Topological data analysis: Concepts, computation, and applications in chemical engineering

[1]  Victor M. Zavala,et al.  Convolutional Network Analysis of Optical Micrographs for Liquid Crystal Sensors , 2020, The Journal of Physical Chemistry C.

[2]  V. Zavala,et al.  Fast predictions of liquid-phase acid-catalyzed reaction rates using molecular dynamics simulations and convolutional neural networks† , 2019, Chemical science.

[3]  Jose A. Perea Topological Time Series Analysis , 2018, Notices of the American Mathematical Society.

[4]  Yankai Cao,et al.  Machine Learning Algorithms for Liquid Crystal-Based Sensors. , 2018, ACS sensors.

[5]  Hernando Ombao,et al.  Topological Data Analysis of Single-Trial Electroencephalographic Signals. , 2018, The annals of applied statistics.

[6]  Berend Smit,et al.  High-Throughput Screening Approach for Nanoporous Materials Genome Using Topological Data Analysis: Application to Zeolites , 2018, Journal of chemical theory and computation.

[7]  Firas A. Khasawneh,et al.  Chatter Classification in Turning Using Machine Learning and Topological Data Analysis , 2018, IFAC-PapersOnLine.

[8]  James A. Dumesic,et al.  Universal kinetic solvent effects in acid-catalyzed reactions of biomass-derived oxygenates , 2018 .

[9]  Yasuaki Hiraoka,et al.  Persistent Homology and Materials Informatics , 2018 .

[10]  Ippei Obayashi,et al.  Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homology , 2017, SIAM J. Appl. Algebra Geom..

[11]  Steve Oudot,et al.  Sliced Wasserstein Kernel for Persistence Diagrams , 2017, ICML.

[12]  N. Attoh-Okine Topological Data Analysis , 2017 .

[13]  George W. Fitzmaurice,et al.  Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing , 2017, CHI.

[14]  Yuhei Umeda,et al.  Time Series Classification via Topological Data Analysis , 2017 .

[15]  Marian Gidea,et al.  Topological Data Analysis of Financial Time Series: Landscapes of Crashes , 2017, 1703.04385.

[16]  L. Wasserman Topological Data Analysis , 2016, 1609.08227.

[17]  Matthew Berger,et al.  On Time-Series Topological Data Analysis: New Data and Opportunities , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).

[18]  Heather A. Harrington,et al.  Persistent homology of time-dependent functional networks constructed from coupled time series. , 2016, Chaos.

[19]  Jorge Cadima,et al.  Principal component analysis: a review and recent developments , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[20]  Jose A. Perea,et al.  SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data , 2015, BMC Bioinformatics.

[21]  Saeed Amizadeh,et al.  Generic and Scalable Framework for Automated Time-series Anomaly Detection , 2015, KDD.

[22]  Henry Adams,et al.  Persistence Images: A Stable Vector Representation of Persistent Homology , 2015, J. Mach. Learn. Res..

[23]  Konstantin Mischaikow,et al.  Analysis of Kolmogorov flow and Rayleigh–Bénard convection using persistent homology , 2015, 1505.06168.

[24]  Emerson G. Escolar,et al.  Persistent homology and many-body atomic structure for medium-range order in the glass , 2015, Nanotechnology.

[25]  Pawel Dlotko,et al.  A persistence landscapes toolbox for topological statistics , 2014, J. Symb. Comput..

[26]  Ulrich Bauer,et al.  A stable multi-scale kernel for topological machine learning , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[27]  Yiying Tong,et al.  Persistent homology for the quantitative prediction of fullerene stability , 2014, J. Comput. Chem..

[28]  Brittany Terese Fasy,et al.  Introduction to the R package TDA , 2014, ArXiv.

[29]  Dennis van Hoof,et al.  Simultaneous flow cytometric analysis of IFN‐γ and CD4 mRNA and protein expression kinetics in human peripheral blood mononuclear cells during activation , 2014, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[30]  Robert Ghrist,et al.  Elementary Applied Topology , 2014 .

[31]  Mikael Vejdemo-Johansson,et al.  javaPlex: A Research Software Package for Persistent (Co)Homology , 2014, ICMS.

[32]  Mariette Yvinec,et al.  The Gudhi Library: Simplicial Complexes and Persistent Homology , 2014, ICMS.

[33]  Kelin Xia,et al.  Persistent homology analysis of protein structure, flexibility, and folding , 2014, International journal for numerical methods in biomedical engineering.

[34]  S. Mukherjee,et al.  Topological Consistency via Kernel Estimation , 2014, 1407.5272.

