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The union of balls and its dual shape
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/978-1-4612-4576-6openalex-snapshot
An Introduction to Algebraic Topology
inferredcites →https://doi.org/10.1007/bf01901190openalex-snapshot
Computing the volume of the union of spheres
inferredcites →https://doi.org/10.1016/0196-6774(88)90035-1openalex-snapshot
Improved algorithms for discs and balls using power diagrams
inferredcites →https://doi.org/10.1016/b978-0-08-016160-0.50028-2openalex-snapshot
ELEMENTS OF ALGEBRAIC TOPOLOGY
inferredcites →https://doi.org/10.1107/s0021889883010985openalex-snapshot
Analytical molecular surface calculation
inferredcites →https://doi.org/10.1109/hicss.1995.375331openalex-snapshot
Measuring proteins and voids in proteins
inferredcites →https://doi.org/10.1109/tit.1983.1056714openalex-snapshot
On the shape of a set of points in the plane
inferredcites →https://doi.org/10.1137/0208040openalex-snapshot
Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
inferredcites →https://doi.org/10.1145/142675.142688openalex-snapshot
Incremental topological flipping works for regular triangulations
inferredcites →https://doi.org/10.1145/160985.161140openalex-snapshot
An incremental algorithm for Betti numbers of simplicial complexes
inferredcites →https://doi.org/10.1145/66888.66892openalex-snapshot
Residual hermite normal form computations
inferredcites →https://doi.org/10.1145/77635.77639openalex-snapshot
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
inferredcites →https://doi.org/10.1146/annurev.bb.06.060177.001055openalex-snapshot
AREAS, VOLUMES, PACKING, AND PROTEIN STRUCTURE
inferredcites →https://doi.org/10.1214/aos/1176348512openalex-snapshot
Inclusion-Exclusion-Bonferroni Identities and Inequalities for Discrete Tube-Like Problems via Euler Characteristics
inferredcites →https://doi.org/10.1515/crll.1850.40.209openalex-snapshot
Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen.
inferredcites →https://doi.org/10.1515/crll.1908.133.97openalex-snapshot
Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape
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Geometric Models of Protein Structure and Function Prediction
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Fragment‐based Drug Design and Drug Discovery
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Joint neighbors approximation of macromolecular solvent accessible surface area
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Enveloping triangulation method for detecting internal cavities in proteins and algorithm for computing their surface areas and volumes
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Derivatives of molecular surface area and volume: Simple and exact analytical formulas
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Geometric measures of large biomolecules: Surface, volume, and pockets
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Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets
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An analytical method for computing atomic contact areas in biomolecules
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Structural and dynamic roles of permanent water molecules in ligand molecular recognition by chicken liver bile acid binding protein
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Structural model of ρ1 GABA C receptor based on evolutionary analysis: Testing of predicted protein–protein interactions involved in receptor assembly and function
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Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design
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Geometric cooperativity and anticooperativity of three‐body interactions in native proteins
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On the nature of cavities on protein surfaces: Application to the identification of drug‐binding sites
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Protein cutoff scanning: A comparative analysis of cutoff dependent and cutoff free methods for prospecting contacts in proteins
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Defining and characterizing protein surface using alpha shapes
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Generation of finite element meshes on molecular surfaces
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An algorithmic solution for computing circle intersection areas and its applications to wireless communications
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A Note on Zeilberger's Abstract Lace Expansion
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Helix-helix packing and interfacial pairwise interactions of residues in membrane proteins
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Computing the Betti Numbers of Arrangements in Practice
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Topologically Correct Image Segmentation Using Alpha Shapes
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Covering an Invariant Manifold with Fat Trajectories
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Area and Perimeter Derivatives of a Union of Disks
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Computational Topology for Point Data: Betti Numbers of α-Shapes
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Smooth surfaces for multi-scale shape representation
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Computation of Protein Geometry and Its Applications: Packing and Function Prediction
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A Topological Characterization of Protein Structure
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Spheres Unions and Intersections and Some of their Applications in Molecular Modeling
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Contractions of Sphere Arrangements
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Geometric Potentials for Computational Protein Sequence Design
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Persistent Topology of Protein Space
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A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images
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Global Nonlinear Fitness Function for Protein Structures
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Coverage and Connectivity
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Simplicial Complex Entropy
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Real-Time Triangulation of Molecular Surfaces
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Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples
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Modeling Macromolecular Complexes: A Journey Across Scales
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Connect the Dots: The Reconstruction of Region Boundaries from Contour Sampling Points
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Simplicial Models and Topological Inference in Biological Systems
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Voronoi-Based Medial Axis Approximation from Samples: Issues and Solutions
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Comparative Analysis of Techniques Oriented on the Recognition of Ligand Binding Area in Proteins
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Fragment-Based Drug Design in Lead Discovery
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Shape reconstruction with Delaunay complex
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Inclusion-exclusion complexes for pseudodisk collections
