Permutation Step Research Articles

Stouffer's test in a large scale simultaneous hypothesis testing.

In microarray data analysis, we are often required to combine several dependent partial test results. To overcome this, many suggestions have been made in previous literature; Tippett’s test and Fisher’s omnibus test are most popular. Both tests have known null distributions when the partial tests are independent. However, for dependent tests, their (even, asymptotic) null distributions are unknown and additional numerical procedures are required. In this paper, we revisited Stouffer’s test based on z-scores and showed its advantage over the two aforementioned methods in the analysis of large-scale microarray data. The combined statistic in Stouffer’s test has a normal distribution with mean 0 from the normality of the z-scores. Its variance can be estimated from the scores of genes in the experiment without an additional numerical procedure. We numerically compared the errors of Stouffer’s test and the two p-value based methods, Tippett’s test and Fisher’s omnibus test. We also analyzed our microarray data to find differentially expressed genes by non-genotoxic and genotoxic carcinogen compounds. Both numerical study and the real application showed that Stouffer’s test performed better than Tippett’s method and Fisher’s omnibus method with additional permutation steps.

A value transformation and random permutation-based coloured image encryption technique

With the recent advances in multimedia transmission and storage, security becomes an important issue to protect data from unauthorised access. There are several methods proposed to secure data including watermarking, encryption, steganography and others. Image encryption, which is widely used in many applications to provide high levels of security such as internet communication, multimedia systems and medical imaging, is proposed in this paper. The proposed encryption method is based on value transformation in which the image pixels are transformed to new values and random permutations in which the rows and the columns of the image are shuffled. The value transformation step is applied on pixels values through performing logical AND operation between their values and specific value in order to get new transformed image with new pixels values unrelated to the original pixels. Moreover, the random permutation step is applied to the columns and rows of the transformed image. In this step the rows and the columns are shuffled respectively using random permutation key to produce the encrypted image. The same generated key is used to shuffle both the rows and the columns of the image. The simulation results show the effectiveness and the security of the proposed method.

CDH13is associated with working memory performance in attention deficit/hyperactivity disorder

Different analytic strategies, including linkage, association and meta-analysis support a role of CDH13 in the susceptibility to attention deficit/hyperactivity disorder (ADHD). CDH13 codes for cadherin 13 (or H-cadherin), which is a member of a family of calcium-dependent cell-cell adhesion proteins and a regulator of neural cell growth. We tested the association between CDH13 on three executive functioning tasks that are promising endophenotypes of ADHD. An adjusted linear regression analysis was performed in 190 ADHD-affected Dutch probands of the IMAGE project. Three executive functions were examined: inhibition, verbal and visuo-spatial working memory (WM). We tested 2632 single nucleotide polymorphisms (SNPs) within CDH13 and 20 kb up- and downstream of the gene (capturing regulatory sequences). To adjust for multiple testing within the gene, we applied stringent permutation steps. Intronic SNP rs11150556 is associated with performance on the Verbal WM task. No other SNP showed gene-wide significance with any of the analyzed traits, but a 72-kb SNP block located 446 kb upstream of SNP rs111500556 showed suggestive evidence for association (P-value range 1.20E-03 to 1.73E-04) with performance in the same Verbal WM task. This study is the first to examine CDH13 and neurocognitive functioning. The mechanisms underlying the associations between CDH13 and the clinical phenotype of ADHD and verbal WM are still unknown. As such, our study may be viewed as exploratory, with the results presented providing interesting hypotheses for further testing.

CNAnova: a new approach for finding recurrent copy number abnormalities in cancer SNP microarray data

The current generation of single nucleotide polymorphism (SNP) arrays allows measurement of copy number aberrations (CNAs) in cancer at more than one million locations in the genome in hundreds of tumour samples. Most research has focused on single-sample CNA discovery, the so-called segmentation problem. The availability of high-density, large sample-size SNP array datasets makes the identification of recurrent copy number changes in cancer, an important issue that can be addressed using the cross-sample information. We present a novel approach for finding regions of recurrent copy number aberrations, called CNAnova, from Affymetrix SNP 6.0 array data. The method derives its statistical properties from a control dataset composed of normal samples and, in contrast to previous methods, does not require segmentation and permutation steps. For rigorous testing of the algorithm and comparison to existing methods, we developed a simulation scheme that uses the noise distribution present in Affymetrix arrays. Application of the method to 128 acute lymphoblastic leukaemia samples shows that CNAnova achieves lower error rate than a popular alternative approach. We also describe an extension of the CNAnova framework to identify recurrent CNA regions with intra-tumour heterogeneity, present in either primary or relapsed samples from the same patients. The CNAnova package and synthetic datasets are available at http://www.compbio.group.cam.ac.uk/software.html.

Adaptive Chosen-Ciphertext Attack on Secure Arithmetic Coding

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The paper “Secure Arithmetic Coding” (in <emphasis emphasistype="bold"><emphasis emphasistype="smcaps">IEEE Transactions on Signal Processing</emphasis></emphasis>, vol. 55, no. 5, pp. 2263–2272, May 2007) presented a novel encryption scheme called the secure arithmetic coding (SAC) based on the interval splitting arithmetic coding (ISAC) and a series of permutations. In the current work, we study the security of the SAC under an adaptive chosen-ciphertext attack. It is shown that the key vectors used in the codeword permutation step can be recovered with complexity <formula formulatype="inline"><tex Notation="TeX">${\cal O}(N)$</tex></formula>, where <formula formulatype="inline"><tex Notation="TeX">$N$</tex> </formula> is the symbol sequence length. After getting these key vectors, we can remove the codeword permutation step, and the resulting system has already been shown to be insecure in the original paper. This implies that the SAC is not suitable for the applications where the attacker can have access to the decoder. In addition, we discuss a method to jointly enhance the security and the performance of the SAC. </para>

On the capability of (T, U) permutation decoding method

Error-trapping decoding techniques are attractive due to their simple structure. Since 1962 several improved error-trapping methods have been devised in an effort to extend the capability and effectiveness in decoding multiple-error-correcting cyclic codes. Prange (1962) and MacWilliams (1964) introduced a (T, U) permutation group applied to this error-trapping decoding strategy by making use of a set of code-preserving permutation to obtain k error-free positions from which the rest of the code word could be reconstructed. Recently, exact lower bounds on the code length n for (n, k, 2t+1) cyclic codes have been found by using 5-step and 3-step (T, U) permutation groups. The present paper presents a study on the relationship between the code parameters n, k, t and the number of permutation steps s, with t being odd. Some examples on the capability of (T, U) permutation decodable (PD) cyclic codes are illustrated. >

Achieving optimality for gate matrix layout and PLA folding: a graph theoretic approach

We present O( n 3) heuristic algorithms for multiple/ simple PLA folding, which also apply to the matrix layout problem. Our heuristic is based on a new approach, where both problems are shown to be composed by a permutation step followed by a compaction step. Therefore we are able to show that the exponential complexity of the problem stems from the permutation step—where a good configuration is searched—, since the compaction step—where the actual folding takes place—is optimally solved in polynomial time. We discuss bounds on the distance of the obtained solution to the optimal and give sufficient conditions for the solution to be optimal. Verification of the sufficient conditions constitutes part of the proposed algorithms, and is in fact used to construct the heuristic solution. An example showing the multiple folding of a 58 × 19 PLA produced by the proposed algorithm is presented.

An algorithm for computing the mixed radix fast Fourier transform

This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.