---
OA_place: publisher
OA_type: free access
_id: '18443'
abstract:
- lang: eng
text: "In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry
relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli
spaces. As a consequence, they\r\nconjecture an equivalence between categories
of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given
by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable
systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler
structures and the\r\ncorresponding branes on affine torus bundles. We use the
techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures
are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for
generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality
between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles
and connections. This T-duality in the appropriate context specializes to\r\nT-duality
between BBB and BAA-branes.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Maria A
full_name: Sisak, Maria A
id: 44A03D04-AEA4-11E9-B225-EA2DE6697425
last_name: Sisak
citation:
ama: Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443
apa: Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute
of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443
chicago: Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of
Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443.
ieee: M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science
and Technology Austria, 2024.
ista: Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science
and Technology Austria.
mla: Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of
Science and Technology Austria, 2024, doi:10.15479/at:ista:18443.
short: M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science
and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-10-19T12:00:37Z
date_published: 2024-10-24T00:00:00Z
date_updated: 2026-04-07T12:42:44Z
day: '24'
ddc:
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: TaHa
doi: 10.15479/at:ista:18443
file:
- access_level: open_access
checksum: 8c4893e726aaa4b3efb82758da9b6851
content_type: application/pdf
creator: msisak
date_created: 2024-10-23T14:42:45Z
date_updated: 2024-10-23T14:42:45Z
file_id: '18467'
file_name: MASisak_dissertation.pdf
file_size: 1672547
relation: main_file
success: 1
- access_level: closed
checksum: 1831b072e861a1e5481024ca9d02b036
content_type: application/x-zip-compressed
creator: msisak
date_created: 2024-10-23T14:43:56Z
date_updated: 2024-10-24T08:09:13Z
file_id: '18468'
file_name: MASisak_source.zip
file_size: 617913
relation: source_file
file_date_updated: 2024-10-24T08:09:13Z
has_accepted_license: '1'
keyword:
- hyperkaehler geometry
- branes
- mirror symmetry
- T-duality
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '10'
oa: 1
oa_version: Published Version
page: '178'
project:
- _id: 6286e8c4-2b32-11ec-9570-f5297902f67f
grant_number: '26069'
name: Branes on hyperkähler manifolds
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
title: T-dual branes on hyperkähler manifolds
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
_id: '17485'
abstract:
- lang: eng
text: "Large language models (LLMs) have made tremendous progress in the past few
years, from being able to generate coherent text to matching or surpassing humans
in a wide variety of creative, knowledge or reasoning tasks. Much of this can
be attributed to massively increased scale, both in the size of the model as well
as the amount of training data, from 100s of millions to 100s of billions, or
even trillions. This trend is expected to continue, which, although exciting,
also raises major practical concerns. Already today's 100+ billion parameter LLMs
require top-of-the-line hardware just to run. Hence, it is clear that sustaining
these developments will require significant efficiency advances.\r\n\r\nHistorically,
one of the most practical ways of improving model efficiency has been compression,
especially in the form of sparsity or quantization. While this has been studied
extensively in the past, existing accurate methods are all designed for models
around 100 million parameters; scaling them up to ones literally 1000x larger
is highly challenging. In this thesis, we introduce a new unified sparsification
and quantization approach OBC, which through additional algorithmic enhancements
leads to GPTQ and SparseGPT, the first techniques fast and accurate enough to
compress 100+ billion parameter models to 4- or even 3-bit precision and 50% weight-sparsity,
respectively. Additionally, we show how weight-only quantizion does not just bring
space savings but also up to 4.5x faster generation speed, via custom GPU kernels.\r\n\r\nIn
fact, we show for the first time that it is possible to develop an FP16 times
INT4 mixed-precision matrix multiplication kernel, called Marlin, which comes
close to simultaneously maximizing both memory and compute utilization, making
weight-only quantization highly practical even for multi-user serving. Further,
we demonstrate that GPTQ can be scaled to widely overparametrized trillion-parameter
models, where extreme sub-1-bit compression rates can be achieved without any
inference slow-down, by co-designing a bespoke entropy coding scheme together
with an efficient kernel.\r\n\r\nFinally, we also study compression from the perspective
of someone with access to massive amounts of compute resources for training large
models completely from scratch. Here the key questions evolve around the joint
scaling behavior between compression, model size, and amount of training data
used. Based on extensive experimental results for both vision and text models,
we introduce the first scaling law which accurately captures the relationship
between weight-sparsity, number of non-zero weights and data. This further allows
us to characterize the optimal sparsity, which we find to increase the longer
a fixed cost model is being trained.\r\n\r\nOverall, this thesis presents contributions
to three different angles of large model efficiency: affordable but accurate algorithms,
highly efficient systems implementations, and fundamental scaling laws for compressed
training."
acknowledged_ssus:
- _id: ScienComp
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Elias
full_name: Frantar, Elias
id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f
last_name: Frantar
citation:
ama: 'Frantar E. Compressing large neural networks : Algorithms, systems and scaling
laws. 2024. doi:10.15479/at:ista:17485'
apa: 'Frantar, E. (2024). Compressing large neural networks : Algorithms, systems
and scaling laws. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17485'
chicago: 'Frantar, Elias. “Compressing Large Neural Networks : Algorithms, Systems
and Scaling Laws.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17485.'
ieee: 'E. Frantar, “Compressing large neural networks : Algorithms, systems and
scaling laws,” Institute of Science and Technology Austria, 2024.'
ista: 'Frantar E. 2024. Compressing large neural networks : Algorithms, systems
and scaling laws. Institute of Science and Technology Austria.'
mla: 'Frantar, Elias. Compressing Large Neural Networks : Algorithms, Systems
and Scaling Laws. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17485.'
short: 'E. Frantar, Compressing Large Neural Networks : Algorithms, Systems and
Scaling Laws, Institute of Science and Technology Austria, 2024.'
corr_author: '1'
date_created: 2024-09-02T11:01:48Z
date_published: 2024-09-05T00:00:00Z
date_updated: 2026-04-07T12:43:04Z
day: '05'
ddc:
- '000'
degree_awarded: PhD
department:
- _id: GradSch
- _id: DaAl
doi: 10.15479/at:ista:17485
ec_funded: 1
file:
- access_level: closed
checksum: 5d785645805a78c5b4ce7cc3df557b09
content_type: application/zip
creator: efrantar
date_created: 2024-09-05T12:04:11Z
date_updated: 2024-09-05T12:04:11Z
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file_size: 1615167
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creator: efrantar
date_created: 2024-09-06T16:24:59Z
date_updated: 2024-09-06T16:24:59Z
file_id: '17880'
file_name: frantar_thesis_final.pdf
file_size: 2376611
relation: main_file
success: 1
file_date_updated: 2024-09-06T16:24:59Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '129'
project:
- _id: 268A44D6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '805223'
name: Elastic Coordination for Scalable Machine Learning
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '18062'
relation: part_of_dissertation
status: public
- id: '18061'
relation: part_of_dissertation
status: public
- id: '17378'
relation: part_of_dissertation
status: public
- id: '17087'
relation: part_of_dissertation
status: public
- id: '14458'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
title: 'Compressing large neural networks : Algorithms, systems and scaling laws'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '18061'
abstract:
- lang: eng
text: 'Mixture-of-Experts (MoE) architectures offer a general solution to the high
inference costs of large language models (LLMs) via sparse routing, bringing faster
and more accurate models, at the cost of massive parameter counts. For example,
the SwitchTransformer-c2048 model has 1.6 trillion parameters, requiring 3.2TB
of accelerator memory to run efficiently, which makes practical deployment challenging
and expensive. In this paper, we present a solution to this memory problem, in
form of a new compression and execution framework called QMoE. Specifically, QMoE
consists of a scalable algorithm which accurately compresses trillion-parameter
MoEs to less than 1 bit per parameter, in a custom format co-designed with bespoke
GPU decoding kernels to facilitate efficient end-to-end compressed inference,
with minor runtime overheads relative to uncompressed execution. Concretely, QMoE
can compress the 1.6 trillion parameter SwitchTransformer-c2048 model to less
than 160GB (20x compression, 0.8 bits per parameter) at only minor accuracy loss,
in less than a day on a single GPU. This enables, for the first time, the execution
of a trillion-parameter model on affordable commodity hardware, like a single
server with 4x NVIDIA A6000 or 8x NVIDIA 3090 GPUs, at less than 5% runtime overhead
relative to ideal uncompressed inference. The anonymized code is available at:
github.com/mlsys24-qmoe/qmoe.'
