Zobrazeno 1 - 10
of 15
pro vyhledávání: '"Emerson G Escolar"'
Autor:
Yusuke Imoto, Tomonori Nakamura, Emerson G Escolar, Michio Yoshiwaki, Yoji Kojima, Yukihiro Yabuta, Yoshitaka Katou, Takuya Yamamoto, Yasuaki Hiraoka, Mitinori Saitou
Publikováno v:
Life Science Alliance. 5(12)
Single-cell RNA sequencing (scRNA-seq) can determine gene expression in numerous individual cells simultaneously, promoting progress in the biomedical sciences. However, scRNA-seq data are high-dimensional with substantial technical noise, including
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ead2fe8f6e355f9e52f368310ff087b0
http://hdl.handle.net/2433/275925
http://hdl.handle.net/2433/275925
Autor:
Emerson G. Escolar, Mickaël Buchet
Publikováno v:
Journal of Applied and Computational Topology. 4:387-424
A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with finite su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6f0d5e152bb9949229f19d98d41a8640
https://doi.org/10.1007/s41468-020-00053-z
https://doi.org/10.1007/s41468-020-00053-z
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing.
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, sh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80141f88761a08c038349a556af3c4a1
https://doi.org/10.1007/s00200-021-00530-7
https://doi.org/10.1007/s00200-021-00530-7
Publikováno v:
Computational Geometry. :101879
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the classification of all indecomposable modules is known to be a wild proble
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e59e7cdad9ed4f7c3461c20b077bbbc8
https://doi.org/10.1016/j.comgeo.2022.101879
https://doi.org/10.1016/j.comgeo.2022.101879
Publikováno v:
SSRN Electronic Journal.
Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. We propose a new method to characterize firms’ inventive activities via topological data analysis (TDA) that repre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b3f5826e7a8ac3f3804b7d06af42aa46
https://doi.org/10.2139/ssrn.3445703
https://doi.org/10.2139/ssrn.3445703
Publikováno v:
Japan Journal of Industrial and Applied Mathematics. 36:97-130
The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persiste
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf2186514a09517555a80fb30978915b
https://doi.org/10.1007/s13160-018-0331-y
https://doi.org/10.1007/s13160-018-0331-y
Autor:
Kaname Matsue, Emerson G. Escolar, Yasumasa Nishiura, Yasuaki Hiraoka, Akihiko Hirata, Takenobu Nakamura
Publikováno v:
Proceedings of the National Academy of Sciences. 113:7035-7040
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is gi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92d6259a6305ebb95ddf49a9d4f44637
https://doi.org/10.1073/pnas.1520877113
https://doi.org/10.1073/pnas.1520877113
Autor:
Yasuaki Hiraoka, Emerson G. Escolar
Publikováno v:
Discrete & Computational Geometry. 55:100-157
We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems. A new alge
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fe189abed13fd89a30c22853203bd2a
https://doi.org/10.1007/s00454-015-9746-2
https://doi.org/10.1007/s00454-015-9746-2
Autor:
Yasuaki Hiraoka, Emerson G. Escolar
Publikováno v:
Journal of the Indonesian Mathematical Society, Vol 20, Iss 1, Pp 47-75 (2014)
A paper by Mischaikow and Nanda [14] uses filtered acyclic matchingsto form a Morse filtration for a filtered complex. The Morse filtration is smallerin size, yet has persistent homology equivalent to that of the original. We give anextension of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::668b09c02c0e9de9781d40b2b0d4e94b
https://doi.org/10.22342/jims.20.1.177.47-75
https://doi.org/10.22342/jims.20.1.177.47-75
Autor:
Emerson G. Escolar, Yasuaki Hiraoka
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9784431561026
This is a summary paper of Escolar and Hiraoka (Persistence modules on commutative ladders of finite type. Discrete Comput Geom 55, 100–157 (2016)) which presents an extension of persistence modules as representations on quivers with nontrivial rel
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b7615a00d50269d696a97103867bd54
https://doi.org/10.1007/978-4-431-56104-0_4
https://doi.org/10.1007/978-4-431-56104-0_4
