인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

Chromatin state annotation using combinations of chromatin modification patterns has emerged as a powerful approach for discovering regulatory regions and their cell type specific activity patterns, and for interpreting disease-association studies1-5. However, the computational challenge of learning chromatin state models from large numbers of chromatin modification datasets in multiple cell types still requires extensive bioinformatics expertise making it inaccessible to the wider scientific community. To address this challenge, we have developed ChromHMM, an automated computational system for learning chromatin states, characterizing their biological functions and correlations with large-scale functional datasets, and visualizing the resulting genome-wide maps of chromatin state annotations.

ChromHMM: automating chromatin-state discovery and characterization

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Classical Algebraic Geometry

Introduction.- Birational Geometry of Surfaces.- Logarithmic Category.- Overview of Mori's Program.- Singularities.- Vanishing Theorems.- Base Point Freeness of Linear Systems.- Cone Theorem.- Contraction Theorem.- Flip.- Cone Theorem Revisited.- Logarithmic Mori's Program.- Birational Relations among Minimal Models.- Birational Relations among Mori Fiber Spaces.- Birational Geometry of Toric Varieties.

Introduction to the Mori Program

Lectures on elliptic curves, London Mathematical Society Student Texts 24, by J. W. S. Cassels. Pp 137. £13-95 (paper) £27-95 (hard). 1991. ISBN 0-521-42530-1, -41517-9. (Cambridge University Press)

A smooth plane curve is said to admit a symmetric determinantal representation if it can be defined by the determinant of a symmetric matrix with entries in linear forms in three variables. We study the local–global principle for the existence of symmetric determinantal representations of smooth plane curves over a global field of characteristic different from two. When the degree of the plane curve is less than or equal to three, we relate the problem of finding symmetric determinantal representations to more familiar Diophantine problems on the Severi–Brauer varieties and mod 2 Galois representations, and prove that the local–global principle holds for conics and cubics. We also construct counterexamples to the local–global principle for quartics using the results of Mumford, Harris, and Shioda on theta characteristics.

The local–global principle for symmetric determinantal representations of smooth plane curves

We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross–Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.

On the symmetric determinantal representations of the Fermat curves of prime degree

The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two

A smooth plane curve is said to admit a symmetric determinantal representation if it can be defined by the determinant of a symmetric matrix with entries in linear forms in three variables. We study the local-global principle for the existence of symmetric determinantal representations of smooth plane curves over a global field of characteristic different from two. When the degree of the plane curve is less than or equal to three, we relate the problem of finding symmetric determinantal representations to more familiar Diophantine problems on the Severi-Brauer varieties and mod 2 Galois representations, and prove that the local-global principle holds for conics and cubics. We also construct counterexamples to the local-global principle for quartics using the results of Mumford, Harris, and Shioda on theta characteristics.

The local-global principle for symmetric determinantal representations of smooth plane curves

It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of three quadrics. We generalize this bijection to possibly singular hypersurfaces of any dimension over arbitrary fields including those of characteristic two. It is accomplished in terms of linear orbits of tuples of symmetric matrices instead of smooth complete intersections of quadrics. As an application of our methods, we give a description of the projective automorphism groups of complete intersections of quadrics generalizing Beauville's results.

Yasuhiro Ishitsuka

Papers

The local–global principle for symmetric determinantal representations of smooth plane curves

On the symmetric determinantal representations of the Fermat curves of prime degree

The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two

The local-global principle for symmetric determinantal representations of smooth plane curves

Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields