Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Iron Uptake and Homeostasis in Microorganisms

Preface. Iron is considered to be a minor element employed, in a variety of forms, by nearly all living organisms. In some cases, it is utilised in large quantities, for instance for the formation of magnetosomes within magnetotactic bacteria or during use of iron as a respiratory donor or acceptor by iron oxidising or reducing bacteria. However, in most cases the role of iron is restricted to its use as a cofactor or prosthetic group assisting the biological activity of many different types of protein. The key metabolic processes that are dependent on iron as a cofactor are numerous; they include respiration, light harvesting, nitrogen fixation, the Krebs cycle, redox stress resistance, amino acid synthesis and oxygen transport. Indeed, it is clear that Life in its current form would be impossible in the absence of iron. One of the main reasons for the reliance of Life upon this metal is the ability of iron to exist in multiple redox states, in particular the relatively stable ferrous (Fe2+) and ferric (Fe3+) forms. The availability of these stable oxidation states allows iron to engage in redox reactions over a wide range of midpoint potentials, depending on the coordination environment, making it an extremely adaptable mediator of electron exchange processes. Iron is also one of the most common elements within the Earth’s crust (5% abundance) and thus is considered to have been readily available when Life evolved on our early, anaerobic planet. However, as oxygen accumulated (the ‘Great oxidation event’) within the atmosphere some 2.4 billion years ago, and as the oceans became less acidic, the iron within primordial oceans was converted from its soluble reduced form to its weakly-soluble oxidised ferric form, which precipitated (~1.8 billion years ago) to form the ‘banded iron formations’ (BIFs) observed today in Precambrian sedimentary rocks around the world. These BIFs provide a geological record marking a transition point away from the ancient anaerobic world towards modern aerobic Earth. They also indicate a period over which the bio-availability of iron shifted from abundance to limitation, a condition that extends to the modern day. Thus, it is considered likely that the vast majority of extant organisms face the common problem of securing sufficient iron from their environment – a problem that Life on Earth has had to cope with for some 2 billion years. This struggle for iron is exemplified by the competition for this metal amongst co-habiting microorganisms who resort to stealing (pirating) each others iron supplies! The reliance of micro-organisms upon iron can be disadvantageous to them, and to our innate immune system it represents a chink in the microbial armour, offering an opportunity that can be exploited to ward off pathogenic invaders. In order to infect body tissues and cause disease, pathogens must secure all their iron from the host. To fight such infections, the host specifically withdraws available iron through the action of various iron depleting processes (e.g. the release of lactoferrin and lipocalin-2) – this represents an important strategy in our defence against disease. However, pathogens are frequently able to deploy iron acquisition systems that target host iron sources such as transferrin, lactoferrin and hemoproteins, and thus counteract the iron-withdrawal approaches of the host. Inactivation of such host-targeting iron-uptake systems often attenuates the pathogenicity of the invading microbe, illustrating the importance of ‘the battle for iron’ in the infection process. The role of iron sequestration systems in facilitating microbial infections has been a major driving force in research aimed at unravelling the complexities of microbial iron transport processes. But also, the intricacy of such systems offers a challenge that stimulates the curiosity. One such challenge is to understand how balanced levels of free iron within the cytosol are achieved in a way that avoids toxicity whilst providing sufficient levels for metabolic purposes – this is a requirement that all organisms have to meet. Although the systems involved in achieving this balance can be highly variable amongst different microorganisms, the overall strategy is common. On a coarse level, the homeostatic control of cellular iron is maintained through strict control of the uptake, storage and utilisation of available iron, and is co-ordinated by integrated iron-regulatory networks. However, much yet remains to be discovered concerning the fine details of these different iron regulatory processes. As already indicated, perhaps the most difficult task in maintaining iron homeostasis is simply the procurement of sufficient iron from external sources. The importance of this problem is demonstrated by the plethora of distinct iron transporters often found within a single bacterium, each targeting different forms (complex or redox state) of iron or a different environmental condition. Thus, microbes devote considerable cellular resource to securing iron from their surroundings, reflecting how successful acquisition of iron can be crucial in the competition for survival. The aim of this book is provide the reader with an overview of iron transport processes within a range of microorganisms and to provide an indication of how microbial iron levels are controlled. This aim is promoted through the inclusion of expert reviews on several well studied examples that illustrate the current state of play concerning our comprehension of how iron is translocated into the bacterial (or fungal) cell and how iron homeostasis is controlled within microbes. The first two chapters (1-2) consider the general properties of microbial iron-chelating compounds (known as ‘siderophores’), and the mechanisms used by bacteria to acquire haem and utilise it as an iron source. The following twelve chapters (3-14) focus on specific types of microorganism that are of key interest, covering both an array of pathogens for humans, animals and plants (e.g. species of Bordetella, Shigella, , Erwinia, Vibrio, Aeromonas, Francisella, Campylobacter and Staphylococci, and EHEC) as well as a number of prominent non-pathogens (e.g. the rhizobia, E. coli K-12, Bacteroides spp., cyanobacteria, Bacillus spp. and yeasts). The chapters relay the common themes in microbial iron uptake approaches (e.g. the use of siderophores, TonB-dependent transporters, and ABC transport systems), but also highlight many distinctions (such as use of different types iron regulator and the impact of the presence/absence of a cell wall) in the strategies employed. We hope that those both within and outside the field will find this book useful, stimulating and interesting. We intend that it will provide a source for reference that will assist relevant researchers and provide an entry point for those initiating their studies within this subject. Finally, it is important that we acknowledge and thank wholeheartedly the many contributors who have provided the 14 excellent chapters from which this book is composed. Without their considerable efforts, this book, and the understanding that it relays, would not have been possible. Simon C Andrews and Pierre Cornelis

