---
_id: '14664'
abstract:
- lang: eng
text: The architecture of self-assembled host molecules can profoundly affect the
properties of the encapsulated guests. For example, a rigid cage with small windows
can efficiently protect its contents from the environment; in contrast, tube-shaped,
flexible hosts with large openings and an easily accessible cavity are ideally
suited for catalysis. Here, we report a “Janus” nature of a Pd6L4 coordination
host previously reported to exist exclusively as a tube isomer (T). We show that
upon encapsulating various tetrahedrally shaped guests, T can reconfigure into
a cage-shaped host (C) in quantitative yield. Extracting the guest affords empty
C, which is metastable and spontaneously relaxes to T, and the T⇄C interconversion
can be repeated for multiple cycles. Reversible toggling between two vastly different
isomers paves the way toward controlling functional properties of coordination
hosts “on demand”.
acknowledgement: We acknowledge funding from the European Union’s Horizon 2020 Research
and Innovation Program under the European Research Council (grant agreement 820008).We
also thank the Deutsche Forschungsgemeinschaft (DFG) for support through priority
program SPP1807(CL489/3-2) and RESOLV Cluster of Excellence EXC2033 (project number
390677874). A.B.G. acknowledges funding from the Zuckerman STEM Leadership Program.
DFT calculations were carried out using resources provided by the Wrocław Center
for Networking and Supercomputing, grant 329.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Kuntrapakam
full_name: Hema, Kuntrapakam
last_name: Hema
- first_name: Angela B.
full_name: Grommet, Angela B.
last_name: Grommet
- first_name: Michał J.
full_name: Białek, Michał J.
last_name: Białek
- first_name: Jinhua
full_name: Wang, Jinhua
last_name: Wang
- first_name: Laura
full_name: Schneider, Laura
last_name: Schneider
- first_name: Christoph
full_name: Drechsler, Christoph
last_name: Drechsler
- first_name: Oksana
full_name: Yanshyna, Oksana
last_name: Yanshyna
- first_name: Yael
full_name: Diskin-Posner, Yael
last_name: Diskin-Posner
- first_name: Guido H.
full_name: Clever, Guido H.
last_name: Clever
- first_name: Rafal
full_name: Klajn, Rafal
id: 8e84690e-1e48-11ed-a02b-a1e6fb8bb53b
last_name: Klajn
citation:
ama: Hema K, Grommet AB, Białek MJ, et al. Guest encapsulation alters the thermodynamic
landscape of a coordination host. Journal of the American Chemical Society.
2023;145(45):24755-24764. doi:10.1021/jacs.3c08666
apa: Hema, K., Grommet, A. B., Białek, M. J., Wang, J., Schneider, L., Drechsler,
C., … Klajn, R. (2023). Guest encapsulation alters the thermodynamic landscape
of a coordination host. Journal of the American Chemical Society. American
Chemical Society. https://doi.org/10.1021/jacs.3c08666
chicago: Hema, Kuntrapakam, Angela B. Grommet, Michał J. Białek, Jinhua Wang, Laura
Schneider, Christoph Drechsler, Oksana Yanshyna, Yael Diskin-Posner, Guido H.
Clever, and Rafal Klajn. “Guest Encapsulation Alters the Thermodynamic Landscape
of a Coordination Host.” Journal of the American Chemical Society. American
Chemical Society, 2023. https://doi.org/10.1021/jacs.3c08666.
ieee: K. Hema et al., “Guest encapsulation alters the thermodynamic landscape
of a coordination host,” Journal of the American Chemical Society, vol.
145, no. 45. American Chemical Society, pp. 24755–24764, 2023.
ista: Hema K, Grommet AB, Białek MJ, Wang J, Schneider L, Drechsler C, Yanshyna
O, Diskin-Posner Y, Clever GH, Klajn R. 2023. Guest encapsulation alters the thermodynamic
landscape of a coordination host. Journal of the American Chemical Society. 145(45),
24755–24764.
mla: Hema, Kuntrapakam, et al. “Guest Encapsulation Alters the Thermodynamic Landscape
of a Coordination Host.” Journal of the American Chemical Society, vol.
145, no. 45, American Chemical Society, 2023, pp. 24755–64, doi:10.1021/jacs.3c08666.
short: K. Hema, A.B. Grommet, M.J. Białek, J. Wang, L. Schneider, C. Drechsler,
O. Yanshyna, Y. Diskin-Posner, G.H. Clever, R. Klajn, Journal of the American
Chemical Society 145 (2023) 24755–24764.
date_created: 2023-12-10T23:00:59Z
date_published: 2023-11-02T00:00:00Z
date_updated: 2023-12-11T11:47:07Z
day: '02'
ddc:
- '540'
department:
- _id: RaKl
doi: 10.1021/jacs.3c08666
external_id:
pmid:
- '37917939'
file:
- access_level: open_access
checksum: a1f37df6b83f88f51ba64468ce0c1589
content_type: application/pdf
creator: dernst
date_created: 2023-12-11T11:44:54Z
date_updated: 2023-12-11T11:44:54Z
file_id: '14675'
file_name: 2023_JACS_Hema.pdf
file_size: 4304472
relation: main_file
success: 1
file_date_updated: 2023-12-11T11:44:54Z
has_accepted_license: '1'
intvolume: ' 145'
issue: '45'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 24755-24764
pmid: 1
publication: Journal of the American Chemical Society
publication_identifier:
eissn:
- 1520-5126
issn:
- 0002-7863
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Guest encapsulation alters the thermodynamic landscape of a coordination host
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: 145
year: '2023'
...
---
_id: '14665'
abstract:
- lang: eng
text: We derive lower bounds on the maximal rates for multiple packings in high-dimensional
Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of
points in R n such that any point in R n lies in the intersection of at most L
- 1 balls of radius √ nN around points in C . This is a natural generalization
of the sphere packing problem. We study the multiple packing problem for both
bounded point sets whose points have norm at most √ nP for some constant P > 0,
and unbounded point sets whose points are allowed to be anywhere in R n . Given
a well-known connection with coding theory, multiple packings can be viewed as
the Euclidean analog of list-decodable codes, which are well-studied over finite
fields. We derive the best known lower bounds on the optimal multiple packing
density. This is accomplished by establishing an inequality which relates the
list-decoding error exponent for additive white Gaussian noise channels, a quantity
of average-case nature, to the list-decoding radius, a quantity of worst-case
nature. We also derive novel bounds on the list-decoding error exponent for infinite
constellations and closed-form expressions for the list-decoding error exponents
for the power-constrained AWGN channel, which may be of independent interest beyond
multiple packing.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. IEEE
Transactions on Information Theory. 2023. doi:10.1109/TIT.2023.3334032'
apa: 'Zhang, Y., & Vatedka, S. (2023). Multiple packing: Lower bounds via error
exponents. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2023.3334032'
chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
Error Exponents.” IEEE Transactions on Information Theory. IEEE, 2023.
https://doi.org/10.1109/TIT.2023.3334032.'
ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,”
IEEE Transactions on Information Theory. IEEE, 2023.'
ista: 'Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via error exponents.
IEEE Transactions on Information Theory.'
mla: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error
Exponents.” IEEE Transactions on Information Theory, IEEE, 2023, doi:10.1109/TIT.2023.3334032.'
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory (2023).
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-16T00:00:00Z
date_updated: 2023-12-18T07:46:45Z
day: '16'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3334032
external_id:
arxiv:
- '2211.04408'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.04408
month: '11'
oa: 1
oa_version: Preprint
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: epub_ahead
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple packing: Lower bounds via error exponents'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14666'
abstract:
- lang: eng
text: So-called spontaneous activity is a central hallmark of most nervous systems.
Such non-causal firing is contrary to the tenet of spikes as a means of communication,
and its purpose remains unclear. We propose that self-initiated firing can serve
as a release valve to protect neurons from the toxic conditions arising in mitochondria
from lower-than-baseline energy consumption. To demonstrate the viability of our
hypothesis, we built a set of models that incorporate recent experimental results
indicating homeostatic control of metabolic products—Adenosine triphosphate (ATP),
adenosine diphosphate (ADP), and reactive oxygen species (ROS)—by changes in firing.
We explore the relationship of metabolic cost of spiking with its effect on the
temporal patterning of spikes and reproduce experimentally observed changes in
intrinsic firing in the fruitfly dorsal fan-shaped body neuron in a model with
ROS-modulated potassium channels. We also show that metabolic spiking homeostasis
can produce indefinitely sustained avalanche dynamics in cortical circuits. Our
theory can account for key features of neuronal activity observed in many studies
ranging from ion channel function all the way to resting state dynamics. We finish
with a set of experimental predictions that would confirm an integrated, crucial
role for metabolically regulated spiking and firmly link metabolic homeostasis
and neuronal function.
acknowledgement: We thank Prof. C. Nazaret and Prof. J.-P. Mazat for sharing the code
of their mitochondrial model. We also thank G. Miesenböck, E. Marder, L. Abbott,
A. Kempf, P. Hasenhuetl, W. Podlaski, F. Zenke, E. Agnes, P. Bozelos, J. Watson,
B. Confavreux, and G. Christodoulou, and the rest of the Vogels Lab for their feedback.
This work was funded by Wellcome Trust and Royal Society Sir Henry Dale Research
Fellowship (WT100000), a Wellcome Trust Senior Research Fellowship (214316/Z/18/Z),
and a UK Research and Innovation, Biotechnology and Biological Sciences Research
Council grant (UKRI-BBSRC BB/N019512/1).
article_number: e2306525120
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Chaitanya
full_name: Chintaluri, Chaitanya
id: E4EDB536-3485-11EA-98D2-20AF3DDC885E
last_name: Chintaluri
- first_name: Tim P
full_name: Vogels, Tim P
id: CB6FF8D2-008F-11EA-8E08-2637E6697425
last_name: Vogels
orcid: 0000-0003-3295-6181
citation:
ama: Chintaluri C, Vogels TP. Metabolically regulated spiking could serve neuronal
energy homeostasis and protect from reactive oxygen species. Proceedings of
the National Academy of Sciences of the United States of America. 2023;120(48).
doi:10.1073/pnas.2306525120
apa: Chintaluri, C., & Vogels, T. P. (2023). Metabolically regulated spiking
could serve neuronal energy homeostasis and protect from reactive oxygen species.
Proceedings of the National Academy of Sciences of the United States of America.
National Academy of Sciences. https://doi.org/10.1073/pnas.2306525120
chicago: Chintaluri, Chaitanya, and Tim P Vogels. “Metabolically Regulated Spiking
Could Serve Neuronal Energy Homeostasis and Protect from Reactive Oxygen Species.”
Proceedings of the National Academy of Sciences of the United States of America.
National Academy of Sciences, 2023. https://doi.org/10.1073/pnas.2306525120.
ieee: C. Chintaluri and T. P. Vogels, “Metabolically regulated spiking could serve
neuronal energy homeostasis and protect from reactive oxygen species,” Proceedings
of the National Academy of Sciences of the United States of America, vol.
120, no. 48. National Academy of Sciences, 2023.
ista: Chintaluri C, Vogels TP. 2023. Metabolically regulated spiking could serve
neuronal energy homeostasis and protect from reactive oxygen species. Proceedings
of the National Academy of Sciences of the United States of America. 120(48),
e2306525120.
mla: Chintaluri, Chaitanya, and Tim P. Vogels. “Metabolically Regulated Spiking
Could Serve Neuronal Energy Homeostasis and Protect from Reactive Oxygen Species.”
Proceedings of the National Academy of Sciences of the United States of America,
vol. 120, no. 48, e2306525120, National Academy of Sciences, 2023, doi:10.1073/pnas.2306525120.
short: C. Chintaluri, T.P. Vogels, Proceedings of the National Academy of Sciences
of the United States of America 120 (2023).
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-21T00:00:00Z
date_updated: 2023-12-11T12:47:41Z
day: '21'
ddc:
- '570'
department:
- _id: TiVo
doi: 10.1073/pnas.2306525120
external_id:
pmid:
- '37988463'
file:
- access_level: open_access
checksum: bf4ec38602a70dae4338077a5a4d497f
content_type: application/pdf
creator: dernst
date_created: 2023-12-11T12:45:12Z
date_updated: 2023-12-11T12:45:12Z
file_id: '14678'
file_name: 2023_PNAS_Chintaluri.pdf
file_size: 16891602
relation: main_file
success: 1
file_date_updated: 2023-12-11T12:45:12Z
has_accepted_license: '1'
intvolume: ' 120'
issue: '48'
language:
- iso: eng
month: '11'
oa: 1
oa_version: None
pmid: 1
project:
- _id: c084a126-5a5b-11eb-8a69-d75314a70a87
grant_number: 214316/Z/18/Z
name: What’s in a memory? Spatiotemporal dynamics in strongly coupled recurrent
neuronal networks.
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- 1091-6490
issn:
- 0027-8424
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/ccluri/metabolic_spiking
scopus_import: '1'
status: public
title: Metabolically regulated spiking could serve neuronal energy homeostasis and
protect from reactive oxygen species
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: 120
year: '2023'
...
---
_id: '14667'
abstract:
- lang: eng
text: 'For large dimensional non-Hermitian random matrices X with real or complex
independent, identically distributed, centered entries, we consider the fluctuations
of f (X) as a matrix where f is an analytic function around the spectrum of X.
We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
Gaussian fluctuations as the matrix size grows to infinity, which consists of
two independent modes corresponding to the tracial and traceless parts of A. We
find a new formula for the variance of the traceless part that involves the Frobenius
norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
pour la variance de la composante de trace nulle, qui fait intervenir la norme
de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
editor for carefully reading this paper and providing helpful comments that improved
the quality of the article. Also the authors would like to thank Peter Forrester
for pointing out the reference [12] that was absent in the previous version of the
manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105.
doi:10.1214/22-AIHP1304
apa: Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random
matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304
chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304.
ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
Annales de l’institut Henri Poincare (B) Probability and Statistics, vol.
