Publications
Selected publications
- A Higher-Dimensional Homologically Persistent Skeleton (Journal article - 2017)
- A one-dimensional homologically persistent skeleton of an unstructured point cloud in any metric space (Journal article - 2015)
- All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron (Journal article - 2008)
- Compressed Drinfeld associators (Journal article - 2004)
- Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives (Conference Paper - 2023)
- Mathematics of 2-Dimensional Lattices (Journal article - 2022)
- Geographic style maps for two-dimensional lattices (Journal article - 2023)
- Resolving the data ambiguity for periodic crystals (Conference Paper - 2022)
- Analogy Powered by Prediction and Structural Invariants: Computationally Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal (Journal article - 2022)
- A fast and robust algorithm to count topologically persistent holes in noisy clouds (Conference Paper - 2013)
2024
Generic families of finite metric spaces with identical or trivial 1-dimensional persistence
Smith, P., & Kurlin, V. (n.d.). Generic families of finite metric spaces with identical or trivial 1-dimensional persistence. Journal of Applied and Computational Topology. doi:10.1007/s41468-024-00177-6
Applications of isometry invariants on material property prediction
Balasingham, J., Zamaraev, V., & Kurlin, V. (2024). Applications of isometry invariants on material property prediction. Acta Crystallographica Section A Foundations and Advances, 80(a1), e574. doi:10.1107/s2053273324094257
Richard Feynman's visual hint gave birth to a new area of continuous crystallography
Anosova, O., & Kurlin, V. (2024). Richard Feynman's visual hint gave birth to a new area of continuous crystallography. Acta Crystallographica Section A Foundations and Advances, 80(a1), e630. doi:10.1107/s2053273324093690
The crystal isometry principle has made transparent the black boxes of structural databases
Widdowson, D., & Kurlin, V. (2024). The crystal isometry principle has made transparent the black boxes of structural databases. Acta Crystallographica Section A Foundations and Advances, 80(a1), e643. doi:10.1107/s2053273324093562
Ultra-fast detection of (near-)duplicate structures across major crystal databases
Widdowson, D., & Kurlin, V. (2024). Ultra-fast detection of (near-)duplicate structures across major crystal databases. Acta Crystallographica Section A Foundations and Advances, 80(a1), e333. doi:10.1107/s2053273324096669
Continuous Invariant-Based Maps of the Cambridge Structural Database.
Widdowson, D. E., & Kurlin, V. A. (2024). Continuous Invariant-Based Maps of the Cambridge Structural Database.. Crystal growth & design, 24(13), 5627-5636. doi:10.1021/acs.cgd.4c00410
The importance of definitions in crystallography.
Anosova, O., Kurlin, V., & Senechal, M. (2024). The importance of definitions in crystallography.. IUCrJ, 11(Pt 4), 453-463. doi:10.1107/s2052252524004056
A data-driven analysis of HDPE post-consumer recyclate for sustainable bottle packaging
Smith, P., McLauchlin, A., Franklin, T., Yan, P., Cunliffe, E., Hasell, T., . . . McDonald, T. O. (2024). A data-driven analysis of HDPE post-consumer recyclate for sustainable bottle packaging. Resources, Conservation and Recycling, 205, 107538. doi:10.1016/j.resconrec.2024.107538
Material Property Prediction Using Graphs Based on Generically Complete Isometry Invariants
Balasingham, J., Zamaraev, V., & Kurlin, V. (2024). Material Property Prediction Using Graphs Based on Generically Complete Isometry Invariants. Integrating Materials and Manufacturing Innovation, 13(2), 555-568. doi:10.1007/s40192-024-00351-9
Accelerating material property prediction using generically complete isometry invariants.
Balasingham, J., Zamaraev, V., & Kurlin, V. (2024). Accelerating material property prediction using generically complete isometry invariants.. Scientific reports, 14(1), 10132. doi:10.1038/s41598-024-59938-z
Accelerating Material Property Prediction using Generically Complete Isometry Invariants.
Complete and bi-continuous invariant of protein backbones under rigid motion.
Anosova, O., Gorelov, A., Jeffcott, W., Jiang, Z., & Kurlin, V. (2024). Complete and bi-continuous invariant of protein backbones under rigid motion.. CoRR, abs/2410.08203.
Computing the bridge length: the key ingredient in a continuous isometry classification of periodic point sets.
