Job assignment in large-scale service systems with affinity relations

We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be assigned to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job–server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that assign jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.

     

Lines,Trees, and Branch Spaces

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.     

Mathematics Assessment: Practices and Reporting Methods

The curriculum, teaching, and assessment Standards of the National Council of Teachers of Mathematics advocate the use of various assessment techniques in mathematics, K-12. Practitioners from 35 school districts in two regions of a midwestern state completed a questionnaire and reported information about their assessment practices, reporting methods, and other issues that affect change in mathematics. The results of the survey suggest that current reporting practices are limiting the use of alternative classroom assessment practices. Delays in the use of alternative mathematics assessment practice can probably be expected until the reporting systems used in school districts become consistent with the assessment systems and teachers participate in ongoing professional development programs to learn more about alternative assessment practices.     

Circumventing air bubbles in microfluidic systems and quantitative continuous-flow PCR applications

Polymerase chain reaction (PCR) is an essential part of research based on genomics or cell analysis. The development of a microfluidic device that would be suitable for high-temperature-based reactions therefore becomes an important contribution towards the integration of micro-total analysis systems (μTAS). However, problems associated with the generation of air bubbles in the microchannels before the introduction of the assay liquid, which we call the “initial start-up” in this study, made the flow irregular and unstable. In this report, we have tried to address these problems by adapting a novel liquid-flow method for high-temperature-based reactions. A PDMS-based microfluidic device was fabricated by soft-lithography techniques and placed on a cartridge heater. The generation of the air bubbles was prevented by introducing the fluorinated oil, an inert and highly viscous liquid, as the cap just before the introduction of the sample solutions into the microchannels. The technique was applied for continuous-flow PCR, which could perform PCR on-chip in a microfluidic system. For the evaluation of practical accuracy, plasmid DNA that serves as a reference molecule for the quantification of genetically modified (GM) maize was used as the template DNA for continuous-flow PCR. After PCR, the products were collected in a vial and analyzed by gel electrophoresis to confirm the accuracy of the results. Additionally, quantitative continuous-flow PCR was performed using TaqMan technology on our PCR device. A laser detection system was also used for the quantitative PCR method. We observed a linear relationship between the threshold cycle (Ct) and the initial DNA concentration. These results showed that it would be possible to quantify the initial copies of the template DNA on our microfluidic device. Accurate quantitative DNA analysis in microfluidic systems is required for the integration of PCR with μTAS, thus we anticipate that our device would have promising potential for applications in a wide range of research.