Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies

<p>Abstract</p> <p>Background</p> <p>The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters.</p> <p>Results</p> <p>In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods.</p> <p>Conclusion</p> <p>We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.</p

Electrical spin injection in GaAs/AlGaAs quantum-well LEDs

We have studied the electroluminescence spectra resulting from spin injection in several ZnMnSe/AlGaAs(n)/GaAs/AlGaAs(p) light-emitting diodes(LEDs) as a function of magnetic field and temperature in the Faraday geometry. The top ZnMnSe layer through which electrons are injected into the GaAs well acts as a spin aligner due to its large conduction band spin splitting. Electrons leave the ZnMnSe layer predominantly in the m(s) = -1/2 spin state; the heavy holes which participate in the elh, transition are injected into the GaAs well from the substrate with equal numbers in the m(s) = +3/2 and m(s) = -3/2 spin states. As a result, the emitted electroluminescence associated with the e(1)h(1) exciton is strongly circularly polarized. The maximum value of the optical polarization P at T = 4.2 K is 0.5 which corresponds to 75% of the injected electrons in the m(s) = -1/2 state.X11sciescopuskciothe