McManus, J., & Kurlin, V. (2024). Computing the bridge length: the key ingredient in a continuous isometry classification of periodic point sets.. CoRR, abs/2410.23288.
Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points
Kurlin, V. (2024). Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points. Match - Communications in Mathematical and in Computer Chemistry, 91(1), 79-108. doi:10.46793/match.91-1.079k
2023
Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances
Schwalbe-Koda, D., Widdowson, D. E., Pham, T. A., & Kurlin, V. A. (2023). Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances. Digital Discovery. doi:10.1039/d3dd00134b
Entropic Trust Region for Densest Crystallographic Symmetry Group Packings.
Torda, M., Goulermas, J. Y., Púcek, R., & Kurlin, V. (2023). Entropic Trust Region for Densest Crystallographic Symmetry Group Packings.. SIAM J. Sci. Comput., 45. doi:10.1137/22M147983X
A continuous map of 2.6+ million 2D lattices from the Cambridge Structural Database
Bright, M., Cooper, A., & Kurlin, V. (2023). A continuous map of 2.6+ million 2D lattices from the Cambridge Structural Database. Acta Crystallographica Section A Foundations and Advances, 79(a2), C513. doi:10.1107/s2053273323091027
A continuous map of the Cambridge Structural Database in meaningful coordinates
Widdowson, D. E., & Kurlin, V. A. (2023). A continuous map of the Cambridge Structural Database in meaningful coordinates. Acta Crystallographica Section A Foundations and Advances, 79(a2), C515. doi:10.1107/s2053273323091003
Continuous maps of molecules and atomic clouds in large databases
Widdowson, D., Elkin, Y., & Kurlin, V. (2023). Continuous maps of molecules and atomic clouds in large databases. Acta Crystallographica Section A Foundations and Advances, 79(a2), C517-C518. doi:10.1107/s2053273323090988
Continuous metrics can improve PDB validation and protein folding prediction
Gorelov, A., & Kurlin, V. (2023). Continuous metrics can improve PDB validation and protein folding prediction. Acta Crystallographica Section A Foundations and Advances, 79(a2), C1381. doi:10.1107/s2053273323082402
Potential materials genome for mapping the continuous space of all periodic crystals
Widdowson, D., & Kurlin, V. (2023). Potential materials genome for mapping the continuous space of all periodic crystals. Acta Crystallographica Section A Foundations and Advances, 79(a2), C1025. doi:10.1107/s2053273323085960
The crystal isometry principle justifies a new data standard for all periodic crystals
Cooper, A. I., Widdowson, D. E., Bright, M. J., & Kurlin, V. A. (2023). The crystal isometry principle justifies a new data standard for all periodic crystals. Acta Crystallographica Section A Foundations and Advances, 79(a2), C76. doi:10.1107/s2053273323095335
Density Functions of Periodic Sequences of Continuous Events.
Anosova, O., & Kurlin, V. (2023). Density functions of periodic sequences of continuous events. Journal of Mathematical Imaging and Vision.
A New Near-linear Time Algorithm For k-Nearest Neighbor Search Using a Compressed Cover Tree
Elkin, Y., & Kurlin, V. (2023). A New Near-linear Time Algorithm For k-Nearest Neighbor Search Using a Compressed Cover Tree. In Proceedings of Machine Learning Research Vol. 202 (pp. 9267-9311).
Geographic style maps for two-dimensional lattices
Bright, M., Cooper, A. I., & Kurlin, V. (2023). Geographic style maps for two-dimensional lattices. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 79, 1-13. doi:10.1107/S2053273322010075
Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives
Widdowson, D., & Kurlin, V. (2023). Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (pp. 1275-1284). IEEE. doi:10.1109/cvpr52729.2023.00129
Simplexwise Distance Distributions for finite spaces with metrics and measures.
The strength of a simplex is the key to a continuous isometry classification of Euclidean clouds of unlabelled points.
