---
_id: '1089'
abstract:
- lang: eng
text: We discuss properties of distributions that are multivariate totally positive
of order two (MTP2) related to conditional independence. In particular, we show
that any independence model generated by an MTP2 distribution is a compositional
semigraphoid which is upward-stable and singleton-transitive. In addition, we
prove that any MTP2 distribution satisfying an appropriate support condition is
faithful to its concentration graph. Finally, we analyze factorization properties
of MTP2 distributions and discuss ways of constructing MTP2 distributions; in
particular we give conditions on the log-linear parameters of a discrete distribution
which ensure MTP2 and characterize conditional Gaussian distributions which satisfy
MTP2.
article_processing_charge: No
author:
- first_name: Shaun
full_name: Fallat, Shaun
last_name: Fallat
- first_name: Steffen
full_name: Lauritzen, Steffen
last_name: Lauritzen
- first_name: Kayvan
full_name: Sadeghi, Kayvan
last_name: Sadeghi
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Nanny
full_name: Wermuth, Nanny
last_name: Wermuth
- first_name: Piotr
full_name: Zwiernik, Piotr
last_name: Zwiernik
citation:
ama: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. Total positivity
in Markov structures. Annals of Statistics. 2017;45(3):1152-1184. doi:10.1214/16-AOS1478
apa: Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., & Zwiernik,
P. (2017). Total positivity in Markov structures. Annals of Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/16-AOS1478
chicago: Fallat, Shaun, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny
Wermuth, and Piotr Zwiernik. “Total Positivity in Markov Structures.” Annals
of Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AOS1478.
ieee: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, and P. Zwiernik,
“Total positivity in Markov structures,” Annals of Statistics, vol. 45,
no. 3. Institute of Mathematical Statistics, pp. 1152–1184, 2017.
ista: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. 2017. Total
positivity in Markov structures. Annals of Statistics. 45(3), 1152–1184.
mla: Fallat, Shaun, et al. “Total Positivity in Markov Structures.” Annals of
Statistics, vol. 45, no. 3, Institute of Mathematical Statistics, 2017, pp.
1152–84, doi:10.1214/16-AOS1478.
short: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, P. Zwiernik, Annals
of Statistics 45 (2017) 1152–1184.
date_created: 2018-12-11T11:50:05Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T11:46:53Z
day: '01'
department:
- _id: CaUh
doi: 10.1214/16-AOS1478
external_id:
isi:
- '000404395900008'
intvolume: ' 45'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1510.01290
month: '06'
oa: 1
oa_version: Submitted Version
page: 1152 - 1184
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Annals of Statistics
publication_identifier:
issn:
- '00905364'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6288'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Total positivity in Markov structures
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 45
year: '2017'
...
---
_id: '1168'
abstract:
- lang: eng
text: Optimum experimental design theory has recently been extended for parameter
estimation in copula models. The use of these models allows one to gain in flexibility
by considering the model parameter set split into marginal and dependence parameters.
However, this separation also leads to the natural issue of estimating only a
subset of all model parameters. In this work, we treat this problem with the application
of the (Formula presented.)-optimality to copula models. First, we provide an
extension of the corresponding equivalence theory. Then, we analyze a wide range
of flexible copula models to highlight the usefulness of (Formula presented.)-optimality
in many possible scenarios. Finally, we discuss how the usage of the introduced
design criterion also relates to the more general issue of copula selection and
optimal design for model discrimination.