59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics,
vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.
short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
Statistics 59 (2023) 2083–2105.
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-12-11T12:36:56Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
arxiv:
- '2112.11382'
intvolume: ' 59'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2023'
...
---
_id: '14683'
abstract:
- lang: eng
text: "Mosaic analysis with double markers (MADM) technology enables the generation
of genetic mosaic tissue in mice and high-resolution phenotyping at the individual
cell level. Here, we present a protocol for isolating MADM-labeled cells with
high yield for downstream molecular analyses using fluorescence-activated cell
sorting (FACS). We describe steps for generating MADM-labeled mice, perfusion,
single-cell suspension, and debris removal. We then detail procedures for cell
sorting by FACS and downstream analysis. This protocol is suitable for embryonic
to adult mice.\r\nFor complete details on the use and execution of this protocol,
please refer to Contreras et al. (2021).1"
acknowledged_ssus:
- _id: Bio
- _id: PreCl
acknowledgement: This research was supported by the Scientific Service Units (SSU)
at IST Austria through resources provided by the Imaging & Optics Facility (IOF)
and Preclinical Facilities (PCF). N.A. received support from FWF Firnberg-Programme
(T 1031). G.C. received support from the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411
as an ISTplus postdoctoral fellow. This work was also supported by IST Austria institutional
funds, FWF SFB F78 to S.H., and the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement no. 725780
LinPro) to S.H.
article_number: '102771'
article_processing_charge: No
article_type: review
author:
- first_name: Nicole
full_name: Amberg, Nicole
id: 4CD6AAC6-F248-11E8-B48F-1D18A9856A87
last_name: Amberg
orcid: 0000-0002-3183-8207
- first_name: Giselle T
full_name: Cheung, Giselle T
id: 471195F6-F248-11E8-B48F-1D18A9856A87
last_name: Cheung
orcid: 0000-0001-8457-2572
- first_name: Simon
full_name: Hippenmeyer, Simon
id: 37B36620-F248-11E8-B48F-1D18A9856A87
last_name: Hippenmeyer
orcid: 0000-0003-2279-1061
citation:
ama: Amberg N, Cheung GT, Hippenmeyer S. Protocol for sorting cells from mouse brains
labeled with mosaic analysis with double markers by flow cytometry. STAR Protocols.
2023;5(1). doi:10.1016/j.xpro.2023.102771
apa: Amberg, N., Cheung, G. T., & Hippenmeyer, S. (2023). Protocol for sorting
cells from mouse brains labeled with mosaic analysis with double markers by flow
cytometry. STAR Protocols. Elsevier. https://doi.org/10.1016/j.xpro.2023.102771
chicago: Amberg, Nicole, Giselle T Cheung, and Simon Hippenmeyer. “Protocol for
Sorting Cells from Mouse Brains Labeled with Mosaic Analysis with Double Markers
by Flow Cytometry.” STAR Protocols. Elsevier, 2023. https://doi.org/10.1016/j.xpro.2023.102771.
ieee: N. Amberg, G. T. Cheung, and S. Hippenmeyer, “Protocol for sorting cells from
mouse brains labeled with mosaic analysis with double markers by flow cytometry,”
STAR Protocols, vol. 5, no. 1. Elsevier, 2023.
ista: Amberg N, Cheung GT, Hippenmeyer S. 2023. Protocol for sorting cells from
mouse brains labeled with mosaic analysis with double markers by flow cytometry.
STAR Protocols. 5(1), 102771.
mla: Amberg, Nicole, et al. “Protocol for Sorting Cells from Mouse Brains Labeled
with Mosaic Analysis with Double Markers by Flow Cytometry.” STAR Protocols,
vol. 5, no. 1, 102771, Elsevier, 2023, doi:10.1016/j.xpro.2023.102771.
short: N. Amberg, G.T. Cheung, S. Hippenmeyer, STAR Protocols 5 (2023).
date_created: 2023-12-13T11:48:05Z
date_published: 2023-12-08T00:00:00Z
date_updated: 2023-12-18T08:06:14Z
day: '08'
ddc:
- '570'
department:
- _id: SiHi
doi: 10.1016/j.xpro.2023.102771
ec_funded: 1
external_id:
pmid:
- '38070137'
intvolume: ' 5'
issue: '1'
keyword:
- General Immunology and Microbiology
- General Biochemistry
- Genetics and Molecular Biology
- General Neuroscience
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.xpro.2023.102771
month: '12'
oa: 1
oa_version: Submitted Version
pmid: 1
project:
- _id: 268F8446-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: T0101031
name: Role of Eed in neural stem cell lineage progression
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 059F6AB4-7A3F-11EA-A408-12923DDC885E
grant_number: F07805
name: Molecular Mechanisms of Neural Stem Cell Lineage Progression
- _id: 260018B0-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '725780'
name: Principles of Neural Stem Cell Lineage Progression in Cerebral Cortex Development
publication: STAR Protocols
publication_identifier:
issn:
- 2666-1667
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Protocol for sorting cells from mouse brains labeled with mosaic analysis with
double markers by flow cytometry
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: 5
year: '2023'
...
---
_id: '14687'
abstract:
- lang: eng
text: The short history of research on Li-O2 batteries has seen a remarkable number
of mechanistic U-turns over the years. From the initial use of carbonate electrolytes,
that were then found to be entirely unsuitable, to the belief that (su)peroxide
was solely responsible for degradation, before the more reactive singlet oxygen
was found to form, to the hypothesis that capacity depends on a competing surface/solution
mechanism before a practically exclusive solution mechanism was identified. Herein,
we argue for an ever-fresh look at the reported data without bias towards supposedly
established explanations. We explain how the latest findings on rate and capacity
limits, as well as the origin of side reactions, are connected via the disproportionation
(DISP) step in the (dis)charge mechanism. Therefrom, directions emerge for the
design of electrolytes and mediators on how to suppress side reactions and to
enable high rate and high reversible capacity.
article_number: e202316476
article_processing_charge: Yes (via OA deal)
article_type: review
author:
- first_name: Rajesh B
full_name: Jethwa, Rajesh B
id: 4cc538d5-803f-11ed-ab7e-8139573aad8f
last_name: Jethwa
orcid: 0000-0002-0404-4356
- first_name: Soumyadip
full_name: Mondal, Soumyadip
id: d25d21ef-dc8d-11ea-abe3-ec4576307f48
last_name: Mondal
- first_name: Bhargavi
full_name: Pant, Bhargavi
id: 50c64d4d-eb97-11eb-a6c2-d33e5e14f112
last_name: Pant
- first_name: Stefan Alexander
full_name: Freunberger, Stefan Alexander
id: A8CA28E6-CE23-11E9-AD2D-EC27E6697425
last_name: Freunberger
orcid: 0000-0003-2902-5319
citation:
ama: Jethwa RB, Mondal S, Pant B, Freunberger SA. To DISP or not? The far‐reaching
reaction mechanisms underpinning Lithium‐air batteries. Angewandte Chemie International
Edition. 2023. doi:10.1002/anie.202316476
apa: Jethwa, R. B., Mondal, S., Pant, B., & Freunberger, S. A. (2023). To DISP
or not? The far‐reaching reaction mechanisms underpinning Lithium‐air batteries.
Angewandte Chemie International Edition. Wiley. https://doi.org/10.1002/anie.202316476
chicago: Jethwa, Rajesh B, Soumyadip Mondal, Bhargavi Pant, and Stefan Alexander
Freunberger. “To DISP or Not? The Far‐reaching Reaction Mechanisms Underpinning
Lithium‐air Batteries.” Angewandte Chemie International Edition. Wiley,
2023. https://doi.org/10.1002/anie.202316476.
ieee: R. B. Jethwa, S. Mondal, B. Pant, and S. A. Freunberger, “To DISP or not?
The far‐reaching reaction mechanisms underpinning Lithium‐air batteries,” Angewandte
Chemie International Edition. Wiley, 2023.
ista: Jethwa RB, Mondal S, Pant B, Freunberger SA. 2023. To DISP or not? The far‐reaching
reaction mechanisms underpinning Lithium‐air batteries. Angewandte Chemie International
Edition., e202316476.
mla: Jethwa, Rajesh B., et al. “To DISP or Not? The Far‐reaching Reaction Mechanisms
Underpinning Lithium‐air Batteries.” Angewandte Chemie International Edition,
e202316476, Wiley, 2023, doi:10.1002/anie.202316476.
short: R.B. Jethwa, S. Mondal, B. Pant, S.A. Freunberger, Angewandte Chemie International
Edition (2023).
date_created: 2023-12-15T16:10:13Z
date_published: 2023-12-14T00:00:00Z
date_updated: 2024-02-15T14:43:05Z
day: '14'
department:
- _id: StFr
- _id: GradSch
doi: 10.1002/anie.202316476
keyword:
- General Chemistry
- Catalysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.1002/anie.202316476'
month: '12'
oa: 1
oa_version: Published Version
publication: Angewandte Chemie International Edition
publication_identifier:
eissn:
- 1521-3773
issn:
- 1433-7851
publication_status: epub_ahead
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: To DISP or not? The far‐reaching reaction mechanisms underpinning Lithium‐air
batteries
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14689'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Elizabeth
full_name: Ing-Simmons, Elizabeth
last_name: Ing-Simmons
- first_name: Nick N
full_name: Machnik, Nick N
id: 3591A0AA-F248-11E8-B48F-1D18A9856A87
last_name: Machnik
orcid: 0000-0001-6617-9742
- first_name: Juan M.
full_name: Vaquerizas, Juan M.
last_name: Vaquerizas
citation:
ama: 'Ing-Simmons E, Machnik NN, Vaquerizas JM. Reply to: Revisiting the use of
structural similarity index in Hi-C. Nature Genetics. 2023;55(12):2053-2055.
doi:10.1038/s41588-023-01595-5'
apa: 'Ing-Simmons, E., Machnik, N. N., & Vaquerizas, J. M. (2023). Reply to:
Revisiting the use of structural similarity index in Hi-C. Nature Genetics.
Springer Nature. https://doi.org/10.1038/s41588-023-01595-5'
chicago: 'Ing-Simmons, Elizabeth, Nick N Machnik, and Juan M. Vaquerizas. “Reply
to: Revisiting the Use of Structural Similarity Index in Hi-C.” Nature Genetics.
Springer Nature, 2023. https://doi.org/10.1038/s41588-023-01595-5.'
ieee: 'E. Ing-Simmons, N. N. Machnik, and J. M. Vaquerizas, “Reply to: Revisiting
the use of structural similarity index in Hi-C,” Nature Genetics, vol.
55, no. 12. Springer Nature, pp. 2053–2055, 2023.'
ista: 'Ing-Simmons E, Machnik NN, Vaquerizas JM. 2023. Reply to: Revisiting the
use of structural similarity index in Hi-C. Nature Genetics. 55(12), 2053–2055.'
mla: 'Ing-Simmons, Elizabeth, et al. “Reply to: Revisiting the Use of Structural
Similarity Index in Hi-C.” Nature Genetics, vol. 55, no. 12, Springer Nature,
2023, pp. 2053–55, doi:10.1038/s41588-023-01595-5.'
short: E. Ing-Simmons, N.N. Machnik, J.M. Vaquerizas, Nature Genetics 55 (2023)
2053–2055.
date_created: 2023-12-17T23:00:53Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2023-12-18T08:51:38Z
day: '01'
department:
- _id: MaRo
doi: 10.1038/s41588-023-01595-5
external_id:
pmid:
- '38052961'
intvolume: ' 55'
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2053-2055
pmid: 1
publication: Nature Genetics
publication_identifier:
eissn:
- 1546-1718
issn:
- 1061-4036
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Reply to: Revisiting the use of structural similarity index in Hi-C'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2023'
...
---
_id: '14690'
abstract:
- lang: eng
text: Generalized multifractality characterizes system size dependence of pure scaling
local observables at Anderson transitions in all 10 symmetry classes of disordered
systems. Recently, the concept of generalized multifractality has been extended
to boundaries of critical disordered noninteracting systems. Here we study the
generalized boundary multifractality in the presence of electron-electron interaction,
focusing on the spin quantum Hall symmetry class (class C). Employing the two-loop
renormalization group analysis within the Finkel'stein nonlinear sigma model,
we compute the anomalous dimensions of the pure scaling operators located at the
boundary of the system. We find that generalized boundary multifractal exponents
are twice larger than their bulk counterparts. Exact symmetry relations between
generalized boundary multifractal exponents in the case of noninteracting systems
are explicitly broken by the interaction.
acknowledgement: The authors are grateful to J. Karcher and A. Mirlin for collaboration
on the related project. We thank I. Gruzberg and A. Mirlin for useful discussions
and comments. I.S.B. is grateful to M. Parfenov and P. Ostrovsky for collaboration
on the related project. The research was supported by Russian Science Foundation
(Grant No. 22-42-04416).
article_number: '205429'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Serafim
full_name: Babkin, Serafim
id: 41e64307-6672-11ee-b9ad-cc7a0075a479
last_name: Babkin
orcid: 0009-0003-7382-8036
- first_name: I
full_name: Burmistrov, I
last_name: Burmistrov
citation:
ama: Babkin S, Burmistrov I. Boundary multifractality in the spin quantum Hall symmetry
class with interaction. Physical Review B. 2023;108(20). doi:10.1103/PhysRevB.108.205429
apa: Babkin, S., & Burmistrov, I. (2023). Boundary multifractality in the spin
quantum Hall symmetry class with interaction. Physical Review B. American
Physical Society. https://doi.org/10.1103/PhysRevB.108.205429
chicago: Babkin, Serafim, and I Burmistrov. “Boundary Multifractality in the Spin
Quantum Hall Symmetry Class with Interaction.” Physical Review B. American
Physical Society, 2023. https://doi.org/10.1103/PhysRevB.108.205429.
ieee: S. Babkin and I. Burmistrov, “Boundary multifractality in the spin quantum
Hall symmetry class with interaction,” Physical Review B, vol. 108, no.
