Institute of Photogrammetry and Remote Sensing (IPF)
Dr. rer. nat.  Patrick Erik Bradley

Dr. rer. nat. Patrick Erik Bradley

I work in the application of mathematics to engineering and science. My main research topic is to apply p-adic or ultrametric methods to spatial information.

Biography

Publications

Teaching

Research Projects

Theses

Code

Research Interests

Biography

1999 Dipl. math. 
2002 Dr. rer. nat. (mathematics)
Oct. 2002 - Dec. 2008 research associate at Institut für Industrielle Bauproduktion (ifib) at Universität Karlsruhe (TH)
20.03. - 19.04.2006 guest scientist at Kyoto University funded  by a JSPS research grant
since
Jan. 2009

senior researcher at Institute of Photogrammetry and Remote Sensing (IPF) at Karlsruhe Institute of Technology

since Sep. 2019 senior researcher at Geodetic Institute Karlsruhe (GIK)

 

Publications


2021
Rebmeister, M.; Schenk, A.; Bradley, P. E.; Dörr, N.; Hinz, S. (2021). OCLeaS – A tomographic PSI Algorithm using Orthogonal Matching Pursuit and Complex Least Squares. Procedia computer science, 181, 220–230. doi:10.1016/j.procs.2021.01.143
2020
Bradley, P. E. (2020). Generalised Diffusion on Moduli Spaces of p-Adic Mumford Curves. P-adic numbers, ultrametric analysis, and applications, 12 (2), 73–89. doi:10.1134/S2070046620020016
Breunig, M.; Bradley, P. E.; Jahn, M.; Kuper, P.; Mazroob, N.; Rösch, N.; Al-Doori, M.; Stefanakis, E.; Jadidi, M. (2020). Geospatial Data Management Research: Progress and Future Directions. ISPRS International Journal of Geo-Information, 9 (2), 95. doi:10.3390/ijgi9020095
2019
Bradley, P. E. (2019). Methodology for the sequence analysis of building stocks. Building research and information, 47 (2), 141–155. doi:10.1080/09613218.2018.1380343
Bradley, P. E. (2019). On the Logistic Behaviour of the Topological Ultrametricity of Data. Journal of classification, 36 (2), 266–276.
Bradley, P. E.; Behnisch, M. (2019). Heavy-tailed distributions for building stock data. Environment and planning / B, 46 (7), 1281–1296. doi:10.1177/2399808318794499
Giovanella, A.; Bradley, P. E.; Wursthorn, S. (2019). Evaluation of Topological Consistency in CityGML. ISPRS International Journal of Geo-Information, 8 (6), Article: 278. doi:10.3390/ijgi8060278
2018
Bradley, P. E.; Paul, N. (2018). Topologically Consistent Space, Time, Version, and Scale Using Alexandrov Topologies. Contemporary Strategies and Approaches in 3-D Information Modeling. Ed.: B. Kumar, 52–82, IGI Global. doi:10.4018/978-1-5225-5625-1.ch003
Giovanella, A.; Bradley, P. E.; Wursthorn, S. (2018). Detection and evaluation of topological consistency in CityGML datasets. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, TC IV Mid-Term Symposium on 3D Spatial Information Science - The Engine of Change; Delft; NL, October 1-5, 2018, 59–66, Copernicus Publications. doi:10.5194/isprs-annals-IV-4-59-2018
2017
Bradley, P. E. (2017). Finding Ultrametricity in Data using Topology. Journal of classification, 34 (1), 76–84. doi:10.1007/s00357-017-9228-8
Jahn, M. W.; Bradley, P. E.; Al Doori, M.; Breunig, M. (2017). Topologically Consistent Models for Efficient Big Geo-Spatio-Temporal Data Distribution. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 12th 3D Geoinfo Conference 2017, Melbourne, Australia, 26th - 27th October 2017, 65–72, Copernicus Publications. doi:10.5194/isprs-annals-IV-4-W5-65-2017
2016
Bradley, P. E. (2016). Ultrametricity indices for the Euclidean and Boolean hypercubes. P-adic numbers, ultrametric analysis, and applications, 8 (4), 298–311. doi:10.1134/S2070046616040038
2015
Bradley, P. E. (2015). Supporting Data Analytics for Smart Cities : An Overview of Data Models and Topology. Statistical Learning and Data Sciences : Proceedings of the 3rd International Symposium, SLDS 2015, Egham, UK, 20th - 23rd April 2015. Ed.: A. Gammerman, 406–413, Springer. doi:10.1007/978-3-319-17091-6_35
Bradley, P. E.; Braun, A. C. (2015). Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data. Applied mathematics, 06 (3), 484–495. doi:10.4236/am.2015.63046
Buchmann, E.; Bradley, P. E.; Böhm, K. (2015). Deriving Bounds on the Size of Spatial Areas. Open Journal of Databases, 2 (1), 1–16.
Paul, N.; Bradley, P. E. (2015). Integrating Space, Time, Version, and Scale using Alexandrov Topologies. International journal of 3-D information modeling, 4 (4), 64–85. doi:10.4018/IJ3DIM.2015100104
2014
Bradley, P. E.; Paul, N. (2014). Comparing G-maps with other topological data structures. Geoinformatica, 18 (3), 595–620. doi:10.1007/s10707-013-0191-1
Paul, N.; Bradley, P. E. (2014). Eine Erweiterung des Relationalen Modells zur Repräsentation räumlichen Wissens. Datenbank-Spektrum, 14 (3), 223–235. doi:10.1007/s13222-014-0163-0
2013
Paul, N.; Bradley, P. E.; Breunig, M. (2013). Integrating Space, Time, Version and Scale Using Alexandrov Topologies [Preprint]. arXiv [cs.DB], arXiv:1303.2595.
2012
