---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21841'
abstract:
- lang: eng
  text: The long-standing notion that genotypes map to phenotypes through simple one
    gene–one trait relationships continues to shape both research in the life sciences
    and public understanding, with implications for policy and funding priorities.
    Yet this paradigm is increasingly recognized as inadequate for explaining continuous
    phenotypic variation and the complex genetic architectures of the genotype–phenotype
    map. Modern genetics emerged from the early 20th-century synthesis of Mendelian
    and biometric schools of heredity, with R.A. Fisher demonstrating early on how
    multiple discrete loci could collectively produce continuous variation. Despite
    this fundamental insight, Mendelism—with its focus on single genes and standardized
    genetic backgrounds—became the dominant framework, shaping current genetics research
    and molecular biology as well as science education. The advent of large-scale
    genomic data has revealed yet again the limitations of this reductionist approach.
    Evidence from quantitative genetics now shows that most phenotypes arise from
    complex networks of many interdependent genes and their dynamic responses to environmental
    perturbations. Here we trace the historical roots of how Mendelian classical genetics
    departed from the biometric school to create the current predominant paradigm
    in genetics, despite fundamentally unresolved issues. Moving on from this one-sided
    paradigm will require systematic development of integrative, evolutionarily grounded
    experimental approaches that better capture the multigenic and context-dependent
    nature of inheritance. Achieving such an extended perspective will require methodological
    innovation, including advances in large-scale (e.g. automated) phenotyping. Dedicated
    research programs will be necessary to advance a new era of genetic research into
    the complex mechanisms underlying phenotypic variation.
acknowledgement: We thank a variety of further colleagues for the many inspiring discussions
  on the nature of heredity, especially the workshops in Berlin. Special thanks also
  to the Stellenbosch Institute for Advanced Studies (STIAS) to provide DT the leisure
  and freedom to write up the first version of this perspective. Thanks also to three
  reviewers who have helped to improve the manuscript. Two dedicated symposia on the
  topic were funded by the Max-Planck Society.
article_number: iyag024
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Diethard
  full_name: Tautz, Diethard
  last_name: Tautz
- first_name: Luisa F
  full_name: Pallares, Luisa F
  last_name: Pallares
- first_name: Leif
  full_name: Andersson, Leif
  last_name: Andersson
- first_name: Neda
  full_name: Barghi, Neda
  last_name: Barghi
- first_name: Nicholas H
  full_name: Barton, Nicholas H
  id: 4880FE40-F248-11E8-B48F-1D18A9856A87
  last_name: Barton
  orcid: 0000-0002-8548-5240
- first_name: Rachael
  full_name: Bay, Rachael
  last_name: Bay
- first_name: Yingguang Frank
  full_name: Chan, Yingguang Frank
  last_name: Chan
- first_name: Angela
  full_name: Hancock, Angela
  last_name: Hancock
- first_name: Tobias S
  full_name: Kaiser, Tobias S
  last_name: Kaiser
- first_name: Daniel
  full_name: Koenig, Daniel
  last_name: Koenig
- first_name: Zacharias
  full_name: Kontarakis, Zacharias
  last_name: Kontarakis
- first_name: Miriam
  full_name: Liedvogel, Miriam
  last_name: Liedvogel
- first_name: Juliette
  full_name: de Meaux, Juliette
  last_name: de Meaux
- first_name: Magnus
  full_name: Nordborg, Magnus
  last_name: Nordborg
- first_name: Abraham A
  full_name: Palmer, Abraham A
  last_name: Palmer
- first_name: Michael
  full_name: Purugganan, Michael
  last_name: Purugganan
- first_name: Christian
  full_name: Schlötterer, Christian
  last_name: Schlötterer
- first_name: Karl
  full_name: Schmid, Karl
  last_name: Schmid
- first_name: Didier Y R
  full_name: Stainier, Didier Y R
  last_name: Stainier
- first_name: Detlef
  full_name: Weigel, Detlef
  last_name: Weigel
- first_name: Jochen B W
  full_name: Wolf, Jochen B W
  last_name: Wolf
- first_name: Dieter
  full_name: Ebert, Dieter
  last_name: Ebert
- first_name: Greg
  full_name: Gibson, Greg
  last_name: Gibson
citation:
  ama: 'Tautz D, Pallares LF, Andersson L, et al. Beyond Mendel: A call to revisit
    the genotype–phenotype map through new experimental paradigms. <i>Genetics</i>.
