An Integrated Design and Simulation Environment for Rapid Prototyping of Laminate Robotic Mechanisms

Laminate mechanisms are a reliable concept in producing lowcost robots for educational and commercial purposes. These mechanisms are produced using low-cost manufacturing techniques which have improved significantly during recent years and are more accessible to novices and hobbyists. However, iterating through the design space to come up with the best design for a robot is still a time consuming and rather expensive task and therefore, there is still a need for model-based analysis before manufacturing. Until now, there has been no integrated design and analysis software for laminate robots. This paper addresses some of the issues surrounding laminate analysis by introducing a companion to an existing laminate design tool that automates the generation of dynamic equations and produces simulation results via rendered plots and videos. We have validated the accuracy of the software by comparing the position, velocity and acceleration of the simulated mechanisms with the measurements taken from physical laminate prototypes using a motion capture system

Leavitt path algebras: Graded direct-finiteness and graded Σ\Sigma-injective simple modules

In this paper, we give a complete characterization of Leavitt path algebras which are graded $\Sigma$-$V$ rings, that is, rings over which a direct sum of arbitrary copies of any graded simple module is graded injective. Specifically, we show that a Leavitt path algebra $L$ over an arbitrary graph $E$ is a graded $\Sigma$-$V$ ring if and only if it is a subdirect product of matrix rings of arbitrary size but with finitely many non-zero entries over $K$ or $K[x,x^{-1}]$ with appropriate matrix gradings. We also obtain a graphical characterization of such a graded $\Sigma$-$V$ ring $L$% . When the graph $E$ is finite, we show that $L$ is a graded $\Sigma$-$V$ ring $\Longleftrightarrow L$ is graded directly-finite $\Longleftrightarrow L$ has bounded index of nilpotence $\Longleftrightarrow$ $L$ is graded semi-simple. Examples show that the equivalence of these properties in the preceding statement no longer holds when the graph $E$ is infinite. Following this, we also characterize Leavitt path algebras $L$ which are non-graded $\Sigma$-$V$ rings. Graded rings which are graded directly-finite are explored and it is shown that if a Leavitt path algebra $L$ is a graded $\Sigma$-$V$ ring, then $L$ is always graded directly-finite. Examples show the subtle differences between graded and non-graded directly-finite rings. Leavitt path algebras which are graded directly-finite are shown to be directed unions of graded semisimple rings. Using this, we give an alternative proof of a theorem of Va\v{s} \cite{V} on directly-finite Leavitt path algebras.Comment: 21 page

EXPERIMENTAL MEASUREMENTS OF FLAME TRANSFER FUNCTION

poster abstractIn order to conform to pollutant-related legislations and minimize NOx emissions, modern household boilers and central heating systems are mov-ing towards premixed combustors. These combustors have been very suc-cessful with regards to emissions along with thermal efficiency. However, there implementation has been associated with acoustical instability prob-lems that are best solved through precise design optimization rather than trial and error experimentation. This poster introduces an experimental setup which is designed to inves-tigate and study, acoustic instability at the flame level. The methodology is an experimental determination of the Flame Transfer Function and compari-son of the experimental data with a theoretical model of the flame-burner. A procedure is designed to diagnose the origins of the combustion instabilities by measurement of the Flame Transfer Function experimentally. The exper-imental setup provides an improved assessment of the acoustic instability problem for industrial applications

Ridge regression and its applications in genetic studies

With the advancement of technology, analysis of large-scale data of gene expression is feasible and has become very popular in the era of machine learning. This paper develops an improved ridge approach for the genome regression modeling. When multicollinearity exists in the data set with outliers, we consider a robust ridge estimator, namely the rank ridge regression estimator, for parameter estimation and prediction. On the other hand, the efficiency of the rank ridge regression estimator is highly dependent on the ridge parameter. In general, it is difficult to provide a satisfactory answer about the selection for the ridge parameter. Because of the good properties of generalized cross validation (GCV) and its simplicity, we use it to choose the optimum value of the ridge parameter. The GCV function creates a balance between the precision of the estimators and the bias caused by the ridge estimation. It behaves like an improved estimator of risk and can be used when the number of explanatory variables is larger than the sample size in high-dimensional problems. Finally, some numerical illustrations are given to support our findings