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Multidimensional Interleavings and Applications to Topological Inference
Multidimensional Interleavings Topological Inference Algebraic Topology
2012/6/27
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at t...
Stochastic Homology. Reduction Formulas for Computing Stochastic Betti Numbers of Maximal Random Complexes with Discrete Probabilities. Computation and Applications
Stochastic Homology Stochastic Betti Numbers Maximal Random Complexes Algebraic Topology
2011/8/25
Abstract: Given a chain complex with the only modi?cation that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be underst...
Theory and applications of lattice point methods for binomial ideals
binomial ideal primary decomposition polynomial ring affine semigroup
2010/12/6
This survey of methods surrounding lattice point methods for binomial ideals begins with a leisurely treatment of the geometric combinatorics of binomial primary decomposition. It then proceeds to thr...
On H-groups and their applications to topological homotopy groups
H-group sub-H-group loop space Topological homotopy
2010/12/13
This paper develops a basic theory of H-groups. We intro-duce a special quotient of H-groups and extend some algebraic construc-tions of topological groups to the category of H-groups and H-maps. We u...
A Splitting Theorem for Local Cohomology and its Applications
Local cohomology split exact sequence generalized Cohen-Macaulay module
2010/12/8
Let R be a commutative Noetherian ring and M a finitely generated R-module. We show in this paper that.
Integral and homothetic indecomposability with applications to irreducibility of polynomials
Absolute irreducibility polytopes integral indecomposability
2010/2/25
Being motivated by some methods for construction of homothetically indecomposable polytopes, we obtain new methods for construction of families of integrally indecomposable polytopes. As a result, we ...
A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asym...
C-Closed Sets in L-Fuzzy Topological Spaces and Some of its Applications
L-fuzzy topology Qa-compactness L-fuzzy C-closed set L-fuzzy C-continuous mappings L-fuzzy net L-fuzzy ideal C-convergence
2010/3/1
We introduce and study the notion of C-closed sets in L-fuzzy topological spaces. Then, C-convergence theory for nets and ideals is established in terms of C-closedness. Finally, we give a new concept...