2022
A database of experimentally measured lithium solid electrolyte conductivities evaluated with machine learning
Hargreaves, C. J. J., Gaultois, M. W. W., Daniels, L. M. M., Watts, E. J. J., Kurlin, V. A. A., Moran, M., . . . Dyer, M. S. S. (2023). A database of experimentally measured lithium solid electrolyte conductivities evaluated with machine learning. NPJ COMPUTATIONAL MATERIALS, 9(1). doi:10.1038/s41524-022-00951-z
Mathematics of 2-Dimensional Lattices
Kurlin, V. (2022). Mathematics of 2-Dimensional Lattices. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS. doi:10.1007/s10208-022-09601-8
Molecular set transformer: attending to the co-crystals in the Cambridge structural database
Vriza, A., Sovago, I., Widdowson, D., Kurlin, V., Wood, P. A., & Dyer, M. S. (n.d.). Molecular set transformer: attending to the co-crystals in the Cambridge structural database. Digital Discovery, 1(6), 834-850. doi:10.1039/d2dd00068g
Densest plane group packings of regular polygons
Torda, M., Goulermas, J. Y., Kurlin, V., & Day, G. M. (2022). Densest plane group packings of regular polygons. PHYSICAL REVIEW E, 106(5). doi:10.1103/PhysRevE.106.054603
Density Functions of Periodic Sequences
Anosova, O., & Kurlin, V. (2022). Density Functions of Periodic Sequences. In Unknown Conference (pp. 395-408). Springer International Publishing. doi:10.1007/978-3-031-19897-7_31
Topological Methods for Pattern Detection in Climate Data
Muszynski, G., Kurlin, V., Morozov, D., Wehner, M., Kashinath, K., & Ram, P. (2022). Topological Methods for Pattern Detection in Climate Data. In Unknown Book (pp. 221-235). Wiley. doi:10.1002/9781119467557.ch13
Algorithms for automated detection of (near-)duplicate periodic crystals
Kurlin, V. (2022). Algorithms for automated detection of (near-)duplicate periodic crystals. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 78 (pp. E775-E776). Retrieved from https://www.webofscience.com/
Mapping the Space of Two-Dimensional Lattices
Bright, M., Kurlin, V., & Cooper, A. (2022). Mapping the Space of Two-Dimensional Lattices. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 78 (pp. E723-E724). doi:10.1107/S2053273322090568
The Crystal Isometry Principle
Kurlin, V., Widdowson, D., Cooper, A., & Bright, M. (2022). The Crystal Isometry Principle. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 78 (pp. E293-E294). Retrieved from https://www.webofscience.com/
The pointwise distance distribution is stronger than the pair distribution function
Kurlin, V., & Widdowson, D. (2022). The pointwise distance distribution is stronger than the pair distribution function. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 78 (pp. E745). doi:10.1107/S2053273322090386
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
Elkin, Y., & Kurlin, V. (2022). Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006. Retrieved from http://arxiv.org/abs/2208.09447v1
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
A Formula for the Linking Number in Terms of Isometry Invariants of Straight Line Segments
Bright, M., Anosova, O., & Kurlin, V. (2022). A Formula for the Linking Number in Terms of Isometry Invariants of Straight Line Segments. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 62(8), 1217-1233. doi:10.1134/S0965542522080024
Fast Predictions of Lattice Energies by Continuous Isometry Invariants of Crystal Structures
Ropers, J., Mosca, M. M., Anosova, O., Kurlin, V., & Cooper, A. I. (2022). Fast Predictions of Lattice Energies by Continuous Isometry Invariants of Crystal Structures. In Unknown Conference (pp. 178-192). Springer International Publishing. doi:10.1007/978-3-031-12285-9_11
Analogy Powered by Prediction and Structural Invariants: Computationally Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal
Zhu, Q., Johal, J., Widdowson, D. E., Pang, Z., Li, B., Kane, C. M., . . . Cooper, A. I. (2022). Analogy Powered by Prediction and Structural Invariants: Computationally Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal. JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 144(22), 9893-9901. doi:10.1021/jacs.2c02653
Density functions of periodic sequences
Average Minimum Distances of periodic point sets are fundamental invariants for mapping all periodic crystals.
Widdowson, D., Mosca, M., Pulido, A., Kurlin, V., & Cooper, A. I. (2022). Average Minimum Distances of periodic point sets are fundamental invariants for mapping all periodic crystals.. MATCH Communications in Mathematical and in Computer Chemistry, 87(3), 529-559. doi:10.46793/match.87-3.529W
A Practical Algorithm for Degree-<i>k</i> Voronoi Domains of Three-Dimensional Periodic Point Sets
Smith, P., & Kurlin, V. (2022). A Practical Algorithm for Degree-<i>k</i> Voronoi Domains of Three-Dimensional Periodic Point Sets. In ADVANCES IN VISUAL COMPUTING, ISVC 2022, PT I Vol. 13598 (pp. 377-391). doi:10.1007/978-3-031-20713-6_29
A computable and continuous metric on isometry classes of high-dimensional periodic sequences.