    2026;232(4). doi:<a href="https://doi.org/10.1093/genetics/iyag024">10.1093/genetics/iyag024</a>'
  apa: 'Tautz, D., Pallares, L. F., Andersson, L., Barghi, N., Barton, N. H., Bay,
    R., … Gibson, G. (2026). Beyond Mendel: A call to revisit the genotype–phenotype
    map through new experimental paradigms. <i>Genetics</i>. Oxford University Press.
    <a href="https://doi.org/10.1093/genetics/iyag024">https://doi.org/10.1093/genetics/iyag024</a>'
  chicago: 'Tautz, Diethard, Luisa F Pallares, Leif Andersson, Neda Barghi, Nicholas
    H Barton, Rachael Bay, Yingguang Frank Chan, et al. “Beyond Mendel: A Call to
    Revisit the Genotype–Phenotype Map through New Experimental Paradigms.” <i>Genetics</i>.
    Oxford University Press, 2026. <a href="https://doi.org/10.1093/genetics/iyag024">https://doi.org/10.1093/genetics/iyag024</a>.'
  ieee: 'D. Tautz <i>et al.</i>, “Beyond Mendel: A call to revisit the genotype–phenotype
    map through new experimental paradigms,” <i>Genetics</i>, vol. 232, no. 4. Oxford
    University Press, 2026.'
  ista: 'Tautz D, Pallares LF, Andersson L, Barghi N, Barton NH, Bay R, Chan YF, Hancock
    A, Kaiser TS, Koenig D, Kontarakis Z, Liedvogel M, de Meaux J, Nordborg M, Palmer
    AA, Purugganan M, Schlötterer C, Schmid K, Stainier DYR, Weigel D, Wolf JBW, Ebert
    D, Gibson G. 2026. Beyond Mendel: A call to revisit the genotype–phenotype map
    through new experimental paradigms. Genetics. 232(4), iyag024.'
  mla: 'Tautz, Diethard, et al. “Beyond Mendel: A Call to Revisit the Genotype–Phenotype
    Map through New Experimental Paradigms.” <i>Genetics</i>, vol. 232, no. 4, iyag024,
    Oxford University Press, 2026, doi:<a href="https://doi.org/10.1093/genetics/iyag024">10.1093/genetics/iyag024</a>.'
  short: D. Tautz, L.F. Pallares, L. Andersson, N. Barghi, N.H. Barton, R. Bay, Y.F.
    Chan, A. Hancock, T.S. Kaiser, D. Koenig, Z. Kontarakis, M. Liedvogel, J. de Meaux,
