Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7. Regular rings 8. Flatness revisited 9. Derivations 10. I-smoothness 11. Applications of complete local rings Appendices References Index.

Commutative Ring Theory

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plucker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

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Combinatorial Commutative Algebra

Preface Part I. Introduction to the Four Themes: 1. Statistics L. Pachter and B. Sturmfels 2. Computation L. Pachter and B. Sturmfels 3. Algebra L. Pachter and B. Sturmfels 4. Biology L. Pachter and B. Sturmfels Part II. Studies on the Four Themes: 5. Parametric inference R. Mihaescu 6. Polytope propagation on graphs M. Joswig 7. Parametric sequence alignment C. Dewey and K. Woods 8. Bounds for optimal sequence alignment S. Elizalde 9. Inference functions S. Elizalde 10. Geometry of Markov chains E. Kuo 11. Equations defining hidden Markov models N. Bray and J. Morton 12. The EM algorithm for hidden Markov models I. B. Hallgrimsdottir, A. Milowski and J. Yu 13. Homology mapping with Markov random fields A. Caspi 14. Mutagenetic tree models N. Beerenwinkel and M. Drton 15. Catalog of small trees M. Casanellas, L. Garcia and S. Sullivant 16. The strand symmetric model M. Casanellas and S. Sullivant 17. Extending statistical models from trees to splits graphs D. Bryant 18. Small trees and generalized neighbor-joining M. Contois and D. Levy 19. Tree construction using Singular Value Decomposition N. Eriksson 20. Applications of interval methods to phylogenetics R. Sainudiin and R. Yoshida 21. Analysis of point mutations in vertebrate genomes J. Al-Aidroos and S. Snir 22. Ultra-conserved elements in vertebrate genomes M. Drton, N. Eriksson and G. Leung Index.

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Algebraic Statistics for Computational Biology

Computing the Continuous Discretely

Monomial Ideals

/pdf/distributive-lattices-affine-semigroup-rings-and-algebras-13dzy9gu6h.pdf

Distributive Lattices, Affine Semigroup Rings and Algebras with Straightening Laws

Binomial edge ideals and conditional independence statements

A componentwise linear ideal is a graded ideal $I$ of a polynomial ring such that, for each degree $q$, the ideal generated by all homogeneous polynomials of degree $q$ belonging to $I$ has a linear resolution. Examples of componentwise linear ideals include stable monomial ideals and Gotzmann ideals. The graded Betti numbers of a componentwise linear ideal can be determined by the graded Betti numbers of its components. Combinatorics on squarefree componentwise linear ideals will be especially studied. It turns out that the Stanley-Reisner ideal $I_{\Delta}$ arising from a simplicial complex $\Delta$ is componentwise linear if and only if the Alexander dual of $\Delta$ is sequentially Cohen-Macaulay. This result generalizes the theorem by Eagon and Reiner which says that the Stanley-Reisner ideal of a simplicial complex has a linear resolution if and only if its Alexander dual is Cohen-Macaulay.

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Componentwise linear ideals

A certain squarefree monomial ideal HP arising from a finite partially ordered set P will be studied from viewpoints of both commutative algbera and combinatorics. First, it is proved that the defining ideal of the Rees algebra of HP possesses a quadratic Grobner basis. Thus in particular all powers of HP have linear resolutions. Second, the minimal free graded resolution of HP will be constructed explicitly and a combinatorial formula to compute the Betti numbers of HP will be presented. Third, by using the fact that the Alexander dual of the simplicial complex ? whose Stanley---Reisner ideal coincides with HP is Cohen---Macaulay, all the Cohen---Macaulay bipartite graphs will be classified.

/pdf/distributive-lattices-bipartite-graphs-and-alexander-duality-2ldli2lulr.pdf

Takayuki Hibi

Papers

Monomial Ideals

Distributive Lattices, Affine Semigroup Rings and Algebras with Straightening Laws

Binomial edge ideals and conditional independence statements

Componentwise linear ideals

Distributive Lattices, Bipartite Graphs and Alexander Duality