Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs

In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth

Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.Comment: v2: 4 pages, 1 figure. Published versio

Automation of a Positron-emission Tomography (PET) Radiotracer Synthesis Protocol for Clinical Production.

The development of new positron-emission tomography (PET) tracers is enabling researchers and clinicians to image an increasingly wide array of biological targets and processes. However, the increasing number of different tracers creates challenges for their production at radiopharmacies. While historically it has been practical to dedicate a custom-configured radiosynthesizer and hot cell for the repeated production of each individual tracer, it is becoming necessary to change this workflow. Recent commercial radiosynthesizers based on disposable cassettes/kits for each tracer simplify the production of multiple tracers with one set of equipment by eliminating the need for custom tracer-specific modifications. Furthermore, some of these radiosynthesizers enable the operator to develop and optimize their own synthesis protocols in addition to purchasing commercially-available kits. In this protocol, we describe the general procedure for how the manual synthesis of a new PET tracer can be automated on one of these radiosynthesizers and validated for the production of clinical-grade tracers. As an example, we use the ELIXYS radiosynthesizer, a flexible cassette-based radiochemistry tool that can support both PET tracer development efforts, as well as routine clinical probe manufacturing on the same system, to produce [18F]Clofarabine ([18F]CFA), a PET tracer to measure in vivo deoxycytidine kinase (dCK) enzyme activity. Translating a manual synthesis involves breaking down the synthetic protocol into basic radiochemistry processes that are then translated into intuitive chemistry "unit operations" supported by the synthesizer software. These operations can then rapidly be converted into an automated synthesis program by assembling them using the drag-and-drop interface. After basic testing, the synthesis and purification procedure may require optimization to achieve the desired yield and purity. Once the desired performance is achieved, a validation of the synthesis is carried out to determine its suitability for the production of the radiotracer for clinical use

Mg-Ni-H films as selective coatings: tunable reflectance by layered hydrogenation

Unlike other switchable mirrors, Mg2NiHx films show large changes in reflection that yield very low reflectance (high absorptance) at different hydrogen contents, far before reaching the semiconducting state. The resulting reflectance patterns are of interference origin, due to a self-organized layered hydrogenation mechanism that starts at the substrate interface, and can therefore be tuned by varying the film thickness. This tunability, together with the high absorptance contrast observed between the solar and the thermal energies, strongly suggests the use of these films in smart coatings for solar applications.Comment: Three two-column pages with 3 figures embedded; RevTE

Scaling of running time of quantum adiabatic algorithm for propositional satisfiability

We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially with their size. Worst case complexity of quantum adiabatic algorithm therefore seems to be exponential.Comment: 7 page

Rapid, efficient, and economical synthesis of PET tracers in a droplet microreactor: application to O-(2-[18F]fluoroethyl)-L-tyrosine ([18F]FET).

BackgroundConventional scale production of small batches of PET tracers (e.g. for preclinical imaging) is an inefficient use of resources. Using O-(2-[18F]fluoroethyl)-L-tyrosine ([18F]FET), we demonstrate that simple microvolume radiosynthesis techniques can improve the efficiency of production by consuming tiny amounts of precursor, and maintaining high molar activity of the tracers even with low starting activity.ProceduresThe synthesis was carried out in microvolume droplets manipulated on a disposable patterned silicon "chip" affixed to a heater. A droplet of [18F]fluoride containing TBAHCO3 was first deposited onto a chip and dried at 100 °C. Subsequently, a droplet containing 60 nmol of precursor was added to the chip and the fluorination reaction was performed at 90 °C for 5 min. Removal of protecting groups was accomplished with a droplet of HCl heated at 90 °C for 3 min. Finally, the crude product was collected in a methanol-water mixture, purified via analytical-scale radio-HPLC and formulated in saline. As a demonstration, using [18F]FET produced on the chip, we prepared aliquots with different molar activities to explore the impact on preclinical PET imaging of tumor-bearing mice.ResultsThe microdroplet synthesis exhibited an overall decay-corrected radiochemical yield of 55 ± 7% (n = 4) after purification and formulation. When automated, the synthesis could be completed in 35 min. Starting with < 370 MBq of activity, ~ 150 MBq of [18F]FET could be produced, sufficient for multiple in vivo experiments, with high molar activities (48-119 GBq/μmol). The demonstration imaging study revealed the uptake of [18F]FET in subcutaneous tumors, but no significant differences in tumor uptake as a result of molar activity differences (ranging 0.37-48 GBq/μmol) were observed.ConclusionsA microdroplet synthesis of [18F]FET was developed demonstrating low reagent consumption, high yield, and high molar activity. The approach can be expanded to tracers other than [18F]FET, and adapted to produce higher quantities of the tracer sufficient for clinical PET imaging

Trees with a large Laplacian eigenvalue multiplicity

In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order $n$ that have a multiplicity that is close to the upper bound $\frac{n-3}{2}$, and emphasize the particular role of the algebraic connectivity.Comment: 11 pages, 5 figure

Flow optimization study of a batch microfluidics PET tracer synthesizing device.

We present numerical modeling and experimental studies of flow optimization inside a batch microfluidic micro-reactor used for synthesis of human-scale doses of Positron Emission Tomography (PET) tracers. Novel techniques are used for mixing within, and eluting liquid out of, the coin-shaped reaction chamber. Numerical solutions of the general incompressible Navier Stokes equations along with time-dependent elution scalar field equation for the three dimensional coin-shaped geometry were obtained and validated using fluorescence imaging analysis techniques. Utilizing the approach presented in this work, we were able to identify optimized geometrical and operational conditions for the micro-reactor in the absence of radioactive material commonly used in PET related tracer production platforms as well as evaluate the designed and fabricated micro-reactor using numerical and experimental validations

Generating sequential space-filling designs using genetic algorithms and Monte Carlo methods

In this paper, the authors compare a Monte Carlo method and an optimization-based approach using genetic algorithms for sequentially generating space-filling experimental designs. It is shown that Monte Carlo methods perform better than genetic algorithms for this specific problem