Retrospective correction for T1-weighting bias in T2 values obtained with various spectroscopic spin-echo acquisition schemes

Localized tissue transverse relaxation time (T₂) is obtained by fitting a decaying exponential to the signals from several spin-echo experiments at different echo times (TE). Unfortunately, time constraints in magnetic resonance spectroscopy (MRS) often mandate in vivo acquisition schemes at short repetition times (TR), that is, comparable with the longitudinal relaxation constant (T₁). This leads to different T₁-weighting of the signals at each TE. Unaccounted for, this varying weighting causes systematic underestimation of the T₂'s, sometimes by as mush as 30%. In this article, we (i) analyze the phenomenon for common MRS spin-echo T₂ acquisition schemes; (ii) propose a general post hoc T₁-bias correction for any (TR, TE) combination; (iii) show that approximate knowledge of T₁ is sufficient, since a 20% uncertainty in T₁ leads to under 3% bias in T₂; and consequently, (iv) efficient, precision-optimized short TR spin-echo T₂ measurement protocols can be designed and used without risk of accuracy loss. Tables of correction for single-refocusing (conventional) spin-echo and double refocusing, such as, PRESS acquisitions, are provided.     

Luminescence studies of Nd- and Yb-doped α-Y(IO3)3 and β-Y(IO3)3, transparent host matrix in the mid- and beginning of the far-infrared

α-Y(IO₃)₃ and β-Y(IO₃)₃ are transparent until 12.8 and 13.4 μm, respectively; thus they are interesting as a potential laser matrix in the mid- and beginning of the far-infrared. So, in order to investigate the properties of lanthanides- doped anhydrous yttrium iodate, polycrystalline samples of α-Y_1−xNd_x(IO₃)₃ (0.01?x?0.05), β-Y_1−xNd_x(IO₃)₃ (0.001?x?0.1), α-Y_1−xYb_x(IO₃)₃ (0.01?x?0.33) and β-Y_1−xYb_x(IO₃)₃ (0.01?x?0.25) were synthesized. For Nd³⁺ ions, fluorescent emissions from the ⁴F_3/2 multiplet were observed at 300 K under pulsed laser excitations at 750 nm and for Yb³⁺, fluorescent emissions from the ²F_5/2 multiplet were observed at 300 K under pulsed laser excitations at 980 nm. The decays of all these emissions were measured. They are exponential and the fluorescence lifetimes are in the range 0.093-0.193 ms for Nd³⁺ and 0.370-0.541 ms for Yb³⁺, depending on the nature of the host and the concentration of doping.     

Enhanced resolution comprehensive two-dimensional gas chromatography applied to the analysis of roasted coffee volatiles

The present research is based on the full exploitation of the separation power of a 0.05 mm internal diameter (ID) capillary, as a comprehensive two-dimensional (2D) GC (GC × GC) secondary column, with the objective of attaining very high-resolution second dimension separations. The aim was achieved by using a split-flow system developed in previous research [P.Q. Tranchida, A. Casilli, P. Dugo, G. Dugo, L. Mondello, Anal. Chem. 79 (2007) 2266], and a dual-oven GC × GC instrument. The column combination employed consisted of a polar 30 m × 0.25 mm ID column connected, by means of a T union, to a detector-linked high-resolution 1.1 m × 0.05 mm ID apolar analytical column and to a 0.33 m × 0.05 mm ID retention gap; the latter was connected to a manually operated split valve. As previously demonstrated, the use of a split valve enables the regulation of gas flows through both analytical columns, generating the most appropriate gas linear velocities. Comprehensive 2D GC experiments were carried out on Arabica roasted coffee volatiles (previously extracted by means of solid-phase microextraction) with the split-valve closed (equal to what can be defined as conventional GC × GC) and with the split-valve opened at various degrees. The reasons why it is absolutely not effective to use a 0.05 mm ID column as second dimension in a conventional GC × GC instrument will be discussed and demonstrated. On the contrary, the use of a 0.05 mm ID column as second dimension, under ideal conditions in a split-flow, twin-oven system, will also be illustrated and discussed.     