Compact Graph Representation of molecular crystals using Point-wise Distance Distributions.
Computable complete invariants for finite clouds of unlabeled points under Euclidean isometry.
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
Elkin, Y., & Kurlin, V. (2022). Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006. In 2022 IEEE WORKSHOP ON TOPOLOGICAL DATA ANALYSIS AND VISUALIZATION (TOPOINVIS 2022) (pp. 9-17). doi:10.1109/TopoInVis57755.2022.00008
Density Functions of Periodic Sequences.
Anosova, O., & Kurlin, V. (2022). Density Functions of Periodic Sequences.. In É. Baudrier, B. Naegel, A. Krähenbühl, & M. Tajine (Eds.), DGMM Vol. 13493 (pp. 395-408). Springer. Retrieved from https://doi.org/10.1007/978-3-031-19897-7
Families of point sets with identical 1D persistence.
Paired compressed cover trees guarantee a near linear parametrized complexity for all k-nearest neighbors search in an arbitrary metric space.
Resolving the data ambiguity for periodic crystals
Widdowson, D. E., & Kurlin, V. A. (2022). Resolving the data ambiguity for periodic crystals. In Advances in Neural Information Processing Systems Vol. 35.
2021
Isometry Invariant Shape Recognition of Projectively Perturbed Point Clouds by the Mergegram Extending 0D Persistence
Elkin, Y., & Kurlin, V. (2021). Isometry Invariant Shape Recognition of Projectively Perturbed Point Clouds by the Mergegram Extending 0D Persistence. MATHEMATICS, 9(17). doi:10.3390/math9172121
Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence
Introduction to invariant-based machine learning for periodic crystals
Ropers, J., Mosca, M. M., Anosova, O., & Kurlin, V. (2021). Introduction to invariant-based machine learning for periodic crystals. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 77 (pp. C671). Retrieved from https://www.webofscience.com/
Atmospheric Blocking Pattern Recognition in Global Climate Model Simulation Data
Muszynski, G., Prabhat., Balewski, J., Kashinath, K., Wehner, M., Kurlin, V., & SOC, I. C. (2021). Atmospheric Blocking Pattern Recognition in Global Climate Model Simulation Data. In 2020 25TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR) (pp. 677-684). doi:10.1109/ICPR48806.2021.9412736
The Density Fingerprint of a Periodic Point Set
A Fast Approximate Skeleton with Guarantees for Any Cloud of Points in a Euclidean Space
Elkin, Y., Liu, D., & Kurlin, V. (2021). A Fast Approximate Skeleton with Guarantees for Any Cloud of Points in a Euclidean Space. In Topological Methods in Data Analysis and Visualization VI (pp. 245-269). Springer Nature. doi:10.1007/978-3-030-83500-2_13
A Proof of the Invariant-Based Formula for the Linking Number and Its Asymptotic Behaviour
Bright, M., Anosova, O., & Kurlin, V. (2021). A Proof of the Invariant-Based Formula for the Linking Number and Its Asymptotic Behaviour. In Numerical Geometry, Grid Generation and Scientific Computing (Vol. 143, pp. 37-60). Springer Nature. doi:10.1007/978-3-030-76798-3_3
An Isometry Classification of Periodic Point Sets
Anosova, O., & Kurlin, V. (2021). An Isometry Classification of Periodic Point Sets. In Unknown Conference (pp. 229-241). Springer International Publishing. doi:10.1007/978-3-030-76657-3_16
Easily computable continuous metrics on the space of isometry classes of all 2-dimensional lattices.