20. American Physical Society, 2023.
ista: Babkin S, Burmistrov I. 2023. Boundary multifractality in the spin quantum
Hall symmetry class with interaction. Physical Review B. 108(20), 205429.
mla: Babkin, Serafim, and I. Burmistrov. “Boundary Multifractality in the Spin Quantum
Hall Symmetry Class with Interaction.” Physical Review B, vol. 108, no.
20, 205429, American Physical Society, 2023, doi:10.1103/PhysRevB.108.205429.
short: S. Babkin, I. Burmistrov, Physical Review B 108 (2023).
date_created: 2023-12-17T23:00:53Z
date_published: 2023-11-15T00:00:00Z
date_updated: 2023-12-18T08:45:28Z
day: '15'
department:
- _id: MaSe
doi: 10.1103/PhysRevB.108.205429
external_id:
arxiv:
- '2308.16852'
intvolume: ' 108'
issue: '20'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2308.16852'
month: '11'
oa: 1
oa_version: Preprint
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Boundary multifractality in the spin quantum Hall symmetry class with interaction
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 108
year: '2023'
...
---
_id: '14691'
abstract:
- lang: eng
text: "Continuous Group-Key Agreement (CGKA) allows a group of users to maintain
a shared key. It is the fundamental cryptographic primitive underlying group messaging
schemes and related protocols, most notably TreeKEM, the underlying key agreement
protocol of the Messaging Layer Security (MLS) protocol, a standard for group
messaging by the IETF. CKGA works in an asynchronous setting where parties only
occasionally must come online, and their messages are relayed by an untrusted
server. The most expensive operation provided by CKGA is that which allows for
a user to refresh their key material in order to achieve forward secrecy (old
messages are secure when a user is compromised) and post-compromise security (users
can heal from compromise). One caveat of early CGKA protocols is that these update
operations had to be performed sequentially, with any user wanting to update their
key material having had to receive and process all previous updates. Late versions
of TreeKEM do allow for concurrent updates at the cost of a communication overhead
per update message that is linear in the number of updating parties. This was
shown to be indeed necessary when achieving PCS in just two rounds of communication
by [Bienstock et al. TCC’20].\r\nThe recently proposed protocol CoCoA [Alwen et
al. Eurocrypt’22], however, shows that this overhead can be reduced if PCS requirements
are relaxed, and only a logarithmic number of rounds is required. The natural
question, thus, is whether CoCoA is optimal in this setting.\r\nIn this work we
answer this question, providing a lower bound on the cost (concretely, the amount
of data to be uploaded to the server) for CGKA protocols that heal in an arbitrary
k number of rounds, that shows that CoCoA is very close to optimal. Additionally,
we extend CoCoA to heal in an arbitrary number of rounds, and propose a modification
of it, with a reduced communication cost for certain k.\r\nWe prove our bound
in a combinatorial setting where the state of the protocol progresses in rounds,
and the state of the protocol in each round is captured by a set system, each
set specifying a set of users who share a secret key. We show this combinatorial
model is equivalent to a symbolic model capturing building blocks including PRFs
and public-key encryption, related to the one used by Bienstock et al.\r\nOur
lower bound is of order k•n1+1/(k-1)/log(k), where 2≤k≤log(n) is the number of
updates per user the protocol requires to heal. This generalizes the n2 bound
for k=2 from Bienstock et al.. This bound almost matches the k⋅n1+2/(k-1) or k2⋅n1+1/(k-1)
efficiency we get for the variants of the CoCoA protocol also introduced in this
paper."
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Benedikt
full_name: Auerbach, Benedikt
id: D33D2B18-E445-11E9-ABB7-15F4E5697425
last_name: Auerbach
orcid: 0000-0002-7553-6606
- first_name: Miguel
full_name: Cueto Noval, Miguel
id: ffc563a3-f6e0-11ea-865d-e3cce03d17cc
last_name: Cueto Noval
- first_name: Guillermo
full_name: Pascual Perez, Guillermo
id: 2D7ABD02-F248-11E8-B48F-1D18A9856A87
last_name: Pascual Perez
orcid: 0000-0001-8630-415X
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
citation:
ama: 'Auerbach B, Cueto Noval M, Pascual Perez G, Pietrzak KZ. On the cost of post-compromise
security in concurrent Continuous Group-Key Agreement. In: 21st International
Conference on Theory of Cryptography. Vol 14371. Springer Nature; 2023:271-300.
doi:10.1007/978-3-031-48621-0_10'
apa: 'Auerbach, B., Cueto Noval, M., Pascual Perez, G., & Pietrzak, K. Z. (2023).
On the cost of post-compromise security in concurrent Continuous Group-Key Agreement.
In 21st International Conference on Theory of Cryptography (Vol. 14371,
pp. 271–300). Taipei, Taiwan: Springer Nature. https://doi.org/10.1007/978-3-031-48621-0_10'
chicago: Auerbach, Benedikt, Miguel Cueto Noval, Guillermo Pascual Perez, and Krzysztof
Z Pietrzak. “On the Cost of Post-Compromise Security in Concurrent Continuous
Group-Key Agreement.” In 21st International Conference on Theory of Cryptography,
14371:271–300. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-48621-0_10.
ieee: B. Auerbach, M. Cueto Noval, G. Pascual Perez, and K. Z. Pietrzak, “On the cost
of post-compromise security in concurrent Continuous Group-Key Agreement,” in
21st International Conference on Theory of Cryptography, Taipei, Taiwan,
2023, vol. 14371, pp. 271–300.
ista: 'Auerbach B, Cueto Noval M, Pascual Perez G, Pietrzak KZ. 2023. On the cost
of post-compromise security in concurrent Continuous Group-Key Agreement. 21st
International Conference on Theory of Cryptography. TCC: Theory of Cryptography,
LNCS, vol. 14371, 271–300.'
mla: Auerbach, Benedikt, et al. “On the Cost of Post-Compromise Security in Concurrent
Continuous Group-Key Agreement.” 21st International Conference on Theory of
Cryptography, vol. 14371, Springer Nature, 2023, pp. 271–300, doi:10.1007/978-3-031-48621-0_10.
short: B. Auerbach, M. Cueto Noval, G. Pascual Perez, K.Z. Pietrzak, in:, 21st International
Conference on Theory of Cryptography, Springer Nature, 2023, pp. 271–300.
conference:
end_date: 2023-12-02
location: Taipei, Taiwan
name: 'TCC: Theory of Cryptography'
start_date: 2023-11-29
date_created: 2023-12-17T23:00:53Z
date_published: 2023-11-27T00:00:00Z
date_updated: 2023-12-18T08:36:51Z
day: '27'
department:
- _id: KrPi
doi: 10.1007/978-3-031-48621-0_10
intvolume: ' 14371'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2023/1123
month: '11'
oa: 1
oa_version: Preprint
page: 271-300
publication: 21st International Conference on Theory of Cryptography
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031486203'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the cost of post-compromise security in concurrent Continuous Group-Key
Agreement
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14371
year: '2023'
...
---
_id: '14692'
abstract:
- lang: eng
text: "The generic-group model (GGM) aims to capture algorithms working over groups
of prime order that only rely on the group operation, but do not exploit any additional
structure given by the concrete implementation of the group. In it, it is possible
to prove information-theoretic lower bounds on the hardness of problems like the
discrete logarithm (DL) or computational Diffie-Hellman (CDH). Thus, since its
introduction, it has served as a valuable tool to assess the concrete security
provided by cryptographic schemes based on such problems. A work on the related
algebraic-group model (AGM) introduced a method, used by many subsequent works,
to adapt GGM lower bounds for one problem to another, by means of conceptually
simple reductions.\r\nIn this work, we propose an alternative approach to extend
GGM bounds from one problem to another. Following an idea by Yun [EC15], we show
that, in the GGM, the security of a large class of problems can be reduced to
that of geometric search-problems. By reducing the security of the resulting geometric-search
problems to variants of the search-by-hypersurface problem, for which information
theoretic lower bounds exist, we give alternative proofs of several results that
used the AGM approach.\r\nThe main advantage of our approach is that our reduction
from geometric search-problems works, as well, for the GGM with preprocessing
(more precisely the bit-fixing GGM introduced by Coretti, Dodis and Guo [Crypto18]).
As a consequence, this opens up the possibility of transferring preprocessing
GGM bounds from one problem to another, also by means of simple reductions. Concretely,
we prove novel preprocessing bounds on the hardness of the d-strong discrete logarithm,
the d-strong Diffie-Hellman inversion, and multi-instance CDH problems, as well
as a large class of Uber assumptions. Additionally, our approach applies to Shoup’s
GGM without additional restrictions on the query behavior of the adversary, while
the recent works of Zhang, Zhou, and Katz [AC22] and Zhandry [Crypto22] highlight
that this is not the case for the AGM approach."
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Benedikt
full_name: Auerbach, Benedikt
id: D33D2B18-E445-11E9-ABB7-15F4E5697425
last_name: Auerbach
orcid: 0000-0002-7553-6606
- first_name: Charlotte
full_name: Hoffmann, Charlotte
id: 0f78d746-dc7d-11ea-9b2f-83f92091afe7
last_name: Hoffmann
orcid: 0000-0003-2027-5549
- first_name: Guillermo
full_name: Pascual Perez, Guillermo
id: 2D7ABD02-F248-11E8-B48F-1D18A9856A87
last_name: Pascual Perez
orcid: 0000-0001-8630-415X
citation:
ama: 'Auerbach B, Hoffmann C, Pascual Perez G. Generic-group lower bounds via reductions
between geometric-search problems: With and without preprocessing. In: 21st
International Conference on Theory of Cryptography. Vol 14371. Springer Nature;
2023:301-330. doi:10.1007/978-3-031-48621-0_11'
apa: 'Auerbach, B., Hoffmann, C., & Pascual Perez, G. (2023). Generic-group
lower bounds via reductions between geometric-search problems: With and without
preprocessing. In 21st International Conference on Theory of Cryptography
(Vol. 14371, pp. 301–330). Springer Nature. https://doi.org/10.1007/978-3-031-48621-0_11'
chicago: 'Auerbach, Benedikt, Charlotte Hoffmann, and Guillermo Pascual Perez. “Generic-Group
Lower Bounds via Reductions between Geometric-Search Problems: With and without
Preprocessing.” In 21st International Conference on Theory of Cryptography,
14371:301–30. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-48621-0_11.'
ieee: 'B. Auerbach, C. Hoffmann, and G. Pascual Perez, “Generic-group lower bounds
via reductions between geometric-search problems: With and without preprocessing,”
in 21st International Conference on Theory of Cryptography, 2023, vol.
14371, pp. 301–330.'
ista: 'Auerbach B, Hoffmann C, Pascual Perez G. 2023. Generic-group lower bounds
via reductions between geometric-search problems: With and without preprocessing.
21st International Conference on Theory of Cryptography. , LNCS, vol. 14371, 301–330.'
mla: 'Auerbach, Benedikt, et al. “Generic-Group Lower Bounds via Reductions between
Geometric-Search Problems: With and without Preprocessing.” 21st International
Conference on Theory of Cryptography, vol. 14371, Springer Nature, 2023, pp.
301–30, doi:10.1007/978-3-031-48621-0_11.'
short: B. Auerbach, C. Hoffmann, G. Pascual Perez, in:, 21st International Conference
on Theory of Cryptography, Springer Nature, 2023, pp. 301–330.
date_created: 2023-12-17T23:00:54Z
date_published: 2023-11-27T00:00:00Z
date_updated: 2023-12-18T09:17:03Z
day: '27'
department:
- _id: KrPi
doi: 10.1007/978-3-031-48621-0_11
intvolume: ' 14371'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2023/808
month: '11'
oa: 1
oa_version: Preprint
page: 301-330
publication: 21st International Conference on Theory of Cryptography
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031486203'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Generic-group lower bounds via reductions between geometric-search problems:
With and without preprocessing'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14371
year: '2023'
...
---
_id: '14693'
abstract:
- lang: eng
text: "Lucas sequences are constant-recursive integer sequences with a long history
of applications in cryptography, both in the design of cryptographic schemes and
cryptanalysis. In this work, we study the sequential hardness of computing Lucas
sequences over an RSA modulus.\r\nFirst, we show that modular Lucas sequences
are at least as sequentially hard as the classical delay function given by iterated
modular squaring proposed by Rivest, Shamir, and Wagner (MIT Tech. Rep. 1996)
in the context of time-lock puzzles. Moreover, there is no obvious reduction in
the other direction, which suggests that the assumption of sequential hardness
of modular Lucas sequences is strictly weaker than that of iterated modular squaring.