article_processing_charge: No
author:
- first_name: Elias
full_name: Frantar, Elias
id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f
last_name: Frantar
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
citation:
ama: 'Frantar E, Alistarh D-A. QMoE: Sub-1-bit compression of trillion parameter
models. In: Gibbons P, Pekhimenko G, De Sa C, eds. Proceedings of Machine
Learning and Systems. Vol 6. ; 2024.'
apa: 'Frantar, E., & Alistarh, D.-A. (2024). QMoE: Sub-1-bit compression of
trillion parameter models. In P. Gibbons, G. Pekhimenko, & C. De Sa (Eds.),
Proceedings of Machine Learning and Systems (Vol. 6). Santa Clara, CA,
USA.'
chicago: 'Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression
of Trillion Parameter Models.” In Proceedings of Machine Learning and Systems,
edited by P. Gibbons, G. Pekhimenko, and C. De Sa, Vol. 6, 2024.'
ieee: 'E. Frantar and D.-A. Alistarh, “QMoE: Sub-1-bit compression of trillion parameter
models,” in Proceedings of Machine Learning and Systems, Santa Clara,
CA, USA, 2024, vol. 6.'
ista: 'Frantar E, Alistarh D-A. 2024. QMoE: Sub-1-bit compression of trillion parameter
models. Proceedings of Machine Learning and Systems. MLSys: Machine Learning
and Systems vol. 6.'
mla: 'Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression of Trillion
Parameter Models.” Proceedings of Machine Learning and Systems, edited
by P. Gibbons et al., vol. 6, 2024.'
short: E. Frantar, D.-A. Alistarh, in:, P. Gibbons, G. Pekhimenko, C. De Sa (Eds.), Proceedings
of Machine Learning and Systems, 2024.
conference:
end_date: 2024-05-16
location: Santa Clara, CA, USA
name: 'MLSys: Machine Learning and Systems'
start_date: 2024-05-13
corr_author: '1'
date_created: 2024-09-13T10:01:38Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2026-04-07T12:43:03Z
day: '01'
department:
- _id: DaAl
editor:
- first_name: P.
full_name: Gibbons, P.
last_name: Gibbons
- first_name: G.
full_name: Pekhimenko, G.
last_name: Pekhimenko
- first_name: C.
full_name: De Sa, C.
last_name: De Sa
intvolume: ' 6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://proceedings.mlsys.org/paper_files/paper/2024/hash/c74b624843218d9b6713fcf299d6d5e4-Abstract-Conference.html
month: '05'
oa: 1
oa_version: Published Version
publication: ' Proceedings of Machine Learning and Systems'
publication_status: published
quality_controlled: '1'
related_material:
record:
- id: '17485'
relation: dissertation_contains
status: public
status: public
title: 'QMoE: Sub-1-bit compression of trillion parameter models'
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 6
year: '2024'
...
---
_id: '18062'
abstract:
- lang: eng
text: 'We explore the impact of parameter sparsity on the scaling behavior of Transformers
trained on massive datasets (i.e., "foundation models"), in both vision and language
domains. In this setting, we identify the first scaling law describing the relationship
between weight sparsity, number of non-zero parameters, and amount of training
data, which we validate empirically across model and data scales; on ViT/JFT-4B
and T5/C4. These results allow us to characterize the "optimal sparsity", the
sparsity level which yields the best performance for a given effective model size
and training budget. For a fixed number of non-zero parameters, we identify that
the optimal sparsity increases with the amount of data used for training. We also
extend our study to different sparsity structures (such as the hardware-friendly
n:m pattern) and strategies (such as starting from a pretrained dense model).
Our findings shed light on the power and limitations of weight sparsity across
various parameter and computational settings, offering both theoretical understanding
and practical implications for leveraging sparsity towards computational efficiency
improvements. We provide pruning and scaling law fitting code at: github.com/google-research/jaxpruner/tree/main/jaxpruner/projects/bigsparse.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Elias
full_name: Frantar, Elias
id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f
last_name: Frantar
- first_name: Carlos Riquelme
full_name: Ruiz, Carlos Riquelme
last_name: Ruiz
- first_name: Neil
full_name: Houlsby, Neil
last_name: Houlsby
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
- first_name: Utku
full_name: Evci, Utku
last_name: Evci
citation:
ama: 'Frantar E, Ruiz CR, Houlsby N, Alistarh D-A, Evci U. Scaling laws for sparsely-connected
foundation models. In: The Twelfth International Conference on Learning Representations.
; 2024.'
apa: Frantar, E., Ruiz, C. R., Houlsby, N., Alistarh, D.-A., & Evci, U. (2024).
Scaling laws for sparsely-connected foundation models. In The Twelfth International
Conference on Learning Representations. Vienna, Austria.
chicago: Frantar, Elias, Carlos Riquelme Ruiz, Neil Houlsby, Dan-Adrian Alistarh,
and Utku Evci. “Scaling Laws for Sparsely-Connected Foundation Models.” In The
Twelfth International Conference on Learning Representations, 2024.
ieee: E. Frantar, C. R. Ruiz, N. Houlsby, D.-A. Alistarh, and U. Evci, “Scaling
laws for sparsely-connected foundation models,” in The Twelfth International
Conference on Learning Representations, Vienna, Austria, 2024.
ista: 'Frantar E, Ruiz CR, Houlsby N, Alistarh D-A, Evci U. 2024. Scaling laws for
sparsely-connected foundation models. The Twelfth International Conference on
Learning Representations. ICLR: International Conference on Learning Representations.'
mla: Frantar, Elias, et al. “Scaling Laws for Sparsely-Connected Foundation Models.”
The Twelfth International Conference on Learning Representations, 2024.
short: E. Frantar, C.R. Ruiz, N. Houlsby, D.-A. Alistarh, U. Evci, in:, The Twelfth
International Conference on Learning Representations, 2024.
conference:
end_date: 2024-05-07
location: Vienna, Austria
name: 'ICLR: International Conference on Learning Representations'
start_date: 2024-05-07
corr_author: '1'
date_created: 2024-09-13T10:31:08Z
date_published: 2024-01-16T00:00:00Z
date_updated: 2026-04-07T12:43:03Z
day: '16'
department:
- _id: DaAl
external_id:
arxiv:
- '2309.08520'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/forum?id=i9K2ZWkYIP
month: '01'
oa: 1
oa_version: Published Version
publication: The Twelfth International Conference on Learning Representations
publication_status: published
quality_controlled: '1'
related_material:
record:
- id: '17485'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Scaling laws for sparsely-connected foundation models
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: publisher
_id: '17208'
abstract:
- lang: eng
text: "Can current quantum computers provide a speedup over their classical counterparts
for some kinds of problems? In this thesis, with a focus on ground state search/preparation,
we address some of the challenges that both quantum annealing and variational
quantum algorithms suffer from, hindering any possible practical speedup in comparison
to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we
study the performance of quantum annealing for solving a particular combinatorial
optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem
is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$.
We consider how modifying the initial problem, by adding more interaction terms
to the corresponding Hamiltonian, leads to the emergence of a first-order phase
transition during the annealing process. This phenomenon causes the total annealing
duration, $T$, required to prepare the ground state of $H_C$ with a high probability
to increase exponentially with the size of the problem. Our findings indicate
that with the growing complexity of problem instances, the likelihood of encountering
first-order phase transitions also increases, making quantum annealing an impractical
solution for these types of combinatorial optimization problems.\r\n\r\nIn the
second part, we focus on the problem of barren plateaus in generic variational
quantum algorithms. Barren plateaus correspond to flat regions in the parameter
space where the gradient of the cost function is zero in expectation, and with
the variance decaying exponentially with the system size, thus obstructing an
efficient parameter optimization. We propose an algorithm to circumvent Barren
Plateaus by monitoring the entanglement entropy of k-local reduced density matrices,
alongside a method for estimating entanglement entropy via classical shadow tomography.
We illustrate the approach with the paradigmatic example of the variational quantum
eigensolver, and show that our algorithm effectively avoids barren plateaus in
the initialization as well as during the optimization stage. \r\n\r\nLastly, in
the last two Chapters of this thesis, we focus on the quantum approximate optimization
algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial
optimization problems in near-term quantum devices. Specifically, we focus on
how to develop rigorous initialization strategies with guarantee improvement.