2020
The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions
Hargreaves, C. J., Dyer, M. S., Gaultois, M. W., Kurlin, V. A., & Rosseinsky, M. J. (2020). The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions. Chemistry of Materials, 32(24), 10610-10620. doi:10.1021/acs.chemmater.0c03381
One class classification as a practical approach for accelerating π–π co-crystal discovery
Vriza, A., Canaj, A. B., Vismara, R., Kershaw Cook, L. J., Manning, T. D., Gaultois, M. W., . . . Rosseinsky, M. J. (n.d.). One class classification as a practical approach for accelerating π–π co-crystal discovery. Chemical Science. doi:10.1039/d0sc04263c
A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
The asymptotic behaviour and a near linear time algorithm for isometry invariants of periodic sets
Widdowson, D., Mosca, M., Pulido, A., Kurlin, V., & Cooper, A. I. (2020). The asymptotic behaviour and a near linear time algorithm for isometry invariants of periodic sets. Retrieved from http://arxiv.org/abs/2009.02488v4
The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions
Hargreaves, C., Dyer, M., Gaultois, M., Kurlin, V., & Rosseinsky, M. J. (2020). The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions. doi:10.26434/chemrxiv.12777566.v1
The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions
Encoding and Topological Computation on Textiles
Encoding and topological computation on textile structures
Bright, M., & Kurlin, V. (2020). Encoding and topological computation on textile structures. Computers & Graphics, 90, 51-61. doi:10.1016/j.cag.2020.05.014
The mergegram of a dendrogram and its stability
A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space
Synthesis through Unification Genetic Programming
Welsch, T., & Kurlin, V. (2020). Synthesis through Unification Genetic Programming. In GECCO'20: PROCEEDINGS OF THE 2020 GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE (pp. 1029-1036). doi:10.1145/3377930.3390208
Voronoi-Based Similarity Distances between Arbitrary Crystal Lattices
Mosca, M. M., & Kurlin, V. (2020). Voronoi-Based Similarity Distances between Arbitrary Crystal Lattices. CRYSTAL RESEARCH AND TECHNOLOGY, 55(5). doi:10.1002/crat.201900197
Persistence-based resolution-independent meshes of superpixels
Kurlin, V., & Muszynski, G. (2020). Persistence-based resolution-independent meshes of superpixels. PATTERN RECOGNITION LETTERS, 131, 300-306. doi:10.1016/j.patrec.2020.01.014
Polygonal Meshes of Highly Noisy Images based on a New Symmetric Thinning Algorithm with Theoretical Guarantees
Siddiqui, M. A., & Kurlin, V. (2020). Polygonal Meshes of Highly Noisy Images based on a New Symmetric Thinning Algorithm with Theoretical Guarantees. In VISAPP: PROCEEDINGS OF THE 15TH INTERNATIONAL JOINT CONFERENCE ON COMPUTER VISION, IMAGING AND COMPUTER GRAPHICS THEORY AND APPLICATIONS, VOL 4: VISAPP (pp. 137-146). doi:10.5220/0009340301370146
The Mergegram of a Dendrogram and Its Stability.
Elkin, Y., & Kurlin, V. (2020). The Mergegram of a Dendrogram and Its Stability.. In J. Esparza, & D. Král' (Eds.), MFCS Vol. 170 (pp. 32:1). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. Retrieved from https://www.dagstuhl.de/dagpub/978-3-95977-159-7
2019
The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Quantifying Uncertainties in Atmospheric River Climatology
Rutz, J. J., Shields, C. A., Lora, J. M., Payne, A. E., Guan, B., Ullrich, P., . . . Viale, M. (n.d.). The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Quantifying Uncertainties in Atmospheric River Climatology. Journal of Geophysical Research: Atmospheres. doi:10.1029/2019jd030936
Resolution-Independent Meshes of Superpixels
Kurlin, V., & Smith, P. (2020). Resolution-Independent Meshes of Superpixels. In ADVANCES IN VISUAL COMPUTING, ISVC 2019, PT I Vol. 11844 (pp. 194-205). doi:10.1007/978-3-030-33720-9_15
Resolution-independent meshes of super pixels
HOW TO CORRECTLY SAMPLE UNIT CELLS IN COMPUTER SIMULATIONS OF CRYSTAL STRUCTURES
Kurlin, V. (2019). HOW TO CORRECTLY SAMPLE UNIT CELLS IN COMPUTER SIMULATIONS OF CRYSTAL STRUCTURES. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 75 (pp. E547). doi:10.1107/S2053273319090090
MATHEMATICAL JUSTIFICATIONS FOR CRYSTAL SYSTEMS, BRAVAIS LATTICES AND A NEW CONTINUOUS CLASSIFICATION
Kurlin, V. (2019). MATHEMATICAL JUSTIFICATIONS FOR CRYSTAL SYSTEMS, BRAVAIS LATTICES AND A NEW CONTINUOUS CLASSIFICATION. In ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES Vol. 75 (pp. E768). doi:10.1107/S2053273319087886
Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets
Muszynski, G., Kashinath, K., Kurlin, V., Wehner, M., & Prabhat. (2019). Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets. GEOSCIENTIFIC MODEL DEVELOPMENT, 12(2), 613-628. doi:10.5194/gmd-12-613-2019
Skeletonisation Algorithms with Theoretical Guarantees for Unorganised Point Clouds with High Levels of Noise
Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise
Smith, P., & Kurlin, V. (2021). Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise. PATTERN RECOGNITION, 115. doi:10.1016/j.patcog.2021.107902
Correction: Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method
Ban, N., Yamazaki, W., & Kurlin, V. (2019). Correction: Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2019-2224.c1
Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method
Ban, N., Yamazaki, W., & Kurlin, V. (2019). Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2019-2224
A Persistence-Based Approach to Automatic Detection of Line Segments in Images
Kurlin, V., & Muszynski, G. (2019). A Persistence-Based Approach to Automatic Detection of Line Segments in Images. In COMPUTATIONAL TOPOLOGY IN IMAGE CONTEXT, CTIC 2019 Vol. 11382 (pp. 137-150). doi:10.1007/978-3-030-10828-1_11
Resolution-Independent Meshes of Superpixels.