In other words, the sequential hardness of modular Lucas sequences might hold
even in the case of an algorithmic improvement violating the sequential hardness
of iterated modular squaring.\r\nSecond, we demonstrate the feasibility of constructing
practically-efficient verifiable delay functions based on the sequential hardness
of modular Lucas sequences. Our construction builds on the work of Pietrzak (ITCS
2019) by leveraging the intrinsic connection between the problem of computing
modular Lucas sequences and exponentiation in an appropriate extension field."
acknowledgement: "Home Theory of Cryptography Conference paper\r\n(Verifiable) Delay
Functions from Lucas Sequences\r\nDownload book PDF\r\nDownload book EPUB\r\nSimilar
content being viewed by others\r\n\r\nSlider with three content items shown per
slide. Use the Previous and Next buttons to navigate the slides or the slide controller
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2\r\nGo to slide 3\r\n(Verifiable) Delay Functions from Lucas Sequences\r\nCharlotte
Hoffmann, Pavel Hubáček, Chethan Kamath & Tomáš Krňák \r\nConference paper\r\nFirst
Online: 27 November 2023\r\n83 Accesses\r\n\r\nPart of the Lecture Notes in Computer
Science book series (LNCS,volume 14372)\r\n\r\nAbstract\r\nLucas sequences are constant-recursive
integer sequences with a long history of applications in cryptography, both in the
design of cryptographic schemes and cryptanalysis. In this work, we study the sequential
hardness of computing Lucas sequences over an RSA modulus.\r\n\r\nFirst, we show
that modular Lucas sequences are at least as sequentially hard as the classical
delay function given by iterated modular squaring proposed by Rivest, Shamir, and
Wagner (MIT Tech. Rep. 1996) in the context of time-lock puzzles. Moreover, there
is no obvious reduction in the other direction, which suggests that the assumption
of sequential hardness of modular Lucas sequences is strictly weaker than that of
iterated modular squaring. In other words, the sequential hardness of modular Lucas
sequences might hold even in the case of an algorithmic improvement violating the
sequential hardness of iterated modular squaring.\r\n\r\nSecond, we demonstrate
the feasibility of constructing practically-efficient verifiable delay functions
based on the sequential hardness of modular Lucas sequences. Our construction builds
on the work of Pietrzak (ITCS 2019) by leveraging the intrinsic connection between
the problem of computing modular Lucas sequences and exponentiation in an appropriate
extension field.\r\n\r\nKeywords\r\nDelay functions\r\nVerifiable delay functions\r\nLucas
sequences\r\nDownload conference paper PDF\r\n\r\n1 Introduction\r\nA verifiable
delay function (VDF) \r\n is a function that satisfies two properties. First, it
is a delay function, which means it must take a prescribed (wall) time T to compute
f, irrespective of the amount of parallelism available. Second, it should be possible
for anyone to quickly verify – say, given a short proof \r\n – the value of the
function (even without resorting to parallelism), where by quickly we mean that
the verification time should be independent of or significantly smaller than T (e.g.,
logarithmic in T). If we drop either of the two requirements, then the primitive
turns out trivial to construct. For instance, for an appropriately chosen hash function
h, the delay function \r\n defined by T-times iterated hashing of the input is a
natural heuristic for an inherently sequential task which, however, seems hard to
verify more efficiently than by recomputing. On the other hand, the identity function
\r\n is trivial to verify but also easily computable. Designing a simple function
satisfying the two properties simultaneously proved to be a nontrivial task.\r\n\r\nThe
notion of VDFs was introduced in [31] and later formalised in [9]. In principle,
since the task of constructing a VDF reduces to the task of incrementally-verifiable
computation [9, 53], constructions of VDFs could leverage succinct non-interactive
arguments of knowledge (SNARKs): take any sequentially-hard function f (for instance,
iterated hashing) as the delay function and then use the SNARK on top of it as the
mechanism for verifying the computation of the delay function. However, as discussed
in [9], the resulting construction is not quite practical since we would rely on
a general-purpose machinery of SNARKs with significant overhead.\r\n\r\nEfficient
VDFs via Algebraic Delay Functions. VDFs have recently found interesting applications
in design of blockchains [17], randomness beacons [43, 51], proofs of data replication
[9], or short-lived zero-knowledge proofs and signatures [3]. Since efficiency is
an important factor there, this has resulted in a flurry of constructions of VDFs
that are tailored with application and practicality in mind. They rely on more algebraic,
structured delay functions that often involve iterating an atomic operation so that
one can resort to custom proof systems to achieve verifiability. These constructions
involve a range of algebraic settings like the RSA or class groups [5, 8, 25, 42,
55], permutation polynomials over finite fields [9], isogenies of elliptic curves
[21, 52] and, very recently, lattices [15, 28]. The constructions in [42, 55] are
arguably the most practical and the mechanism that underlies their delay function
is the same: carry out iterated squaring in groups of unknown order, like RSA groups
[47] or class groups [12]. What distinguishes these two proposals is the way verification
is carried out, i.e., how the underlying “proof of exponentiation” works: while
Pietrzak [42] resorts to an LFKN-style recursive proof system [35], Wesolowski [55]
uses a clever linear decomposition of the exponent.\r\n\r\nIterated Modular Squaring
and Sequentiality. The delay function that underlies the VDFs in [5, 25, 42, 55]
is the same, and its security relies on the conjectured sequential hardness of iterated
squaring in a group of unknown order (suggested in the context of time-lock puzzles
by Rivest, Shamir, and Wagner [48]). Given that the practically efficient VDFs all
rely on the above single delay function, an immediate open problem is to identify
additional sources of sequential hardness that are structured enough to support
practically efficient verifiability.\r\n\r\n1.1 Our Approach to (Verifiable) Delay
Functions\r\nIn this work, we study an alternative source of sequential hardness
in the algebraic setting and use it to construct efficient verifiable delay functions.
The sequentiality of our delay function relies on an atomic operation that is related
to the computation of so-called Lucas sequences [29, 34, 57], explained next.\r\n\r\nLucas
Sequences. A Lucas sequence is a constant-recursive integer sequence that satisfies
the recurrence relation\r\n\r\nfor integers P and Q.Footnote1 Specifically, the
Lucas sequences of integers \r\n and \r\n of the first and second type (respectively)
are defined recursively as\r\n\r\nwith \r\n, and\r\n\r\nwith \r\n.\r\n\r\nThese
sequences can be alternatively defined by the characteristic polynomial \r\n. Specifically,
given the discriminant \r\n of the characteristic polynomial, one can alternatively
compute the above sequences by performing operations in the extension field\r\n\r\nusing
the identities\r\n\r\nwhere \r\n and its conjugate \r\n are roots of the characteristic
polynomial. Since conjugation and exponentiation commute in the extension field
(i.e., \r\n), computing the i-th terms of the two Lucas sequences over integers
reduces to computing \r\n in the extension field, and vice versa.\r\n\r\nThe intrinsic
connection between computing the terms in the Lucas sequences and that of exponentiation
in the extension has been leveraged to provide alternative instantiations of public-key
encryption schemes like RSA and ElGamal in terms of Lucas sequences [7, 30]. However,
as we explain later, the corresponding underlying computational hardness assumptions
are not necessarily equivalent.\r\n\r\nOverview of Our Delay Function. The delay
function in [5, 25, 42, 55] is defined as the iterated squaring base x in a (safe)
RSA groupFootnote2 modulo N:\r\n\r\nOur delay function is its analogue in the setting
of Lucas sequences:\r\n\r\nAs mentioned above, computing \r\n can be carried out
equivalently in the extension field \r\n using the known relationship to roots of
the characteristic polynomial of the Lucas sequence. Thus, the delay function can
be alternatively defined as\r\n\r\nNote that the atomic operation of our delay function
is “doubling” the index of an element of the Lucas sequence modulo N (i.e., \r\n)
or, equivalently, squaring in the extension field \r\n (as opposed to squaring in
\r\n). Using the representation of \r\n as \r\n, squaring in \r\n can be expressed
as a combination of squaring, multiplication and addition modulo N, since\r\n\r\n(1)\r\nSince
\r\n is a group of unknown order (provided the factorization of N is kept secret),
iterated squaring remains hard here. In fact, we show in Sect. 3.2 that iterated
squaring in \r\n is at least as hard as iterated squaring for RSA moduli N. Moreover,
we conjecture in Conjecture 1 that it is, in fact, strictly harder (also see discussion
below on advantages of our approach).\r\n\r\nVerifying Modular Lucas Sequence. To
obtain a VDF, we need to show how to efficiently verify our delay function. To this
end, we show how to adapt the interactive proof of exponentiation from [42] to our
setting, which then – via the Fiat-Shamir Transform [22] – yields the non-interactive
verification algorithm.Footnote3 Thus, our main result is stated informally below.\r\n\r\nTheorem
1\r\n(Informally stated, see Theorem 2). Assuming sequential hardness of modular
Lucas sequence, there exists statistically-sound VDF in the random-oracle model.\r\n\r\nHowever,
the modification of Pietrzak’s protocol is not trivial and we have to overcome several
hurdles that we face in this task, which we elaborate on in Sect. 1.2. We conclude
this section with discussions about our results.\r\n\r\nAdvantage of Our Approach.
Our main advantage is the reliance on a potentially weaker (sequential) hardness
assumption while maintaining efficiency: we show in Sect. 3.2 that modular Lucas
sequences are at least as sequentially-hard as the classical delay function given
by iterated modular squaring [48]. Despite the linear recursive structure of Lucas
sequences, there is no obvious reduction in the other direction, which suggests
that the assumption of sequential hardness of modular Lucas sequences is strictly
weaker than that of iterated modular squaring (Conjecture 1). In other words, the
sequential hardness of modular Lucas sequences might hold even in the case of an
algorithmic improvement violating the sequential hardness of iterated modular squaring.
Even though both assumptions need the group order to be hidden, we believe that
there is need for a nuanced analysis of sequential hardness assumptions in hidden
order groups, especially because all current delay functions that provide sufficient
structure for applications are based on iterated modular squaring. If the iterated
modular squaring assumption is broken, our delay function is currently the only
practical alternative in the RSA group.\r\n\r\nDelay Functions in Idealised Models.
Recent works studied the relationship of group-theoretic (verifiable) delay functions
to the hardness of factoring in idealised models such as the algebraic group model
and the generic ring model [27, 50]. In the generic ring model, Rotem and Segev
[50] showed the equivalence of straight-line delay functions in the RSA setting
and factoring. Our construction gives rise to a straight-line delay function and,
by their result, its sequentiality is equivalent to factoring for generic algorithms.
However, their result holds only in the generic ring model and leaves the relationship
between the two assumptions unresolved in the standard model.\r\n\r\nCompare this
with the status of the RSA assumption and factoring. On one hand, we know that in
the generic ring model, RSA and factoring are equivalent [2]. Yet, it is possible
to rule out certain classes of reductions from factoring to RSA in the standard
model [11]. Most importantly, despite the equivalence in the generic ring model,
there is currently no reduction from factoring to RSA in the standard model and
it remains one of the major open problems in number theory related to cryptography
since the introduction of the RSA assumption.\r\n\r\nIn summary, speeding up iterated
squaring by a non-generic algorithm could be possible (necessarily exploiting the
representations of ring elements modulo N), while such an algorithm may not lead
to a speed-up in the computation of modular Lucas sequences despite the result of
Rotem and Segev [50].\r\n\r\n1.2 Technical Overview\r\nPietrzak’s VDF. Let \r\n
be an RSA modulus where p and q are safe primes and let x be a random element from
\r\n. At its core, Pietrzak’s VDF relies on the interactive protocol for the statement\r\n\r\n“(N,
x, y, T) satisfies \r\n”.\r\n\r\nThe protocol is recursive and, in a round-by-round
fashion, reduces the claim to a smaller statement by halving the time parameter.
To be precise, in each round, the (honest) prover sends the “midpoint” \r\n of the
current statement to the verifier and they together reduce the statement to\r\n\r\n“\r\n
satisfies \r\n”,\r\n\r\nwhere \r\n and \r\n for a random challenge r. This is continued
till \r\n is obtained at which point the verifier simply checks whether \r\n using
a single modular squaring.\r\n\r\nSince the challenges r are public, the protocol
can be compiled into a non-interactive one using the Fiat-Shamir transform [22]
and this yields a means to verify the delay function\r\n\r\nIt is worth pointing
out that the choice of safe primes is crucial for proving soundness: in case the
group has easy-to-find elements of small order then it becomes easy to break soundness
(see, e.g., [10]).\r\n\r\nAdapting Pietrzak’s Protocol to Lucas Sequences. For a
modulus \r\n and integers \r\n, recall that our delay function is defined as\r\n\r\nor
equivalently\r\n\r\nfor the discriminant \r\n of the characteristic polynomial \r\n.
Towards building a verification algorithm for this delay function, the natural first
step is to design an interactive protocol for the statement\r\n\r\n“(N, P, Q, y,
T) satisfies \r\n.”\r\n\r\nIt turns out that the interactive protocol from [42]
can be adapted for this purpose. However, we encounter two technicalities in this
process.\r\n\r\nDealing with elements of small order. The main problem that we face
while designing our protocol is avoiding elements of small order. In the case of
[42], this was accomplished by moving to the setting of signed quadratic residues
[26] in which the sub-groups are all of large order. It is not clear whether a corresponding
object exists for our algebraic setting. However, in an earlier draft of Pietrzak’s
protocol [41], this problem was dealt with in a different manner: the prover sends
a square root of \r\n, from which the original \r\n can be recovered easily (by
squaring it) with a guarantee that the result lies in a group of quadratic residues
\r\n. Notice that the prover knows the square root of \r\n, because it is just a
previous term in the sequence he computed.\r\n\r\nIn our setting, we cannot simply
ask for the square root of the midpoint as the subgroup of \r\n we effectively work
in has a different structure. Nevertheless, we can use a similar approach: for an
appropriately chosen small a, we provide an a-th root of \r\n (instead of \r\n itself)
to the prover in the beginning of the protocol. The prover then computes the whole
sequence for \r\n. In the end, he has the a-th root of every term of the original
sequence and he can recover any element of the original sequence by raising to the
a-th power.\r\n\r\nSampling strong modulus. The second technicality is related to
the first one. In order to ensure that we can use the above trick, we require a
modulus where the small subgroups are reasonably small not only in the group \r\n
but also in the extension \r\n. Thus the traditional sampling algorithms that are
used to sample strong primes (e.g., [46]) are not sufficient for our purposes. However,
sampling strong primes that suit our criteria can still be carried out efficiently
as we show in the full version.\r\n\r\nComparing Our Technique with [8, 25]. The
VDFs in [8, 25] are also inspired by [42] and, hence, faced the same problem of
low-order elements. In [8], this is dealt with by amplifying the soundness at the
cost of parallel repetition and hence larger proofs and extra computation. In [25],
the number of repetitions of [8] is reduced significantly by introducing the following
technique: The exponent of the initial instance is reduced by some parameter \r\n
and at the end of an interactive phase, the verifier performs final exponentiation
with \r\n, thereby weeding out potential false low-order elements in the claim.
This technique differs from the approach taken in our work in the following ways:
The technique from [25] works in arbitrary groups but it requires the parameter
\r\n to be large and of a specific form. In particular, the VDF becomes more efficient
when \r\n is larger than \r\n. In our protocol, we work in RSA groups whose modulus
is the product of primes that satisfy certain conditions depending on a. This enables
us to choose a parameter a that is smaller than a statistical security parameter
and thereby makes the final exponentiation performed by the verifier much more efficient.