Our motivation for this study lies in that for random initialization, the optimization
typically leads to local minima with poor performance. Our main result corresponds
to the analytical construction of index-1 saddle points or transition states,
stationary points with a single direction of descent, as a tool for systematically
exploring the QAOA optimization landscape. This leads us to propose a novel greedy
parameter initialization strategy that guarantees for the energy to decrease with
an increasing number of circuit layers. Furthermore, with precise estimates for
the negative Hessian eigenvalue and its eigenvector, we establish a lower bound
for energy improvement following a QAOA iteration."
acknowledged_ssus:
- _id: ScienComp
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Raimel A
full_name: Medina Ramos, Raimel A
id: CE680B90-D85A-11E9-B684-C920E6697425
last_name: Medina Ramos
orcid: 0000-0002-5383-2869
citation:
ama: Medina Ramos RA. Exploring the optimization landscape of variational quantum
algorithms. 2024. doi:10.15479/at:ista:17208
apa: Medina Ramos, R. A. (2024). Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17208
chicago: Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational
Quantum Algorithms.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17208.
ieee: R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum
algorithms,” Institute of Science and Technology Austria, 2024.
ista: Medina Ramos RA. 2024. Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria.
mla: Medina Ramos, Raimel A. Exploring the Optimization Landscape of Variational
Quantum Algorithms. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17208.
short: R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum
Algorithms, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-09T09:14:24Z
date_published: 2024-07-09T00:00:00Z
date_updated: 2026-04-07T12:43:22Z
day: '09'
ddc:
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: MaSe
doi: 10.15479/at:ista:17208
ec_funded: 1
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date_updated: 2024-07-10T11:34:09Z
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checksum: 6724a95bec772dbabc0111b9f08a805e
content_type: application/pdf
creator: rmedinar
date_created: 2024-07-17T09:23:24Z
date_updated: 2024-07-17T09:23:24Z
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relation: main_file
success: 1
file_date_updated: 2024-07-17T09:23:24Z
has_accepted_license: '1'
keyword:
- Quantum computing
- Variational Quantum Algorithms
- Optimization
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '133'
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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- id: '10545'
relation: part_of_dissertation
status: public
- id: '10067'
relation: part_of_dissertation
status: public
- id: '17222'
relation: part_of_dissertation
status: public
- id: '13125'
relation: part_of_dissertation
status: public
- id: '11471'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
title: Exploring the optimization landscape of variational quantum algorithms
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short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: repository
_id: '17222'
abstract:
- lang: eng
text: "The quantum approximate optimization algorithm (QAOA) uses a quantum computer\r\nto
implement a variational method with $2p$ layers of alternating unitary\r\noperators,
optimized by a classical computer to minimize a cost function. While\r\nrigorous
performance guarantees exist for the QAOA at small depths $p$, the\r\nbehavior
at large depths remains less clear, though simulations suggest\r\nexponentially
fast convergence for certain problems. In this work, we gain\r\ninsights into
the deep QAOA using an analytic expansion of the cost function\r\naround transition
states. Transition states are constructed in a recursive\r\nmanner: from the local
minima of the QAOA with $p$ layers we obtain transition\r\nstates of the QAOA
with $p+1$ layers, which are stationary points characterized\r\nby a unique direction
of negative curvature. We construct an analytic estimate\r\nof the negative curvature
and the corresponding direction in parameter space at\r\neach transition state.
The expansion of the QAOA cost function along the\r\nnegative direction to the
quartic order gives a lower bound of the QAOA cost\r\nfunction improvement. We
provide physical intuition behind the analytic\r\nexpressions for the local curvature
and quartic expansion coefficient. Our\r\nnumerical study confirms the accuracy
of our approximations and reveals that\r\nthe obtained bound and the true value
of the QAOA cost function gain have a\r\ncharacteristic exponential decrease with
the number of layers $p$, with the\r\nbound decreasing more rapidly. Our study
establishes an analytical method for\r\nrecursively studying the QAOA that is
applicable in the regime of high circuit\r\ndepth."
article_number: '2405.10125'
article_processing_charge: No
arxiv: 1
author:
- first_name: Raimel A
full_name: Medina Ramos, Raimel A
id: CE680B90-D85A-11E9-B684-C920E6697425
last_name: Medina Ramos
orcid: 0000-0002-5383-2869
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement
of the quantum approximate optimization algorithm. arXiv. doi:10.48550/arXiv.2405.10125
apa: Medina Ramos, R. A., & Serbyn, M. (n.d.). A recursive lower bound on the
energy improvement of the quantum approximate optimization algorithm. arXiv.
https://doi.org/10.48550/arXiv.2405.10125
chicago: Medina Ramos, Raimel A, and Maksym Serbyn. “A Recursive Lower Bound on
the Energy Improvement of the Quantum Approximate Optimization Algorithm.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2405.10125.
ieee: R. A. Medina Ramos and M. Serbyn, “A recursive lower bound on the energy improvement
of the quantum approximate optimization algorithm,” arXiv. .
ista: Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement
of the quantum approximate optimization algorithm. arXiv, 2405.10125.
mla: Medina Ramos, Raimel A., and Maksym Serbyn. “A Recursive Lower Bound on the
Energy Improvement of the Quantum Approximate Optimization Algorithm.” ArXiv,
2405.10125, doi:10.48550/arXiv.2405.10125.
short: R.A. Medina Ramos, M. Serbyn, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-07-10T13:12:09Z
date_published: 2024-05-16T00:00:00Z
date_updated: 2026-04-07T12:43:22Z
day: '16'
department:
- _id: MaSe
doi: 10.48550/arXiv.2405.10125
external_id:
arxiv:
- '2405.10125'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2405.10125
month: '05'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
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relation: dissertation_contains
status: public
status: public
title: A recursive lower bound on the energy improvement of the quantum approximate
optimization algorithm
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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: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: publisher
_id: '18132'
abstract:
- lang: eng
text: "In this thesis, we are dealing with both arithmetic and geometric problems
coming from the\r\nstudy of rational points with a particular focus on function
fields over finite fields:\r\n(1) Using the circle method we produce upper bounds
for the number of rational points of\r\nbounded height on diagonal cubic surfaces
and fourfolds over Fq(t). This is based on\r\njoint work with Leonhard Hochfilzer.\r\n(2)
We study rational points on smooth complete intersections X defined by cubic and\r\nquadratic
hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square”\r\ndeveloped
by Vishe [202] and use the circle method with a Kloosterman refinement to\r\nestablish
an asymptotic formula for the number of rational points of bounded height on\r\nX
when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation.\r\n(3)
In joint work with Hochfilzer, we obtain upper bounds for the number of rational
points of\r\nbounded height on del Pezzo surfaces of low degree over any global
field. Our approach\r\nis to take hyperplane sections, which reduces the problem
to uniform estimates for the\r\nnumber of rational points on curves.\r\n(4) We
develop a version of the circle method capable of counting Fq-points on jet schemes\r\nof
moduli spaces of rational curves on hypersurfaces. Combining this with a spreading\r\nout
argument and a result of Mustaţă [150], this allows us to show that these moduli\r\nspaces
only have canonical singularities under suitable assumptions on the degree and
the\r\ndimension.\r\nIn addition, we give an overview of guiding questions and
conjectures in the field of rational\r\npoints and explain the basic mechanism
underlying the circle method.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
citation:
ama: Glas J. Counting rational points over function fields. 2024. doi:10.15479/at:ista:18132
apa: Glas, J. (2024). Counting rational points over function fields. Institute
of Science and Technology Austria. https://doi.org/10.15479/at:ista:18132
chicago: Glas, Jakob. “Counting Rational Points over Function Fields.” Institute
of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18132.
ieee: J. Glas, “Counting rational points over function fields,” Institute of Science
and Technology Austria, 2024.
ista: Glas J. 2024. Counting rational points over function fields. Institute of
Science and Technology Austria.
mla: Glas, Jakob. Counting Rational Points over Function Fields. Institute
of Science and Technology Austria, 2024, doi:10.15479/at:ista:18132.
short: J. Glas, Counting Rational Points over Function Fields, Institute of Science
and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-09-23T18:58:08Z
date_published: 2024-09-23T00:00:00Z
date_updated: 2026-04-07T12:53:54Z
day: '23'
ddc:
- '512'
degree_awarded: PhD
department:
- _id: GradSch
- _id: TiBr
doi: 10.15479/at:ista:18132
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oa: 1
oa_version: Published Version
page: '195'
project:
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grant_number: P36278
name: Rational curves via function field analytic number theory
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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status: public
- id: '18294'
relation: part_of_dissertation
status: public
- id: '18295'
relation: part_of_dissertation
status: public
- id: '18173'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
title: Counting rational points over function fields
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type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '18173'
abstract:
- lang: eng
text: Using a two-dimensional version of the delta method, we establish an asymptotic
formula for the number of rational points of bounded height on non-singular complete
intersections of cubic and quadric hypersurfaces of dimension at least 23 over
Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.
acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting
this project and many helpful conversations and Pankaj Vishe for useful comments.
Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise
in exponential sums and geometry. While working on this paper, the author was supported
by FWF grant (DOI 10.55776/P36278).
article_number: e12991
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
citation:
ama: Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991
apa: Glas, J. (2024). Rational points on complete intersections of cubic and quadric
hypersurfaces over Fq(t). Journal of the London Mathematical Society. London
Mathematical Society. https://doi.org/10.1112/jlms.12991
chicago: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric
Hypersurfaces over Fq(T).” Journal of the London Mathematical Society.
London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991.
ieee: J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t),” Journal of the London Mathematical Society, vol. 110, no.
4. London Mathematical Society, 2024.
ista: Glas J. 2024. Rational points on complete intersections of cubic and quadric
hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4),
e12991.
mla: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric
Hypersurfaces over Fq(T).” Journal of the London Mathematical Society,
vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991.
short: J. Glas, Journal of the London Mathematical Society 110 (2024).
corr_author: '1'
date_created: 2024-10-06T22:01:11Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-04-07T12:53:53Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/jlms.12991
external_id:
arxiv:
- '2306.02718'
file:
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month: '10'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
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title: Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2024'
...
---
OA_place: repository
_id: '18295'
abstract:
- lang: eng
text: By developing a suitable version of the circle method, we show that the space
of degree e rational curves on a smooth hypersurface of degree d has only canonical
singularities provided its dimension is sufficiently large with respect to e and
d.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
citation:
ama: Glas J. Canonical singularities on moduli spaces of rational curves via the
circle method. arXiv. doi:10.48550/arXiv.2405.16648
apa: Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves
via the circle method. arXiv. https://doi.org/10.48550/arXiv.2405.16648
chicago: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves
via the Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.16648.
ieee: J. Glas, “Canonical singularities on moduli spaces of rational curves via
the circle method,” arXiv. .
ista: Glas J. Canonical singularities on moduli spaces of rational curves via the
circle method. arXiv, 10.48550/arXiv.2405.16648.
mla: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via
the Circle Method.” ArXiv, doi:10.48550/arXiv.2405.16648.
short: J. Glas, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-10-10T13:15:43Z
date_published: 2024-05-26T00:00:00Z
date_updated: 2026-04-07T12:53:53Z
day: '26'
department:
- _id: TiBr
doi: 10.48550/arXiv.2405.16648
external_id:
arxiv:
- '2405.16648'
language:
- iso: eng
main_file_link:
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month: '05'
oa: 1
oa_version: Preprint
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: arXiv
publication_status: submitted
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method
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---
OA_place: publisher
_id: '18667'
abstract:
- lang: eng
text: "Many chemical and physical properties of materials are determined by the
material’s shape,\r\nfor example the size of its pores and the width of its tunnels.
This makes materials science\r\na prime application area for geometrical and topological
methods. Nevertheless many\r\nmethods in topological data analysis have not been
satisfyingly extended to the needs of\r\nmaterials science. This thesis provides
new methods and new mathematical theorems\r\ntargeted at those specific needs
by answering four different research questions. While the\r\nmotivation for each
of the research questions arises from materials science, the methods\r\nare versatile
and can be applied in different areas as well. \r\n\r\nThe first research question
is concerned with image data, for example a three-dimensional\r\ncomputed tomography
(CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies
for digital images and depending on the application either of them might be\r\nrequired.
However, software for computing the topological data analysis method persistence\r\nhomology,
usually supports only one of the two topologies. We answer the question how to\r\ncompute
persistent homology of an image with respect to one of the two topologies using\r\nsoftware
that is intended for the other topology. \r\n\r\nThe second research question
is concerned with image data as well, and asks how much\r\nof the topological
information of an image is lost when the resolution is coarsened. As\r\ncomputer
tomography scanners are more expensive the higher the resolution, it is an\r\nimportant
question in materials science to know which resolution is enough to get satisfying\r\npersistent
homology. We give theoretical bounds on the information loss based on different\r\ngeometrical
properties of the object to be scanned. In addition, we conduct experiments on\r\nsand
and stone CT image data. \r\n\r\nThe third research question is motivated by comparing
crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically,
crystalline materials are either modeled by\r\nunmanageable infinite periodic
point sets, or by one of their fundamental domains, which is\r\nunstable under
perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate
properties such that comparing the crystals can be eased by comparing the\r\nfingerprints
instead. We define the density fingerprint and prove the necessary properties.
\r\n\r\nThe fourth research question is motivated by studying the hole-structure
or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials.
A common way to deal\r\nwith periodicity is to take a fundamental domain and identify
opposite boundaries to form a\r\ntorus. However, computing persistent homology
or merge trees on that torus loses some\r\nof the information materials scientists
are interested in and is additionally not stable under\r\ncertain noise. We therefore
decorate the merge tree stemming from the torus with additional\r\ninformation
describing the density and growth rate of the periodic copies of a component\r\nwithin
a growing spherical window. We prove all desired properties, like stability and
efficient\r\ncomputability."
acknowledgement: "I was supported by the European Research Council (ERC) Horizon 2020
project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship.
In addition,\r\nI am very thankful for having been able to attend the second Workshop
for Women in\r\nComputational Topology in July 2019, funded by the Mathematical
Sciences Institute at\r\nANU, the US National Science Foundation through the award
CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association
for Women in Mathematics. Two of the\r\nprojects presented in this thesis started
there. One of them reached completion thanks to\r\nfunding from the MSRI Summer
Research in Mathematics program awarded to me and my\r\ncollaborators in 2020."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
citation:
ama: Heiss T. New methods for applying topological data analysis to materials science.
2024. doi:10.15479/at:ista:18667
apa: Heiss, T. (2024). New methods for applying topological data analysis to
materials science. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18667
chicago: Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials
Science.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18667.
ieee: T. Heiss, “New methods for applying topological data analysis to materials
science,” Institute of Science and Technology Austria, 2024.
ista: Heiss T. 2024. New methods for applying topological data analysis to materials
science. Institute of Science and Technology Austria.
mla: Heiss, Teresa. New Methods for Applying Topological Data Analysis to Materials
Science. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18667.
short: T. Heiss, New Methods for Applying Topological Data Analysis to Materials
Science, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-12-17T16:17:55Z
date_published: 2024-12-17T00:00:00Z
date_updated: 2026-04-07T12:54:10Z
day: '17'
ddc:
- '514'
- '516'
- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:18667
ec_funded: 1
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keyword:
- persistent homology
- topological data analysis
- periodic
- crystalline materials
- images
- fingerprint
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: '111'
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication_identifier:
isbn:
- 978-3-99078-052-7
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
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status: public
- id: '9345'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: New methods for applying topological data analysis to materials science
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type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: repository
_id: '18673'
abstract:
- lang: eng
text: "Motivated by applications to crystalline materials, we generalize the merge
tree and the related barcode of a filtered complex to the periodic setting in
Euclidean space. They are invariant under isometries, changing bases, and indeed
changing lattices. In addition, we prove stability under perturbations and provide
an algorithm that under mild geometric conditions typically satisfied by crystalline
materials takes O((n+m)logn) time, in which n and m are the numbers of vertices
and edges in the quotient complex, respectively.\r\n"
acknowledgement: "Both authors are partially supported by the European Research Council
(ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The
first author is also partially supported by the DFG\r\nCollaborative Research Center
TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF),
grant no. I 02979-N35."
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
citation:
ama: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv.
doi:10.48550/arXiv.2408.16575
apa: Edelsbrunner, H., & Heiss, T. (n.d.). Merge trees of periodic filtrations.
arXiv. https://doi.org/10.48550/arXiv.2408.16575
chicago: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16575.
ieee: H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” arXiv.
.
ista: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575.
mla: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.”
ArXiv, doi:10.48550/arXiv.2408.16575.
short: H. Edelsbrunner, T. Heiss, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-12-18T14:06:57Z
date_published: 2024-08-29T00:00:00Z
date_updated: 2026-04-07T12:54:09Z
day: '29'
department:
- _id: HeEd
doi: 10.48550/arXiv.2408.16575
ec_funded: 1
external_id:
arxiv:
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- iso: eng
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month: '08'
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call_identifier: H2020
grant_number: '788183'
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call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
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OA_place: publisher
_id: '14711'
abstract:
- lang: eng
text: "In nature, different species find their niche in a range of environments,
each with its unique characteristics. While some thrive in uniform (homogeneous)
landscapes where environmental conditions stay relatively consistent across space,
others traverse the complexities of spatially heterogeneous terrains. Comprehending
how species are distributed and how they interact within these landscapes holds
the key to gaining insights into their evolutionary dynamics while also informing
conservation and management strategies.\r\n\r\nFor species inhabiting heterogeneous
landscapes, when the rate of dispersal is low compared to spatial fluctuations
in selection pressure, localized adaptations may emerge. Such adaptation in response
to varying selection strengths plays an important role in the persistence of populations
in our rapidly changing world. Hence, species in nature are continuously in a
struggle to adapt to local environmental conditions, to ensure their continued
survival. Natural populations can often adapt in time scales short enough for
evolutionary changes to influence ecological dynamics and vice versa, thereby
creating a feedback between evolution and demography. The analysis of this feedback
and the relative contributions of gene flow, demography, drift, and natural selection
to genetic variation and differentiation has remained a recurring theme in evolutionary
biology. Nevertheless, the effective role of these forces in maintaining variation
and shaping patterns of diversity is not fully understood. Even in homogeneous
environments devoid of local adaptations, such understanding remains elusive.
