The Experts below are selected from a list of 40773 Experts worldwide ranked by ideXlab platform
Khandker Muttalib - One of the best experts on this subject based on the ideXlab platform.
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Universality of a family of random matrix ensembles with logarithmic soft-confinement potentials
Physical Review B, 2010Co-Authors: Jinmyung Choi, Khandker MuttalibAbstract:Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\lambda$ describing logarithmic soft-confinement potentials $V(H) \sim [\ln H]^{(1+\lambda)} \:(\lambda>0$). We showed that we can study eigenvalue correlations of these "$\lambda$-ensembles" based on the numerical construction of the corresponding orthogonal polynomials with respect to the weight function $\exp[- (\ln x)^{1+\lambda}]$. In this work, we expand our previous work and show that: i) the eigenvalue density is given by a power-law of the form $\rho(x) \propto [\ln x]^{\lambda-1}/x$ and ii) the two-Level Kernel has an anomalous structure, which is characteristic of the critical ensembles. We further show that the anomalous part, or the so-called "ghost-correlation peak", is controlled by the parameter $\lambda$; decreasing $\lambda$ increases the anomaly. We also identify the two-Level Kernel of the $\lambda$-ensembles in the semiclassical regime, which can be written in a sinh-Kernel form with more general argument that reduces to that of the critical ensembles for $\lambda=1$. Finally, we discuss the universality of the $\lambda$-ensembles, which includes Wigner-Dyson universality ($\lambda \to \infty$ limit), the uncorrelated Poisson-like behavior ($\lambda \to 0$ limit), and a critical behavior for all the intermediate $\lambda$ ($0
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Two-Level correlation function of $\lambda$-ensembles
arXiv: Statistical Mechanics, 2010Co-Authors: Jinmyung Choi, Khandker MuttalibAbstract:Recently we introduced a family of U(N) invariant random matrix ensembles which is a one-paramter ($\lambda$) extension of the q-random matrix ensembles (RMEs), given by the asymptotic weak confining potential $V(H) \sim [\ln H]^{(1+\lambda)}$ \cite{cm-jpa09}. With numerical construction of the corresponding orthogonal polynomials, we showed that the eigenvalue density of the ensembles deviates from the inverse power law and that the two-Level Kernel of the ensembles is qualitatively different from those of Gaussian and the critical ensembles. In this work, we make further efforts to characterize the two-Level Kernel of the $\lambda$-ensembles and discuss its various properties. To this end, we first show that the Kernel of the $\lambda$-ensembles also possess an anomalous structure characteristic of the critical ensembles, namely the ghost correlation peak. We then propose, albeit in a restricted regime, a form of the two-Level Kernel which is distinct from the sine Kernel of the Gaussian ensembles as well as the sinh Kernel of the critical ensembles. We test the proposed form numerically and discuss its implications. In particular, we show that the case $\lambda > 1$ is qualitatively distinct from the case $\lambda
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Power-law eigenvalue density, scaling, and critical random-matrix ensembles.
Physical Review E, 2007Co-Authors: Khandker Muttalib, Mourad E. H. IsmailAbstract:We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a scaling appropriate for such power-law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-Level Kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.
Christopher S. Oehmen - One of the best experts on this subject based on the ideXlab platform.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC Bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection. Results We introduce a new method for feature vector representation based on the physicochemical properties of the primary protein sequence. A distribution of physicochemical property scores are assembled from 4-mers of the sequence and normalized based on the null distribution of the property over all possible 4-mers. With this approach there is little computational cost associated with the transformation of the protein into feature space, and overall performance in terms of remote homology detection is comparable with current state-of-the-art methods. We demonstrate that the features can be used for the task of pairwise remote homology detection with improved accuracy versus sequence-based methods such as BLAST and other feature-based methods of similar computational cost. Conclusions A protein feature method based on physicochemical properties is a viable approach for extracting features in a computationally inexpensive manner while retaining the sensitivity of SVM protein homology detection. Furthermore, identifying features that can be used for generic pairwise homology detection in lieu of family-based homology detection is important for applications such as large database searches and comparative genomics.
Bobbie-jo M. Webb-robertson - One of the best experts on this subject based on the ideXlab platform.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC Bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection. Results We introduce a new method for feature vector representation based on the physicochemical properties of the primary protein sequence. A distribution of physicochemical property scores are assembled from 4-mers of the sequence and normalized based on the null distribution of the property over all possible 4-mers. With this approach there is little computational cost associated with the transformation of the protein into feature space, and overall performance in terms of remote homology detection is comparable with current state-of-the-art methods. We demonstrate that the features can be used for the task of pairwise remote homology detection with improved accuracy versus sequence-based methods such as BLAST and other feature-based methods of similar computational cost. Conclusions A protein feature method based on physicochemical properties is a viable approach for extracting features in a computationally inexpensive manner while retaining the sensitivity of SVM protein homology detection. Furthermore, identifying features that can be used for generic pairwise homology detection in lieu of family-based homology detection is important for applications such as large database searches and comparative genomics.
Mourad E. H. Ismail - One of the best experts on this subject based on the ideXlab platform.
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Power-law eigenvalue density, scaling, and critical random-matrix ensembles.
Physical Review E, 2007Co-Authors: Khandker Muttalib, Mourad E. H. IsmailAbstract:We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a scaling appropriate for such power-law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-Level Kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.
Kyle G Ratuiste - One of the best experts on this subject based on the ideXlab platform.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection.
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Physicochemical property distributions for accurate and rapid pairwise protein homology detection
BMC Bioinformatics, 2010Co-Authors: Bobbie-jo M. Webb-robertson, Kyle G Ratuiste, Christopher S. OehmenAbstract:Background The challenge of remote homology detection is that many evolutionarily related sequences have very little similarity at the amino acid Level. Kernel-based discriminative methods, such as support vector machines (SVMs), that use vector representations of sequences derived from sequence properties have been shown to have superior accuracy when compared to traditional approaches for the task of remote homology detection. Results We introduce a new method for feature vector representation based on the physicochemical properties of the primary protein sequence. A distribution of physicochemical property scores are assembled from 4-mers of the sequence and normalized based on the null distribution of the property over all possible 4-mers. With this approach there is little computational cost associated with the transformation of the protein into feature space, and overall performance in terms of remote homology detection is comparable with current state-of-the-art methods. We demonstrate that the features can be used for the task of pairwise remote homology detection with improved accuracy versus sequence-based methods such as BLAST and other feature-based methods of similar computational cost. Conclusions A protein feature method based on physicochemical properties is a viable approach for extracting features in a computationally inexpensive manner while retaining the sensitivity of SVM protein homology detection. Furthermore, identifying features that can be used for generic pairwise homology detection in lieu of family-based homology detection is important for applications such as large database searches and comparative genomics.