Dispersion strengthening models

Strengthening behavior of crystalline solids containing uniform dispersion of fine particle

Excision for simplicial sheaves on the Stein site and Gromov's Oka principle

A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion \Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to $X$ are given the compact-open topology. Gromov's Oka principle states that if $X$ has a spray, then it has the Oka-Grauert property. The purpose of this paper is to investigate the Oka-Grauert property using homotopical algebra. We embed the category of complex manifolds into the model category of simplicial sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert property is equivalent to $X$ representing a finite homotopy sheaf on the Stein site. This expresses the Oka-Grauert property in purely holomorphic terms, without reference to continuous maps.Comment: Version 3 contains a few very minor improvement

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

Phenotype-genotype association grid: a convenient method for summarizing multiple association analyses

BACKGROUND: High-throughput genotyping generates vast amounts of data for analysis; results can be difficult to summarize succinctly. A single project may involve genotyping many genes with multiple variants per gene and analyzing each variant in relation to numerous phenotypes, using several genetic models and population subgroups. Hundreds of statistical tests may be performed for a single SNP, thereby complicating interpretation of results and inhibiting identification of patterns of association. RESULTS: To facilitate visual display and summary of large numbers of association tests of genetic loci with multiple phenotypes, we developed a Phenotype-Genotype Association (PGA) grid display. A database-backed web server was used to create PGA grids from phenotypic and genotypic data (sample sizes, means and standard errors, P-value for association). HTML pages were generated using Tcl scripts on an AOLserver platform, using an Oracle database, and the ArsDigita Community System web toolkit. The grids are interactive and permit display of summary data for individual cells by a mouse click (i.e. least squares means for a given SNP and phenotype, specified genetic model and study sample). PGA grids can be used to visually summarize results of individual SNP associations, gene-environment associations, or haplotype associations. CONCLUSION: The PGA grid, which permits interactive exploration of large numbers of association test results, can serve as an easily adapted common and useful display format for large-scale genetic studies. Doing so would reduce the problem of publication bias, and would simplify the task of summarizing large-scale association studies

The homotopy theory of simplicial props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat

DG-algebras and derived A-infinity algebras

A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A-infinity algebra. Such a minimal derived A-infinity algebra model for A is a k-projective resolution of the homology algebra of A together with a family of maps satisfying appropriate relations. As in the case of A-infinity algebras, it is possible to recover the dga up to quasi-isomorphism from a minimal derived A-infinity algebra model. Hence the structure we are describing provides a complete description of the quasi-isomorphism type of the dga.Comment: v3: 27 pages. Minor corrections, to appear in Crelle's Journa

Multifactor dimensionality reduction for graphics processing units enables genome-wide testing of epistasis in sporadic ALS

Motivation: Epistasis, the presence of gene–gene interactions, has been hypothesized to be at the root of many common human diseases, but current genome-wide association studies largely ignore its role. Multifactor dimensionality reduction (MDR) is a powerful model-free method for detecting epistatic relationships between genes, but computational costs have made its application to genome-wide data difficult. Graphics processing units (GPUs), the hardware responsible for rendering computer games, are powerful parallel processors. Using GPUs to run MDR on a genome-wide dataset allows for statistically rigorous testing of epistasis

Stroke genetics: prospects for personalized medicine.

Epidemiologic evidence supports a genetic predisposition to stroke. Recent advances, primarily using the genome-wide association study approach, are transforming what we know about the genetics of multifactorial stroke, and are identifying novel stroke genes. The current findings are consistent with different stroke subtypes having different genetic architecture. These discoveries may identify novel pathways involved in stroke pathogenesis, and suggest new treatment approaches. However, the already identified genetic variants explain only a small proportion of overall stroke risk, and therefore are not currently useful in predicting risk for the individual patient. Such risk prediction may become a reality as identification of a greater number of stroke risk variants that explain the majority of genetic risk proceeds, and perhaps when information on rare variants, identified by whole-genome sequencing, is also incorporated into risk algorithms. Pharmacogenomics may offer the potential for earlier implementation of 'personalized genetic' medicine. Genetic variants affecting clopidogrel and warfarin metabolism may identify non-responders and reduce side-effects, but these approaches have not yet been widely adopted in clinical practice

Two-dimensional enrichment analysis for mining high-level imaging genetic associations

Enrichment analysis has been widely applied in the genome-wide association studies (GWAS), where gene sets corresponding to biological pathways are examined for significant associations with a phenotype to help increase statistical power and improve biological interpretation. In this work, we expand the scope of enrichment analysis into brain imaging genetics, an emerging field that studies how genetic variation influences brain structure and function measured by neuroimaging quantitative traits (QT). Given the high dimensionality of both imaging and genetic data, we propose to study Imaging Genetic Enrichment Analysis (IGEA), a new enrichment analysis paradigm that jointly considers meaningful gene sets (GS) and brain circuits (BC) and examines whether any given GS-BC pair is enriched in a list of gene-QT findings. Using gene expression data from Allen Human Brain Atlas and imaging genetics data from Alzheimer's Disease Neuroimaging Initiative as test beds, we present an IGEA framework and conduct a proof-of-concept study. This empirical study identifies 12 significant high level two dimensional imaging genetics modules. Many of these modules are relevant to a variety of neurobiological pathways or neurodegenerative diseases, showing the promise of the proposal framework for providing insight into the mechanism of complex diseases

Genetics of callous-unemotional behavior in children

Callous-unemotional behavior (CU) is currently under consideration as a subtyping index for conduct disorder diagnosis. Twin studies routinely estimate the heritability of CU as greater than 50%. It is now possible to estimate genetic influence using DNA alone from samples of unrelated individuals, not relying on the assumptions of the twin method. Here we use this new DNA method (implemented in a software package called Genome-wide Complex Trait Analysis, GCTA) for the first time to estimate genetic influence on CU. We also report the first genome-wide association (GWA) study of CU as a quantitative trait. We compare these DNA results to those from twin analyses using the same measure and the same community sample of 2,930 children rated by their teachers at ages 7, 9 and 12. GCTA estimates of heritability were near zero, even though twin analysis of CU in this sample confirmed the high heritability of CU reported in the literature, and even though GCTA estimates of heritability were substantial for cognitive and anthropological traits in this sample. No significant associations were found in GWA analysis, which, like GCTA, only detects additive effects of common DNA variants. The phrase ‘missing heritability’ was coined to refer to the gap between variance associated with DNA variants identified in GWA studies versus twin study heritability. However, GCTA heritability, not twin study heritability, is the ceiling for GWA studies because both GCTA and GWA are limited to the overall additive effects of common DNA variants, whereas twin studies are not. This GCTA ceiling is very low for CU in our study, despite its high twin study heritability estimate. The gap between GCTA and twin study heritabilities will make it challenging to identify genes responsible for the heritability of CU