Understanding this feedback is crucial, for example in determining the conditions
under which extinction risk can be mitigated in peripheral populations subject
to deleterious mutation accumulation at the edges of species’ ranges\r\nas well
as in highly fragmented populations.\r\n\r\nIn this thesis we explore both uniform
and spatially heterogeneous metapopulations, investigating and providing theoretical
insights into the dynamics of local adaptation in the latter and examining the
dynamics of load and extinction as well as the impact of joint ecological and
evolutionary (eco-evolutionary) dynamics in the former. The thesis is divided
into 5 chapters.\r\n\r\nChapter 1 provides a general introduction into the subject
matter, clarifying concepts and ideas used throughout the thesis. In chapter 2,
we explore how fast a species distributed across a heterogeneous landscape adapts
to changing conditions marked by alterations in carrying capacity, selection pressure,
and migration rate.\r\n\r\nIn chapter 3, we investigate how migration selection
and drift influences adaptation and the maintenance of variation in a metapopulation
with three habitats, an extension of previous models of adaptation in two habitats.
We further develop analytical approximations for the critical threshold required
for polymorphism to persist.\r\n\r\nThe focus of chapter 4 of the thesis is on
understanding the interplay between ecology and evolution as coupled processes.
We investigate how eco-evolutionary feedback between migration, selection, drift,
and demography influences eco-evolutionary outcomes in marginal populations subject
to deleterious mutation accumulation. Using simulations as well as theoretical
approximations of the coupled dynamics of population size and allele frequency,
we analyze how gene flow from a large mainland source influences genetic load
and population size on an island (i.e., in a marginal population) under genetically
realistic assumptions. Analyses of this sort are important because small isolated
populations, are repeatedly affected by complex interactions between ecological
and evolutionary processes, which can lead to their death. Understanding these
interactions can therefore provide an insight into the conditions under which
extinction risk can be mitigated in peripheral populations thus, contributing
to conservation and restoration efforts.\r\n\r\nChapter 5 extends the analysis
in chapter 4 to consider the dynamics of load (due to deleterious mutation accumulation)
and extinction risk in a metapopulation. We explore the role of gene flow, selection,
and dominance on load and extinction risk and further pinpoint critical thresholds
required for metapopulation persistence.\r\n\r\nOverall this research contributes
to our understanding of ecological and evolutionary mechanisms that shape species’
persistence in fragmented landscapes, a crucial foundation for successful conservation
efforts and biodiversity management."
acknowledged_ssus:
- _id: SSU
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Oluwafunmilola O
full_name: Olusanya, Oluwafunmilola O
id: 41AD96DC-F248-11E8-B48F-1D18A9856A87
last_name: Olusanya
orcid: 0000-0003-1971-8314
citation:
ama: Olusanya OO. Local adaptation, genetic load and extinction in metapopulations.
2024. doi:10.15479/at:ista:14711
apa: Olusanya, O. O. (2024). Local adaptation, genetic load and extinction in
metapopulations. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14711
chicago: Olusanya, Oluwafunmilola O. “Local Adaptation, Genetic Load and Extinction
in Metapopulations.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:14711.
ieee: O. O. Olusanya, “Local adaptation, genetic load and extinction in metapopulations,”
Institute of Science and Technology Austria, 2024.
ista: Olusanya OO. 2024. Local adaptation, genetic load and extinction in metapopulations.
Institute of Science and Technology Austria.
mla: Olusanya, Oluwafunmilola O. Local Adaptation, Genetic Load and Extinction
in Metapopulations. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:14711.
short: O.O. Olusanya, Local Adaptation, Genetic Load and Extinction in Metapopulations,
Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2023-12-26T22:49:53Z
date_published: 2024-01-19T00:00:00Z
date_updated: 2026-04-07T12:54:29Z
day: '19'
ddc:
- '576'
degree_awarded: PhD
department:
- _id: NiBa
- _id: GradSch
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ec_funded: 1
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call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: c08d3278-5a5b-11eb-8a69-fdb09b55f4b8
grant_number: P32896
name: Causes and consequences of population fragmentation
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grant_number: '26380'
name: Polygenic Adaptation in a Metapopulation
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- 2663-337X
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full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Jitka
full_name: Polechova, Jitka
last_name: Polechova
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full_name: Sachdeva, Himani
last_name: Sachdeva
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abstract:
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text: "This dissertation is the summary of the author’s work, concerning the relations
between\r\ncohomology rings of algebraic varieties and rings of functions on zero
schemes and fixed\r\npoint schemes. For most of the thesis, the focus is on smooth
complex varieties with\r\nan action of a principally paired group, e.g. a parabolic
subgroup of a reductive group.\r\nThe fundamental theorem 5.2.11 from co-authored
article [66] says that if the principal\r\nnilpotent has a unique zero, then the
zero scheme over the Kostant section is isomorphic\r\nto the spectrum of the equivariant
cohomology ring, remembering the grading in terms of\r\na C^* action. A similar
statement is proved also for the G-invariant functions on the total\r\nzero scheme
over the whole Lie algebra. Additionally, we are able to prove an analogous\r\nresult
for the GKM spaces, which poses the question on a joint generalisation.\r\nWe
also tackle the situation of a singular variety. As long as it is embedded in
a smooth\r\nvariety with regular action, we are able to study its cohomology as
well by means of\r\nthe zero scheme. In case of e.g. Schubert varieties this determines
the cohomology ring\r\ncompletely. In largest generality, this allows us to see
a significant part of the cohomology\r\nring.\r\nWe also show (Theorem 6.2.1)
that the cohomology ring of spherical varieties appears as\r\nthe ring of functions
on the zero scheme. The computational aspect is not easy, but one\r\ncan hope
that this can bring some concrete information about such cohomology rings.\r\nLastly,
the K-theory conjecture 6.3.1 is studied, with some results attained for GKM\r\nspaces.\r\nThe
thesis includes also an introduction to group actions on algebraic varieties.
In\r\nparticular, the vector fields associated to the actions are extensively
studied. We also\r\nprovide a version of the Kostant section for arbitrary principally
paired group, which\r\nparametrises the regular orbits in the Lie algebra of an
algebraic group. Before proving\r\nthe main theorem, we also include a historical
overview of the field. In particular we bring\r\ntogether the results of Akyildiz,
Carrell and Lieberman on non-equivariant cohomology\r\nrings."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Kamil P
full_name: Rychlewicz, Kamil P
id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
last_name: Rychlewicz
citation:
ama: Rychlewicz KP. Equivariant cohomology and rings of functions. 2024. doi:10.15479/at:ista:17156
apa: Rychlewicz, K. P. (2024). Equivariant cohomology and rings of functions.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17156
chicago: Rychlewicz, Kamil P. “Equivariant Cohomology and Rings of Functions.” Institute
of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17156.
ieee: K. P. Rychlewicz, “Equivariant cohomology and rings of functions,” Institute
of Science and Technology Austria, 2024.
ista: Rychlewicz KP. 2024. Equivariant cohomology and rings of functions. Institute
of Science and Technology Austria.
mla: Rychlewicz, Kamil P. Equivariant Cohomology and Rings of Functions.
Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17156.
short: K.P. Rychlewicz, Equivariant Cohomology and Rings of Functions, Institute
of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-06-23T15:07:06Z
date_published: 2024-06-25T00:00:00Z
date_updated: 2026-04-07T12:55:46Z
day: '25'
ddc:
- '516'
degree_awarded: PhD
department:
- _id: TaHa
- _id: GradSch
doi: 10.15479/at:ista:17156
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- equivariant cohomology
- zero schemes
- algebraic groups
- Lie algebras
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month: '06'
oa: 1
oa_version: Published Version
page: '117'
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grant_number: '26525'
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publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
title: Equivariant cohomology and rings of functions
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---
OA_place: publisher
OA_type: gold
_id: '18515'
abstract:
- lang: eng
text: "Understanding the role of evolutionary processes in shaping genetic variation
has been a\r\nprimary goal in evolutionary genetics. In this regard, a key question
is how genetically\r\ndistinct populations evolve in the face of gene flow, thereby
generating genetic and\r\nphenotypic divergence and reproductive isolation (RI).