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Stresses and Liftings of Cell-Complexes
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Molecular Surface Modeling and Meshing
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Microstructure modeling and computational micromechanics of glued metallic hollow-sphere composites
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Kinetic Connectivity for Unit Disks
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Different Bounds on the Different Betti Numbers of Semi-Algebraic Sets
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The Area Derivative of a Space-Filling Diagram
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Inclusion-Exclusion Formulas from Independent Complexes
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Persistence Modules on Commutative Ladders of Finite Type
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The Central Set and Its Application to the Kneser–Poulsen Conjecture
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Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics
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Computing the Multicover Bifiltration
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Boundary Measures for Geometric Inference
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Geometric Inference for Probability Measures
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A weak characterisation of the Delaunay triangulation
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On determining the cover of a simplex by spheres centered at its vertices
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An armature structure for 3D shapes
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Optimization of the First Dirichlet Laplacian Eigenvalue with Respect to a Union of Balls
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A topological measurement of protein compressibility
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An elegant algorithm of the analytical calculation for the volume of fused spheres with different radii
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Arrangements and Their Applications**Work by PA. was supported by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.–Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-91-22103 and CCR-93-11127, by…
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Data-driven quantification of grain boundary structures and their correlation with migration kinetics
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Dual models of pore spaces
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Connectivity graphs as models of local interactions
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TMBHMM: A frequency profile based HMM for predicting the topology of transmembrane beta barrel proteins and the exposure status of transmembrane residues
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Three-dimensional beta shapes
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Kernel modeling for molecular surfaces using a uniform solution
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A barcode shape descriptor for curve point cloud data
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Geometric models with weigthed topology
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Efficient construction of the Čech complex
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Triangulation of molecular surfaces based on extracting surface atoms
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Geometric filtering of pairwise atomic interactions applied to the design of efficient statistical potentials
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Recursive geometry of the flow complex and topology of the flow complex filtration
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The medial axis of the union of inner Voronoi balls in the plane
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Reconstructing 3D compact sets
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Preserving geometric properties in reconstructing regions from internal and nearby points
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Multiple covers with balls I: Inclusion–exclusion
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Geometric dominating-set and set-cover via local-search
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Statistical analysis and exposure status classification of transmembrane beta barrel residues
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Computational structure analysis of biomacromolecule complexes by interface geometry
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Relationship between periodic dinucleotides and the nucleosome structure revealed by alpha shape modeling
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A Raman spectroscopic study of the conformations of 1,4-dioxane in the pure liquid, methanol, and aqueous solution
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A topological sampling theorem for Robust boundary reconstruction and image segmentation
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From the Kneser–Poulsen conjecture to ball-polyhedra
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Skeleton based solid representation with topology preservation
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A novel projection approximation algorithm for the fast and accurate computation of molecular collision cross sections (I). Method
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A novel projection approximation algorithm for the fast and accurate computation of molecular collision cross sections (III): Application to supramolecular coordination-driven assemblies with complex shapes
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A novel projection approximation algorithm for the fast and accurate computation of molecular collision cross sections (IV). Application to polypeptides
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Interaction pattern of aldose reductase with β-glucogallin: Active site exploration and multiple docking analyses
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Geometric separation and exact solutions for the parameterized independent set problem on disk graphs
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Predicting Protein Function and Binding Profile via Matching of Local Evolutionary and Geometric Surface Patterns
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Sphericity of a protein via the β -complex
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On the estimation of the medial axis and inner parallel body
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FEMME database: topologic and geometric information of macromolecules
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Computational characterization and molecular dynamics simulation of the thermostable direct hemolysin-related hemolysin (TRH) amplified from Vibrio parahaemolyticus
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Provably correct reconstruction of surfaces from sparse noisy samples
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Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise
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A fast persistence-based segmentation of noisy 2D clouds with provable guarantees
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Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
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Are Proteins Well-Packed?