Separation of diisopropylnaphthalene isomers

The separation of diisopropylnaphthalenes was reinvestigated. The application of GC × GC appears to be a clear and necessary improvement over the use of single column techniques, with a polar (CP-Wax-52) column as reference technique, and a non-polar (CP-Sil-8) column as an alternative. Both qualitative and quantitative separations of DIPN isomers showed to be superior on GC × GC. The composition of both a DIPN mixture resulting from a typical experiment with a zeolite catalyst and a commercial one could be quantitatively determined in this way.     

A bicriteria parallel machine scheduling with a learning effect of setup and removal times

In studies on scheduling problems, generally setup times and removal times of jobs have been neglected or by including those into processing times. However, in some production systems, setup times and removal times are very important such that they should be considered independent from processing times. Since, in general jobs are done according to automatic machine processes in production systems processing times do not differ according to process sequence. But, since human factor becomes influential when setup times and removal times are taken into consideration, setup times will be decreasing by repeating setup processes frequently. This fact is defined with learning effect in scheduling literature. In this study, a bicriteria m-identical parallel machines scheduling problem with a learning effect of setup times and removal times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and total tardiness. A mathematical programming model is developed for the problem which belongs to NP-hard class. Results of computational tests show that the proposed model is effective in solving problems with up to 15 jobs and five machines. We also proposed three heuristic approaches for solving large jobs problems. According to the best of our knowledge, no work exists on the minimization of the weighted sum of total completion time and total tardiness with a learning effect of setup times and removal times.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains

An (upward) skip-free Markov chain with the set of nonnegative integers as state space is a chain for which upward jumps may be only of unit size; there is no restriction on downward jumps. In a 1987 paper, Brown and Shao determined, for an irreducible continuous-time skip-free chain and any d, the passage time distribution from state 0 to state d. When the nonzero eigenvalues ν _j of the generator on {0,…,d}, with d made absorbing, are all real, their result states that the passage time is distributed as the sum of d independent exponential random variables with rates ν _j . We give another proof of their theorem. In the case of birth-and-death chains, our proof leads to an explicit representation of the passage time as a sum of independent exponential random variables. Diaconis and Miclo recently obtained the first such representation, but our construction is much simpler. We obtain similar (and new) results for a fastest strong stationary time T of an ergodic continuous-time skip-free chain with stochastically monotone time-reversal started in state 0, and we also obtain discrete-time analogs of all our results. In the paper’s final section we present extensions of our results to more general chains. Research supported by NSF grant DMS–0406104, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement of Research in Statistics.     

带特殊重试时间的M／M／1重试排队模型的另一个特征值

研究对应于带特殊重试时间的M／M／1重试排队模型主算子在左半复平面的谱,证明-（2λ＋α＋β＋√（α＋β）^2＋4λβ/4是该主算子的几何重数为1的特征值．     

GCxGC/TOF MS technique-A new tool in identification of insect pheromones: Analysis of the persimmon bark borer sex pheromone gland

Conventional gas chromatography with electroantennographic detection (GC-EAD) and two-dimensional (GC × GC) gas chromatography using a time-of-flight mass spectrometric detector (TOFMS), were combined to analyse the female sex pheromone gland extract of the persimmon bark borer, Euzophera batangensis. GC-EAD analysis produced two EAD responses in GC areas where no compounds were detected by FID detection. GC × GC/TOFMS analysis of this area indicated the presence of several chemicals, including (Z9,E12)-tetradeca-9,12-dien-1-ol and (Z9)-tetradec-9-en-1-ol, pheromone components of closely related Euzophera species. Spectral characteristics, retention behaviour and the ability to elicit GC-EAD responses imply that both identified unsaturated alcohols are candidates for E. batangensis sex pheromone components. GC × GC/TOFMS facilitated the analysis of complex matrices on a subnanogram level and was shown to have great potential as a powerful tool in the analysis of insect pheromones.