Multidimensional persistence in biomolecular data

Molecular nonlinear dynamics and protein thermal uncertainty quantification

(2014) Kelin Xia et al.   CHAOS

Persistent homology analysis of protein structure, flexibility, and folding

(2014) Kelin Xia et al.   International Journal for Numerical Methods in Biomedical Engineering

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

(2014) Kristopher Opron et al.   JOURNAL OF CHEMICAL PHYSICS

Persistent homology for the quantitative prediction of fullerene stability

(2014) Kelin Xia et al.   JOURNAL OF COMPUTATIONAL CHEMISTRY

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

(2013) Konstantin Mischaikow et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Flow prediction in cerebral aneurysms based on geometry reconstruction from 3D rotational angiography

(2013) J. Mikhal et al.   International Journal for Numerical Methods in Biomedical Engineering

Flow-induced ATP release in patient-specific arterial geometries - a comparative study of computational models

(2013) E. Boileau et al.   International Journal for Numerical Methods in Biomedical Engineering

A fast alternating direction implicit algorithm for geometric flow equations in biomolecular surface generation

(2013) Wufeng Tian et al.   International Journal for Numerical Methods in Biomedical Engineering

Multiscale multiphysics and multidomain models—Flexibility and rigidity

(2013) Kelin Xia et al.   JOURNAL OF CHEMICAL PHYSICS

Multiscale geometric modeling of macromolecules II: Lagrangian representation

(2013) Xin Feng et al.   JOURNAL OF COMPUTATIONAL CHEMISTRY

Multiscale geometric modeling of macromolecules I: Cartesian representation

(2013) Kelin Xia et al.   JOURNAL OF COMPUTATIONAL PHYSICS

MULTISCALE, MULTIPHYSICS AND MULTIDOMAIN MODELS I: BASIC THEORY

(2013) GUO-WEI WEI   JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY

Betti numbers in multidimensional persistent homology are stable functions

(2013) Andrea Cerri et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Reeb Graphs: Approximation and Persistence

(2012) Tamal K. Dey et al.   DISCRETE & COMPUTATIONAL GEOMETRY

A fast algorithm for constructing topological structure in large data

(2012) Xu Liu et al.   Homology Homotopy and Applications

Simulation-Based Joint Estimation of Body Deformation and Elasticity Parameters for Medical Image Analysis

(2012) Huai-Ping Lee et al.   IEEE TRANSACTIONS ON MEDICAL IMAGING

Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures

(2012) B. Rieck et al.   IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

(2012) Xin Feng et al.   International Journal for Numerical Methods in Biomedical Engineering

Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval

(2012) Patrizio Frosini et al.   PATTERN RECOGNITION LETTERS

Variational Multiscale Models for Charge Transport

(2012) Guo-Wei Wei et al.   SIAM REVIEW

A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology

(2012) Y. Dabaghian et al.   PLoS Computational Biology

A Mayer–Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions

(2011) Barbara Di Fabio et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Topology-Based Kernels With Application to Inference Problems in Alzheimer's Disease

(2011) Deepti Pachauri et al.   IEEE TRANSACTIONS ON MEDICAL IMAGING

Branching and Circular Features in High Dimensional Data

(2011) Bei Wang et al.   IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS

Semi-automatic surface and volume mesh generation for subject-specific biomedical geometries

(2011) Igor Sazonov et al.   International Journal for Numerical Methods in Biomedical Engineering

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface

(2011) Duan Chen et al.   International Journal for Numerical Methods in Biomedical Engineering

Partial differential equation transform-Variational formulation and Fourier analysis

(2011) Yang Wang et al.   International Journal for Numerical Methods in Biomedical Engineering

Biomolecular surface construction by PDE transform

(2011) Qiong Zheng et al.   International Journal for Numerical Methods in Biomedical Engineering

Differential geometry based solvation model II: Lagrangian formulation

(2011) Zhan Chen et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Mode Decomposition Evolution Equations

(2011) Yang Wang et al.   JOURNAL OF SCIENTIFIC COMPUTING

A Topological View of Unsupervised Learning from Noisy Data

(2011) P. Niyogi et al.   SIAM JOURNAL ON COMPUTING

Differential Geometry Based Multiscale Models

(2010) Guo-Wei Wei   BULLETIN OF MATHEMATICAL BIOLOGY

Computing Robustness and Persistence for Images

(2010) P Bendich et al.   IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS

Modeling and simulation of electronic structure, material interface and random doping in nano-electronic devices

(2010) Duan Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Differential geometry based solvation model I: Eulerian formulation

(2010) Zhan Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multiscale molecular dynamics using the matched interface and boundary method

(2010) Weihua Geng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Strong solutions for the generalized Perona–Malik equation for image restoration

(2010) Zhengmeng Jin et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Topology and data

(2009) Gunnar Carlsson   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

The Theory of Multidimensional Persistence

(2009) Gunnar Carlsson et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Describing shapes by geometrical-topological properties of real functions

(2008) S. Biasotti et al.   ACM COMPUTING SURVEYS

Localized homology

(2008) Afra Zomorodian et al.   COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS

Geometric and potential driving formation and evolution of biomolecular surfaces

(2008) P. W. Bates et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

(2008) Zeyun Yu et al.   JOURNAL OF MOLECULAR GRAPHICS & MODELLING

Topological analysis of population activity in visual cortex

(2008) G. Singh et al.   JOURNAL OF VISION

Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions

(2007) Jianhan Chen et al.   PHYSICAL CHEMISTRY CHEMICAL PHYSICS