A Deployable In Vivo EPR Tooth Dosimeter for Triage After a Radiation Event Involving Large Populations

In order to meet the potential need for emergency large-scale retrospective radiation biodosimetry following an accident or attack, we have developed instrumentation and methodology for in vivo electron paramagnetic resonance spectroscopy to quantify concentrations of radiation-induced radicals within intact teeth. This technique has several very desirable characteristics for triage, including independence from confounding biologic factors, a non-invasive measurement procedure, the capability to make measurements at any time after the event, suitability for use by non-expert operators at the site of an event, and the ability to provide immediate estimates of individual doses. Throughout development there has been a particular focus on the need for a deployable system, including instrumental requirements for transport and field use, the need for high throughput, and use by minimally trained operators.Numerous measurements have been performed using this system in clinical and other non-laboratory settings, including in vivo measurements with unexposed populations as well as patients undergoing radiation therapies. The collection and analyses of sets of three serially-acquired spectra with independent placements of the resonator, in a data collection process lasting approximately five minutes, provides dose estimates with standard errors of prediction of approximately 1 Gy. As an example, measurements were performed on incisor teeth of subjects who had either received no irradiation or 2 Gy total body irradiation for prior bone marrow transplantation; this exercise provided a direct and challenging test of our capability to identify subjects who would be in need of acute medical care.     

A hybrid evolutionary algorithm for the two-dimensional packing problem

This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.     

Algorithm for quadratic semi-assignment problem with partition size coefficients

This paper discusses the problem of assigning $N$ streams of requests (clients) to $M$ related server machines with the objective to minimize the sum of worst-case processing times. The completion time of a batch of requests is measured as a sum of weights of the subset of clients which share a single machine. Such problem can be seen as minimizing the sum of total weights of blocks of $M$ -partition, each multiplied by the cardinality of a block. We prove that this problem can be solved in polynomial time for any fixed $M$ and present an efficient backward induction algorithm.     

Generalized Stäckel systems

We consider the generalized Stäckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Stäckel transforms.     

A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields

We present a novel NMR approach to the determination of crosslink densities in rubber materials. The method is based on the dipolar correlation effect (DCE) on the stimulated echo examined in a series of rubber samples and linear polyisoprene. The parameter evaluated from the echo attenuation curves is the mean‐squared dipolar fluctuation associated with anisotropic reorientations of macromolecular backbones. The contributions to the DCE of the constraints due to excluded volume effects and chemical crosslinks are estimated. A strong dependence of the mean‐squared dipolar fluctuation on the crosslink density of rubber combined with the simplicity of performing the measurements with inexpensive low‐field instruments suggests that the DCE is a useful tool for routine applications. The potential and problems of performing DCE measurements in low‐magnetic‐field conditions are discussed in detail. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2207–2216, 2001     

Stereocontrolled synthesis of enantiopure anticancer cyclopentenone prostaglandin analogues: (−)- and (+)-TEI-9826

The synthesis of both enantiomers of TEI-9826 has been accomplished in seven steps with an overall yield of 44% starting from diastereomeric camphor protected 3-[(dimethoxyphosphoryl)methyl]-4,5-dihydroxycyclopent-2-enones. The key steps include a fully diastereoselective hydrogenation of the endocyclic carbon–carbon double bond in the cyclopentenone ring controlled with a chiral diol moiety and the conversion of the latter into a new transposed olefinic bond.     

Integers without divisors in a given progression

An asymptotic formula is given for the number of integers n ≤ x which do not have divisors in a fixed arithmetical progression. This extends a previous result of Banks et al. (Forum Math 20:1005–1037, 2008) who considered the case of progressions with prime difference.