acknowledgement: 'This work has been supported by the project ANR-2011-IS01-001-01
“DESIRE” and Austrian Science Fund (FWF) I833-N18. Open access funding is provided
by the Austrian Science Fund (FWF). '
article_processing_charge: No
author:
- first_name: Elisa
full_name: Perrone, Elisa
id: 2A5F8724-F248-11E8-B48F-1D18A9856A87
last_name: Perrone
orcid: 0000-0003-0370-9835
- first_name: Andreas
full_name: Rappold, Andreas
last_name: Rappold
- first_name: Werner
full_name: Müller, Werner
last_name: Müller
citation:
ama: Perrone E, Rappold A, Müller W. D inf s optimality in copula models. Statistical
Methods and Applications. 2017;26(3):403-418. doi:10.1007/s10260-016-0375-6
apa: Perrone, E., Rappold, A., & Müller, W. (2017). D inf s optimality in copula
models. Statistical Methods and Applications. Springer. https://doi.org/10.1007/s10260-016-0375-6
chicago: Perrone, Elisa, Andreas Rappold, and Werner Müller. “D Inf s Optimality
in Copula Models.” Statistical Methods and Applications. Springer, 2017.
https://doi.org/10.1007/s10260-016-0375-6.
ieee: E. Perrone, A. Rappold, and W. Müller, “D inf s optimality in copula models,”
Statistical Methods and Applications, vol. 26, no. 3. Springer, pp. 403–418,
2017.
ista: Perrone E, Rappold A, Müller W. 2017. D inf s optimality in copula models.
Statistical Methods and Applications. 26(3), 403–418.
mla: Perrone, Elisa, et al. “D Inf s Optimality in Copula Models.” Statistical
Methods and Applications, vol. 26, no. 3, Springer, 2017, pp. 403–18, doi:10.1007/s10260-016-0375-6.
short: E. Perrone, A. Rappold, W. Müller, Statistical Methods and Applications 26
(2017) 403–418.
date_created: 2018-12-11T11:50:31Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2023-09-20T11:25:09Z
day: '01'
ddc:
- '519'
department:
- _id: CaUh
doi: 10.1007/s10260-016-0375-6
external_id:
isi:
- '000407973200004'
file:
- access_level: open_access
checksum: 0b2d1b647ca96e9ef13a14b8b6775e0f
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:13Z
date_updated: 2020-07-14T12:44:37Z
file_id: '5199'
file_name: IST-2017-739-v1+2_10260_2016_375_MOESM1_ESM.pdf
file_size: 56664
relation: main_file
- access_level: open_access
checksum: 3321ef34e02e28acfc427f77cf32812a
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:14Z
date_updated: 2020-07-14T12:44:37Z
file_id: '5200'
file_name: IST-2017-739-v1+3_s10260-016-0375-6.pdf
file_size: 688953
relation: main_file
file_date_updated: 2020-07-14T12:44:37Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 403 - 418
publication: Statistical Methods and Applications
publication_status: published
publisher: Springer
publist_id: '6189'
pubrep_id: '739'
quality_controlled: '1'
scopus_import: '1'
status: public
title: D inf s optimality in copula models
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 26
year: '2017'
...
---
_id: '698'
abstract:
- lang: eng
text: 'Extracellular matrix signals from the microenvironment regulate gene expression
patterns and cell behavior. Using a combination of experiments and geometric models,
we demonstrate correlations between cell geometry, three-dimensional (3D) organization
of chromosome territories, and gene expression. Fluorescence in situ hybridization
experiments showed that micropatterned fibroblasts cultured on anisotropic versus
isotropic substrates resulted in repositioning of specific chromosomes, which
contained genes that were differentially regulated by cell geometries. Experiments
combined with ellipsoid packing models revealed that the mechanosensitivity of
chromosomes was correlated with their orientation in the nucleus. Transcription
inhibition experiments suggested that the intermingling degree was more sensitive
to global changes in transcription than to chromosome radial positioning and its
orientations. These results suggested that cell geometry modulated 3D chromosome
arrangement, and their neighborhoods correlated with gene expression patterns
in a predictable manner. This is central to understanding geometric control of
genetic programs involved in cellular homeostasis and the associated diseases. '
author:
- first_name: Yejun
full_name: Wang, Yejun
last_name: Wang
- first_name: Mallika
full_name: Nagarajan, Mallika
last_name: Nagarajan
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Gv
full_name: Shivashankar, Gv
last_name: Shivashankar
citation:
ama: Wang Y, Nagarajan M, Uhler C, Shivashankar G. Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression. Molecular
Biology of the Cell. 2017;28(14):1997-2009. doi:10.1091/mbc.E16-12-0825
apa: Wang, Y., Nagarajan, M., Uhler, C., & Shivashankar, G. (2017). Orientation
and repositioning of chromosomes correlate with cell geometry dependent gene expression.