Kurlin, V., & Smith, P. (2019). Resolution-Independent Meshes of Superpixels.. In G. Bebis, R. Boyle, B. Parvin, D. Koracin, D. Ushizima, S. Chai, . . . P. Xu (Eds.), ISVC (1) Vol. 11844 (pp. 194-205). Springer. Retrieved from https://doi.org/10.1007/978-3-030-33720-9
2018
Towards a topological pattern detection in fluid and climate simulation data
Muszynski, G., Kashinath, K., Kurlin, V., Wehner, M., & Prabhat. (2018, September 19). Towards a topological pattern detection in fluid and climate simulation data. In Climate Informatics (pp. 4 pages). Boulder, Colorado, US. Retrieved from https://www2.cisl.ucar.edu/
Atmospheric River Tracking Method Intercomparison Project (ARTMIP): project goals and experimental design
Kurlin, V., Muszynski, G., Wehner, M., Shields, C., Rutz, J., Leung, L. -Y., & Ralph, M. (2018). Atmospheric River Tracking Method Intercomparison Project (ARTMIP): project goals and experimental design. Geoscientific Model Development, 11(6), 2455-2474. doi:10.5194/gmd-11-2455-2018
Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets
Muszynski, G., Kashinath, K., Kurlin, V., & Wehner, M. (2018). Topological Data Analysis and Machine Learning for RecognizingAtmospheric River Patterns in Large Climate Datasets. doi:10.5194/gmd-2018-53
Superpixels optimized by color and shape
Kurlin, V., & Harvey, D. (2018). Superpixels optimized by color and shape. In Lecture Notes in Computer Science (pp. 14 pages). Venice, Italy: Springer Nature. Retrieved from http://kurlin.org/
Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Project Goals and Experimental Design
2017
Convex constrained meshes for superpixel segmentations of images.
Forsythe, J., & Kurlin, V. (2017). Convex constrained meshes for superpixel segmentations of images. JOURNAL OF ELECTRONIC IMAGING, 26(6). doi:10.1117/1.JEI.26.6.061609
A Higher-Dimensional Homologically Persistent Skeleton
Kalisnik, S., Kurlin, V., & Lesnik, D. (2019). A Higher-Dimensional Homologically Persistent Skeleton. Advances in Applied Mathematics, 102(January 2019), 113-142. doi:10.1016/j.aam.2018.07.004
The Higher-Dimensional Skeletonization Problem
Computing invariants of knotted graphs given by sequences of points in 3-dimensional space
Kurlin, V. (2017). Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space. In Mathematics and Visualization (pp. 349-363). Springer International Publishing. doi:10.1007/978-3-319-44684-4_21
Convex constrained meshes for superpixel segmentations of images.
Forsythe, J., & Kurlin, V. (2017). Convex constrained meshes for superpixel segmentations of images.. J. Electronic Imaging, 26, 61609.