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Modelling natural objects with α-complexes
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Computing the Betti numbers of arrangements via spectral sequences
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A New Method to Detect Related Function Among Proteins Independent of Sequence and Fold Homology
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Inferring Functional Relationships of Proteins from Local Sequence and Spatial Surface Patterns
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Dynamic maintenance and visualization of molecular surfaces
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Triangulating the surface of a molecule
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On the definition and the construction of pockets in macromolecules
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Shape space from deformation
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The medial axis of a union of balls
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Area, perimeter and derivatives of a skin curve
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Spheres, molecules, and hidden surface removal
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The Geometry of Biomolecular Solvation
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Geometric and Topological Inference
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Triangulation of Submanifolds
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Reconstruction of Submanifolds
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Stability of Distance Functions
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Distance to Probability Measures
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Functional norms, condition numbers and numerical algorithms in algebraic geometry
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Power diagrams and interaction processes for unions of discs
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Exact Analytical Algorithm for the Solvent-Accessible Surface Area and Derivatives in Implicit Solvent Molecular Simulations on GPUs
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PbS Clusters Embedded in Sodalite Zeolite Cavities of Different Compositions: Unraveling the Structural Evolution and Optical Properties Using ab Initio Calculations
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The Langevin Hull: Constant Pressure and Temperature Dynamics for Nonperiodic Systems
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On-the-Fly Numerical Surface Integration for Finite-Difference Poisson–Boltzmann Methods
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Volumetric Properties of Hydrated Peptides: Voronoi–Delaunay Analysis of Molecular Simulation Runs
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Effect of Pressure on Conformational Equilibria of 1-Chloropropane and 1-Bromopropane in Water and Organic Solvents: A Raman Spectroscopic Study
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Effect of Solvent and pH on the Structure of PAMAM Dendrimers
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Pressure Effect on Conformational Equilibria of Analog Peptides in Aqueous Solution by Raman Spectroscopy
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Pore configuration landscape of granular crystallization
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Fully developed active turbulence defined through a non-equilibrium phase transition
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Origin of scaling behavior of protein packing density: A sequential Monte Carlo study of compact long chain polymers
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The weighted-volume derivative of a space-filling diagram
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Clique topology reveals intrinsic geometric structure in neural correlations
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Cell division sets a universal flow geometry in cell layers
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A new algorithm to characterise the degree of concaveness of a molecular surface relevant in ion mobility spectrometry
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State of the union (of geometric objects)
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Developing optimal non-linear scoring function for protein design
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On the derivation of propensity scales for predicting exposed transmembrane residues of helical membrane proteins