Molecular Biology of the Cell. American Society for Cell Biology. https://doi.org/10.1091/mbc.E16-12-0825
chicago: Wang, Yejun, Mallika Nagarajan, Caroline Uhler, and Gv Shivashankar. “Orientation
and Repositioning of Chromosomes Correlate with Cell Geometry Dependent Gene Expression.”
Molecular Biology of the Cell. American Society for Cell Biology, 2017.
https://doi.org/10.1091/mbc.E16-12-0825.
ieee: Y. Wang, M. Nagarajan, C. Uhler, and G. Shivashankar, “Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression,” Molecular
Biology of the Cell, vol. 28, no. 14. American Society for Cell Biology, pp.
1997–2009, 2017.
ista: Wang Y, Nagarajan M, Uhler C, Shivashankar G. 2017. Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression. Molecular
Biology of the Cell. 28(14), 1997–2009.
mla: Wang, Yejun, et al. “Orientation and Repositioning of Chromosomes Correlate
with Cell Geometry Dependent Gene Expression.” Molecular Biology of the Cell,
vol. 28, no. 14, American Society for Cell Biology, 2017, pp. 1997–2009, doi:10.1091/mbc.E16-12-0825.
short: Y. Wang, M. Nagarajan, C. Uhler, G. Shivashankar, Molecular Biology of the
Cell 28 (2017) 1997–2009.
date_created: 2018-12-11T11:47:59Z
date_published: 2017-07-07T00:00:00Z
date_updated: 2021-01-12T08:11:17Z
day: '07'
ddc:
- '519'
department:
- _id: CaUh
doi: 10.1091/mbc.E16-12-0825
file:
- access_level: open_access
checksum: de01dac9e30970cfa6ae902480a4e04d
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:53Z
date_updated: 2020-07-14T12:47:46Z
file_id: '4844'
file_name: IST-2017-892-v1+1_Mol._Biol._Cell-2017-Wang-1997-2009.pdf
file_size: 1086097
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: ' 28'
issue: '14'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 1997 - 2009
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Molecular Biology of the Cell
publication_identifier:
issn:
- '10591524'
publication_status: published
publisher: American Society for Cell Biology
publist_id: '7001'
pubrep_id: '892'
quality_controlled: '1'
scopus_import: 1
status: public
title: Orientation and repositioning of chromosomes correlate with cell geometry dependent
gene expression
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...
---
_id: '1208'
abstract:
- lang: eng
text: We study parameter estimation in linear Gaussian covariance models, which
are p-dimensional Gaussian models with linear constraints on the covariance matrix.
Maximum likelihood estimation for this class of models leads to a non-convex optimization
problem which typically has many local maxima. Using recent results on the asymptotic
distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient
conditions for any hill climbing method to converge to the global maximum. Although
we are primarily interested in the case in which n≫p, the proofs of our results
utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably,
our numerical simulations indicate that our results remain valid for p as small
as 2. An important consequence of this analysis is that, for sample sizes n≃14p,
maximum likelihood estimation for linear Gaussian covariance models behaves as
if it were a convex optimization problem. © 2016 The Royal Statistical Society
and Blackwell Publishing Ltd.
article_processing_charge: No
author:
- first_name: Piotr
full_name: Zwiernik, Piotr
last_name: Zwiernik
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Donald
full_name: Richards, Donald
last_name: Richards
citation:
ama: 'Zwiernik P, Uhler C, Richards D. Maximum likelihood estimation for linear
Gaussian covariance models. Journal of the Royal Statistical Society Series
B: Statistical Methodology. 2017;79(4):1269-1292. doi:10.1111/rssb.12217'
apa: 'Zwiernik, P., Uhler, C., & Richards, D. (2017). Maximum likelihood estimation
for linear Gaussian covariance models. Journal of the Royal Statistical Society.
