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.     

Acid/Base‐Triggered Switching of Circularly Polarized Luminescence and Electronic Circular Dichroism in Organic and Organometallic Helicenes

Electronic circular dichroism and circularly polarized luminescence acid/base switching activity has been demonstrated in helicene‐bipyridine proligand 1 a and in its “rollover” cycloplatinated derivative 2 a . Whereas proligand 1 a displays a strong bathochromic shift (>160 nm) of the nonpolarized and circularly polarized luminescence upon protonation, complex 2 a displays slightly stronger emission. This strikingly different behavior between singlet emission in the organic helicene and triplet emission in the organometallic derivative has been rationalized by using quantum‐chemical calculations. The very large bathochromic shift of the emission observed upon protonation of azahelicene‐bipyridine 1 a has been attributed to the decrease in aromaticity (promoting a charge‐transfer‐type transition rather than a π–π* transition) as well as an increase in the HOMO–LUMO character of the transition and stabilization of the LUMO level upon protonation.     

An upper bound on the Chebotarev invariant of a finite group

A subset {g ₁,..., g _d } of a finite group G invariably generates \(\left\{ {g_1^{{x_1}}, \ldots ,g_d^{{x_d}}} \right\}\) generates G for every choice of x _i ∈ G. The Chebotarev invariant C(G) of G is the expected value of the random variable n that is minimal subject to the requirement that n randomly chosen elements of G invariably generate G. The first author recently showed that \(C\left( G \right) \leqslant \beta \sqrt {\left| G \right|} \) for some absolute constant β. In this paper we show that, when G is soluble, then β is at most 5/3. We also show that this is best possible. Furthermore, we show that, in general, for each ε > 0 there exists a constant c _ε such that \(C\left( G \right) \leqslant \left( {1 + \in } \right)\sqrt {\left| G \right|} + {c_ \in }\).     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

Ultraviolet Absorption Induces Hydrogen‐Atom Transfer in G⋅C Watson–Crick DNA Base Pairs in Solution

Ultrafast deactivation pathways bestow photostability on nucleobases and hence preserve the structural integrity of DNA following absorption of ultraviolet (UV) radiation. One controversial recovery mechanism proposed to account for this photostability involves electron‐driven proton transfer (EDPT) in Watson–Crick base pairs. The first direct observation is reported of the EDPT process after UV excitation of individual guanine–cytosine (G?C) Watson–Crick base pairs by ultrafast time‐resolved UV/visible and mid‐infrared spectroscopy. The formation of an intermediate biradical species (G[?H]?C[+H]) with a lifetime of 2.9 ps was tracked. The majority of these biradicals return to the original G?C Watson–Crick pairs, but up to 10 % of the initially excited molecules instead form a stable photoproduct G*?C* that has undergone double hydrogen‐atom transfer. The observation of these sequential EDPT mechanisms across intermolecular hydrogen bonds confirms an important and long debated pathway for the deactivation of photoexcited base pairs, with possible implications for the UV photochemistry of DNA.     

The Structure of Uniform Discrete Defective Crystals

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are satisfied, there is a minimum (non-zero) separation of points in this set, so the set is discrete. We describe the structure of such sets explicitly, and show in particular that any such set is either a simple lattice or a 4-lattice.Paolo Cermelli was partially supported by the Italian MIUR grant ‘Modelli Matematici per la Scienza dei Materiali’.