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**1 - 4**of**4**### COOKED SUMMARY This cooked summary explains the main ideas of the paper ”Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks with Noise

"... Variance Uncertainty ” by referring the equation numbers in the paper. This cooked summary is very helpful for researchers in the field and who would like to know the novelty and key contribution of the paper without reading the whole text. Objective of the paper Given N samples, the objective is to ..."

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Variance Uncertainty ” by referring the equation numbers in the paper. This cooked summary is very helpful for researchers in the field and who would like to know the novelty and key contribution of the paper without reading the whole text. Objective of the paper Given N samples, the objective is to decide between H0 (the N samples contain noise only) and H1 (these N samples contain a transmitted signal + noise). Methodology • Express the baseband transmitted signal x(t) as in Equa-tion (1) of the paper. To do this we ASSUME that the transmitter pulse shaping filter is known to the cognitive receiver. • Introduce a linear combination scalars {αi}Li=1 and DE-FINE a new sample {ỹ[n]}Nn=1 as in Equation (3) (novel part). • Design {αi}Li=1 such that we can get two different signals from {ỹ[n]}Nn=1 such that the SNR of the first signal is different from the SNR of the second signal. This is possible by performing the following tasks: – Solve the optimization problem (6), substitute this optimal solution {αi}Li=1 in Equation (3) and set the resulting samples as {e[n]}Nn=1 (i.e., see Equation (14)) (novel part). – Solve the optimization problem (7), substitute this optimal solution {αi}Li=1 in Equation (3) and set the resulting samples as {z[n]}Nn=1 (i.e., see Equation (14)) (novel part). – Now it is clear that the SNR of z[n] is greater than (and is equal to) the SNR of e[n] under H1 (and H0) hypothesis, respectively. • Due to this mathematical outcome, we propose Equation (20) as our test statistics (novel part). • As we can see, Equation (20) will be closer to 0 and much greater than 0 under H0 and H1 hypothesis, respectively. • The Pf and Pd of this new test statistics is derived in (22) and (23). • All the explanation and analytical equations after Equa-tion (23) are to improve the test statistics (20) by taking into account the effect of synchronization between the transmitter and cognitive receiver, adjacent channel inter-ference, unknown pulse shaping filter and so on, which are very important for practical cognitive radio. ar X iv

### Spectral gene set enrichment (SGSE)

, 2014

"... Motivation: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist ..."

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Motivation: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist for unsupervised gene set testing, they predominantly compute enrich-ment relative to clusters of the genomic variables with performance strongly dependent on the clustering algorithm and number of clusters. Results: We propose a novel method, spectral gene set enrichment (SGSE), for unsupervised competitive testing of the association between gene sets and empirical data sources. SGSE first computes the statistical association between gene sets and principal components (PCs) using our principal component gene set enrichment (PCGSE) method. The overall statistical association between each gene set and the spectral structure of the data is then computed by combining the PC-level p-values using the weighted Z-method with weights set to the PC variance scaled by Tracey-Widom test p-values. Using simulated data, we show that the SGSE algorithm can accurately recover spectral features from noisy data. To illustrate the utility of our method on real data, we demonstrate the superior performance of the SGSE method relative to standard cluster-based techniques for testing the association between MSigDB gene sets and the variance structure of microarray gene expres-sion data. Availability:

### arXiv: arXiv:0000.0000 DISTRIBUTION OF THE LARGEST ROOT OF A MATRIX FOR ROY’S TEST IN MULTIVARIATE ANALYSIS OF VARIANCE

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### DOI 10.1186/s12859-015-0490-7 METHODOLOGY ARTICLE Open Access Spectral gene set enrichment (SGSE)

"... Background: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist ..."

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Background: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist for unsupervised gene set testing, they predominantly compute enrichment relative to clusters of the genomic variables with performance strongly dependent on the clustering algorithm and number of clusters. Results: We propose a novel method, spectral gene set enrichment (SGSE), for unsupervised competitive testing of the association between gene sets and empirical data sources. SGSE first computes the statistical association between gene sets and principal components (PCs) using our principal component gene set enrichment (PCGSE) method. The overall statistical association between each gene set and the spectral structure of the data is then computed by combining the PC-level p-values using the weighted Z-method with weights set to the PC variance scaled by Tracy-Widom test p-values. Using simulated data, we show that the SGSE algorithm can accurately recover spectral features from noisy data. To illustrate the utility of our method on real data, we demonstrate the superior performance of the SGSE method relative to standard cluster-based techniques for testing the association between MSigDB gene sets and the variance structure of microarray gene expression data.