On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale

Characterizations of Pseudo-Codewords of LDPC Codes

An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of properties of this fundamental cone derived from its connection to unramified covers of the graphical models on which the decoding algorithms operate. For the class of cycle codes, these developments naturally lead to a characterization of the fundamental polytope as the Newton polytope of the Hashimoto edge zeta function of the underlying graph.Comment: Submitted, August 200

A study of network-based kernel methods on protein-protein interaction for protein functions prediction

Predicting protein functions is an important issue in the post-genomic era. In this paper, we studied several network-based kernels including Local Linear Embedding (LLE) kernel method, Diffusion kernel and Laplacian Kernel to uncover the relationship between proteins functions and Protein-Protein Interactions (PPI). We first construct kernels based on PPI networks, we then apply Support Vector Machine (SVM) techniques to classify proteins into different functional groups. 5-fold cross validation is then applied to the selected 359 GO terms to compare the performance of different kernels and guilt-by-association methods including neighbor counting methods and Chisquare methods. Finally we made predictions of functions of some unknown genes and verified the preciseness of our prediction in part by the information of other data source.postprintThe 3rd International Symposium on Optimization and Systems Biology (OSB 2009), Zhangjiajie, China, 20-22 September 2009. In Lecture Notes in Operations Research, 2009, v. 11, p. 25-3

Comparative genomics approaches accurately predict deleterious variants in plants

Recent advances in genome resequencing have led to increased interest in prediction of the functional consequences of genetic variants. Variants at phylogenetically conserved sites are of particular interest, because they are more likely than variants at phylogenetically variable sites to have deleterious effects on fitness and contribute to phenotypic variation. Numerous comparative genomic approaches have been developed to predict deleterious variants, but the approaches are nearly always assessed based on their ability to identify known disease-causing mutations in humans. Determining the accuracy of deleterious variant predictions in nonhuman species is important to understanding evolution, domestication, and potentially to improving crop quality and yield. To examine our ability to predict deleterious variants in plants we generated a curated database of 2,910 Arabidopsis thaliana mutants with known phenotypes. We evaluated seven approaches and found that while all performed well, their relative ranking differed from prior benchmarks in humans. We conclude that deleterious mutations can be reliably predicted in A. thaliana and likely other plant species, but that the relative performance of various approaches does not necessarily translate from one species to another

Metabolite biomarker discovery for metabolic diseases by flux analysis

Metabolites can serve as biomarkers and their identification has significant importance in the study of biochemical reaction and signalling networks. Incorporating metabolic and gene expression data to reveal biochemical networks is a considerable challenge, which attracts a lot of attention in recent research. In this paper, we propose a promising approach to identify metabolic biomarkers through integrating available biomedical data and disease-specific gene expression data. A Linear Programming (LP) based method is then utilized to determine flux variability intervals, therefore enabling the analysis of significant metabolic reactions. A statistical approach is also presented to uncover these metabolites. The identified metabolites are then verified by comparing with the results in the existing literature. The proposed approach here can also be applied to the discovery of potential novel biomarkers. © 2012 IEEE.published_or_final_versio

Discovery of metabolite biomarkers: flux analysis and reaction-reaction network approach

published_or_final_versio

Divergence and Shannon information in genomes

Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length-independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.Comment: 4 pages, 3 tables, 2 figure