Bradley, P. E. (2012). p-adic Methods in Stereo Vision. Challenges at the Interface of Data Analysis, Computer Science, and Optimization - Proceedings of the 34th Annual Conference of the Gesellschaft für Klassifikation e. V., Karlsruhe, July 21-23, 2010. Ed.: W. A. Gaul, 173–182, Springer Verlag. doi:10.1007/978-3-642-24466-7_18
2011
Bradley, P. E.; Jutzi, B. (2011). Improved feature detection in fused intensity-range images with Complex SIFT (C SIFT). Remote sensing, 3 (9), 2076–2088. doi:10.3390/rs3092076
2010
Bestehorn, M.; Böhm, K.; Bradley, P. E.; Buchmann, E. (2010). Deriving Spatio-temporal Query Results in Sensor Networks. Scientific and statistical database management : Proceedings of the 22nd international conference, SSDBM 2010, Heidelberg, Germany, 30th June - 2nd July 2010. Ed.: M. Gertz, 6–23, Springer Verlag. doi:10.1007/978-3-642-13818-8_3
Bradley, P. E. (2010). An ultrametric interpretation of building related event data. Construction Management and Economics, 28 (3), 311–326. doi:10.1080/01446190903473790
Bradley, P. E. (2010). A p-adic RanSaC algorithm for stereo vision using Hensel lifting. P-adic numbers, ultrametric analysis, and applications, 2 (1), 55–67.
Bradley, P. E. (2010). Mumford dendrograms. The Computer Journal, 53 (4), 393–404. doi:10.1093/comjnl/bxm088
Bradley, P. E. (2010). From image processing to topological modelling with p-adic numbers. P-adic numbers, ultrametric analysis, and applications, 2 (4), 293–304.
Bradley, P. E.; Paul, N. (2010). Using the relational model to capture topological information of spaces. The Computer Journal, 53 (1), 69–89. doi:10.1093/comjnl/bxn054
2009
Bradley, P. E. (2009). On p-adic Classification. P-Adic Numbers, Ultrametric Analysis, and Application, 1 (4), 271–285.
Bradley, P. E. (2009). Mumford dendrograms and discret p-adic symmetries. P-Adic Numbers, Ultrametric Analysis, and Applications, 1 (2), 118–127.
2008
Bradley, P. E. (2008). Counting plane Mumford curves. Proceedings of the 5th Summer School in Modern Mathematical Physics, MPHYS5, Belgrade, Serbia, 6th -17th July 2008. Ed.: B. Dragovich, 51–64.
Bradley, P. E. (2008). Families of Dendrograms. Data Analysis, Machine Learning and Applications : Proceedings of the 31st Annual Conference of the Gesellschaft für Klassifikation e.V., Freiburg, Germany, 7th - 9th March 2007. Ed.: C. Preisach, 95–102, Springer Verlag. doi:10.1007/978-3-540-78246-9_12
Bradley, P. E. (2008). Degenerating Families of Dendrograms. Journal of classification, 25 (1), 27–42. doi:10.1007/s00357-008-9009-5
2007
Bradley, P. E. (2007). Cyclic coverings of the p-adic projective line by Mumford curves. Manuscripta mathematica, 124 (1), 77–95. doi:10.1007/s00229-007-0120-4
Bradley, P. E.; Kohler, N. (2007). Methodology for the survival analysis of urban building stocks. Building research and information, 35 (5), 529–542. doi:10.1080/09613210701266939
2005
Bischoff, W.; Bradley, P. E.; Ferrara, C.; Kohler, N. (2005). Überlebensanalyse von Gebäudebeständen : Das Beispiel der Stadt Ettlingen. Stadtforschung und Statistik, 1 (5), 32–35.
Bradley, P. E. (2005). Riemann existence theorems of Mumford type. Mathematische Zeitschrift, 251 (2), 393–414. doi:10.1007/s00209-005-0808-7
Bradley, P. E.; Buergel-Goodwin, E.; Ferrara, C. (2005). Survival functions of buildings and building elements. Proceedings of the 10th DBMC International Conference on Durability of Building Materials and Components, Lyon, France, 17th - 20th April 2005, Art.Nr. TT8–65.
Bradley, P. E.; Buergel-Goodwin, E.; Ferrara, C.; Kohler, N. (2005). Survival functions of building stocks and components. Proceedings of the 2005 World Sustainable Building Conference, Tokyo, Japan, 28th - 29th September 2005.
Bradley, P. E.; Ferrara, C.; Kohler, N. (2005). Estimating survival functions of building stocks. Proceedings of the 10th DBMC International Conference on Durability of Building Materials and Components, Lyon, France, 17th - 20th April 2005, Art.Nr. TT5–63.
Paul, N.; Bradley, P. E. (2005). Relationale Datenbanken für die Topologie architektonischer Räume. 17. Forum Bauinformatik Junge Wissenschaftler forschen, Cottbus, Germany, 28. - 30. September, 2005, 10 S., Cottbus.
2004
Bradley, P. E. (2004). Eine Methode zur Schätzung des deutschen Bestandes an nichtlandwirtschaftlichen Betriebsgebäuden. Das Verschwinden der Bauten des Industriezeitalters : Lebenszyklen industrieller Baubestände und Methoden transdisziplinärer Forschung. Hrsg.: U. Hassler, 117–120, Wasmuth.
Bradley, P. E. (2004). Einführung in die Überlebensanalyse von Gebäudebeständen. Das Verschwinden der Bauten des Industriezeitalters : Lebenszyklen industrieller Baubestände und Methoden transdisziplinärer Forschung. Hrsg.: U. Hassler, 256–257, Wasmuth.
2003
Paul, N.; Bradley, P. E. (2003). Topological houses. Digital proceedings / IKM 2003, proceedings 16th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : 10. - 12. Juni 2003, Weimar / Bauhaus-Universität Weimar. Ed.: K. Gürlebeck; L. Hempel; C. Könke, 6 S., Fakultät für Bauingenieurwesen.
2002
Bradley, P. E. (2002). p-adische Hurwitzräume [online]. PhD dissertation. Fak. f. Mathematik, Diss. v. 26.6.2002., Universität Karlsruhe (TH). doi:10.5445/IR/3712002