    M. Nordborg, A.A. Palmer, M. Purugganan, C. Schlötterer, K. Schmid, D.Y.R. Stainier,
    D. Weigel, J.B.W. Wolf, D. Ebert, G. Gibson, Genetics 232 (2026).
date_created: 2026-05-07T08:53:40Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-05-18T07:51:26Z
day: '01'
ddc:
- '570'
department:
- _id: NiBa
doi: 10.1093/genetics/iyag024
external_id:
  pmid:
  - '41701356'
file:
- access_level: open_access
  checksum: 5a862c539f9dec4511277ad8927c549c
  content_type: application/pdf
  creator: dernst
  date_created: 2026-05-18T07:48:45Z
  date_updated: 2026-05-18T07:48:45Z
  file_id: '21890'
  file_name: 2026_Genetics_Tautz.pdf
  file_size: 542844
  relation: main_file
  success: 1
file_date_updated: 2026-05-18T07:48:45Z
fulldoi: https://doi.org/10.1093/genetics/iyag024
has_accepted_license: '1'
intvolume: '       232'
issue: '4'
keyword:
- classic genetics
- quantitative genetics
- genotype–phenotype map
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
pmid: 1
publication: Genetics
publication_identifier:
  eissn:
  - 1943-2631
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Beyond Mendel: A call to revisit the genotype–phenotype map through new experimental
  paradigms'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 232
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22291'
abstract:
- lang: eng
  text: Persistent homology is a fundamental tool in Topological Data Analysis. The
    associated algebraic structure is the persistence module, a sequence of vector
    spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute
    invariant known as the persistence diagram. However, this is no longer the case
    for maps between persistence modules (i.e. persistence maps). We propose a new
    invariant for persistence maps, consisting of a partial matching between the persistence
    diagrams of the domain and codomain modules. We show that this invariant is additive
    with respect to the direct sum decomposition of persistence maps, is more discriminative
    than the image module, and is computable in cubic time. Furthermore, we provide
    an implementation and demonstrate its efficiency by integrating it with edge collapse
    techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical
    contribution, we describe how to induce a persistence map between two flag complexes
    that have been independently simplified via edge collapses, even when a direct
    simplicial map between them is no longer available.
acknowledgement: This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR,
  under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant
  CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting
  this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also
  like to thank Lars M Salbu for fruitful discussions regarding the operators from
  Definition 4.1 and their relation with the order relations introduced in Definition
  3.2.
article_number: '102598'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rocio
  full_name: Gonzalez-Diaz, Rocio
  last_name: Gonzalez-Diaz
- first_name: Manuel
  full_name: Soriano Trigueros, Manuel
  id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
  last_name: Soriano Trigueros
  orcid: 0000-0003-2449-1433
- first_name: Alvaro
  full_name: Torras-Casas, Alvaro
  last_name: Torras-Casas
citation:
  ama: Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings
    induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138.
    doi:<a href="https://doi.org/10.1016/j.jsc.2026.102598">10.1016/j.jsc.2026.102598</a>
  apa: Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive
    partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.jsc.2026.102598">https://doi.org/10.1016/j.jsc.2026.102598</a>
  chicago: Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas.
    “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic
    Computation</i>. Elsevier, 2026. <a href="https://doi.org/10.1016/j.jsc.2026.102598">https://doi.org/10.1016/j.jsc.2026.102598</a>.
  ieee: R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial
    matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>,
    vol. 138. Elsevier, 2026.
  ista: Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial
    matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.
  mla: Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence
    Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026,
    doi:<a href="https://doi.org/10.1016/j.jsc.2026.102598">10.1016/j.jsc.2026.102598</a>.
  short: R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic
    Computation 138 (2026).
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: The code used for the computational experiments is available
  in https://github.com/Cimagroup/IBloFunMatch
date_created: 2026-07-13T09:43:38Z
date_published: 2026-06-23T00:00:00Z
date_updated: 2026-07-13T12:00:07Z
day: '23'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2026.102598
external_id:
  arxiv:
  - '2006.11100'
fulldoi: https://doi.org/10.1016/j.jsc.2026.102598
has_accepted_license: '1'
intvolume: '       138'
keyword:
- Persistence module
- Persistence map
- Persistent homology
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1016/j.jsc.2026.102598
mathsc:
- 55N31
- 16G20
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Symbolic Computation
publication_identifier:
  eissn:
  - 1095-855X
  issn:
  - 0747-7171
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: no
title: Additive partial matchings induced by persistence maps
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 138
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '22294'
abstract:
- lang: eng
  text: 'Modern computer systems store vast amounts of personal data, enabling advances
    in AI and ML but risking user privacy and trust. For privacy reasons, it is sometimes
    desired for an ML model to forget part of the data it was trained on. In this
    paper, we introduce a novel unlearning approach based on Forgetting Neural Networks
    (FNNs), a neuroscience-inspired architecture that explicitly encodes forgetting
    through multiplicative decay factors. While FNNs had previously been studied as
    a theoretical construct, we provide the first concrete implementation and demonstrate
    their effectiveness for targeted unlearning. We propose several variants with
    per-neuron forgetting factors, including rank-based assignments guided by activation
    levels, and evaluate them on MNIST and Fashion-MNIST benchmarks. Our method systematically
    removes information associated with forget sets while preserving performance on
    retained data. Membership inference attacks confirm the effectiveness of FNN-based
    unlearning in erasing information about the training data from the neural network.