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Prediction of the translocon-mediated membrane insertion free energies of protein sequences
inferred← citeshttps://doi.org/10.1093/bioinformatics/btp599openalex-snapshot
Roll: a new algorithm for the detection of protein pockets and cavities with a rolling probe sphere
inferred← citeshttps://doi.org/10.1093/bioinformatics/btt644openalex-snapshot
Computing cavities, channels, pores and pockets in proteins from non-spherical ligands models
inferred← citeshttps://doi.org/10.1093/pnasnexus/pgag003openalex-snapshot
Can solvents tie knots? Helical folds of biopolymers in liquid environments
inferred← citeshttps://doi.org/10.1098/rspa.2020.0170openalex-snapshot
Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases
inferred← citeshttps://doi.org/10.1101/2020.12.31.424985openalex-snapshot
The growing topology of the C. elegans connectome
inferred← citeshttps://doi.org/10.1101/379768openalex-snapshot
Multiscale analysis of structurally conserved motifs
inferred← citeshttps://doi.org/10.1103/physreve.74.061107openalex-snapshot
Betti number signatures of homogeneous Poisson point processes
inferred← citeshttps://doi.org/10.1103/physrevlett.133.228301openalex-snapshot
Active Particles Knead Three-Dimensional Gels into Porous Structures
inferred← citeshttps://doi.org/10.1109/38.511855openalex-snapshot
Viewing geometric protein structures from inside a CAVE
inferred← citeshttps://doi.org/10.1109/3dv.2015.67openalex-snapshot
Towards Skeleton Based Reconstruction: From Projective Skeletonization to Canal Surface Estimation
inferred← citeshttps://doi.org/10.1109/cdc.2004.1428617openalex-snapshot
Connectivity graphs as models of local interactions
inferred← citeshttps://doi.org/10.1109/cec.2007.4425018openalex-snapshot
Virtual Reality High Dimensional Objective Spaces for Multi-objective Optimization: An Improved Representation
inferred← citeshttps://doi.org/10.1109/cvpr.2014.189openalex-snapshot
A Fast and Robust Algorithm to Count Topologically Persistent Holes in Noisy Clouds
inferred← citeshttps://doi.org/10.1109/embc53108.2024.10782681openalex-snapshot
Predicting Functional Surface Topographies Combining Topological Data Analysis and Deep Learning Across the Human Protein Universe
inferred← citeshttps://doi.org/10.1109/hicss.1995.375331openalex-snapshot
Measuring proteins and voids in proteins
inferred← citeshttps://doi.org/10.1109/icasspw59220.2023.10193167openalex-snapshot
Topological Analysis of Low Dimensional Phase Space Trajectories of High Dimensional EEG Signals For Classification of Interictal Epileptiform Discharges
inferred← citeshttps://doi.org/10.1109/iccsa.2014.53openalex-snapshot
BetaConcept: A Program for Voronoi Diagrams, Dual Structures, and Complexes in the Plane
inferred← citeshttps://doi.org/10.1109/icpr.2008.4761263openalex-snapshot
Topologically correct surface reconstruction using alpha shapes and relations to ball-pivoting
inferred← citeshttps://doi.org/10.1109/iembs.2009.5335112openalex-snapshot
Geometry of protein shape and its evolutionary pattern for function prediction and characterization
inferred← citeshttps://doi.org/10.1109/isvd.2006.35openalex-snapshot
The B-shape and B-complex for three-dimensional spheres
inferred← citeshttps://doi.org/10.1109/isvd.2007.1openalex-snapshot
\beta-shape Based Computation of Blending Surfaces on a Molecule
inferred← citeshttps://doi.org/10.1109/isvd.2009.14openalex-snapshot
Simulation of Random Set Models for Unions of Discs and the Use of Power Tessellations
inferred← citeshttps://doi.org/10.1109/jmass.2020.3026633openalex-snapshot
Minimization of Delta-v for Satellite Swarm Maintenance Using a Virtual Chief
inferred← citeshttps://doi.org/10.1109/pccga.1998.732056openalex-snapshot
Shape space from deformation
inferred← citeshttps://doi.org/10.1109/synasc.2014.85openalex-snapshot
Auto-completion of Contours in Sketches, Maps, and Sparse 2D Images Based on Topological Persistence
inferred← citeshttps://doi.org/10.1109/tdsc.2025.3616852openalex-snapshot
An Algorithm for Persistent Homology Computation Using Homomorphic Encryption
inferred← citeshttps://doi.org/10.1109/titb.2005.863875openalex-snapshot
Automatic 3-D Grayscale Volume Matching and Shape Analysis
inferred← citeshttps://doi.org/10.1109/tvcg.2015.2467432openalex-snapshot
Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials
inferred← citeshttps://doi.org/10.1109/tvcg.2018.2873633openalex-snapshot
Beta-complex vs. Alpha-complex: Similarities and Dissimilarities
inferred← citeshttps://doi.org/10.1109/visual.2000.885737openalex-snapshot
Case study: a methodology for plume visualization with application to real-time acquisition and navigation
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