Further, a can be any natural number, while \r\n must be set as powers of all small
prime numbers up a certain bound in [25].\r\n\r\n1.3 More Related Work\r\nTimed
Primitives. The notion of VDFs was introduced in [31] and later formalised in [9].
VDFs are closely related to the notions of time-lock puzzles [48] and proofs of
sequential work [36]. Roughly speaking, a time-lock puzzle is a delay function that
additionally allows efficient sampling of the output via a trapdoor. A proof of
sequential work, on the other hand, is a delay “multi-function”, in the sense that
the output is not necessarily unique. Constructions of time-lock puzzles are rare
[6, 38, 48], and there are known limitations: e.g., that it cannot exist in the
random-oracle model [36]. However, we know how to construct proofs of sequential
work in the random-oracle model [1, 16, 19, 36].\r\n\r\nSince VDFs have found several
applications, e.g., in the design of resource-efficient blockchains [17], randomness
beacons [43, 51] and proof of data replication [9], there have been several constructions.
Among them, the most notable are the iterated-squaring based construction from [8,
25, 42, 55], the permutation-polynomial based construction from [9], the isogenies-based
construction from [13, 21, 52] and the construction from lattice problems [15, 28].
The constructions in [42, 55] are quite practical (see the survey [10]) and the
VDF deployed in the cryptocurrency Chia is basically their construction adapted
to the algebraic setting of class groups [17]. This is arguably the closest work
to ours. On the other hand, the constructions from [21, 52], which work in the algebraic
setting of isogenies of elliptic curves where no analogue of square and multiply
is known, simply rely on “exponentiation”. Although, these constructions provide
a certain form of quantum resistance, they are presently far from efficient. Freitag
et al. [23] constructed VDFs from any sequentially hard function and polynomial
hardness of learning with errors, the first from standard assumptions. The works
of Cini, Lai, and Malavolta [15, 28] constructed the first VDF from lattice-based
assumptions and conjectured it to be post-quantum secure.\r\n\r\nSeveral variants
of VDFs have also been proposed. A VDF is said to be unique if the proof that is
used for verification is unique [42]. Recently, Choudhuri et al. [5] constructed
unique VDFs from the sequential hardness of iterated squaring in any RSA group and
polynomial hardness of LWE. A VDF is tight [18] if the gap between simply computing
the function and computing it with a proof is small. Yet another extension is a
continuous VDF [20]. The feasibility of time-lock puzzles and proofs of sequential
works were recently extended to VDFs. It was shown [50] that the latter requirement,
i.e., working in a group of unknown order, is inherent in a black-box sense. It
was shown in [18, 37] that there are barriers to constructing tight VDFs in the
random-oracle model.\r\n\r\nVDFs also have surprising connection to complexity theory
[14, 20, 33].\r\n\r\nWork Related to Lucas Sequences. Lucas sequences have long
been studied in the context of number theory: see for example [45] or [44] for a
survey of its applications to number theory. Its earliest application to cryptography
can be traced to the \r\n factoring algorithm [56]. Constructive applications were
found later thanks to the parallels with exponentiation. Several encryption and
signature schemes were proposed, most notably the LUC family of encryption and signatures
[30, 39]. It was later shown that some of these schemes can be broken or that the
advantages it claimed were not present [7]. Other applications can be found in [32].\r\n\r\n2
Preliminaries\r\n2.1 Interactive Proof Systems\r\nInteractive Protocols. An interactive
protocol consists of a pair \r\n of interactive Turing machines that are run on
a common input \r\n. The first machine \r\n is the prover and is computationally
unbounded. The second machine \r\n is the verifier and is probabilistic polynomial-time.\r\n\r\nIn
an \r\n-round (i.e., \r\n-message) interactive protocol, in each round \r\n, first
\r\n sends a message \r\n to \r\n and then \r\n sends a message \r\n to \r\n, where
\r\n is a finite alphabet. At the end of the interaction, \r\n runs a (deterministic)
Turing machine on input \r\n. The interactive protocol is public-coin if \r\n is
a uniformly distributed random string in \r\n.\r\n\r\nInteractive Proof Systems.
The notion of an interactive proof for a language L is due to Goldwasser, Micali
and Rackoff [24].\r\n\r\nDefinition 1\r\nFor a function \r\n, an interactive protocol
\r\n is an \r\n-statistically-sound interactive proof system for L if:\r\n\r\nCompleteness:
For every \r\n, if \r\n interacts with \r\n on common input \r\n, then \r\n accepts
with probability 1.\r\n\r\nSoundness: For every \r\n and every (computationally-unbounded)
cheating prover strategy \r\n, the verifier \r\n accepts when interacting with \r\n
with probability less than \r\n, where \r\n is called the soundness error.\r\n\r\n2.2
Verifiable Delay Functions\r\nWe adapt the definition of verifiable delay functions
from [9] but we decouple the verifiability and sequentiality properties for clarity
of exposition of our results. First, we present the definition of a delay function.\r\n\r\nDefinition
2\r\nA delay function \r\n consists of a triple of algorithms with the following
syntax:\r\n\r\n:\r\n\r\nOn input a security parameter \r\n, the algorithm \r\n outputs
public parameters \r\n.\r\n\r\n:\r\n\r\nOn input public parameters \r\n and a time
parameter \r\n, the algorithm \r\n outputs a challenge x.\r\n\r\n:\r\n\r\nOn input
a challenge pair (x, T), the (deterministic) algorithm \r\n outputs the value y
of the delay function in time T.\r\n\r\nThe security property required of a delay
function is sequential hardness as defined below.\r\n\r\nDefinition 3\r\n(Sequentiality).
We say that a delay function \r\n satisfies the sequentiality property, if there
exists an \r\n such that for all \r\n and for every adversary \r\n, where \r\n uses
\r\n processors and runs in time \r\n, there exists a negligible function \r\n such
that\r\n\r\nfigure a\r\nA few remarks about our definition of sequentiality are
in order:\r\n\r\n1.\r\nWe require computing \r\n to be hard in less than T sequential
steps even using any polynomially-bounded amount of parallelism and precomputation.
Note that it is necessary to bound the amount of parallelism, as an adversary could
otherwise break the underlying hardness assumption (e.g. hardness of factorization).
Analogously, T should be polynomial in \r\n as, otherwise, breaking the underlying
hardness assumptions becomes easier than computing \r\n itself for large values
of T.\r\n\r\n2.\r\nAnother issue is what bound on the number of sequential steps
of the adversary should one impose. For example, the delay function based on T repeated
modular squarings can be computed in sequential time \r\n using polynomial parallelism
[4]. Thus, one cannot simply bound the sequential time of the adversary by o(T).
Similarly to [38], we adapt the \r\n bound for \r\n which, in particular, is asymptotically
smaller than \r\n.\r\n\r\n3.\r\nWithout loss of generality, we assume that the size
of \r\n is at least linear in n and the adversary A does not have to get the unary
representation of the security parameter \r\n as its input.\r\n\r\nThe definition
of verifiable delay function extends a delay function with the possibility to compute
publicly-verifiable proofs of correctness of the output value.\r\n\r\nDefinition
4\r\nA delay function \r\n is a verifiable delay function if it is equipped with
two additional algorithms \r\n and \r\n with the following syntax:\r\n\r\n:\r\n\r\nOn
input public parameters and a challenge pair (x, T), the \r\n algorithm outputs
\r\n, where \r\n is a proof that the output y is the output of \r\n.\r\n\r\n:\r\n\r\nOn
input public parameters, a challenge pair (x, T), and an output/proof pair \r\n,
the (deterministic) algorithm \r\n outputs either \r\n or \r\n.\r\n\r\nIn addition
to sequentiality (inherited from the underlying delay function), the \r\n and \r\n
algorithms must together satisfy correctness and (statistical) soundness as defined
below.\r\n\r\nDefinition 5\r\n(Correctness). A verifiable delay function \r\n is
correct if for all \r\n\r\nfigure b\r\nDefinition 6\r\n(Statistical soundness).
A verifiable delay function \r\n is statistically sound if for every (computationally
unbounded) malicious prover \r\n there exists a negligible function \r\n such that
for all \r\n\r\nfigure c\r\n3 Delay Functions from Lucas Sequences\r\nIn this section,
we propose a delay function based on Lucas sequences and prove its sequentiality
assuming that iterated squaring in a group of unknown order is sequential (Sect.
3.1). Further, we conjecture (Sect. 3.2) that our delay function candidate is even
more robust than its predecessor proposed by Rivest, Shamir, and Wagner [48]. Finally,
we turn our delay function candidate into a verifiable delay function (Sect. 4).\r\n\r\n3.1
The Atomic Operation\r\nOur delay function is based on subsequences of Lucas sequences,
whose indexes are powers of two. Below, we use \r\n to denote the set of non-negative
integers.\r\n\r\nDefinition 7\r\nFor integers \r\n, the Lucas sequences \r\n and
\r\n are defined for all \r\n as\r\n\r\nwith \r\n and \r\n, and\r\n\r\nwith \r\n
and \r\n.\r\n\r\nWe define subsequences \r\n, respectively \r\n, of \r\n, respectively
\r\n for all \r\n as\r\n\r\n(2)\r\nAlthough the value of \r\n depends on parameters
(P, Q), we omit (P, Q) from the notation because these parameters will be always
obvious from the context.\r\n\r\nThe underlying atomic operation for our delay function
is\r\n\r\nThere are several ways to compute \r\n in T sequential steps, and we describe
two of them below.\r\n\r\nAn Approach Based on Squaring in a Suitable Extension
Ring. To compute the value \r\n, we can use the extension ring \r\n, where \r\n
is the discriminant of the characteristic polynomial \r\n of the Lucas sequence.
The characteristic polynomial f(z) has a root \r\n, and it is known that, for all
\r\n, it holds that\r\n\r\nThus, by iterated squaring of \r\n, we can compute terms
of our target subsequences. To get a better understanding of squaring in the extension
ring, consider the representation of the root \r\n for some \r\n. Then,\r\n\r\nThen,
the atomic operation of our delay function can be interpreted as \r\n, defined for
all \r\n as\r\n\r\n(3)\r\nAn Approach Based on Known Identities. Many useful identities
for members of modular Lucas sequences are known, such as\r\n\r\n(4)\r\nSetting
\r\n we get\r\n\r\n(5)\r\nThe above identities are not hard to derive (see, e.g.,
Lemma 12.5 in [40]). Indexes are doubled on each of application of the identities
in Eq. (5), and, thus, for \r\n, we define an auxiliary sequence \r\n by \r\n. Using
the identities in Eq. (5), we get recursive equations\r\n\r\n(6)\r\nThen, the atomic
operation of our delay function can be interpreted as \r\n, defined for all \r\n
as\r\n\r\n(7)\r\nAfter a closer inspection, the reader may have an intuition that
an auxiliary sequence \r\n, which introduces a third state variable, is redundant.
This intuition is indeed right. In fact, there is another easily derivable identity\r\n\r\n(8)\r\nwhich
can be found, e.g., as Lemma 12.2 in [40]. On the other hand, Eq. (8) is quite interesting
because it allows us to compute large powers of an element \r\n using two Lucas
sequences. We use this fact in the security reduction in Sect. 3.2. Our construction
of a delay function, denoted \r\n, is given in Fig. 1.\r\n\r\nFig. 1.\r\nfigure
1\r\nOur delay function candidate \r\n based on a modular Lucas sequence.\r\n\r\nFull
size image\r\nOn the Discriminant D. Notice that whenever D is a quadratic residue
modulo N, the value \r\n is an element of \r\n and hence \r\n. By definition, LCS.Gen
generates a parameter D that is a quadratic residue with probability 1/4, so it
might seem that in one fourth of the cases there is another approach to compute
\r\n: find the element \r\n and then perform n sequential squarings in the group
\r\n. However, it is well known that finding square roots of uniform elements in
\r\n is equivalent to factoring the modulus N, so this approach is not feasible.
We can therefore omit any restrictions on the discriminant D in the definition of
our delay function LCS.\r\n\r\n3.2 Reduction from RSW Delay Function\r\nIn order
to prove the sequentiality property (Definition 3) of our candidate \r\n, we rely
on the standard conjecture of the sequentiality of the \r\n time-lock puzzles, implicitly
stated in [48] as the underlying hardness assumption.\r\n\r\nDefinition 8\r\n(\r\n
delay function). The \r\n delay function is defined as follows:\r\n\r\n: Samples
two n-bit primes p and q and outputs \r\n.\r\n\r\n: Outputs an x sampled from the
uniform distribution on \r\n.\r\n\r\n: Outputs \r\n.\r\n\r\nTheorem 2\r\nIf the
\r\n delay function has the sequentiality property, then the \r\n delay function
has the sequentiality property.\r\n\r\nProof\r\nSuppose there exists an adversary
\r\n who contradicts the sequentiality of \r\n, where \r\n is a precomputation algorithm
and \r\n is an online algorithm. We construct an adversary \r\n who contradicts
the sequentiality of \r\n as follows:\r\n\r\nThe algorithm \r\n is defined identically
to the algorithm \r\n.\r\n\r\nOn input \r\n, \r\n picks a P from the uniform distribution
on \r\n, sets\r\n\r\nand it runs \r\n to compute \r\n. The algorithm \r\n computes
\r\n using the identity in Eq. (8).\r\n\r\nNote that the input distribution for
the algorithm \r\n produced by \r\n differs from the one produced by \r\n, because
the \r\n generator samples Q from the uniform distribution on \r\n (instead of \r\n).