An old problem revisited - and solved: Upton and Dalton's linear production response: A note

This note presents a robust method for estimating response surfaces that consist of linear response regimes and a linear plateau. The linear response-and-plateau model has fascinated production scientists since von Liebig (1855) and, as Upton and Dalton indicated, some years ago in this Journal, the response-and-plateau model seems to fit the data in many empirical studies. The estimation algorithm evolves from Bayesian implementation of a switching-regression (finite mixtures) model and demonstrates routine application of Gibbs sampling and data augmentation-techniques that are now in widespread application in other disciplines.

Dissociative electron attachment to dinitrogen pentoxide, N2O5

Electron attachment was studied in gaseous dinitrogen pentoxide, N2O5, for incident electron energies between a few meV and 10 eV. No stable parent anion N2O5- was observed but several anionic fragments (NO3-, NO2-, NO-, O-, and O-2(-)) were detected using quadrupole mass spectrometry. Many of these dissociative pathways were found to be coupled and provide detailed information on the dynamics of N2O5 fragmentation. Estimates of the cross sections for production of each of the anionic fragments were made and suggest that electron attachment to N2O5 is amongst the most efficient attachment reactions recorded for nonhalogenated polyatomic systems. (C) 2004 American Institute of Physics.

Molecular t-matrices for low-energy electron diffraction (TMOL v1.1)*1

We describe a FORTRAN-90 program that computes scattering t-matrices for a molecule. These can be used in a Low-Energy Electron Diffraction program to solve the molecular structural problem very efficiently. The intramolecular multiple scattering is computed within a Dyson-like approach, using free space Green propagators in a basis of spherical waves. The advantage of this approach is related to exploiting the chemical identity of the molecule, and to the simplicity to translate and rotate these t-matrices without performing a new multiple-scattering calculation for each configuration. FORTRAN-90 routines for rotating the resulting t-matrices using Wigner matrices are also provided.

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.

Curriculum theory, curriculum policy and the problem of ill-disciplined thinking

This paper examines the implications of policy fracture and arms length governance within the decision making processes currently shaping curriculum design within the English education system. In particular it argues that an unresolved ‘ideological fracture’ at government level has been passed down to school leaders whose response to the dilemma is distorted by the target-driven agenda of arms length agencies. Drawing upon the findings of a large scale on-line survey of history teaching in English secondary schools, this paper illustrates the problems that occur when policy making is divorced from curriculum theory, and in particular from any consideration of the nature of knowledge. Drawing on the social realist theory of knowledge elaborated by Young (2008), we argue that the rapid spread of alternative curricular arrangements, implemented in the absence of an understanding of curriculum theory, undermines the value of disciplined thinking to the detriment of many young people, particularly those in areas of social and economic deprivation.

The acrylamide problem: a plant and agronomic science issue.

Acrylamide, a chemical that is probably carcinogenic in humans and has neurological and reproductive effects, forms from free asparagine and reducing sugars during high-temperature cooking and processing of common foods. Potato and cereal products are major contributors to dietary exposure to acrylamide and while the food industry reacted rapidly to the discovery of acrylamide in some of the most popular foods, the issue remains a difficult one for many sectors. Efforts to reduce acrylamide formation would be greatly facilitated by the development of crop varieties with lower concentrations of free asparagine and/or reducing sugars, and of best agronomic practice to ensure that concentrations are kept as low as possible. This review describes how acrylamide is formed, the factors affecting free asparagine and sugar concentrations in crop plants, and the sometimes complex relationship between precursor concentration and acrylamide-forming potential. It covers some of the strategies being used to reduce free asparagine and sugar concentrations through genetic modification and other genetic techniques, such as the identification of quantitative trait loci. The link between acrylamide formation, flavour, and colour is discussed, as well as the difficulty of balancing the unknown risk of exposure to acrylamide in the levels that are present in foods with the well-established health benefits of some of the foods concerned. Key words: Amino acids, asparagine, cereals, crop quality, food safety, Maillard reaction, potato, rye, sugars, wheat.

On the quantum mechanical scattering statistics of many particles

The probability of a quantum particle being detected in a given solid angle is determined by the S-matrix. The explanation of this fact in time-dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the S-matrix probability emerges in the limit of large distances.

The potential for skill across the range of the seamless weather-climate prediction problem: a stimulus for our science

Predictability is considered in the context of the seamless weather-climate prediction problem, and the notion is developed that there can be predictive power on all time-scales. On all scales there are phenomena that occur as well as longer time-scales and external conditions that should combine to give some predictability. To what extent this theoretical predictability may actually be realised and, further, to what extent it may be useful is not clear. However the potential should provide a stimulus to, and high profile for, our science and its application for many years.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.