate pollution is considerable in most basins; (v) the estimated potential water savings by partial relocation of crops to basins where they consume less water and by reducing water footprints of crops down to benchmark levels are significant compared to demand reducing and supply increasing measures considered in Morocco’s national water strateg