    These results establish FNNs as a promising foundation for efficient and interpretable
    unlearning. '
article_processing_charge: No
arxiv: 1
author:
- first_name: Amartya
  full_name: Hatua, Amartya
  last_name: Hatua
- first_name: Trung
  full_name: Nguyen, Trung
  last_name: Nguyen
- first_name: Filip
  full_name: Cano Cordoba, Filip
  id: 708cad98-e86a-11ef-8098-bdae2d7c6af1
  last_name: Cano Cordoba
  orcid: 0000-0002-0783-904X
- first_name: Andrew
  full_name: Sung, Andrew
  last_name: Sung
citation:
  ama: 'Hatua A, Nguyen T, Cano Cordoba F, Sung A. Machine unlearning using forgetting
    neural networks. In: <i>Proceedings of the 18th International Conference on Agents
    and Artificial Intelligence</i>. Vol 2. SciTePress; 2026:1536-1546. doi:<a href="https://doi.org/10.5220/0014326500004052">10.5220/0014326500004052</a>'
  apa: 'Hatua, A., Nguyen, T., Cano Cordoba, F., &#38; Sung, A. (2026). Machine unlearning
    using forgetting neural networks. In <i>Proceedings of the 18th International
    Conference on Agents and Artificial Intelligence</i> (Vol. 2, pp. 1536–1546).
    Marbella, Spain: SciTePress. <a href="https://doi.org/10.5220/0014326500004052">https://doi.org/10.5220/0014326500004052</a>'
  chicago: Hatua, Amartya, Trung Nguyen, Filip Cano Cordoba, and Andrew Sung. “Machine
    Unlearning Using Forgetting Neural Networks.” In <i>Proceedings of the 18th International
    Conference on Agents and Artificial Intelligence</i>, 2:1536–46. SciTePress, 2026.
    <a href="https://doi.org/10.5220/0014326500004052">https://doi.org/10.5220/0014326500004052</a>.
  ieee: A. Hatua, T. Nguyen, F. Cano Cordoba, and A. Sung, “Machine unlearning using
    forgetting neural networks,” in <i>Proceedings of the 18th International Conference
    on Agents and Artificial Intelligence</i>, Marbella, Spain, 2026, vol. 2, pp.
    1536–1546.
  ista: 'Hatua A, Nguyen T, Cano Cordoba F, Sung A. 2026. Machine unlearning using
    forgetting neural networks. Proceedings of the 18th International Conference on
    Agents and Artificial Intelligence. ICAART: International Conference on Agents
    and Artificial Intelligence vol. 2, 1536–1546.'
  mla: Hatua, Amartya, et al. “Machine Unlearning Using Forgetting Neural Networks.”
    <i>Proceedings of the 18th International Conference on Agents and Artificial Intelligence</i>,
    vol. 2, SciTePress, 2026, pp. 1536–46, doi:<a href="https://doi.org/10.5220/0014326500004052">10.5220/0014326500004052</a>.
  short: A. Hatua, T. Nguyen, F. Cano Cordoba, A. Sung, in:, Proceedings of the 18th
    International Conference on Agents and Artificial Intelligence, SciTePress, 2026,
    pp. 1536–1546.