However, this is not a problem since the size of \r\n is negligible compared to
the size of \r\n, so the statistical distance between the distribution of D produced
by \r\n and the distribution of D sampled by \r\n is negligible in the security
parameter. Thus, except for a negligible multiplicative loss, the adversary \r\n
attains the same success probability of breaking the sequentiality of \r\n as the
probability of \r\n breaking the sequentiality of \r\n – a contradiction to the
assumption of the theorem. \r\n\r\nWe believe that the converse implication to
Theorem 2 is not true, i.e., that breaking the sequentiality of \r\n does not necessarily
imply breaking the sequentiality of \r\n. Below, we state it as a conjecture.\r\n\r\nConjecture
1\r\nSequentiality of \r\n cannot be reduced to sequentiality of \r\n.\r\n\r\nOne
reason why the above conjecture might be true is that, while the \r\n delay function
is based solely only on multiplication in the group \r\n, our \r\n delay function
uses the full arithmetic (addition and multiplication) of the commutative ring \r\n.\r\n\r\nOne
way to support the conjecture would be to construct an algorithm that speeds up
iterated squaring but is not immediately applicable to Lucas sequences. By [49]
we know that this cannot be achieved by a generic algorithm. A non-generic algorithm
that solves iterated squaring in time \r\n is presented in [4]. The main tool of
their construction is the Explicit Chinese Remainder Theorem modulo N. However,
a similiar theorem exists also for univariate polynomial rings, which suggests that
a similar speed-up can be obtained for our delay function by adapting the techniques
in [4] to our setting.\r\n\r\n4 VDF from Lucas Sequences\r\nIn Sect. 3.1 we saw
different ways of computing the atomic operation of the delay function. Computing
\r\n in the extension field seems to be the more natural and time and space effective
approach. Furthermore, writing the atomic operation \r\n as \r\n is very clear,
and, thus, we follow this approach throughout the rest of the paper.\r\n\r\n4.1
Structure of \r\nTo construct a VDF based on Lucas sequences, we use an algebraic
extension\r\n\r\n(9)\r\nwhere N is an RSA modulus and \r\n. In this section, we
describe the structure of the algebraic extension given in Expression (9). Based
on our understanding of the structure of the above algebraic extension, we can conclude
that using modulus N composed of safe primes (i.e., for all prime factors p of N,
\r\n has a large prime divisor) is necessary but not sufficient condition for security
of our construction. We specify some sufficient conditions on factors of N in the
subsequent Sect. 4.2.\r\n\r\nFirst, we introduce some simplifying notation for quotient
rings.\r\n\r\nDefinition 9\r\nFor \r\n and \r\n, we denote by \r\n the quotient
ring \r\n, where (m, f(x)) denotes the ideal of the ring \r\n generated by m and
f(x).\r\n\r\nObservation 1, below, allows us to restrict our analysis only to the
structure of \r\n for prime \r\n.\r\n\r\nObservation 1\r\nLet \r\n be distinct primes,
\r\n and \r\n. Then\r\n\r\nProof\r\nUsing the Chinese reminder theorem, we get\r\n\r\nas
claimed. \r\n\r\nThe following lemma characterizes the structure of \r\n with
respect to the discriminant of f. We use \r\n to denote the standard Legendre symbol.\r\n\r\nLemma
1\r\nLet \r\n and \r\n be a polynomial of degree 2 with the discriminant D. Then\r\n\r\nProof\r\nWe
consider each case separately:\r\n\r\nIf \r\n, then f(x) is irreducible over \r\n
and \r\n is a field with \r\n elements. Since \r\n is a finite field, \r\n is cyclic
and contains \r\n elements.\r\n\r\nIf \r\n, then \r\n and f has some double root
\r\n and it can be written as \r\n for some \r\n. Since the ring \r\n is isomorphic
to the ring \r\n (consider the isomorphism \r\n), we can restrict ourselves to describing
the structure of \r\n.\r\n\r\nWe will prove that the function \r\n,\r\n\r\nis an
isomorphism. First, the polynomial \r\n is invertible if and only if \r\n (inverse
is \r\n). For the choice \r\n, we have\r\n\r\nThus \r\n is onto. Second, \r\n is,
in fact, a bijection, because\r\n\r\n(10)\r\nFinally, \r\n is a homomorphism, because\r\n\r\nIf
\r\n, then f(x) has two roots \r\n. We have an isomorphism\r\n\r\nand \r\n. \r\n\r\n4.2
Strong Groups and Strong Primes\r\nTo achieve the verifiability property of our
construction, we need \r\n to contain a strong subgroup (defined next) of order
asymptotically linear in p. We remark that our definition of strong primes is stronger
than the one by Rivest and Silverman [46].\r\n\r\nDefinition 10\r\n(Strong groups).
For \r\n, we say that a non-trivial group \r\n is \r\n-strong, if the order of each
non-trivial subgroup of \r\n is greater than \r\n.\r\n\r\nObservation 2\r\nIf \r\n
and \r\n are \r\n-strong groups, then \r\n is a \r\n-strong group.\r\n\r\nIt can
be seen from Lemma 1 that \r\n always contains groups of small order (e.g. \r\n).
To avoid these, we descend into the subgroup of a-th powers of elements of \r\n.
Below, we introduce the corresponding notation.\r\n\r\nDefinition 11\r\nFor an Abelian
group \r\n and \r\n, we define the subgroup \r\n of \r\n in the multiplicative notation
and \r\n in the additive notation.\r\n\r\nFurther, we show in Lemma 2 below that
\r\n-strong primality (defined next) is a sufficient condition for \r\n to be a
\r\n-strong group.\r\n\r\nDefinition 12\r\n(Strong primes). Let \r\n and \r\n. We
say that p is a \r\n-strong prime, if \r\n and there exists \r\n, \r\n, such that
\r\n and every prime factor of W is greater than \r\n.\r\n\r\nSince a is a public
parameter in our setup, super-polynomial a could reveal partial information about
the factorization of N. However, we could allow a to be polynomial in \r\n while
maintaining hardness of factoring N.Footnote4 For the sake of simplicity of Definition
12, we rather use stronger condition \r\n. The following simple observation will
be useful for proving Lemma 2.\r\n\r\nObservation 3\r\nFor \r\n.\r\n\r\nLemma 2\r\nLet
p be a \r\n-strong prime and \r\n be a quadratic polynomial. Then, \r\n is a \r\n-strong
group.\r\n\r\nProof\r\nFrom definition of the strong primes, there exists \r\n,
whose factors are bigger than \r\n and \r\n. We denote \r\n a factor of W. Applying
Observation 3 to Lemma 1, we get\r\n\r\nIn particular, we used above the fact that
Observation 2 implies that \r\n as explained next. Since \r\n, all divisors of \r\n
are divisors of aW. By definition of a and W in Definition 12, we also have that
\r\n, which implies that any factor of \r\n divides either a or W, but not both.
When we divide \r\n by all the common divisors with a, only the common divisors
with W are left, which implies \r\n. The proof of the lemma is now completed by
Observation 2.\r\n\r\nCorollary 1\r\nLet p be a \r\n-strong prime, q be a \r\n-strong
prime, \r\n, \r\n, \r\n and \r\n. Then \r\n is \r\n-strong.\r\n\r\n4.3 Our Interactive
Protocol\r\nOur interactive protocol is formally described in Fig. 3. To understand
this protocol, we first recall the outline of Pietrzak’s interactive protocol from
Sect. 1.2 and then highlight the hurdles. Let \r\n be an RSA modulus where p and
q are strong primes and let x be a random element from \r\n. The interactive protocol
in [42] allows a prover to convince the verifier of the statement\r\n\r\n“(N, x,
y, T) satisfies \r\n”.\r\n\r\nThe protocol is recursive and in a round-by-round
fashion reduces the claim to a smaller statement by halving the time parameter.
To be precise, in each round the (honest) prover sends the “midpoint” \r\n of the
current statement to the verifier and they together reduce the statement to\r\n\r\n“\r\n
satisfies \r\n”,\r\n\r\nwhere \r\n and \r\n for a random challenge r. This is continued
until \r\n is obtained at which point the verifier simply checks whether \r\n.\r\n\r\nThe
main problem, we face while designing our protocol is ensuring that the verifier
can check whether \r\n sent by prover lies in an appropriate subgroup of \r\n. In
the first draft of Pietrzak’s protocol [41], prover sends a square root of \r\n,
from which the original \r\n can be recovered easily (by simply squaring it) with
a guarantee, that the result lies in a group of quadratic residues \r\n. Notice
that the prover knows the square root of \r\n, because it is just a previous term
in the sequence he computed.\r\n\r\nUsing Pietrzak’s protocol directly for our delay
function would require computing a-th roots in RSA group for some arbitrary a. Since
this is a computationally hard problem, we cannot use the same trick. In fact, the
VDF construction of Wesolowski [54] is based on similar hardness assumption.\r\n\r\nWhile
Pietrzak shifted from \r\n to the group of signed quadratic residues \r\n in his
following paper [42] to get unique proofs, we resort to his old idea of ‘squaring
a square root’ and generalise it.\r\n\r\nThe high level idea is simple. First, on
input \r\n, prover computes the sequence \r\n. Next, during the protocol, verifier
maps all elements sent by the prover by homomorphism\r\n\r\n(11)\r\ninto the target
strong group \r\n. This process is illustrated in Fig. 2. Notice that the equality
\r\n for the original sequence implies the equality \r\n for the mapped sequence
\r\n.\r\n\r\nFig. 2.\r\nfigure 2\r\nIllustration of our computation of the iterated
squaring using the a-th root of \r\n. Horizontal arrows are \r\n and diagonal arrows
are \r\n.\r\n\r\nFull size image\r\nRestriction to Elements of \r\n. Mapping Eq.
(11) introduces a new technical difficulty. Since \r\n is not injective, we narrow
the domain inputs, for which the output of our VDF is verifiable, from \r\n to \r\n.
Furthermore, the only way to verify that a certain x is an element of \r\n is to
get an a-th root of x and raise it to the ath power. So we have to represent elements
of \r\n by elements of \r\n anyway. To resolve these two issues, we introduce a
non-unique representation of elements of \r\n.\r\n\r\nDefinition 13\r\nFor \r\n
and \r\n, we denote \r\n (an element of \r\n) by [x]. Since this representation
of \r\n is not unique, we define an equality relation by\r\n\r\nWe will denote by
tilde () the elements that were already powered to the a by a verifier (i.e. ).
Thus tilded variables verifiably belong to the target group \r\n.\r\n\r\nIn the
following text, the goal of the brackets notation in Definition 13 is to distinguish
places where the equality means the equality of elements of \r\n from those places,
where the equality holds up to \r\n. A reader can also see the notation in Definition
13 as a concrete representation of elements of a factor group \r\n.\r\n\r\nOur security
reduction 2 required the delay function to operate everywhere on \r\n. This is not
a problem if the \r\n algorithm is modified to output the set \r\n.\r\n\r\nFig.
3.\r\nfigure 3\r\nOur Interactive Protocol for \r\n.\r\n\r\nFull size image\r\n4.4
Security\r\nRecall here that \r\n is \r\n-strong group, so there exist\r\n\r\n and
\r\n such that\r\n\r\n(12)\r\nDefinition 14\r\nFor \r\n and \r\n, we define \r\n
as i-th coordinate of \r\n, where \r\n is the isomorphism given by Eq. (12).\r\n\r\nLemma
3\r\nLet \r\n and \r\n. If \r\n, then\r\n\r\n\t(13)\r\nProof\r\nFix \r\n, \r\n and
y. Let some \r\n satisfy\r\n\r\n(14)\r\nUsing notation from Definition 14, we rewrite
Eq. (14) as a set of equations\r\n\r\nFor every \r\n, by reordering the terms, the
j-th equation becomes\r\n\r\n(15)\r\nIf \r\n, then \r\n. Further for every \r\n.
It follows that \r\n. Putting these two equations together gives us \r\n, which
contradicts our assumption \r\n.\r\n\r\nIt follows that there exists \r\n such that\r\n\r\n(16)\r\nThereafter
there exists \r\n such that \r\n divides \r\n and\r\n\r\n(17)\r\nFurthermore, from
Eq. (15), \r\n divides \r\n. Finally, dividing eq. Eq. (15) by \r\n, we get that
r is determined uniquely (\r\n),\r\n\r\nUsing the fact that \r\n, this uniqueness
of r upper bounds number of \r\n, such that Eq. (14) holds, to one. It follows that
the probability that Eq. (14) holds for r chosen randomly from the uniform distribution
over \r\n is less than \r\n. \r\n\r\nCorollary 2\r\nThe halving protocol will
turn an invalid input tuple (i.e. \r\n) into a valid output tuple (i.e. \r\n) with
probability less than \r\n.\r\n\r\nTheorem 3\r\nFor any computationally unbounded
prover who submits anything other than \r\n such that \r\n in phase 2 of the protocol,
the soundness error is upper-bounded by \r\n\r\nProof\r\nIn each round of the protocol,
T decreases to \r\n. It follows that the number of rounds of the halving protocol
before reaching \r\n is upper bounded by \r\n.\r\n\r\nIf the verifier accepts the
solution tuple \r\n in the last round, then the equality \r\n must hold. It follows
that the initial inequality must have turned into equality in some round of the
halving protocol. By Lemma 3, the probability of this event is bounded by \r\n.
Finally, using the union bound for all rounds, we obtain the upper bound (\r\n.
\ \r\n\r\n4.5 Our VDF\r\nAnalogously to the VDF of Pietrzak [42], we compile our
public-coin interactive proof given in Fig. 3 into a VDF using the Fiat-Shamir heuristic.
The complete construction is given in Fig. 4. For ease of exposition, we assume
that the time parameter T is always a power of two.\r\n\r\nFig. 4.\r\nfigure 4\r\n
based on Lucas sequences\r\n\r\nFull size image\r\nAs discussed in Sect. 4.3, it
is crucial for the security of the protocol that the prover computes a sequence
of powers of the a-th root of the challenge and the resulting value (as well as
the intermediate values) received from the prover is lifted to the appropriate group
by raising it to the a-th power. We use the tilde notation in Fig. 4 in order to
denote elements on the sequence relative to the a-th root.\r\n\r\nNote that, by
the construction, the output of our VDF is the \r\n-th power of the root of the
characteristic polynomial for Lucas sequence with parameters P and Q. Therefore,
the value of the delay function implicitly corresponds to the \r\n-th term of the
Lucas sequence.\r\n\r\nTheorem 4\r\nLet \r\n be the statistical security parameter.
