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Welcome to the wiki of [[STRUCTURES|STRUCTURES | EP Mathematics and Data]].
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This wiki is centered around the [[STRUCTURES#Organization|exploratory project]] '''EP Mathematics and Data''' within STRUCTURES and is meant to provide a platform for collaborative work on data analysis across the fields of pure mathematics and natural sciences.
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== Purpose ==
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The purpose of this wiki is to provide a public platform where people can learn about recent approaches to data analysis via topological and geometrical techniques. We take two complementary approaches to achieve this:
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<div style="font-size:162%; padding:.1em;">WELCOME TO [[STRUCTURES| STRUCTURES | EP Mathematics and Data]]</div>
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* The foundations of topology and geometry are well known to most mathematicians, but less so to researchers in the natural sciences, who we believe might benefit greatly from incorporating related techniques into their toolbox. To remedy this we collect the most important elements of the underlying theory and provide introductory articles to the relevant subjects.
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<div style="font-size:95%;"> a collaboration at the intersection of mathematics and data analysis based at Heidelberg University.</div>
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* Analysing and handling real-life data is an art well-developed in the natural sciences, but may at times seem enigmatic to mathematicians, who usually are not exposed to large sets of data on a daily basis. It is apparent that an implementation of the theoretical ideas on computers is paramount for applications, so we provide a list of existing software and offer a number of short tutorials. We furthermore present case studies of real-life applications.
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We hope that in establishing this wiki from these two perspectives, researchers from both mathematics and natural sciences are provided with the relevant background to easily approach each other, laying ground for fruitful collaborations.
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== Structure of this wiki ==
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<ul style="position:absolute; right:-1em; top:50%; margin-top:-2.4em; width:40%; min-width:25em; font-size:95%;">
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In this wiki a brief introduction to computational topological methods shall be given, beginning with an example analysis. A primer on computational topology theory follows, including the most important theorems of the topological constructions undertaken, leading over to a few recent research examples, in which these methods are applied. Subsequently, several numerical examples are given, which might serve as points of entry for individual first steps with computational topology methods.
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<li style="position:absolute; left:33%; top:0;">[[Portal:Society|Society]]</li>
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<li style="position:absolute; left:33%; top:1.6em;">[[Portal:Mathematics|Mathematics]]</li>
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<li style="position:absolute; left:33%; top:3.2em;">[[Portal:Science|Science]]</li>
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<li style="position:absolute; left:25%; top:0em;">[[Introductory reading|Introductory Literature]]</li>
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<li style="position:absolute; left:25%; top:1.6em;">[[List of Software]]</li>
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<li style="position:absolute; left:75%; top:0em;">[[Activities]]</li>
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<li style="position:absolute; left:75%; top:1.6em;"><strong>[[Main Page#Structure of this wiki|About]]</strong></li>
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About</h2>
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<div style="padding:0.1em 0.6em;">
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This wiki is centered around the [[STRUCTURES#Organization|exploratory project (EP)]] '''Mathematics and Data''' within [[STRUCTURES]] and is meant to provide a platform for collaborative work on data analysis across the fields of pure mathematics and natural sciences.
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</div>
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<div style="padding:0.1em 0.6em;">
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If you want to find out more about these topics you can follow one of the links below
 
* [[What is Topological Data Analysis? - A Primer]]
 
* [[What is Topological Data Analysis? - A Primer]]
 
* [[Mathematical Background]]
 
* [[Mathematical Background]]
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* [[List of Software]] and respective [[tutorials]]
 
* [[List of Software]] and respective [[tutorials]]
 
* [[Case Studies]]
 
* [[Case Studies]]
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== Current and Upcoming Activities ==
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{{main|Activities}}
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'''Lecture''' - ''[https://www.mathi.uni-heidelberg.de/~aott/geodata.html Geometric Methods in Data Analysis] -'' Tue 16:15 - 17:45 - Mathematikon SR C
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Upcoming Events</h2>
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May 27 11h-13h SR C <br>
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Mapper - Fabian Klos <br>
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Stability - Peter Albers
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Related Activities</h2>
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<div style="padding:0.1em 1em;"> {{main|Activities}} </div>
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'''Lecture''' <br>
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''[https://www.mathi.uni-heidelberg.de/~aott/geodata.html Geometric Methods in Data Analysis]'' <br>
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Tue 16:15 - 17:45, Mathematikon SR C
  
 
'''Block Seminar''' - ''[https://www.mathi.uni-heidelberg.de/~swoboda/teaching/SS19/Seminarankuendigung.pdf High-dimensional geometry and probability with view towards applications in data science] -'' June 28 & July 5 (all day) - Mathematikon SR 4
 
'''Block Seminar''' - ''[https://www.mathi.uni-heidelberg.de/~swoboda/teaching/SS19/Seminarankuendigung.pdf High-dimensional geometry and probability with view towards applications in data science] -'' June 28 & July 5 (all day) - Mathematikon SR 4
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'''Summer School''' - ''[https://sites.google.com/view/persistenthomologyandbarcodes/ Persistent Homology and Barcodes] -'' August 5-9 - JLU Gießen, Schloß Rauischholzhausen
 
'''Summer School''' - ''[https://sites.google.com/view/persistenthomologyandbarcodes/ Persistent Homology and Barcodes] -'' August 5-9 - JLU Gießen, Schloß Rauischholzhausen
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== Disclaimer ==
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One goal of this wiki is to help make information widely available and usefully related to other information. In this users and contributors are expected to follow traditional academic practice. Whenever useful, references and pointers to related literature are given, providing further information to the reader.  
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<h2 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
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Purpose
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</h2>
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<div style="padding:0.1em 0.6em;">
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The purpose of this wiki is to provide a public platform where people can learn about recent approaches to data analysis via topological and geometrical techniques. To achieve this we follow two complementary approaches:
 +
* The foundations of topology and geometry are well known to most mathematicians, but less so to researchers in the natural sciences, who we believe might benefit greatly from incorporating related techniques into their toolbox. To remedy this we collect the most important elements of the underlying theory and provide introductory articles to the relevant subjects.
 +
* Analysing and handling real-life data is an art well-developed in the natural sciences, but may at times seem enigmatic to mathematicians, who usually are not exposed to large sets of data on a daily basis. It is apparent that an implementation of the theoretical ideas on computers is paramount for applications, so we provide a list of existing software and offer a number of short tutorials. We furthermore present case studies of real-life applications.
 +
We hope that in establishing this wiki from these two perspectives, researchers from both mathematics and natural sciences are provided with the relevant background to easily approach each other, laying ground for fruitful collaborations.
 +
</div>
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<!--        DISCLAIMER        -->
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<h2 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
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Disclaimer</h2>
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<div style="padding:0.1em 0.6em;">
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One goal of this wiki is to help make information widely available and usefully related to other information. In this users and contributors are expected to follow traditional academic practice. Whenever useful, references for further reading are given, providing additional information to the reader.  
  
 
Nonetheless, this wiki is meant neither to be complete nor original.  
 
Nonetheless, this wiki is meant neither to be complete nor original.  
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== Contributing to this wiki ==
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Contributing to this wiki</h2>
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Everyone is invited to contribute to this wiki. If you are interested, get in touch with us via mail:
 
Everyone is invited to contribute to this wiki. If you are interested, get in touch with us via mail:
  
 
structures-hiwi@mathi.uni-heidelberg.de
 
structures-hiwi@mathi.uni-heidelberg.de
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Revision as of 16:58, 16 May 2019

a collaboration at the intersection of mathematics and data analysis based at Heidelberg University.
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