conference:
  end_date: 2026-03-08
  location: Marbella, Spain
  name: 'ICAART: International Conference on Agents and Artificial Intelligence'
  start_date: 2026-03-05
das_tickbox: '1'
date_created: 2026-07-13T09:46:46Z
date_published: 2026-06-30T00:00:00Z
date_updated: 2026-07-16T09:02:53Z
day: '30'
department:
- _id: ToHe
doi: 10.5220/0014326500004052
external_id:
  arxiv:
  - '2410.22374'
fulldoi: https://doi.org/10.5220/0014326500004052
intvolume: '         2'
keyword:
- Machine Unlearning
- Neuroscience-Inspired Machine Learning
- Membership Inference Attacks
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2410.22374
month: '06'
oa: 1
oa_version: Preprint
page: 1536-1546
publication: Proceedings of the 18th International Conference on Agents and Artificial
  Intelligence
publication_identifier:
  eissn:
  - 2184-433X
  isbn:
  - '9789897587962'
publication_status: published
publisher: SciTePress
quality_controlled: '1'
scopus_import: '1'
status: public
title: Machine unlearning using forgetting neural networks
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22693'
abstract:
- lang: eng
  text: We study torus-equivariant algebraic K-theory of affine Schubert varieties
    in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant
    Hochschild homology of perfect complexes, which has a geometric description in
    terms of global functions on certain fixed-point schemes. We prove that Fp-linearly,
    this comparison is an isomorphism. Our approach is quite constructive, resulting
    in new computations of these K-theory rings. We establish various structural results
    for equivariant perfect algebraic K-theory on the way; we believe these are of
    independent interest.
acknowledgement: "I would like to thank the following people for fruitful discussions,\r\nhelpful
  sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt,
  Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck,
  Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil
  Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further
  like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin
  a previous version.\r\nThis work was done during author’s PhD at the Institute of
  Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the
  Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847.
  For open access\r\npurposes, the author has applied a CC BY public copyright license
  to any author-accepted\r\nmanuscript version arising from this submission."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
  full_name: Löwit, Jakub
  id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
  last_name: Löwit
citation:
  ama: Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta
    Mathematica</i>. 2026. doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a>
  apa: Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection.
    <i>Documenta Mathematica</i>. EMS Press. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a>
  chicago: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.”
    <i>Documenta Mathematica</i>. EMS Press, 2026. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a>.
  ieee: J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” <i>Documenta
    Mathematica</i>. EMS Press, 2026.
  ista: Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta
    Mathematica.
  mla: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta
    Mathematica</i>, EMS Press, 2026, doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a>.
  short: J. Löwit, Documenta Mathematica (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-12T13:29:17Z
date_published: 2026-03-26T00:00:00Z
date_updated: 2026-08-26T06:53:54Z
day: '26'
ddc:
- '500'
department:
- _id: GradSch
- _id: TaHa
doi: 10.4171/dm/1064
external_id:
  arxiv:
  - '2409.18925'
fulldoi: https://doi.org/10.4171/dm/1064
has_accepted_license: '1'
keyword:
- equivariant algebraic K-theory
- perfection in positive characteristic
- affine Grassmannian
- affine Schubert varieties
- Dennis trace map
- equivariant Hochschild homology
- fixed-point schemes
- toric varieties
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.4171/DM/1064
mathsc:
- '19E08'
- 19L47
- 20G44
- 14G17
- 19D55
- 14F43
- 14L30
- 14D24
- 14M25
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
  grant_number: P35847
  name: Geometry of the tip of the global nilpotent cone
publication: Documenta Mathematica
publication_identifier:
  eissn:
  - 1431-0643
  issn:
  - 1431-0635
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
related_material:
  record:
  - id: '22694'
    relation: dissertation_contains
    status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Equivariant K-theory, affine Grassmannian and perfection
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22954'
abstract:
- lang: eng
  text: The aim of the present paper is to propose and study a dissipative variant
    of symplectic billiards within planar strictly convex domains. The associated
    billiard map is dissipative, thus it admits a compact invariant set, the so-called
    Birkhoff attractor. Its complexity depends on the rate of dissipation as well
    as on the geometry of the billiard table. We prove that (a) for strong dissipation,
    the Birkhoff attractor is a normally contracted graph over the zero section; (b)
    for mild dissipation, the Birkhoff attractor within a centrally symmetric domain
    is an indecomposable continuum whose restricted dynamics has positive topological
    entropy. We compare these results with those for dissipative Birkhoff billiards,
    studied in [15].