The \r\n VDF defined in Fig. 4 is correct and statistically-sound with a negligible
soundness error if \r\n is modelled as a random oracle, against any adversary that
makes \r\n oracle queries.\r\n\r\nProof\r\nThe correctness follows directly by construction.\r\n\r\nTo
prove its statistical soundness, we proceed in a similar way to [42]. We cannot
apply Fiat-Shamir transformation directly, because our protocol does not have constant
number of rounds, thus we use Fiat-Shamir heuristic to each round separately.\r\n\r\nFirst,
we use a random oracle as the \r\n function. Second, if a malicious prover computed
a proof accepted by verifier for some tuple \r\n such that\r\n\r\n(19)\r\nthen he
must have succeeded in turning inequality from Eq. (19) into equality in some round.
By Lemma 3, probability of such a flipping is bounded by \r\n. Every such an attempt
requires one query to random oracle. Using a union bound, it follows that the probability
that a malicious prover who made q queries to random oracle succeeds in flipping
initial inequality into equality in some round is upper-bounded by \r\n.\r\n\r\nSince
q is \r\n, \r\n is a negligible function and thus the soundness error is negligible.
\ \r\n\r\nNotes\r\n1.\r\nNote that integer sequences like Fibonacci numbers and
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references\r\n\r\nAcknowledgements\r\nWe thank Krzysztof Pietrzak and Alon Rosen
for several fruitful discussions about this work and the anonymous reviewers of
SCN 2022 and TCC 2023 for valuable suggestions.\r\n\r\nPavel Hubáček is supported
by the Czech Academy of Sciences (RVO 67985840), by the Grant Agency of the Czech
Republic under the grant agreement no. 19-27871X, and by the Charles University
project UNCE/SCI/004. Chethan Kamath is supported by Azrieli International Postdoctoral
Fellowship, by the European Research Council (ERC) under the European Union’s Horizon
Europe research and innovation programme (grant agreement No. 101042417, acronym
SPP), and by ISF grant 1789/19."
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short: C. Hoffmann, P. Hubáček, C. Kamath, T. Krňák, in:, 21st International Conference
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Discussions.'
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X. Gao, L.J. Hardwick, G. Horwitz, J. Janek, L.R. Johnson, J.W. Jordan, S. Matsuda,
S. Menkin, S. Mondal, Q. Qiu, T. Samarakoon, I. Temprano, K. Uosaki, G. Vailaya,
E.D. Wachsman, Y. Wu, S. Ye, Faraday Discussions (2023).
date_created: 2023-12-20T10:48:09Z
date_published: 2023-12-19T00:00:00Z
date_updated: 2023-12-20T11:54:06Z
day: '19'
department:
- _id: StFr
doi: 10.1039/d3fd90062b
keyword:
- Physical and Theoretical Chemistry
language:
- iso: eng
month: '12'
oa_version: None
publication: Faraday Discussions
publication_identifier:
eissn:
- 1364-5498
issn:
- 1359-6640
publication_status: epub_ahead
publisher: Royal Society of Chemistry
quality_controlled: '1'
status: public
title: 'Towards practical metal–oxygen batteries: General discussion'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14702'
article_processing_charge: No
article_type: review
author:
- first_name: Gary A.
full_name: Attard, Gary A.
last_name: Attard
- first_name: Ernesto J.
full_name: Calvo, Ernesto J.
last_name: Calvo
- first_name: Larry A.
full_name: Curtiss, Larry A.
last_name: Curtiss
- first_name: Daniel
full_name: Dewar, Daniel
last_name: Dewar
- first_name: James H. J.
full_name: Ellison, James H. J.
last_name: Ellison
- first_name: Xiangwen
full_name: Gao, Xiangwen
last_name: Gao
- first_name: Clare P.
full_name: Grey, Clare P.
last_name: Grey
- first_name: Laurence J.
full_name: Hardwick, Laurence J.
last_name: Hardwick
- first_name: Gabriela
full_name: Horwitz, Gabriela
last_name: Horwitz
- first_name: Juergen
full_name: Janek, Juergen
last_name: Janek
- first_name: Lee R.
full_name: Johnson, Lee R.
last_name: Johnson
- first_name: Jack W.
full_name: Jordan, Jack W.
last_name: Jordan
- first_name: Shoichi
full_name: Matsuda, Shoichi
last_name: Matsuda
- first_name: Soumyadip
full_name: Mondal, Soumyadip
id: d25d21ef-dc8d-11ea-abe3-ec4576307f48
last_name: Mondal
- first_name: Alex R.
full_name: Neale, Alex R.
last_name: Neale
- first_name: Nagore
full_name: Ortiz-Vitoriano, Nagore
last_name: Ortiz-Vitoriano
- first_name: Israel
full_name: Temprano, Israel
last_name: Temprano
- first_name: Ganesh
full_name: Vailaya, Ganesh
last_name: Vailaya
- first_name: Eric D.
full_name: Wachsman, Eric D.
last_name: Wachsman
- first_name: Hsien-Hau
full_name: Wang, Hsien-Hau
last_name: Wang
- first_name: Yiying
full_name: Wu, Yiying
last_name: Wu
- first_name: Shen
full_name: Ye, Shen
last_name: Ye
citation:
ama: 'Attard GA, Calvo EJ, Curtiss LA, et al. Materials for stable metal–oxygen
battery cathodes: general discussion. Faraday Discussions. 2023. doi:10.1039/d3fd90059b'
apa: 'Attard, G. A., Calvo, E. J., Curtiss, L. A., Dewar, D., Ellison, J. H. J.,
Gao, X., … Ye, S. (2023). Materials for stable metal–oxygen battery cathodes:
general discussion. Faraday Discussions. Royal Society of Chemistry. https://doi.org/10.1039/d3fd90059b'
chicago: 'Attard, Gary A., Ernesto J. Calvo, Larry A. Curtiss, Daniel Dewar, James
H. J. Ellison, Xiangwen Gao, Clare P. Grey, et al. “Materials for Stable Metal–Oxygen
Battery Cathodes: General Discussion.” Faraday Discussions. Royal Society
of Chemistry, 2023. https://doi.org/10.1039/d3fd90059b.'
ieee: 'G. A. Attard et al., “Materials for stable metal–oxygen battery cathodes:
general discussion,” Faraday Discussions. Royal Society of Chemistry, 2023.'
ista: 'Attard GA, Calvo EJ, Curtiss LA, Dewar D, Ellison JHJ, Gao X, Grey CP, Hardwick
LJ, Horwitz G, Janek J, Johnson LR, Jordan JW, Matsuda S, Mondal S, Neale AR,
Ortiz-Vitoriano N, Temprano I, Vailaya G, Wachsman ED, Wang H-H, Wu Y, Ye S. 2023.
Materials for stable metal–oxygen battery cathodes: general discussion. Faraday
Discussions.'
mla: 'Attard, Gary A., et al. “Materials for Stable Metal–Oxygen Battery Cathodes:
General Discussion.” Faraday Discussions, Royal Society of Chemistry, 2023,
doi:10.1039/d3fd90059b.'
short: G.A. Attard, E.J. Calvo, L.A. Curtiss, D. Dewar, J.H.J. Ellison, X. Gao,
C.P. Grey, L.J. Hardwick, G. Horwitz, J. Janek, L.R. Johnson, J.W. Jordan, S.
Matsuda, S. Mondal, A.R. Neale, N. Ortiz-Vitoriano, I. Temprano, G. Vailaya, E.D.
Wachsman, H.-H. Wang, Y. Wu, S. Ye, Faraday Discussions (2023).
date_created: 2023-12-20T10:49:43Z
date_published: 2023-12-18T00:00:00Z
date_updated: 2023-12-20T11:58:12Z
day: '18'
department:
- _id: StFr
doi: 10.1039/d3fd90059b
keyword:
- Physical and Theoretical Chemistry
language:
- iso: eng
month: '12'
oa_version: None
publication: Faraday Discussions
publication_identifier:
eissn:
- 1364-5498
issn:
- 1359-6640
publication_status: epub_ahead
publisher: Royal Society of Chemistry
quality_controlled: '1'
status: public
title: 'Materials for stable metal–oxygen battery cathodes: general discussion'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14703'
abstract:
- lang: eng
text: We present a discretization of the dynamic optimal transport problem for which
we can obtain the convergence rate for the value of the transport cost to its
continuous value when the temporal and spatial stepsize vanish. This convergence
result does not require any regularity assumption on the measures, though experiments
suggest that the rate is not sharp. Via an analysis of the duality gap we also
obtain the convergence rates for the gradient of the optimal potentials and the
velocity field under mild regularity assumptions. To obtain such rates we discretize
the dual formulation of the dynamic optimal transport problem and use the mature
literature related to the error due to discretizing the Hamilton-Jacobi equation.
acknowledgement: "The authors would like to thank Chris Wojtan for his continuous
support and several interesting discussions. Part of this research was performed
during two visits: one of SI to the BIDSA research center at Bocconi University,
and one of HL to the Institute of Science and Technology Austria. Both host institutions
are warmly acknowledged for the hospital-\r\nity. HL is partially supported by the
MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with
Applications to Optimization and Machine Learning”, funded by the European Union
- Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083
“CoDiNA” funded by the European Research Council."
article_number: '2312.12213'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
- first_name: Hugo
full_name: Lavenant, Hugo
last_name: Lavenant
citation:
ama: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. arXiv. doi:10.48550/arXiv.2312.12213
apa: Ishida, S., & Lavenant, H. (n.d.). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. arXiv. https://doi.org/10.48550/arXiv.2312.12213
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2312.12213.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” arXiv. .
ista: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. arXiv, 2312.12213.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, 2312.12213,
doi:10.48550/arXiv.2312.12213.
short: S. Ishida, H. Lavenant, ArXiv (n.d.).
date_created: 2023-12-21T10:14:37Z
date_published: 2023-12-19T00:00:00Z
date_updated: 2023-12-27T13:44:33Z
day: '19'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2312.12213
external_id:
arxiv:
- '2312.12213'
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2312.12213
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: arXiv
publication_status: submitted
status: public
title: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
type: preprint
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14709'
abstract:
- lang: eng
text: Amid the delays due to the global pandemic, in early October 2022, the auxin
community gathered in the idyllic peninsula of Cavtat, Croatia. More than 170
scientists from across the world converged to discuss the latest advancements
in fundamental and applied research in the field. The topics, from signalling
and transport to plant architecture and response to the environment, show how
auxin research must bridge from the molecular realm to macroscopic developmental
responses. This is mirrored in this collection of reviews, contributed by participants
of the Auxin 2022 meeting.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Marta
full_name: Del Bianco, Marta
last_name: Del Bianco
- first_name: Jiří
full_name: Friml, Jiří
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
- first_name: Lucia
full_name: Strader, Lucia
last_name: Strader
- first_name: Stefan
full_name: Kepinski, Stefan
last_name: Kepinski
citation:
ama: 'Del Bianco M, Friml J, Strader L, Kepinski S. Auxin research: Creating tools
for a greener future. Journal of Experimental Botany. 2023;74(22):6889-6892.
doi:10.1093/jxb/erad420'
apa: 'Del Bianco, M., Friml, J., Strader, L., & Kepinski, S. (2023). Auxin research:
Creating tools for a greener future. Journal of Experimental Botany. Oxford
University Press. https://doi.org/10.1093/jxb/erad420'
chicago: 'Del Bianco, Marta, Jiří Friml, Lucia Strader, and Stefan Kepinski. “Auxin
Research: Creating Tools for a Greener Future.” Journal of Experimental Botany.
Oxford University Press, 2023. https://doi.org/10.1093/jxb/erad420.'
ieee: 'M. Del Bianco, J. Friml, L. Strader, and S. Kepinski, “Auxin research: Creating
tools for a greener future,” Journal of Experimental Botany, vol. 74, no.
22. Oxford University Press, pp. 6889–6892, 2023.'
ista: 'Del Bianco M, Friml J, Strader L, Kepinski S. 2023. Auxin research: Creating
tools for a greener future. Journal of Experimental Botany. 74(22), 6889–6892.'
mla: 'Del Bianco, Marta, et al. “Auxin Research: Creating Tools for a Greener Future.”
Journal of Experimental Botany, vol. 74, no. 22, Oxford University Press,
2023, pp. 6889–92, doi:10.1093/jxb/erad420.'
short: M. Del Bianco, J. Friml, L. Strader, S. Kepinski, Journal of Experimental
Botany 74 (2023) 6889–6892.
date_created: 2023-12-24T23:00:53Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T09:29:24Z
day: '01'
ddc:
- '580'
department:
- _id: JiFr
doi: 10.1093/jxb/erad420
external_id:
pmid:
- '38038239'
file:
- access_level: open_access
checksum: f66fb960fd791dea53fd0e087f2fbbe8
content_type: application/pdf
creator: dernst
date_created: 2024-01-02T09:23:57Z
date_updated: 2024-01-02T09:23:57Z
file_id: '14724'
file_name: 2023_JourExperimentalBotany_DelBianco.pdf
file_size: 425194
relation: main_file
success: 1
file_date_updated: 2024-01-02T09:23:57Z
has_accepted_license: '1'
intvolume: ' 74'
issue: '22'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 6889-6892
pmid: 1
publication: Journal of Experimental Botany
publication_identifier:
eissn:
- 1460-2431
issn:
- 0022-0957
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Auxin research: Creating tools for a greener future'
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: 74
year: '2023'
...
