Matriks Jordan Dan Aplikasinya Pada Sistem Linier Waktu Diskrit

Matrix is diagonalizable (similar with matrix diagonal) if and only if the sum of geometric multiplicities of its eigenvalues is n.If we search for an upper triangular form that is nearly diagonal as possible but is still attainable by similarity for every matrix, especially the sum of geometric multiplicities of its eigenvalues is less than n, the result is the Jordan canonical form, which is denoted by , and . In this paper, will be described how to get matrix S(in order to get matrix ) by using generalized eigenvector. In addition, it will also describe the Jordan canonical form and its properties, and some observation and application on discrete time linear system

A Highly Efficient Gene Expression Programming (GEP) Model for Auxiliary Diagnosis of Small Cell Lung Cancer

<div><p>Background</p><p>Lung cancer is an important and common cancer that constitutes a major public health problem, but early detection of small cell lung cancer can significantly improve the survival rate of cancer patients. A number of serum biomarkers have been used in the diagnosis of lung cancers; however, they exhibit low sensitivity and specificity.</p><p>Methods</p><p>We used biochemical methods to measure blood levels of lactate dehydrogenase (LDH), C-reactive protein (CRP), Na⁺, Cl^-, carcino-embryonic antigen (CEA), and neuron specific enolase (NSE) in 145 small cell lung cancer (SCLC) patients and 155 non-small cell lung cancer and 155 normal controls. A gene expression programming (GEP) model and Receiver Operating Characteristic (ROC) curves incorporating these biomarkers was developed for the auxiliary diagnosis of SCLC.</p><p>Results</p><p>After appropriate modification of the parameters, the GEP model was initially set up based on a training set of 115 SCLC patients and 125 normal controls for GEP model generation. Then the GEP was applied to the remaining 60 subjects (the test set) for model validation. GEP successfully discriminated 281 out of 300 cases, showing a correct classification rate for lung cancer patients of 93.75% (225/240) and 93.33% (56/60) for the training and test sets, respectively. Another GEP model incorporating four biomarkers, including CEA, NSE, LDH, and CRP, exhibited slightly lower detection sensitivity than the GEP model, including six biomarkers. We repeat the models on artificial neural network (ANN), and our results showed that the accuracy of GEP models were higher than that in ANN. GEP model incorporating six serum biomarkers performed by NSCLC patients and normal controls showed low accuracy than SCLC patients and was enough to prove that the GEP model is suitable for the SCLC patients.</p><p>Conclusion</p><p>We have developed a GEP model with high sensitivity and specificity for the auxiliary diagnosis of SCLC. This GEP model has the potential for the wide use for detection of SCLC in less developed regions.</p></div

Serum levels of six biomarkers in SCLC patients and NSCLC patients.

<p>* Statistics were conducted using the non-parametric Wilcoxon test (Mann–Whitney U test).</p><p>Serum levels of six biomarkers in SCLC patients and NSCLC patients.</p

Histopathologic test of SCLC patients.

<p>A. hematoxylin-eosin staining of biopsy specimen slice. B. CD56(+) findings in immunohistochemical method. C. Syn (+) findings in immunohistochemical method. D.TTF-1(+) findings in immunohistochemical method</p

Parameter settings for the GEP algorithm.

<p>Parameter settings for the GEP algorithm.</p

The detection capability of GEP model 1 with six biomarkers in SCLC and NSCLC patients.

<p>The detection capability of GEP model 1 with six biomarkers in SCLC and NSCLC patients.</p

SCLC detection rate of GEP model 1 and model 2.

<p>CC = Correlation Coefficient; MSE = Mean Squared Error; RAE = Root Mean Squared Error; MAE = Mean Absolute Error; RSE = Relative Squared Error.</p><p>SCLC detection rate of GEP model 1 and model 2.</p

The flowchart of the GEP modeling in this study.

<p>The flowchart of the GEP modeling in this study.</p

The detection capability of ANN models in SCLC patients and normal controls.

<p>The detection capability of ANN models in SCLC patients and normal controls.</p

The correlation analysis of the biomarkers were depended on Spearman rank correlation analysis (r = correlation coefficient, P value <i>of 0 <0</i>.<i>0001</i>).

<p>The correlation analysis of the biomarkers were depended on Spearman rank correlation analysis (r = correlation coefficient, P value <i>of 0 <0</i>.<i>0001</i>).</p