Comparison of fast field-cycling magnetic resonance imaging methods and future perspectives

ABSTRACT

Fast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents.     

T1Effects in Sequential Dynamic Susceptibility Contrast Experiments

Residual effects of an initial bolus of gadolinium contrast agent have been previously demonstrated in sequential dynamic susceptibility contrast MR experiments. While these residual effects quickly reach a saturation steady state, their etiology is uncertain, and they can lead to spurious estimates of hemodynamic parameters in activation experiments. The possible influence ofT₁effects is now investigated with experiments in whichT₁weighting is varied as well as with serial regionalT₁measurements. Little evidence for significant residualT₁effects is found, suggesting instead that susceptibility effects underlie these observations. An initial saturation dose of contrast agent minimizes this effect.     

Signed graphs for portfolio analysis in risk management

We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable.     

On isomorphic factorizations of circulant graphs

We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

A Faster Deterministic Maximum Flow Algorithm

Cheriyan and Hagerup developed a randomized algorithm to compute the maximum flow in a graph with n nodes and m edges in O(mn + n² log²n) expected time. The randomization is used to efficiently play a certain combinatorial game that arises during the computation. We give a version of their algorithm where a general version of their game arises. Then we give a strategy for the game that yields a deterministic algorithm for computing the maximum flow in a directed graph with n nodes and m edges that runs in time O(mn(log_{m/n log n}n)). Our algorithm gives an O(mn) deterministic algorithm for all m/n = Ω(n^ε) for any positive constant ε, and is currently the fastest deterministic algorithm for computing maximum flow as long as m/n = ω(log n).     

How to Build Robust Shared Control Systems

Previous researchers have designed shared control schemes with a view to minimising the likelihood that participants will conspire to perform an unauthorised act. But, human nature being what it is, systems inevitably fail; so shared control schemes should also be designed so that the police can identify conspirators after the fact. This requirement leads us to search for schemes with sparse access structures. We show how this can be done using ideas from coding theory. In particular, secret sharing schemes based on geometric codes whose dual [n,k,d] codes have d and n as their only nonzero weights are suitable. We determine their access structures and analyse their properties. We have found almost all of them, and established some relations among codes, designs and secret-sharing schemes.     

Supersymmetry,vacuum statistics,and the fundamental theorem of algebra

I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degreen need not haven real zeroes, while a complex polynomial of degreen must haven complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.     

Connections Between Pedagogical and Epistemological Constructivism: Questions for Teaching and Research in Chemistry

The rich and ongoing debate about constructivism in chemistry education includes questions about the relationship, for better or worse, between applications of the theory in pedagogy and in epistemology. This paper presents an examination of the potential to use connections of epistemological and pedagogical constructivism to one another. It examines connections linked to the content, processes, and premises of science with a goal of prompting further research in these areas.