Huy L. Nguyen

An STS-Based Map of the Human Genome

A physical map has been constructed of the human genome containing 15,086 sequence-tagged sites (STSs), with an average spacing of 199 kilobases. The project involved assembly of a radiation hybrid map of the human genome containing 6193 loci and incorporated a genetic linkage map of the human genome containing 5264 loci. This information was combined with the results of STS-content screening of 10,850 loci against a yeast artificial chromosome library to produce an integrated map, anchored by the radiation hybrid and genetic maps. The map provides radiation hybrid coverage of 99 percent and physical coverage of 94 percent of the human genome. The map also represents an early step in an international project to generate a transcript map of the human genome, with more than 3235 expressed sequences localized. The STSs in the map provide a scaffold for initiating large-scale sequencing of the human genome.

An Optimized Set of Human Telomere Clones for Studying Telomere Integrity and Architecture

Telomere-specific clones are a valuable resource for the characterization of chromosomal rearrangements. We previously reported a first-generation set of human telomere probes consisting of 34 genomic clones, which were a known distance from the end of the chromosome ( approximately 300 kb), and 7 clones corresponding to the most distal markers on the integrated genetic/physical map (1p, 5p, 6p, 9p, 12p, 15q, and 20q). Subsequently, this resource has been optimized and completed: the size of the genomic clones has been expanded to a target size of 100-200 kb, which is optimal for use in genome-scanning methodologies, and additional probes for the remaining seven telomeres have been identified. For each clone we give an associated mapped sequence-tagged site and provide distances from the telomere estimated using a combination of fiberFISH, interphase FISH, sequence analysis, and radiation-hybrid mapping. This updated set of telomeric clones is an invaluable resource for clinical diagnosis and represents an important contribution to genetic and physical mapping efforts aimed at telomeric regions.

Radiation hybrid map of the mouse genome.

Radiation hybrid (RH) maps are a useful tool for genome analysis, providing a direct method for localizing genes and anchoring physical maps and genomic sequence along chromosomes. The construction of a comprehensive RH map for the human genome has resulted in gene maps reflecting the location of more than 30,000 human genes. Here we report the first comprehensive RH map of the mouse genome. The map contains 2,486 loci screened against an RH panel of 93 cell lines. Most loci (93%) are simple sequence length polymorphisms (SSLPs) taken from the mouse genetic map, thereby providing direct integration between these two key maps. We performed RH mapping by a new and efficient approach in which we replaced traditional gel- or hybridization-based assays by a homogeneous 5´-nuclease assay involving a single common probe for all genetic markers. The map provides essentially complete connectivity and coverage across the genome, and good resolution for ordering loci, with 1 centiRay (cR) corresponding to an average of approximately 100 kb. The RH map, together with an accompanying World-Wide Web server, makes it possible for any investigator to rapidly localize sequences in the mouse genome. Together with the previously constructed genetic map and a YAC-based physical map reported in a companion paper, the fundamental maps required for mouse genomics are now available.

OSNAP: Faster Numerical Linear Algebra Algorithms via Sparser Subspace Embeddings

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over matrices Π ∈ R^m×n such that for any linear subspace W ⊆ Rⁿ with dim(W) = d, P_Π~D(∀x ∈ W ||Πx||₂ ∈ (1 ± ε)||x||₂) > 2/3. We show that a certain class of distributions, Oblivious Sparse Norm-Approximating Projections (OSNAPs), provides OSEs with m = O(d^1+γ/ε²), and where every matrix Π in the support of the OSE has only s = O_γ(1/ε) non-zero entries per column, for γ > 0 any desired constant. Plugging OSNAPs into known algorithms for approximate least squares regression, ℓ_p regression, low rank approximation, and approximating leverage scores implies faster algorithms for all these problems. Our main result is essentially a Bai-Yin type theorem in random matrix theory and is likely to be of independent interest: we show that for any fixed U ∈ R^n×d with orthonormal columns and random sparse Π, all singular values of ΠU lie in [1 - ε, 1 + ε] with good probability. This can be seen as a generalization of the sparse Johnson-Lindenstrauss lemma, which was concerned with d = 1. Our methods also recover a slightly sharper version of a main result of [Clarkson-Woodruff, STOC 2013], with a much simpler proof. That is, we show that OSNAPs give an OSE with m = O(d²/ε²), s = 1.

