Personalized drug design requires the classification of cancer patients as accurate as possible. With advances in genome sequencing and microarray technology, a large amount of gene expression data has been and will continuously be produced from various cancerous patients. Such cancer-alerted gene expression data allows us to classify tumors at the genomewide level. However, cancer-alerted gene expression datasets typically have much more number of genes (features) than that of samples (patients), which imposes a challenge for classification of tumors. In this paper, a new method is proposed for cancer diagnosis using gene expression data by casting the classification problem as finding sparse representations of test samples with respect to training samples. The sparse representation is computed by the l 1 -regularized least square method. To investigate its performance, the proposed method is applied to six tumor gene expression datasets and compared with various support vector machine (SVM) methods. The experimental results have shown that the performance of the proposed method is comparable with or better than those of SVMs. In addition, the proposed method is more efficient than SVMs as it has no need of model selection.

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Real-time, 30 color Doppler echocardiography (RT3D) i s capable of quantibing flow at the LV outjlow tract (LVOT). However, previous works have found significant underestimation for flow rate estimation due to jinite scanning time (ST) of the color Doppler. We have, therefore, developed a mathematical model to correct the impact of ST on flow quantification and validated it by an animal study.Scanning time to cover the entire cross-sectional image of the LVOT was calculated as 60 ms, and the underestimation due to temporal averaging effect was predicted as 1827%. In the animal experiment, peak flow rates were obtained by spatially integrating the velocity data f o m he cross-sectional color images of the LVOT. By applying a correction factor, there was an excellent agreement between reference flow rate by an electromagnetic flow meter and RT3D (A = -5.6 ml/s, r=0.93, which was signifiantly better than without correction (p< 0.001).Real-time, color 30 echocardiography was capable of quantifiing flow accurately by applying the mathematical correction. IntroductionReal-time, three -dimensional (RT3D) color Doppler echocardiography is capable of quantifying flow velocities in cross-sectional (c-plane) images of the flow tract I. The RT3D system, originally developed in the Duke University Center for Emerging Cardiovascular Technology, utilizes a two-dimensional matrix array probe that electronically scans the ultrasound beam to detect the echo signals from 3D volumetric space in real-time '. The volumetric frame rate of the system is around 25 Hz for B-mode, and 10 Hz for color Doppler imaging, depending on scanning conditions. By using the cross-sectional color Doppler images, calculation of flow rate is possible without any geometric assumptions about flow velocity distributions4.However, previous works have assumed an infinitesimal scanning time to obtain the cross-sectional color Doppler images, and have found significant underestimation for peak flow rate estimation. The aim of the present study was, therefore, to develop a mathematical model to correct the impact of the scanning time or temporal resolution on flow quantification by R n D color Doppler. Methods Numerical modelingFor the numerical modeling, ultrasonic scanning time (ST) to cover the entire cross-sectional area of the flow tract using RT3D was first calculated from the following parameters: pulse repetition frequency (PRF; kHz), packet size of the color Doppler (number of the ultrasound interrogations per scanning line) (PS), and the parallel processing number (PP). E E 0 TP ET' Time Figure 1. Schematic diagram of the temporal flow profile and its relation to the scanning time (ST). Qp: peak flow rate; Tp (Time to peak); ET (ejection time).

The performance of most methods for cancer diagnosis using gene expression data greatly depends on careful model selection. Least square for classification has no need of model selection. However, a major drawback prevents it from successful application in microarray data classification: lack of robustness to outliers. In this paper we cast linear regression as a constrained l 1 -norm minimization problem to greatly alleviate its sensitivity to outliers, and hence the name l 1 least square. The numerical experiment shows that l 1 least square can match the best performance achieved by support vector machines (SVMs) with careful model selection.