This requires quantifying the role\r\nand relative contributions of prezygotic
and postzygotic isolating mechanisms on the\r\nreduction of gene exchange between
populations, and identifying regions in the genome\r\nthat mediate RI, which is
often polygenic. Further, this needs distinguishing neutral and\r\nselected regions
in the genome, and discerning how selection influences patterns of neutral\r\ndivergence.\r\nPopulation
structure, defined as any deviation from panmixia, such as geographic distribution,
movement and mating patterns of individuals, influences how genetic variation
is\r\nstructured in space and shapes the neutral null model. Availability of large
scale spatial\r\ngenomic datasets now enables us to detect signatures of population
structure in genetic\r\ndata and infer population genetic parameters. Such inferences
are crucial and have wide\r\napplications in biodiversity, conservation genetics,
population management and medical\r\ngenetics. However, inferences are based on
assumptions that do not always match the\r\ncomplex reality, thus leading to erroneous
conclusions. Moreover, the role and interaction\r\nof heterogeneous population
density and dispersal, which are ubiquitous in nature, has\r\nbeen challenging
to study owing to their mathematical complexity. In such scenarios,\r\nfeedback
between theory, data and simulations can prove to be useful.\r\nIn this thesis,
I examine the effect of population structure on neutral genetic variation\r\nand
barriers to gene exchange in hybridising populations, thereby bridging together
the\r\nfields of spatial population genetics and speciation.\r\nDespite being
a key concept in speciation, reproductive isolation (RI) lacks a quantitative\r\ndefinition
and has been used and measured differently across different fields. Chapter 2\r\ngives
a quantitative definition of RI, in terms of the effect of genetic differences
on gene\r\nflow. We give analytical predictions for RI in a range of scenarios,
in terms of effective migration rates for discrete populations and barrier strength
for continuous populations.\r\nIn addition to this, we discuss current measures
of RI and their limitations, and propose\r\nthe need for new measures that combine
organismal and genetic perspectives of RI.\r\nIn chapter 3, I examine the combined
effect of assortative mating, sexual selection\r\nand viability selection on RI.
For this, we consider a polygenic ‘magic’ trait under a\r\nmainland-island model.
We obtain novel theoretical predictions for molecular divergence\r\nin terms of
effective migration rates, which bears a simple relationship to measurable\r\nfitness
components of migrants and various early generation hybrids. We explore the\r\nconditions
under which local adaptation can be maintained despite maladaptive gene flow\r\nand
quantify the relative contributions of viability and sexual selection to genome-wide\r\nbarriers
to gene flow.\r\nThe next two chapters of the thesis focus on a hybrid zone of
Antirrhinum majus that\r\nconsist of two subspecies- the magenta flowered A. m.
pseudomajus and the yellow\r\nflowered A.m. striatum. Previous studies have suggested
that flower colour is target of\r\npollinator mediated selection and is influenced
only by few genes. While these regions\r\nshow high genetic differentiation between
the subspecies, the rest of the genome is seen\r\nto be well mixed. Chapter 4
examines the effects of heterogeneous population density\r\nand leptokurtic dispersal
on isolation by distance and the distribution of heterozygosity\r\nby focusing
on non-flower colour markers.\r\nChapter 5 analyses cline shapes and associations
among 6 focal flower colour markers to\r\nunderstand how selection and dispersal
maintain this hybrid zone. We see sharp coincident\r\nstepped clines at all loci
and positive associations throughout the hybrid zone, contrary to\r\nthe expected
patterns from diffusive gene flow. With a novel scheme of inferring dispersal\r\ncombined
with multilocus simulations, we show that stepped clines do not reflect genetic\r\nbarriers
to gene flow, but are rather a result of long-distance migration. This framework\r\nallows
us to get realistic estimates gene flow and selection and shows how traditional
cline\r\nanalysis may lead to inaccurate conclusions when assumptions of the theory
are not met.\r\nOverall, this thesis investigates how different features of population
structure leave\r\ndetectable signatures in genetic variation, namely in patterns
of isolation by distance,\r\nlinkage disequilibrium and genetic divergence. It
also highlights how effective migration\r\nrates provide useful way of analysing
polygenic architectures and shed new light into\r\nhybrid zones. In doing so,
I identify scenarios when simple models become insufficient\r\nand suggest possibe
directions by combining genetic data with simulations."
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "I also acknowledge the funding agencies Marie Curie COFUND Doctoral
Fellowship,\r\nAustrian Science Fund FWF (grant P32166) and ERC (grant PR1000ERC02)
for financially\r\nsupporting my research over the years."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Parvathy
full_name: Surendranadh, Parvathy
id: 455235B8-F248-11E8-B48F-1D18A9856A87
last_name: Surendranadh
orcid: 0000-0001-6395-386X
citation:
ama: Surendranadh P. Effect of population structure on neutral genetic variation
and barriers to gene exchange. 2024. doi:10.15479/at:ista:18515
apa: Surendranadh, P. (2024). Effect of population structure on neutral genetic
variation and barriers to gene exchange. Institute of Science and Technology
Austria. https://doi.org/10.15479/at:ista:18515
chicago: Surendranadh, Parvathy. “Effect of Population Structure on Neutral Genetic
Variation and Barriers to Gene Exchange.” Institute of Science and Technology
Austria, 2024. https://doi.org/10.15479/at:ista:18515.
ieee: P. Surendranadh, “Effect of population structure on neutral genetic variation
and barriers to gene exchange,” Institute of Science and Technology Austria, 2024.
ista: Surendranadh P. 2024. Effect of population structure on neutral genetic variation
and barriers to gene exchange. Institute of Science and Technology Austria.
mla: Surendranadh, Parvathy. Effect of Population Structure on Neutral Genetic
Variation and Barriers to Gene Exchange. Institute of Science and Technology
Austria, 2024, doi:10.15479/at:ista:18515.
short: P. Surendranadh, Effect of Population Structure on Neutral Genetic Variation
and Barriers to Gene Exchange, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-11-06T21:25:37Z
date_published: 2024-11-07T00:00:00Z
date_updated: 2026-04-07T12:56:52Z
day: '07'
ddc:
- '576'
degree_awarded: PhD
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- _id: GradSch
- _id: NiBa
doi: 10.15479/at:ista:18515
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oa_version: Published Version
page: '219'
project:
- _id: 05959E1C-7A3F-11EA-A408-12923DDC885E
grant_number: P32166
name: Snapdragon Speciation
- _id: bd6958e0-d553-11ed-ba76-86eba6a76c00
grant_number: '101055327'
name: Understanding the evolution of continuous genomes
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
title: Effect of population structure on neutral genetic variation and barriers to
gene exchange
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short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: repository
_id: '18689'
abstract:
- lang: eng
text: Multiplexed fluorescence microscopy imaging is widely used in biomedical applications.
However, simultaneous imaging of multiple fluorophores can result in spectral
leaks and overlapping, which greatly degrades image quality and subsequent analysis.
Existing popular spectral unmixing methods are mainly based on computational intensive
linear models and the performance is heavily dependent on the reference spectra,
which may greatly preclude its further applications. In this paper, we propose
a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate
the physical spectral mixing process. A tranfer learning framework is further
devised to allow our AutoUnmix adapting to a variety of imaging systems without
retraining the network. Our proposed method has demonstrated real-time unmixing
capabilities, surpassing existing methods by up to 100-fold in terms of unmixing
speed. We further validate the reconstruction performance on both synthetic datasets
and biological samples. The unmixing results of AutoUnmix achieve a highest SSIM
of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than
other popular unmixing methods. Due to the desirable property of data independency
and superior blind unmixing performance, we believe AutoUnmix is a powerful tool
to study the interaction process of different organelles labeled by multiple fluorophores.
acknowledged_ssus:
- _id: Bio
- _id: LifeSc
- _id: M-Shop
- _id: E-Lib
acknowledgement: "We gratefully acknowledge support by the Scientific Service Units
at ISTA, including the Imaging and Optics and Lab Support facilities and the mechanical
workshop and Library. We thank Philipp Velicky for STED microscope alignment.\r\n\r\nThis
project has received funding from the Austrian Science Fund (FWF): I 3630-B25 (J.G.D)
and the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 742985, J.F.). It has also
received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 665385. S.T. has
received funding as an ISTplus Fellow from the European Union’s Horizon 2020 Research
and Innovation Programme under Marie Skłodowska-Curie grant agreement no. 754411
and from an EMBO Long-Term Fellowship (grant number ALTF 679-2018). It has further
received funding from the Austrian Science Fund (FWF) grant DK W1232 (M.T, N.A-D.,
J.G.D). W.J. received funding via a Human Frontier Science Program postdoctoral
fellowship LT000557/2018.\r\n\r\nThe funders had no role in study design, data collection
and analysis, decision to publish or preparation of the manuscript."