2016
Resolution-independent superpixels based on convex constrained meshes without small angles
Kurlin, V., Forsythe, J., & Fitzgibbon, A. (2016). Resolution-independent superpixels based on convex constrained meshes without small angles. In Lecture Notes in Computer Science. Las-Vegas, USA: Springer Verlag (Germany): Series. doi:10.1007/978-3-319-50835-1_21
A fast persistence-based segmentation of noisy 2D clouds with provable guarantees
Kurlin, V. (2016). A fast persistence-based segmentation of noisy 2D clouds with provable guarantees. Pattern Recognition Letters, 83(1), 3-12. doi:10.1016/j.patrec.2015.11.025
A Linear Time Algorithm for Embedding Arbitrary Knotted Graphs into a 3-Page Book
Kurlin, V., & Smithers, C. (2016). A Linear Time Algorithm for Embedding Arbitrary Knotted Graphs into a 3-Page Book. In Unknown Book (Vol. 598, pp. 99-122). doi:10.1007/978-3-319-29971-6_6
2015
Relaxed Disk Packing
Edelsbrunner, H., Iglesias-Ham, M., & Kurlin, V. (2015). Relaxed Disk Packing. Retrieved from http://arxiv.org/abs/1505.03402v1
Relaxed Disk Packing
Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence
Kurlin, V. (2014). Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence. In 16TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING (SYNASC 2014) (pp. 594-601). doi:10.1109/SYNASC.2014.85
A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images
Kurlin, V. (2015). A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images. In COMPUTER ANALYSIS OF IMAGES AND PATTERNS, CAIP 2015, PT I Vol. 9256 (pp. 606-617). doi:10.1007/978-3-319-23192-1_51
A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages
Kurlin, V. (2015). A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages. In Proceedings of the 6th International Conference on Information Visualization Theory and Applications (pp. 5-16). SCITEPRESS - Science and and Technology Publications. doi:10.5220/0005259900050016
A one-dimensional homologically persistent skeleton of an unstructured point cloud in any metric space
Kurlin, V. (2015). A one-dimensional homologically persistent skeleton of an unstructured point cloud in any metric space. Computer Graphics Forum, 34(5), 253-262. doi:10.1111/cgf.12713
Relaxed Disk Packing.
Ham, M. I., Edelsbrunner, H., & Kurlin, V. (2015). Relaxed Disk Packing.. In CCCG. Queen's University, Ontario, Canada. Retrieved from https://cccg.ca/proceedings/2015/
2014
Computing a configuration skeleton for motion planning of two round robots on a metric graph
Kurlin, V., & Safi-Samghabadi, M. (2014). Computing a configuration skeleton for motion planning of two round robots on a metric graph. In 2014 SECOND RSI/ISM INTERNATIONAL CONFERENCE ON ROBOTICS AND MECHATRONICS (ICROM) (pp. 723-729). Retrieved from https://www.webofscience.com/
2013
A fast and robust algorithm to count topologically persistent holes in noisy clouds
A fast and robust algorithm to count topologically persistent holes in noisy clouds
Kurlin, V. (2014). A fast and robust algorithm to count topologically persistent holes in noisy clouds. In 2014 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) (pp. 1458-1463). doi:10.1109/CVPR.2014.189
2010
Recognizing trace graphs of closed braids
Fiedler, T., & Kurlin, V. (2010). Recognizing trace graphs of closed braids. Osaka Journal of Mathematics, 47(4), 885-909. doi:10.18910/7426
2009
Computing braid groups of graphs with applications to robot motion planning
Kurlin, V. (2012). COMPUTING BRAID GROUPS OF GRAPHS WITH APPLICATIONS TO ROBOT MOTION PLANNING. HOMOLOGY HOMOTOPY AND APPLICATIONS, 14(1), 159-180. doi:10.4310/HHA.2012.v14.n1.a8
Computing braid groups of graphs with applications to robot motion planning
On Descriptional Complexity of the Planarity Problem for Gauss Words
2008
Recognizing trace graphs of closed braids
Fiedler, T., & Kurlin, V. (2010). RECOGNIZING TRACE GRAPHS OF CLOSED BRAIDS. OSAKA JOURNAL OF MATHEMATICS, 47(4), 885-909. Retrieved from https://www.webofscience.com/
Recognizing trace graphs of closed braids
All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron
Kearton, C., & Kurlin, V. (2008). All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 8(3), 1223-1247. doi:10.2140/agt.2008.8.1223
All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron
2007
How many wireless sensors are needed to guarantee connectivity of a 1-dimensional network with random inter-node spacings?