acknowledgement: Open access funding provided by Università degli Studi di Padova
  within the CRUI-CARE Agreement. A.F. is partially supported by the ANR project CoSyDy
  (ANR-CE40-0014), the ANR project GALS (ANR-23-CE40-0001) and PEPS project “Jeuns
  chercheurs et jeunes chercheuses” 2025. L.B. and O.B. have been partially supported
  by the PRIN project 2022FPZEES “Stability in Hamiltonian Dynamics and Beyond”.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Luca
  full_name: Baracco, Luca
  last_name: Baracco
- first_name: Olga
  full_name: Bernardi, Olga
  last_name: Bernardi
- first_name: Anna
  full_name: Florio, Anna
  last_name: Florio
- first_name: Alessandra
  full_name: Nardi, Alessandra
  id: 3e9c89df-ff0c-11f0-9fd7-c11e36d36769
  last_name: Nardi
citation:
  ama: Baracco L, Bernardi O, Florio A, Nardi A. Birkhoff attractors for dissipative
    symplectic billiards. <i>Journal of Dynamics and Differential Equations</i>. 2026.
    doi:<a href="https://doi.org/10.1007/s10884-026-10528-9">10.1007/s10884-026-10528-9</a>
  apa: Baracco, L., Bernardi, O., Florio, A., &#38; Nardi, A. (2026). Birkhoff attractors
    for dissipative symplectic billiards. <i>Journal of Dynamics and Differential
    Equations</i>. Springer. <a href="https://doi.org/10.1007/s10884-026-10528-9">https://doi.org/10.1007/s10884-026-10528-9</a>
  chicago: Baracco, Luca, Olga Bernardi, Anna Florio, and Alessandra Nardi. “Birkhoff
    Attractors for Dissipative Symplectic Billiards.” <i>Journal of Dynamics and Differential
    Equations</i>. Springer, 2026. <a href="https://doi.org/10.1007/s10884-026-10528-9">https://doi.org/10.1007/s10884-026-10528-9</a>.
  ieee: L. Baracco, O. Bernardi, A. Florio, and A. Nardi, “Birkhoff attractors for
    dissipative symplectic billiards,” <i>Journal of Dynamics and Differential Equations</i>.
    Springer, 2026.
  ista: Baracco L, Bernardi O, Florio A, Nardi A. 2026. Birkhoff attractors for dissipative
    symplectic billiards. Journal of Dynamics and Differential Equations.
  mla: Baracco, Luca, et al. “Birkhoff Attractors for Dissipative Symplectic Billiards.”
    <i>Journal of Dynamics and Differential Equations</i>, Springer, 2026, doi:<a
    href="https://doi.org/10.1007/s10884-026-10528-9">10.1007/s10884-026-10528-9</a>.
  short: L. Baracco, O. Bernardi, A. Florio, A. Nardi, Journal of Dynamics and Differential
    Equations (2026).
das_tickbox: '0'
date_created: 2026-09-17T11:05:59Z
date_published: 2026-07-27T00:00:00Z
date_updated: 2026-09-24T12:26:26Z
day: '27'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.1007/s10884-026-10528-9
external_id:
  arxiv:
  - '2509.13086'
fulldoi: https://doi.org/10.1007/s10884-026-10528-9
has_accepted_license: '1'
keyword:
- Dissipative symplectic billiard
- Birkhoff attractor
- Conformally symplectic twist map
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s10884-026-10528-9
month: '07'
oa: 1
oa_version: Published Version
publication: Journal of Dynamics and Differential Equations
publication_identifier:
  eissn:
  - 1572-9222
  issn:
  - 1040-7294
publication_status: epub_ahead
publisher: Springer
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Birkhoff attractors for dissipative symplectic billiards
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
_id: '5561'
abstract:
- lang: eng
  text: 'Graph matching problems as described in "Active Graph Matching for Automatic
    Joint Segmentation and Annotation of C. Elegans." by Kainmueller, Dagmar and Jug,
    Florian and Rother, Carsten and Myers, Gene, MICCAI 2014. Problems are in OpenGM2
    hdf5 format (see http://hciweb2.iwr.uni-heidelberg.de/opengm/) and a custom text
    format used by the feature matching solver described in "Feature Correspondence
    via Graph Matching: Models and Global Optimization." by Lorenzo Torresani, Vladimir
    Kolmogorov and Carsten Rother, ECCV 2008, code at http://pub.ist.ac.at/~vnk/software/GraphMatching-v1.02.src.zip. '
acknowledgement: We thank Vladimir Kolmogorov and Stephan Saalfeld forinspiring discussions.
