Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.Comment: 24 pages, 5 figure

Silicon Membrane Thickness Monitoring System based on Optical Sensing system

Silicon wafer etching is frequently used in micromachining and microelectronic fabrication processes. How to precisely control the thickness of etched silicon membrane is very challenging. Controlling the etching depth by controlling the etching time can result in large errors due to fluctuation of etching rate. A more accurate in-situ silicon membrane thickness monitoring system during silicon wafer etching is very necessary. In this poster, we proposed a silicon membrane thickness in-situ monitoring system based on optical sensing. A halogen lamp generates light to be passed through the silicon membrane. The light is partially absorbed while transmitting the silicon wafer depending on the thickness of the membrane. Two photodiodes are used to detect the lights passing through the silicon membrane at different wavelengths. The difference of the readings is used to cancel out the common errors, hence leading to improved accuracy. The system is designed and simulated to verify its optical responses. The experimental setup of the system is implemented and the results are analyzed. The proposed Silicon membrane thickness monitoring system can be used to monitor and control the etching depth to achieve precise silicon membrane thickness as needed

Central Dogma at the Single-Molecule Level in Living Cells

Gene expression originates from individual DNA molecules within living cells. Like many single-molecule processes, gene expression and regulation are stochastic, that is, sporadic in time. This leads to heterogeneity in the messenger RNA and protein copy numbers in a population of cells with identical genomes. With advanced single-cell fluorescence microscopy, it is now possible to quantify transcriptomes and proteomes with single-molecule sensitivity. Dynamic processes such as transcription factor binding, transcription and translation can be monitored in real time, providing quantitative descriptions of gene expression and regulation, and the demonstration that a single-molecule event can determine the phenotype of a cell.Chemistry and Chemical Biolog