Familial Eosinophilia Maps to the Cytokine Gene Cluster on Human Chromosomal Region 5q31-q33

Familial eosinophilia (FE) is an autosomal dominant disorder characterized by peripheral hypereosinophilia of unidentifiable cause with or without other organ involvement. To localize the gene for FE, we performed a genomewide search in a large U.S. kindred, using 312 different polymorphic markers. Seventeen affected subjects, 28 unaffected bloodline relatives, and 8 spouses were genotyped. The initial linkage results from the genome scan provided evidence for linkage on chromosome 5q31-q33. Additional genotyping of genetic markers located in this specific region demonstrated significant evidence that the FE locus is situated between the chromosome 5q markers D5S642 and D5S816 (multipoint LOD score of 6.49). Notably, this region contains the cytokine gene cluster, which includes three genes-namely, those for interleukin (IL)-3, IL-5, and granulocyte/macrophage colony-stimulating factor (GM-CSF)-whose products play important roles in the development and proliferation of eosinophils. These three cytokine genes were screened for potential disease-specific mutations by resequencing of a subgroup of individuals from the present kindred. No functional sequence polymorphisms were found within the promoter, the exons, or the introns of any of these genes or within the IL-3/GM-CSF enhancer, suggesting that the primary defect in FE is not caused by a mutation in any one of these genes but, rather, is caused by another gene in the area.

A radiation hybrid map of mouse genes.

A comprehensive gene-based map of a genome is a powerful tool for genetic studies and is especially useful for the positional cloning and positional candidate approaches. The availability of gene maps for multiple organisms provides the foundation for detailed conserved-orthology maps showing the correspondence between conserved genomic segments. These maps make it possible to use cross-species information in gene hunts and shed light on the evolutionary forces that shape the genome. Here we report a radiation hybrid map of mouse genes, a combined project of the Whitehead Institute/Massachusetts Institute of Technology Center for Genome Research, the Medical Research Council UK Mouse Genome Centre, and the National Center for Biotechnology Information. The map contains 11,109 genes, screened against the T31 RH panel and positioned relative to a reference map containing 2,280 mouse genetic markers. It includes 3,658 genes homologous to the human genome sequence and provides a framework for overlaying the human genome sequence to the mouse and for sequencing the mouse genome.

On the convergence of the Hegselmann-Krause system

We study convergence of the following discrete-time non-linear dynamical system:

Turnstile streaming algorithms might as well be linear sketches

n

Sublinear Time Algorithms for Earth Mover’s Distance

agents are located in Rd and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly studied system was introduced by Krause to model the dynamics of opinion formation and is often referred to as the Hegselmann-Krause model. We prove the first polynomial time bound for the convergence of this system in arbitrary dimensions. This improves on the bound of nO(n) resulting from a more general theorem of Chazelle [4]. Also, we show a quadratic lower bound and improve the upper bound for one-dimensional systems to O(n3).

Constrained Submodular Maximization: Beyond 1/e

In the turnstile model of data streams, an underlying vector x ∈ {--m,--m+1,..., m--1,m}n is presented as a long sequence of positive and negative integer updates to its coordinates. A randomized algorithm seeks to approximate a function f(x) with constant probability while only making a single pass over this sequence of updates and using a small amount of space. All known algorithms in this model are linear sketches: they sample a matrix A from a distribution on integer matrices in the preprocessing phase, and maintain the linear sketch A·x while processing the stream. At the end of the stream, they output an arbitrary function of A · x. One cannot help but ask: are linear sketches universal? In this work we answer this question by showing that any 1-pass constant probability streaming algorithm for approximating an arbitrary function f of x in the turnstile model can also be implemented by sampling a matrix A from the uniform distribution on O(n logm) integer matrices, with entries of magnitude poly(n), and maintaining the linear sketch Ax. Furthermore, the logarithm of the number of possible states of Ax, as x ranges over {--m,--m + 1,..., m}n, plus the amount of randomness needed to store A, is at most a logarithmic factor larger than the space required of the space-optimal algorithm. Our result shows that to prove space lower bounds for 1-pass streaming algorithms, it suffices to prove lower bounds in the simultaneous model of communication complexity, rather than the stronger 1-way model. Moreover, the fact that we can assume we have a linear sketch with polynomially-bounded entries further simplifies existing lower bounds, e.g., for frequency moments we present a simpler proof of the Ω(n1-2/k) bit complexity lower bound without using communication complexity.