Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Genomic Sequence is Highly Predictive of Local Nucleosome Depletion

The regulation of DNA accessibility through nucleosome positioning is important for transcription control. Computational models have been developed to predict genome-wide nucleosome positions from DNA sequences, but these models consider only nucleosome sequences, which may have limited their power. We developed a statistical multi-resolution approach to identify a sequence signature, called the N-score, that distinguishes nucleosome binding DNA from non-nucleosome DNA. This new approach has significantly improved the prediction accuracy. The sequence information is highly predictive for local nucleosome enrichment or depletion, whereas predictions of the exact positions are only modestly more accurate than a null model, suggesting the importance of other regulatory factors in fine-tuning the nucleosome positions. The N-score in promoter regions is negatively correlated with gene expression levels. Regulatory elements are enriched in low N-score regions. While our model is derived from yeast data, the N-score pattern computed from this model agrees well with recent high-resolution protein-binding data in human.Statistic

Genomic Sequence Is Highly Predictive of Local Nucleosome Depletion

The regulation of DNA accessibility through nucleosome positioning is important for transcription control. Computational models have been developed to predict genome-wide nucleosome positions from DNA sequences, but these models consider only nucleosome sequences, which may have limited their power. We developed a statistical multi-resolution approach to identify a sequence signature, called the N-score, that distinguishes nucleosome binding DNA from non-nucleosome DNA. This new approach has significantly improved the prediction accuracy. The sequence information is highly predictive for local nucleosome enrichment or depletion, whereas predictions of the exact positions are only modestly more accurate than a null model, suggesting the importance of other regulatory factors in fine-tuning the nucleosome positions. The N-score in promoter regions is negatively correlated with gene expression levels. Regulatory elements are enriched in low N-score regions. While our model is derived from yeast data, the N-score pattern computed from this model agrees well with recent high-resolution protein-binding data in human

Assessing the effects of data selection and representation on the development of reliable E. coli sigma 70 promoter region predictors

As the number of sequenced bacterial genomes increases, the need for rapid and reliable tools for the annotation of functional elements (e.g., transcriptional regulatory elements) becomes more desirable. Promoters are the key regulatory elements, which recruit the transcriptional machinery through binding to a variety of regulatory proteins (known as sigma factors). The identification of the promoter regions is very challenging because these regions do not adhere to specific sequence patterns or motifs and are difficult to determine experimentally. Machine learning represents a promising and cost-effective approach for computational identification of prokaryotic promoter regions. However, the quality of the predictors depends on several factors including: i) training data; ii) data representation; iii) classification algorithms; iv) evaluation procedures. In this work, we create several variants of E. coli promoter data sets and utilize them to experimentally examine the effect of these factors on the predictive performance of E. coli σ70 promoter models. Our results suggest that under some combinations of the first three criteria, a prediction model might perform very well on cross-validation experiments while its performance on independent test data is drastically very poor. This emphasizes the importance of evaluating promoter region predictors using independent test data, which corrects for the over-optimistic performance that might be estimated using the cross-validation procedure. Our analysis of the tested models shows that good prediction models often perform well despite how the non-promoter data was obtained. On the other hand, poor prediction models seems to be more sensitive to the choice of non-promoter sequences. Interestingly, the best performing sequence-based classifiers outperform the best performing structure-based classifiers on both cross-validation and independent test performance evaluation experiments. Finally, we propose a meta-predictor method combining two top performing sequence-based and structure-based classifiers and compare its performance with some of the state-of-the-art E. coli σ70 promoter prediction methods.NPRP grant No. 4-1454-1-233 from the Qatar National Research Fund (a member of Qatar Foundation).Scopu

View-based models for visual tracking and recognition

Ph.DDOCTOR OF PHILOSOPH

Prediction of DNase I Hypersensitive Sites by Using Pseudo Nucleotide Compositions

DNase I hypersensitive sites (DHS) associated with a wide variety of regulatory DNA elements. Knowledge about the locations of DHS is helpful for deciphering the function of noncoding genomic regions. With the acceleration of genome sequences in the postgenomic age, it is highly desired to develop cost-effective computational methods to identify DHS. In the present work, a support vector machine based model was proposed to identify DHS by using the pseudo dinucleotide composition. In the jackknife test, the proposed model obtained an accuracy of 83%, which is competitive with that of the existing method. This result suggests that the proposed model may become a useful tool for DHS identifications

Identifying the molecular components that matter: a statistical modelling approach to linking functional genomics data to cell physiology

Functional genomics technologies, in which thousands of mRNAs, proteins, or metabolites can be measured in single experiments, have contributed to reshape biological investigations. One of the most important issues in the analysis of the generated large datasets is the selection of relatively small sub-sets of variables that are predictive of the physiological state of a cell or tissue. In this thesis, a truly multivariate variable selection framework using diverse functional genomics data has been developed, characterized, and tested. This framework has also been used to prove that it is possible to predict the physiological state of the tumour from the molecular state of adjacent normal cells. This allows us to identify novel genes involved in cell to cell communication. Then, using a network inference technique networks representing cell-cell communication in prostate cancer have been inferred. The analysis of these networks has revealed interesting properties that suggests a crucial role of directional signals in controlling the interplay between normal and tumour cell to cell communication. Experimental verification performed in our laboratory has provided evidence that one of the identified genes could be a novel tumour suppressor gene. In conclusion, the findings and methods reported in this thesis have contributed to further understanding of cell to cell interaction and multivariate variable selection not only by applying and extending previous work, but also by proposing novel approaches that can be applied to any functional genomics data

Predicting Human Nucleosome Occupancy from Primary Sequence

Nucleosomes are the fundamental repeating unit of chromatin and comprise the structural building blocks of the living eukaryotic genome. Micrococcal nuclease (MNase) has long been used to delineate nucleosomal organization. Microarray-based nucleosome mapping experiments in yeast chromatin have revealed regularly-spaced translational phasing of nucleosomes. These data have been used to train computational models of sequence-directed nuclesosome positioning, which have identified ubiquitous strong intrinsic nucleosome positioning signals. Here, we successfully apply this approach to nucleosome positioning experiments from human chromatin. The predictions made by the human-trained and yeast-trained models are strongly correlated, suggesting a shared mechanism for sequence-based determination of nucleosome occupancy. In addition, we observed striking complementarity between classifiers trained on experimental data from weakly versus heavily digested MNase samples. In the former case, the resulting model accurately identifies nucleosome-forming sequences; in the latter, the classifier excels at identifying nucleosome-free regions. Using this model we are able to identify several characteristics of nucleosome-forming and nucleosome-disfavoring sequences. First, by combining results from each classifier applied de novo across the human ENCODE regions, the classifier reveals distinct sequence composition and periodicity features of nucleosome-forming and nucleosome-disfavoring sequences. Short runs of dinucleotide repeat appear as a hallmark of nucleosome-disfavoring sequences, while nucleosome-forming sequences contain short periodic runs of GC base pairs. Second, we show that nucleosome phasing is most frequently predicted flanking nucleosome-free regions. The results suggest that the major mechanism of nucleosome positioning in vivo is boundary-event-driven and affirm the classical statistical positioning theory of nucleosome organization