[35]  Ulrich Bauer,et al.  Induced Matchings of Barcodes and the Algebraic Stability of Persistence , 2013, SoCG.

[36]  Konstantin Mischaikow,et al.  Morse Theory for Filtrations and Efficient Computation of Persistent Homology , 2013, Discret. Comput. Geom..

[37]  Bung-Nyun Kim,et al.  Persistent Brain Network Homology From the Perspective of Dendrogram , 2012, IEEE Transactions on Medical Imaging.

[38]  Josef Spidlen,et al.  FlowRepository: A resource of annotated flow cytometry datasets associated with peer‐reviewed publications , 2012, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[39]  Peter Bubenik,et al.  Statistical topological data analysis using persistence landscapes , 2012, J. Mach. Learn. Res..

[40]  Peter Bubenik,et al.  Statistical topology using persistence landscapes , 2012, ArXiv.

[41]  Steve Oudot,et al.  The Structure and Stability of Persistence Modules , 2012, Springer Briefs in Mathematics.

[42]  Andrew J. Blumberg,et al.  Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces , 2012, Found. Comput. Math..

[43]  Ingrid Hotz,et al.  Noname manuscript No. (will be inserted by the editor) Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory , 2022 .

[44]  Christine Bachoc,et al.  Tight p-fusion frames , 2012, ArXiv.

[45]  H. Poincaré,et al.  On Analysis Situs , 2010 .

[46]  Tamal K. Dey,et al.  Optimal homologous cycles, total unimodularity, and linear programming , 2010, STOC '10.

[47]  G. Carlsson,et al.  Statistical topology via Morse theory, persistence and nonparametric estimation , 2009, 0908.3668.

[48]  Leonidas J. Guibas,et al.  Proximity of persistence modules and their diagrams , 2009, SCG '09.

[49]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[50]  Raphael Gottardo,et al.  Automated gating of flow cytometry data via robust model‐based clustering , 2008, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[51]  R. Ghrist Barcodes: The persistent topology of data , 2007 .

[52]  Travis E. Oliphant,et al.  Python for Scientific Computing , 2007, Computing in Science & Engineering.

[53]  Philip K. Chan,et al.  Modeling multiple time series for anomaly detection , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[54]  David Cohen-Steiner,et al.  Stability of Persistence Diagrams , 2005, Discret. Comput. Geom..

[55]  Leonidas J. Guibas,et al.  Persistence barcodes for shapes , 2004, SGP '04.

[56]  Afra Zomorodian,et al.  Computing Persistent Homology , 2004, SCG '04.

[57]  Andrew Stein,et al.  Analysis of blood vessel topology by cubical homology , 2002, Proceedings. International Conference on Image Processing.

[58]  Konstantin Mischaikow,et al.  Cubical homology and the topological classification of 2D and 3D imagery , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[59]  Rahul R. Shah,et al.  Principles for Measurement of Chemical Exposure Based on Recognition-Driven Anchoring Transitions in Liquid Crystals , 2001, Science.

[60]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[61]  R. J. Wilson,et al.  Analysis situs , 1985 .

[62]  T. Rothenberg Identification in Parametric Models , 1971 .

[63]  D. M. Kan,et al.  ABSTRACT HOMOTOPY. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[64]  P. Alexandroff,et al.  Über den allgemeinen Dimensionsbegriff und seine Beziehungen zur elementaren geometrischen Anschauung , 1928 .

[65]  Yasuaki Hiraoka,et al.  Persistent homology analysis of craze formation. , 2017, Physical review. E.

[66]  Lovekesh Vig,et al.  Long Short Term Memory Networks for Anomaly Detection in Time Series , 2015, ESANN.

[67]  Jose A. Perea,et al.  Foundations of Computational Mathematics SLIDING WINDOWS AND PERSISTENCE : AN APPLICATION OF TOPOLOGICAL METHODS TO SIGNAL ANALYSIS , 2014 .

[68]  Christopher Rao,et al.  Graphs in Statistical Analysis , 2010 .

[69]  Günter Rote,et al.  Effective Computational Geometry for Curves and Surfaces Chapter 7 Computational Topology : An Introduction , 2007 .

[70]  Stéphane Lafon,et al.  Diffusion maps , 2006 .

[71]  Phyllis F. Dorflinger Department of Brain and Cognitive Sciences , 2005 .

[72]  S. Sheather Density Estimation , 2004 .

[73]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[74]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[75]  R. Ho Algebraic Topology , 2022 .

[76]  Leonidas J. Guibas,et al.  BIOINFORMATICS ORIGINAL PAPER doi:10.1093/bioinformatics/btm250 Structural bioinformatics Persistent voids: a new structural metric for membrane fusion , 2022 .