17788065ecfc — Benedikt Fluhr <http://bfluhr.com> 6 years ago
Added Citations to recent Research

Added citations to both, the recent paper by
de Silva, Munch, and Stefanou and our poster.
4 files changed, 34 insertions(+), 1 deletions(-)

A => bib/deSilva17.bib
M bib/diFabio14.bib
A => bib/fluhr17.bib
M intro.md
A => bib/deSilva17.bib +10 -0
@@ 0,0 1,10 @@ 
+@article{deSilva2017b,
+author = {Vin {de Silva} and Elizabeth Munch and Anastasios Stefanou},
+eprint = {1706.04095v1},
+eprintclass = {math.CT},
+eprinttype = {arXiv},
+journal = {arXiv:1706.04095v1},
+link = {http://arxiv.org/pdf/1706.04095v1},
+title = {Theory of interleavings on $[0,\infty)$-actegories},
+year = {2017}
+}

          
M bib/diFabio14.bib +1 -1
@@ 1,5 1,5 @@ 
 @article{diFabio2014,
-  author    = {Barbara Di Fabio and
+  author    = {Barbara {Di Fabio} and
                Claudia Landi},
   title     = {The edit distance for Reeb graphs of surfaces},
   journal   = {CoRR},

          
A => bib/fluhr17.bib +10 -0
@@ 0,0 1,10 @@ 
+@misc{fluhr2017,
+ author       = {Benedikt Fluhr},
+ title        = {Generic 1{D}-Interleavings},
+ year         = {2017},
+ type         = {Poster},
+ language     = {en},
+ url          = {http://bfluhr.com/bucket/poster-acat01.pdf},
+ howpublished = {Spring School on Applied and Computational Algebraic Topology \url{https://www.him.uni-bonn.de/programs/future-programs/future-trimester-programs/acat-2017/spring-school/schedule/} April 25th},
+ organization = {Hausdorff Research Institute for Mathematics},
+}

          
M intro.md +13 -0
@@ 416,3 416,16 @@ There is much more prior art and the pap
 our primary references.
 Most of the papers mentioned by @deSilva2016 and @bubenik2014
 in their introductions are antecedents to our work as well.
+We presented some of the abstract ideas we use here in the form
+of a poster [@fluhr2017].
+Little did we know that @deSilva2017b
+were developing a very similar framework.
+Some differences between their approach and ours is that
+they work in a very general setup with an arbitrary metric space
+whereas we merely consider the real numbers as a base space.
+This made it feasible for us to treat
+the absolute and the relative interleaving distance in one go.
+Very loosely speaking one might say, that in applying this theory
+to topological data analysis @deSilva2017b
+use the approach of *thickening* whereas we mostly use the approach
+of *smoothing*.