article_processing_charge: No
author:
- first_name: Michelle C
full_name: Gallei, Michelle C
id: 35A03822-F248-11E8-B48F-1D18A9856A87
last_name: Gallei
orcid: 0000-0003-1286-7368
- first_name: Sven M
full_name: Truckenbrodt, Sven M
id: 45812BD4-F248-11E8-B48F-1D18A9856A87
last_name: Truckenbrodt
- first_name: Caroline
full_name: Kreuzinger, Caroline
id: 382077BA-F248-11E8-B48F-1D18A9856A87
last_name: Kreuzinger
- first_name: Syamala
full_name: Inumella, Syamala
id: F8660870-D756-11E9-98C5-34DFE5697425
last_name: Inumella
orcid: 0009-0002-5890-120X
- first_name: Vitali
full_name: Vistunou, Vitali
id: 7e146587-8972-11ed-ae7b-d7a32ea86a81
last_name: Vistunou
- first_name: Christoph M
full_name: Sommer, Christoph M
id: 4DF26D8C-F248-11E8-B48F-1D18A9856A87
last_name: Sommer
orcid: 0000-0003-1216-9105
- first_name: Mojtaba
full_name: Tavakoli, Mojtaba
id: 3A0A06F4-F248-11E8-B48F-1D18A9856A87
last_name: Tavakoli
orcid: 0000-0002-7667-6854
- first_name: Nathalie
full_name: Agudelo Duenas, Nathalie
id: 40E7F008-F248-11E8-B48F-1D18A9856A87
last_name: Agudelo Duenas
- first_name: Jakob
full_name: Vorlaufer, Jakob
id: 937696FA-C996-11E9-8C7C-CF13E6697425
last_name: Vorlaufer
orcid: 0009-0000-7590-3501
- first_name: Wiebke
full_name: Jahr, Wiebke
id: 425C1CE8-F248-11E8-B48F-1D18A9856A87
last_name: Jahr
orcid: 0000-0003-0201-2315
- first_name: Marek
full_name: Randuch, Marek
id: 6ac4636d-15b2-11ec-abd3-fb8df79972ae
last_name: Randuch
- first_name: Alexander J
full_name: Johnson, Alexander J
id: 46A62C3A-F248-11E8-B48F-1D18A9856A87
last_name: Johnson
orcid: 0000-0002-2739-8843
- first_name: Eva
full_name: Benková, Eva
id: 38F4F166-F248-11E8-B48F-1D18A9856A87
last_name: Benková
orcid: 0000-0002-8510-9739
- first_name: Jiří
full_name: Friml, Jiří
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
- first_name: Johann G
full_name: Danzl, Johann G
id: 42EFD3B6-F248-11E8-B48F-1D18A9856A87
last_name: Danzl
orcid: 0000-0001-8559-3973
citation:
ama: Gallei MC, Truckenbrodt SM, Kreuzinger C, et al. Super-resolution expansion
microscopy in plant roots. bioRxiv. doi:10.1101/2024.02.21.581330
apa: Gallei, M. C., Truckenbrodt, S. M., Kreuzinger, C., Inumella, S., Vistunou,
V., Sommer, C. M., … Danzl, J. G. (n.d.). Super-resolution expansion microscopy
in plant roots. bioRxiv. https://doi.org/10.1101/2024.02.21.581330
chicago: Gallei, Michelle C, Sven M Truckenbrodt, Caroline Kreuzinger, Syamala Inumella,
Vitali Vistunou, Christoph M Sommer, Mojtaba Tavakoli, et al. “Super-Resolution
Expansion Microscopy in Plant Roots.” BioRxiv, n.d. https://doi.org/10.1101/2024.02.21.581330.
ieee: M. C. Gallei et al., “Super-resolution expansion microscopy in plant
roots,” bioRxiv. .
ista: Gallei MC, Truckenbrodt SM, Kreuzinger C, Inumella S, Vistunou V, Sommer CM,
Tavakoli M, Agudelo Duenas N, Vorlaufer J, Jahr W, Randuch M, Johnson AJ, Benková
E, Friml J, Danzl JG. Super-resolution expansion microscopy in plant roots. bioRxiv,
10.1101/2024.02.21.581330.
mla: Gallei, Michelle C., et al. “Super-Resolution Expansion Microscopy in Plant
Roots.” BioRxiv, doi:10.1101/2024.02.21.581330.
short: M.C. Gallei, S.M. Truckenbrodt, C. Kreuzinger, S. Inumella, V. Vistunou,
C.M. Sommer, M. Tavakoli, N. Agudelo Duenas, J. Vorlaufer, W. Jahr, M. Randuch,
A.J. Johnson, E. Benková, J. Friml, J.G. Danzl, BioRxiv (n.d.).
corr_author: '1'
date_created: 2024-12-19T12:28:00Z
date_published: 2024-02-21T00:00:00Z
date_updated: 2026-04-07T12:56:36Z
day: '21'
department:
- _id: EvBe
- _id: JoDa
- _id: JiFr
doi: 10.1101/2024.02.21.581330
ec_funded: 1
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.1101/2024.02.21.581330
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 261099A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '742985'
name: Tracing Evolution of Auxin Transport and Polarity in Plants
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 26AA4EF2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1232-B24
name: Molecular Drug Targets
- _id: 269B5B22-B435-11E9-9278-68D0E5697425
grant_number: ALTF 679-2018
name: UltraX - achieving sub-nanometer resolution in light microscopy using iterative
X10 microscopy in combination with nanobodies and STED
publication: bioRxiv
publication_status: draft
related_material:
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status: public
title: Super-resolution expansion microscopy in plant roots
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_embargo: '20'
OA_place: publisher
_id: '18681'
acknowledged_ssus:
- _id: Bio
- _id: PreCl
- _id: LifeSc
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Mojtaba
full_name: Tavakoli, Mojtaba
id: 3A0A06F4-F248-11E8-B48F-1D18A9856A87
last_name: Tavakoli
orcid: 0000-0002-7667-6854
citation:
ama: 'Tavakoli M. Developing molecular and structural tools for studying brain architecture
with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics
reconstruction with light microscopy. 2024. doi:10.15479/at:ista:18681'
apa: 'Tavakoli, M. (2024). Developing molecular and structural tools for studying
brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed
connectomics reconstruction with light microscopy. Institute of Science and
Technology Austria. https://doi.org/10.15479/at:ista:18681'
chicago: 'Tavakoli, Mojtaba. “Developing Molecular and Structural Tools for Studying
Brain Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed
Connectomics Reconstruction with Light Microscopy.” Institute of Science and Technology
Austria, 2024. https://doi.org/10.15479/at:ista:18681.'
ieee: 'M. Tavakoli, “Developing molecular and structural tools for studying brain
architecture with super resolution expansion microscopy. LICONN: Molecularly-informed
connectomics reconstruction with light microscopy,” Institute of Science and Technology
Austria, 2024.'
ista: 'Tavakoli M. 2024. Developing molecular and structural tools for studying
brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed
connectomics reconstruction with light microscopy. Institute of Science and Technology
Austria.'
mla: 'Tavakoli, Mojtaba. Developing Molecular and Structural Tools for Studying
Brain Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed
Connectomics Reconstruction with Light Microscopy. Institute of Science and
Technology Austria, 2024, doi:10.15479/at:ista:18681.'
short: 'M. Tavakoli, Developing Molecular and Structural Tools for Studying Brain
Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed
Connectomics Reconstruction with Light Microscopy, Institute of Science and Technology
Austria, 2024.'
corr_author: '1'
date_created: 2024-12-19T02:30:39Z
date_published: 2024-12-20T00:00:00Z
date_updated: 2026-04-07T12:56:37Z
day: '20'
ddc:
- '600'
- '570'
degree_awarded: PhD
department:
- _id: GradSch
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doi: 10.15479/at:ista:18681
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date_updated: 2024-12-20T10:25:12Z
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embargo_to: open_access
file_id: '18700'
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file_date_updated: 2024-12-20T10:31:37Z
has_accepted_license: '1'
language:
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license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '12'
oa_version: Published Version
page: '230'
project:
- _id: 6285a163-2b32-11ec-9570-8e204ca2dba5
grant_number: '26137'
name: Studying Organelle Structure and Function at Nanoscale Resolution with Expansion
Microscopy
- _id: 26AA4EF2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1232-B24
name: Molecular Drug Targets
publication_identifier:
isbn:
- 978-3-99078-048-0
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
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relation: part_of_dissertation
status: public
- id: '18688'
relation: part_of_dissertation
status: public
- id: '18677'
relation: part_of_dissertation
status: public
- id: '18689'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Johann G
full_name: Danzl, Johann G
id: 42EFD3B6-F248-11E8-B48F-1D18A9856A87
last_name: Danzl
orcid: 0000-0001-8559-3973
title: 'Developing molecular and structural tools for studying brain architecture
with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics
reconstruction with light microscopy'
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
_id: '15094'
abstract:
- lang: eng
text: "Point sets, geometric networks, and arrangements of hyperplanes are fundamental
objects in\r\ndiscrete geometry that have captivated mathematicians for centuries,
if not millennia. This\r\nthesis seeks to cast new light on these structures by
illustrating specific instances where a\r\ntopological perspective, specifically
through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt
first glance, the topology of these geometric objects might seem uneventful: point
sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition
of Rd, which\r\nis a contractible space, and the topology of a network primarily
involves the enumeration\r\nof connected components and cycles within the network.