article_processing_charge: No
author:
- first_name: Dagmar
  full_name: Kainmueller, Dagmar
  last_name: Kainmueller
- first_name: Florian
  full_name: Jug, Florian
  last_name: Jug
- first_name: Carsten
  full_name: Rother, Carsten
  last_name: Rother
- first_name: Gene
  full_name: Meyers, Gene
  last_name: Meyers
citation:
  ama: Kainmueller D, Jug F, Rother C, Meyers G. Graph matching problems for annotating
    C. Elegans. 2017. doi:<a href="https://doi.org/10.15479/AT:ISTA:57">10.15479/AT:ISTA:57</a>
  apa: Kainmueller, D., Jug, F., Rother, C., &#38; Meyers, G. (2017). Graph matching
    problems for annotating C. Elegans. Institute of Science and Technology Austria.
    <a href="https://doi.org/10.15479/AT:ISTA:57">https://doi.org/10.15479/AT:ISTA:57</a>
  chicago: Kainmueller, Dagmar, Florian Jug, Carsten Rother, and Gene Meyers. “Graph
    Matching Problems for Annotating C. Elegans.” Institute of Science and Technology
    Austria, 2017. <a href="https://doi.org/10.15479/AT:ISTA:57">https://doi.org/10.15479/AT:ISTA:57</a>.
  ieee: D. Kainmueller, F. Jug, C. Rother, and G. Meyers, “Graph matching problems
    for annotating C. Elegans.” Institute of Science and Technology Austria, 2017.
  ista: Kainmueller D, Jug F, Rother C, Meyers G. 2017. Graph matching problems for
    annotating C. Elegans, Institute of Science and Technology Austria, <a href="https://doi.org/10.15479/AT:ISTA:57">10.15479/AT:ISTA:57</a>.
  mla: Kainmueller, Dagmar, et al. <i>Graph Matching Problems for Annotating C. Elegans</i>.
    Institute of Science and Technology Austria, 2017, doi:<a href="https://doi.org/10.15479/AT:ISTA:57">10.15479/AT:ISTA:57</a>.
  short: D. Kainmueller, F. Jug, C. Rother, G. Meyers, (2017).
datarep_id: '57'
date_created: 2018-12-12T12:31:32Z
date_published: 2017-02-13T00:00:00Z
date_updated: 2024-02-21T13:46:31Z
day: '13'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.15479/AT:ISTA:57
file:
- access_level: open_access
  checksum: 3dc3e1306a66028a34181ebef2923139
  content_type: application/zip
  creator: system
  date_created: 2018-12-12T13:02:54Z
  date_updated: 2020-07-14T12:47:03Z
  file_id: '5614'
  file_name: IST-2017-57-v1+1_wormMatchingProblems.zip
  file_size: 327042819
  relation: main_file
file_date_updated: 2020-07-14T12:47:03Z
fulldoi: https://doi.org/10.15479/AT:ISTA:57
has_accepted_license: '1'
keyword:
- graph matching
- feature matching
- QAP
- MAP-inference
license: https://creativecommons.org/publicdomain/zero/1.0/
month: '02'
oa: 1
oa_version: Published Version
publisher: Institute of Science and Technology Austria
status: public
title: Graph matching problems for annotating C. Elegans
tmp:
  image: /images/cc_0.png
  legal_code_url: https://creativecommons.org/publicdomain/zero/1.0/legalcode
  name: Creative Commons Public Domain Dedication (CC0 1.0)
  short: CC0 (1.0)
type: research_data
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...