---
_id: '14710'
abstract:
- lang: eng
text: The self-assembly of complex structures from a set of non-identical building
blocks is a hallmark of soft matter and biological systems, including protein
complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence
of the equilibrium assembly yield on the concentrations and interaction energies
of building blocks is highly challenging, owing to the difficulty of computing
the entropic contributions to the free energy of the many structures that compete
with the ground state configuration. While these calculations yield well known
results for spherically symmetric building blocks, they do not hold when the building
blocks have internal rotational degrees of freedom. Here we present an approach
for solving this problem that works with arbitrary building blocks, including
proteins with known structure and complex colloidal building blocks. Our algorithm
combines classical statistical mechanics with recently developed computational
tools for automatic differentiation. Automatic differentiation allows efficient
evaluation of equilibrium averages over configurations that would otherwise be
intractable. We demonstrate the validity of our framework by comparison to molecular
dynamics simulations of simple examples, and apply it to calculate the yield curves
for known protein complexes and for the assembly of colloidal shells.
acknowledgement: 'We thank Lucy Colwell for suggesting that we use covariance based
methods to predict contacts and Yang Hsia, Scott Boyken, Zibo Chen, and David Baker
for collaborations on designed protein complexes. We also thank Ned Wingreen for
suggesting the alternative derivation of (11). This research was supported by the
Office of Naval Research through ONR N00014-17-1-3029, the Simons Foundation the
NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard
(award number #1764269), the Peter B. Lewis ’55 Lewis-Sigler Institute/Genomics
Fund through the Lewis-Sigler Institute of Integrative Genomics at Princeton University,
and the National Science Foundation through the Center for the Physics of Biological
Function (PHY-1734030).'
article_number: '8328'
article_processing_charge: Yes
article_type: original
author:
- first_name: Agnese I.
full_name: Curatolo, Agnese I.
last_name: Curatolo
- first_name: Ofer
full_name: Kimchi, Ofer
last_name: Kimchi
- first_name: Carl Peter
full_name: Goodrich, Carl Peter
id: EB352CD2-F68A-11E9-89C5-A432E6697425
last_name: Goodrich
orcid: 0000-0002-1307-5074
- first_name: Ryan K.
full_name: Krueger, Ryan K.
last_name: Krueger
- first_name: Michael P.
full_name: Brenner, Michael P.
last_name: Brenner
citation:
ama: Curatolo AI, Kimchi O, Goodrich CP, Krueger RK, Brenner MP. A computational
toolbox for the assembly yield of complex and heterogeneous structures. Nature
Communications. 2023;14. doi:10.1038/s41467-023-43168-4
apa: Curatolo, A. I., Kimchi, O., Goodrich, C. P., Krueger, R. K., & Brenner,
M. P. (2023). A computational toolbox for the assembly yield of complex and heterogeneous
structures. Nature Communications. Springer Nature. https://doi.org/10.1038/s41467-023-43168-4
chicago: Curatolo, Agnese I., Ofer Kimchi, Carl Peter Goodrich, Ryan K. Krueger,
and Michael P. Brenner. “A Computational Toolbox for the Assembly Yield of Complex
and Heterogeneous Structures.” Nature Communications. Springer Nature,
2023. https://doi.org/10.1038/s41467-023-43168-4.
ieee: A. I. Curatolo, O. Kimchi, C. P. Goodrich, R. K. Krueger, and M. P. Brenner,
“A computational toolbox for the assembly yield of complex and heterogeneous structures,”
Nature Communications, vol. 14. Springer Nature, 2023.
ista: Curatolo AI, Kimchi O, Goodrich CP, Krueger RK, Brenner MP. 2023. A computational
toolbox for the assembly yield of complex and heterogeneous structures. Nature
Communications. 14, 8328.
mla: Curatolo, Agnese I., et al. “A Computational Toolbox for the Assembly Yield
of Complex and Heterogeneous Structures.” Nature Communications, vol. 14,
8328, Springer Nature, 2023, doi:10.1038/s41467-023-43168-4.
short: A.I. Curatolo, O. Kimchi, C.P. Goodrich, R.K. Krueger, M.P. Brenner, Nature
Communications 14 (2023).
date_created: 2023-12-24T23:00:53Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T11:36:46Z
day: '01'
ddc:
- '530'
department:
- _id: CaGo
doi: 10.1038/s41467-023-43168-4
file:
- access_level: open_access
checksum: fd9e9d527c2691f03fbc24031a75a3b3
content_type: application/pdf
creator: kschuh
date_created: 2023-12-27T08:40:43Z
date_updated: 2023-12-27T08:40:43Z
file_id: '14714'
file_name: 2023_NatureComm_Curatolo.pdf
file_size: 1342319
relation: main_file
success: 1
file_date_updated: 2023-12-27T08:40:43Z
has_accepted_license: '1'
intvolume: ' 14'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Nature Communications
publication_identifier:
eissn:
- '20411723'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A computational toolbox for the assembly yield of complex and heterogeneous
structures
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: 14
year: '2023'
...
---
_id: '14715'
abstract:
- lang: eng
text: We consider N trapped bosons in the mean-field limit with coupling constant
λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation.
We prove that the probability of finding ℓ particles outside the condensate wave
function decays exponentially in ℓ.
acknowledgement: We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful
remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum
Systems and Their Collective Phenomena.”
article_number: '121901'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Peter
full_name: Pickl, Peter
last_name: Pickl
citation:
ama: Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the
weakly interacting Bose gas. Journal of Mathematical Physics. 2023;64(12).
doi:10.1063/5.0172199
apa: Mitrouskas, D. J., & Pickl, P. (2023). Exponential decay of the number
of excitations in the weakly interacting Bose gas. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/5.0172199
chicago: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the
Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics. AIP Publishing, 2023. https://doi.org/10.1063/5.0172199.
ieee: D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations
in the weakly interacting Bose gas,” Journal of Mathematical Physics, vol.
64, no. 12. AIP Publishing, 2023.
ista: Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations
in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901.
mla: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number
of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical
Physics, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:10.1063/5.0172199.
short: D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023).
date_created: 2023-12-31T23:01:02Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T08:51:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1063/5.0172199
external_id:
arxiv:
- '2307.11062'
file:
- access_level: open_access
checksum: 66572f718a36465576cf0d6b3f7e01fc
content_type: application/pdf
creator: dernst
date_created: 2024-01-02T08:45:07Z
date_updated: 2024-01-02T08:45:07Z
file_id: '14722'
file_name: 2023_JourMathPhysics_Mitrouskas.pdf
file_size: 4346922
relation: main_file
success: 1
file_date_updated: 2024-01-02T08:45:07Z
has_accepted_license: '1'
intvolume: ' 64'
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Exponential decay of the number of excitations in the weakly interacting Bose
gas
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: 64
year: '2023'
...
---
_id: '14716'
abstract:
- lang: eng
text: "Background: Antimicrobial resistance (AMR) poses a significant global health
threat, and an accurate prediction of bacterial resistance patterns is critical
for effective treatment and control strategies. In recent years, machine learning
(ML) approaches have emerged as powerful tools for analyzing large-scale bacterial
AMR data. However, ML methods often ignore evolutionary relationships among bacterial
strains, which can greatly impact performance of the ML methods, especially if
resistance-associated features are attempted to be detected. Genome-wide association
studies (GWAS) methods like linear mixed models accounts for the evolutionary
relationships in bacteria, but they uncover only highly significant variants which
have already been reported in literature.\r\n\r\nResults: In this work, we introduce
a novel phylogeny-related parallelism score (PRPS), which measures whether a certain
feature is correlated with the population structure of a set of samples. We demonstrate
that PRPS can be used, in combination with SVM- and random forest-based models,
to reduce the number of features in the analysis, while simultaneously increasing
models’ performance. We applied our pipeline to publicly available AMR data from
PATRIC database for Mycobacterium tuberculosis against six common antibiotics.\r\n\r\nConclusions:
Using our pipeline, we re-discovered known resistance-associated mutations as
well as new candidate mutations which can be related to resistance and not previously
reported in the literature. We demonstrated that taking into account phylogenetic
relationships not only improves the model performance, but also yields more biologically
relevant predicted most contributing resistance markers."
acknowledgement: Open Access funding enabled and organized by Projekt DEAL. A.Y. and
O.V.K. acknowledge financial support from the Klaus Faber Foundation. A.A.A. was
funded by the Helmholtz AI project AMR-XAI. The work of O.O.B. is funded by Fonds
zur Förderung der Wissenschaftlichen Forschung (FWF), Grant ESP 253-B.
article_number: '404'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Alper
full_name: Yurtseven, Alper
last_name: Yurtseven
- first_name: Sofia
full_name: Buyanova, Sofia
id: 2F54A7BC-3902-11EA-AC87-BC9F3DDC885E
last_name: Buyanova
- first_name: Amay Ajaykumar A.
full_name: Agrawal, Amay Ajaykumar A.
last_name: Agrawal
- first_name: Olga
full_name: Bochkareva, Olga
id: C4558D3C-6102-11E9-A62E-F418E6697425
last_name: Bochkareva
orcid: 0000-0003-1006-6639
- first_name: Olga V V.
full_name: Kalinina, Olga V V.
last_name: Kalinina
citation:
ama: Yurtseven A, Buyanova S, Agrawal AAA, Bochkareva O, Kalinina OVV. Machine learning
and phylogenetic analysis allow for predicting antibiotic resistance in M. tuberculosis.
BMC Microbiology. 2023;23(1). doi:10.1186/s12866-023-03147-7
apa: Yurtseven, A., Buyanova, S., Agrawal, A. A. A., Bochkareva, O., & Kalinina,
O. V. V. (2023). Machine learning and phylogenetic analysis allow for predicting
antibiotic resistance in M. tuberculosis. BMC Microbiology. Springer Nature.
https://doi.org/10.1186/s12866-023-03147-7
chicago: Yurtseven, Alper, Sofia Buyanova, Amay Ajaykumar A. Agrawal, Olga Bochkareva,
and Olga V V. Kalinina. “Machine Learning and Phylogenetic Analysis Allow for
Predicting Antibiotic Resistance in M. Tuberculosis.” BMC Microbiology.
Springer Nature, 2023. https://doi.org/10.1186/s12866-023-03147-7.
ieee: A. Yurtseven, S. Buyanova, A. A. A. Agrawal, O. Bochkareva, and O. V. V. Kalinina,
“Machine learning and phylogenetic analysis allow for predicting antibiotic resistance
in M. tuberculosis,” BMC Microbiology, vol. 23, no. 1. Springer Nature,
2023.
ista: Yurtseven A, Buyanova S, Agrawal AAA, Bochkareva O, Kalinina OVV. 2023. Machine
learning and phylogenetic analysis allow for predicting antibiotic resistance
in M. tuberculosis. BMC Microbiology. 23(1), 404.
mla: Yurtseven, Alper, et al. “Machine Learning and Phylogenetic Analysis Allow
for Predicting Antibiotic Resistance in M. Tuberculosis.” BMC Microbiology,
vol. 23, no. 1, 404, Springer Nature, 2023, doi:10.1186/s12866-023-03147-7.
short: A. Yurtseven, S. Buyanova, A.A.A. Agrawal, O. Bochkareva, O.V.V. Kalinina,
BMC Microbiology 23 (2023).
date_created: 2023-12-31T23:01:02Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T09:20:57Z
day: '01'
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doi: 10.1186/s12866-023-03147-7
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publication_identifier:
eissn:
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title: Machine learning and phylogenetic analysis allow for predicting antibiotic
resistance in M. tuberculosis
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...
---
_id: '14717'
abstract:
- lang: eng
text: We count primitive lattices of rank d inside Zn as their covolume tends to
infinity, with respect to certain parameters of such lattices. These parameters
include, for example, the subspace that a lattice spans, namely its projection
to the Grassmannian; its homothety class and its equivalence class modulo rescaling
and rotation, often referred to as a shape. We add to a prior work of Schmidt
by allowing sets in the spaces of parameters that are general enough to conclude
the joint equidistribution of these parameters. In addition to the primitive d-lattices
Λ themselves, we also consider their orthogonal complements in Zn, A1, and show
that the equidistribution occurs jointly for Λ and A1. Finally, our asymptotic
formulas for the number of primitive lattices include an explicit bound on the
error term.
acknowledgement: This work was done when both authors were visiting Institute of Science
and Technology (IST) Austria. T.H. was being supported by Engineering and Physical
Sciences Research Council grant EP/P026710/1. Y.K. had a great time there and is
grateful for the hospitality. The appendix to this paper is largely based on a mini
course T.H. had given at IST in February 2020.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Tal
full_name: Horesh, Tal
id: C8B7BF48-8D81-11E9-BCA9-F536E6697425
last_name: Horesh
- first_name: Yakov
full_name: Karasik, Yakov
last_name: Karasik
citation:
ama: Horesh T, Karasik Y. Equidistribution of primitive lattices in ℝn. Quarterly
Journal of Mathematics. 2023;74(4):1253-1294. doi:10.1093/qmath/haad008
apa: Horesh, T., & Karasik, Y. (2023). Equidistribution of primitive lattices
in ℝn. Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haad008
chicago: Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices
in ℝn.” Quarterly Journal of Mathematics. Oxford University Press, 2023.
https://doi.org/10.1093/qmath/haad008.
ieee: T. Horesh and Y. Karasik, “Equidistribution of primitive lattices in ℝn,”
Quarterly Journal of Mathematics, vol. 74, no. 4. Oxford University Press,
pp. 1253–1294, 2023.
ista: Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly
Journal of Mathematics. 74(4), 1253–1294.
mla: Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in
ℝn.” Quarterly Journal of Mathematics, vol. 74, no. 4, Oxford University
Press, 2023, pp. 1253–94, doi:10.1093/qmath/haad008.
short: T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294.
date_created: 2023-12-31T23:01:03Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-02T07:39:55Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1093/qmath/haad008
external_id:
arxiv:
- '2012.04508'
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oa: 1
oa_version: Published Version
page: 1253-1294
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
grant_number: EP-P026710-2
name: Between rational and integral points
publication: Quarterly Journal of Mathematics
publication_identifier:
eissn:
- 1464-3847
issn:
- 0033-5606
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equidistribution of primitive lattices in ℝn
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: 74
year: '2023'
...