However, beneath this apparent\r\nsimplicity, there lies an array of intriguing
structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused
on three case studies, each addressing one of the mentioned objects, this work\r\nwill
showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry,
algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
citation:
ama: Cultrera di Montesano S. Persistence and Morse theory for discrete geometric
structures. 2024. doi:10.15479/at:ista:15094
apa: Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete
geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094
chicago: Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete
Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094.
ieee: S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric
structures,” Institute of Science and Technology Austria, 2024.
ista: Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric
structures. Institute of Science and Technology Austria.
mla: Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete
Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094.
short: S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric
Structures, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-03-08T15:28:10Z
date_published: 2024-03-08T00:00:00Z
date_updated: 2026-04-07T12:58:48Z
day: '08'
ddc:
- '514'
- '500'
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:15094
ec_funded: 1
file:
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creator: scultrer
date_created: 2024-03-14T08:55:07Z
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file_name: Thesis Sebastiano.pdf
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file_size: 4746234
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has_accepted_license: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: '108'
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '15091'
relation: part_of_dissertation
status: public
- id: '11660'
relation: part_of_dissertation
status: public
- id: '15090'
relation: part_of_dissertation
status: public
- id: '15093'
relation: part_of_dissertation
status: public
- id: '13182'
relation: part_of_dissertation
status: public
- id: '11658'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Persistence and Morse theory for discrete geometric structures
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '13182'
abstract:
- lang: eng
text: "We characterize critical points of 1-dimensional maps paired in persistent
homology\r\ngeometrically and this way get elementary proofs of theorems about
the symmetry\r\nof persistence diagrams and the variation of such maps. In particular,
we identify\r\nbranching points and endpoints of networks as the sole source of
asymmetry and\r\nrelate the cycle basis in persistent homology with a version
of the stable marriage\r\nproblem. Our analysis provides the foundations of fast
algorithms for maintaining a\r\ncollection of sorted lists together with its persistence
diagram."
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This
project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme, grant no. 788183,
from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and
from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of
this paper thank anonymous reviewers for their constructive criticism and Monika
Henzinger for detailed comments on an earlier version of this paper.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera Di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera Di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization
of the persistence of 1D maps. Journal of Applied and Computational Topology.
2024;8:1101-1119. doi:10.1007/s41468-023-00126-9
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2024). Geometric characterization of the persistence of 1D maps. Journal of
Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.”
Journal of Applied and Computational Topology. Springer Nature, 2024. https://doi.org/10.1007/s41468-023-00126-9.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric
characterization of the persistence of 1D maps,” Journal of Applied and Computational
Topology, vol. 8. Springer Nature, pp. 1101–1119, 2024.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric
characterization of the persistence of 1D maps. Journal of Applied and Computational
Topology. 8, 1101–1119.
mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D
Maps.” Journal of Applied and Computational Topology, vol. 8, Springer
Nature, 2024, pp. 1101–19, doi:10.1007/s41468-023-00126-9.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal
of Applied and Computational Topology 8 (2024) 1101–1119.
corr_author: '1'
date_created: 2023-07-02T22:00:44Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-04-07T12:58:47Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00126-9
ec_funded: 1
external_id:
pmid:
- '39678706'
file:
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intvolume: ' 8'
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month: '10'
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oa_version: Published Version
page: 1101-1119
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
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call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Geometric characterization of the persistence of 1D 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: 8
year: '2024'
...
---
_id: '15093'
abstract:
- lang: eng
text: We present a dynamic data structure for maintaining the persistent homology
of a time series of real numbers. The data structure supports local operations,
including the insertion and deletion of an item and the cutting and concatenating
of lists, each in time O(log n + k), in which n counts the critical items and
k the changes in the augmented persistence diagram. To achieve this, we design
a tailor-made tree structure with an unconventional representation, referred to
as banana tree, which may be useful in its own right.
acknowledgement: The first and second authors are funded by the European Research Council under the
European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha
Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31,
and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The
third author received funding by the European Research Council under the European
Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures
(MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize
with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant
no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The
fourth author is funded by the Vienna Graduate School on Computational Optimization,
FWF project no. W1260-N35.
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Lara
full_name: Ost, Lara
last_name: Ost
citation:
ama: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining
the persistent homology of time series. In: Woodruff DP, ed. Proceedings of
the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society
for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11'
apa: 'Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., & Ost, L.
(2024). Dynamically maintaining the persistent homology of time series. In D.
P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete
Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11'
chicago: Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger,
and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.”
In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms
(SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied
Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11.
ieee: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically
maintaining the persistent homology of time series,” in Proceedings of the
2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria,
VA, USA, 2024, pp. 243–295.
ista: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically
maintaining the persistent homology of time series. Proceedings of the 2024 Annual
ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete
Algorithms, 243–295.'
mla: Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent
Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium
on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial
and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11.
short: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P.
Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete
Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.
conference:
end_date: 2024-01-10
location: Alexandria, VA, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2024-01-07
corr_author: '1'
date_created: 2024-03-08T10:27:39Z
date_published: 2024-01-04T00:00:00Z
date_updated: 2026-04-07T12:58:47Z
day: '04'
department:
- _id: HeEd
- _id: MoHe
doi: 10.1137/1.9781611977912.11
ec_funded: 1
editor:
- first_name: David P.
full_name: Woodruff, David P.
last_name: Woodruff
external_id:
arxiv:
- '2311.01115'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2311.01115
month: '01'
oa: 1
oa_version: Preprint
page: 243 - 295
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62
call_identifier: H2020
grant_number: '101019564'
name: The design and evaluation of modern fully dynamic data structures
- _id: 34def286-11ca-11ed-8bc3-da5948e1613c
grant_number: Z00422
name: Efficient algorithms
- _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe
grant_number: P33775
name: Fast Algorithms for a Reactive Network Layer
publication: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms
(SODA)
publication_identifier:
eisbn:
- '9781611977912'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Dynamically maintaining the persistent homology of time series
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
_id: '15091'
abstract:
- lang: eng
text: "Motivated by applications in the medical sciences, we study finite chromatic\r\nsets
in Euclidean space from a topological perspective. Based on the persistent\r\nhomology
for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers
that describe the geometric micro- and macro-structure\r\nof how the color classes
mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay
and alpha complexes, and code that does these\r\ncomputations is provided."
article_number: '2212.03128'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
orcid: 0000-0003-0464-3823
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. arXiv. doi:10.48550/arXiv.2212.03128
apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian,
M. (n.d.). Chromatic alpha complexes. arXiv. https://doi.org/10.48550/arXiv.2212.03128
chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner,
and Morteza Saghafian. “Chromatic Alpha Complexes.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2212.03128.
ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian,
“Chromatic alpha complexes,” arXiv. .
ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic
alpha complexes. arXiv, 2212.03128.
mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” ArXiv,
2212.03128, doi:10.48550/arXiv.2212.03128.
short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv
(n.d.).
corr_author: '1'
date_created: 2024-03-08T10:13:59Z
date_published: 2024-02-07T00:00:00Z
date_updated: 2026-04-07T12:58:47Z
day: '07'
department:
- _id: HeEd
doi: 10.48550/arXiv.2212.03128
external_id:
arxiv:
- '2212.03128'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2212.03128
month: '02'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20585'
relation: later_version
status: public
- id: '18979'
relation: dissertation_contains
status: public
- id: '15094'
relation: dissertation_contains
status: public
status: public
title: Chromatic alpha complexes
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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...