Kurlin, V., & Mihaylova, L. (2007). Connectivity of Random 1-Dimensional Networks. Retrieved from http://arxiv.org/abs/0710.1001v2
Fiber quadrisecants in knot isotopies
Fiber quadrisecants in knot isotopies
Fiedler, T., & Kurlin, V. (2008). FIBER QUADRISECANTS IN KNOT ISOTOPIES. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 17(11), 1415-1428. doi:10.1142/S0218216508006695
2006
Gauss paragraphs of classical links and a characterization of virtual link groups
Kurlin, V. (2008). Gauss paragraphs of classical links and a characterization of virtual link groups. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 145, 129-140. doi:10.1017/S0305004108001151
Gauss paragraphs of classical links and a characterization of virtual link groups
A 1-parameter approach to links in a solid torus
Fiedler, T., & Kurlin, V. (2010). A 1-parameter approach to links in a solid torus. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62(1), 167-211. doi:10.2969/jmsj/06210167
A 1-parameter approach to links in a solid torus
The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra
The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra
Kurlin, V. (2007). The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra. JOURNAL OF LIE THEORY, 17(3), 525-538. Retrieved from https://www.webofscience.com/
2005
Peripherally specified homomorphs of link groups
Kurlin, V., & Lines, D. (2007). Peripherally specified homomorphs of link groups. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 16(6), 719-740. doi:10.1142/S0218216507005440
Peripherally specified homomorphs of link groups
2004
Compressed Drinfeld associators
Kurlin, V. (2005). Compressed Drinfeld associators. JOURNAL OF ALGEBRA, 292(1), 184-242. doi:10.1016/j.jalgebra.2005.05.013
Compressed Drinfeld associators
Three-page encoding and complexity theory for spatial graphs
Kurlin, V. (2007). Three-page encoding and complexity theory for spatial graphs. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 16(1), 59-102. doi:10.1142/S021821650700521X
Трехстраничные вложения сингулярных узлов
Вершинин, В. В., Vershinin, V. V., Вершинин, В. В., Vershinin, V. V., Курлин, В. А., & Kurlin, V. A. (2004). Трехстраничные вложения сингулярных узлов. Функциональный анализ и его приложения, 38(1), 16-33. doi:10.4213/faa93
2003
Three-page embeddings of singular knots
Kurlin, V. A., & Vershinin, V. V. (2004). Three-page embeddings of singular knots. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 38(1), 14-27. doi:10.1023/B:FAIA.0000024864.64045.de
Three-page embeddings of singular knots
Basic embeddings of graphs and Dynnikov's three-page embedding method
Kurlin, V. A. (2003). Basic embeddings of graphs and Dynnikov's three-page embedding method. RUSSIAN MATHEMATICAL SURVEYS, 58(2), 372-374. doi:10.1070/RM2003v058n02ABEH000617
Базисные вложения графов и метод трехстраничных вложений Дынникова
Курлин, В. А., & Kurlin, V. A. (2003). Базисные вложения графов и метод трехстраничных вложений Дынникова. Успехи математических наук, 58(2), 163-164. doi:10.4213/rm617
2001
Dynnikov three-page diagrams of spatial 3-valent graphs
Kurlin, V. A. (2001). Dynnikov three-page diagrams of spatial 3-valent graphs. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 35(3), 230-233. doi:10.1023/A:1012339231182
Three-page Dynnikov's Diagrams of Spatial 3-valent Graphs
Kurlin, V. (2001). Three-page Dynnikov's Diagrams of Spatial 3-valent Graphs. Functional Analysis and Its Applications, 35(3), 230-233.
Трехстраничные диаграммы Дынникова заузленных $3$-валентных графов
Курлин, В. А., & Kurlin, V. A. (2001). Трехстраничные диаграммы Дынникова заузленных $3$-валентных графов. Функциональный анализ и его приложения, 35(3), 84-88. doi:10.4213/faa264
2000
Basic embeddings into a product of graphs
Kurlin, V. (2000). Basic embeddings into a product of graphs. TOPOLOGY AND ITS APPLICATIONS, 102(2), 113-137. doi:10.1016/S0166-8641(98)00147-3
1999
Invariants of colored links
Kurlin, V. A. (1999). Invariants of colored links. Vestnik Moskovskogo Universiteta. Ser. 1 Matematika Mekhanika, (4), 61-63.
The reduction of framed links to ordinary ones
Kurlin, V. (1999). The reduction of framed links to ordinary ones. RUSSIAN MATHEMATICAL SURVEYS, 54(4), 845-846. doi:10.1070/RM1999v054n04ABEH000190
Редукция оснащенных зацеплений к обычным
Курлин, В. А., & Kurlin, V. A. (1999). Редукция оснащенных зацеплений к обычным. Успехи математических наук, 54(4), 177-178. doi:10.4213/rm190