Microchips and their significance in isolation of circulating tumor cells and monitoring of cancers

In micro-fluid systems, fluids are injected into extremely narrow polymer channels in small amounts such as micro-, nano-, or pico-liter scales. These channels themselves are embedded on tiny chips. Various specialized structures in the chips including pumps, valves, and channels allow the chips to accept different types of fluids to be entered the channel and along with flowing through the channels, exert their effects in the framework of different reactions. The chips are generally crystal, silicon, or elastomer in texture. These highly organized structures are equipped with discharging channels through which products as well as wastes of the reactions are secreted out. A particular advantage regarding the use of fluids in micro-scales over macro-scales lies in the fact that these fluids are much better processed in the chips when they applied as micro-scales. When the laboratory is miniaturized as a microchip and solutions are injected on a micro-scale, this combination makes a specialized construction referred to as "lab-on-chip". Taken together, micro-fluids are among the novel technologies which further than declining the costs; enhancing the test repeatability, sensitivity, accuracy, and speed; are emerged as widespread technology in laboratory diagnosis. They can be utilized for monitoring a wide spectrum of biological disorders including different types of cancers. When these microchips are used for cancer monitoring, circulatory tumor cells play a fundamental role

Bandwidth Borrowing Schemes for Instantaneous Video-on-Demand Systems

A controlled multicast scheme provides instantaneous service, but limited server bandwidth causes some user requests to be either delayed or rejected when insufficient free bandwidth is available. Two borrowing schemes are proposed for instantaneous video-on-demand (VOD) that reduce the user request blocking rate by borrowing bandwidth from ongoing video streams when there is insufficient free bandwidth for the server to deliver a new video stream. Both these new schemes have proved to be successful in reducing blocking rate and increasing bandwidth utilization at the expense of temporarily degrading the video quality

Analytical performance modelling of adaptive wormhole routing in the star interconnection network

The star graph was introduced as an attractive alternative to the well-known hypercube and its properties have been well studied in the past. Most of these studies have focused on topological properties and algorithmic aspects of this network. Although several analytical models have been proposed in the literature for different interconnection networks, none of them have dealt with star graphs. This paper proposes the first analytical model to predict message latency in wormhole-switched star interconnection networks with fully adaptive routing. The analysis focuses on a fully adaptive routing algorithm which has shown to be the most effective for star graphs. The results obtained from simulation experiments confirm that the proposed model exhibits a good accuracy under different operating conditions

On computing joint invariants of vector fields

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}

A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms

We provide an algorithmic approach to the construction of point transformations for scalar ordinary differential equations that admit three-dimensional symmetry algebras which lead to their respective canonical forms