Teaching

Geometric models of geodesy

Lectures and exercises in the bachelor course of studies Geodesy and Geoinformatics (2+1). Annually since winter semester 2019/2020

Basics of kinematic and dynamic models of geodesy
Lectures and exercises in the bachelor course of studies Geodesy and Geoinformatics (2+1). Annually since summer semester 2017

numerical mathematics
Lecture and tutorial in the master course of studies Geodesy and Geoinformatics (3+1). Annually since winter semester 2011/2012

Lecture at the Duale Hochschule Karlsruhe since June 2016

Topology
Accompanying course to the DFG project Modeling and Management of Topology for Building Information Models with special consideration of planning alternatives and versions. Institute for Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology.

Start: December 9, 2009. 90 minutes per week. End: 30 June 2010. topics: Set theory and algebraic topology for geoinformatics.

Space-time related information systems and geodesy
Working group on the DFG project Architectural Complexes. Institute for Industrial Building Production, Universität Karlsruhe (TH).
Start: 10.01.2006. Tuesdays approx. 9.30 a.m. to approx. 11.00 a.m. in the seminar room of the ifib. End: After 10 sessions.
The program.

Mathematics for Architects

Lecture with exercise and computer exercise. Summer term 2005. home page of the lecture. Faculty of Architecture, Universität Karlsruhe (TH).

Introduction to algebraic topology for architecture

Accompanying course to the DFG project Architectural Complexes. Institute for Industrial Building Production, Universität Karlsruhe (TH).

Start: 17.09.2004. Weekly 90-120 minutes.
Since January 2005, alternating with Norbert Paul (Themen: Applications of Chain Complexes in Architecture and Relational Database Schemas for Topological Spaces).
End: March 2005


Theses

Supervised theses

  1. Matthieu Rebmeister. Parameter Estimation for Persistent Scatterer Interferometry using Compressive Sensing. Master thesis, Karlsruhe Institute of Technology (2020)
  2. Anna Krimmelbein. Topology in CityGML. Diploma thesis, Karlsruhe Institute of Technology (2011)
  3. Anna Krimmelbein. Topology of graphs in the context of geoinformatics. Student research project, Karlsruhe Institute of Technology (2010)
  4. Norbert Paul. Topological databases for architectural spaces. Dissertation, University of Karlsruhe (2008)
  5. Martin Behnisch. Classification of municipalities according to building stock related characteristics. Diploma thesis, University of Karlsruhe (2004)
  6. Pablo Viejo García. Ettlingen. Past, present, future. Diploma thesis, University of Karlsruhe (2003)

Own theses

  1. p-adic Hurwitz spaces. Dissertation, University of Karlsruhe (2002)
  2. Mumford curves and reduction of analytic maps. Diploma thesis, University of Karlsruhe (1998)

Code

Here is Java code for computing Betti numbers of finite topological spaces. Download

Based on this, there is a CityGML Parser.

Research interests

  • Topology in spatial information systems and data

  • Non-Archimedean Geometry, p-adic numbers and applications

  • dynamics of building stocks