Series B: Statistical Methodology. Wiley-Blackwell. https://doi.org/10.1111/rssb.12217'
chicago: 'Zwiernik, Piotr, Caroline Uhler, and Donald Richards. “Maximum Likelihood
Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical
Society. Series B: Statistical Methodology. Wiley-Blackwell, 2017. https://doi.org/10.1111/rssb.12217.'
ieee: 'P. Zwiernik, C. Uhler, and D. Richards, “Maximum likelihood estimation for
linear Gaussian covariance models,” Journal of the Royal Statistical Society.
Series B: Statistical Methodology, vol. 79, no. 4. Wiley-Blackwell, pp. 1269–1292,
2017.'
ista: 'Zwiernik P, Uhler C, Richards D. 2017. Maximum likelihood estimation for
linear Gaussian covariance models. Journal of the Royal Statistical Society. Series
B: Statistical Methodology. 79(4), 1269–1292.'
mla: 'Zwiernik, Piotr, et al. “Maximum Likelihood Estimation for Linear Gaussian
Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical
Methodology, vol. 79, no. 4, Wiley-Blackwell, 2017, pp. 1269–92, doi:10.1111/rssb.12217.'
short: 'P. Zwiernik, C. Uhler, D. Richards, Journal of the Royal Statistical Society.
Series B: Statistical Methodology 79 (2017) 1269–1292.'
date_created: 2018-12-11T11:50:43Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-20T11:17:21Z
day: '01'
department:
- _id: CaUh
doi: 10.1111/rssb.12217
external_id:
isi:
- '000411712300012'
intvolume: ' 79'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.5604
month: '09'
oa: 1
oa_version: Submitted Version
page: 1269 - 1292
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: 'Journal of the Royal Statistical Society. Series B: Statistical Methodology'
publication_identifier:
issn:
- '13697412'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6142'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximum likelihood estimation for linear Gaussian covariance models
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 79
year: '2017'
...
---
_id: '1833'
abstract:
- lang: eng
text: 'Relational models for contingency tables are generalizations of log-linear
models, allowing effects associated with arbitrary subsets of cells in the table,
and not necessarily containing the overall effect, that is, a common parameter
in every cell. Similarly to log-linear models, relational models can be extended
to non-negative distributions, but the extension requires more complex methods.
An extended relational model is defined as an algebraic variety, and it turns
out to be the closure of the original model with respect to the Bregman divergence.
In the extended relational model, the MLE of the cell parameters always exists
and is unique, but some of its properties may be different from those of the MLE
under log-linear models. The MLE can be computed using a generalized iterative
scaling procedure based on Bregman projections. '
author:
- first_name: Anna
full_name: Klimova, Anna
id: 31934120-F248-11E8-B48F-1D18A9856A87
last_name: Klimova
- first_name: Tamás
full_name: Rudas, Tamás
last_name: Rudas
citation:
ama: Klimova A, Rudas T. On the closure of relational models. Journal of Multivariate
Analysis. 2016;143:440-452. doi:10.1016/j.jmva.2015.10.005
apa: Klimova, A., & Rudas, T. (2016). On the closure of relational models. Journal
of Multivariate Analysis. Elsevier. https://doi.org/10.1016/j.jmva.2015.10.005
chicago: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.”
Journal of Multivariate Analysis. Elsevier, 2016. https://doi.org/10.1016/j.jmva.2015.10.005.
ieee: A. Klimova and T. Rudas, “On the closure of relational models,” Journal
of Multivariate Analysis, vol. 143. Elsevier, pp. 440–452, 2016.
ista: Klimova A, Rudas T. 2016. On the closure of relational models. Journal of
Multivariate Analysis. 143, 440–452.
mla: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” Journal
of Multivariate Analysis, vol. 143, Elsevier, 2016, pp. 440–52, doi:10.1016/j.jmva.2015.10.005.
short: A. Klimova, T. Rudas, Journal of Multivariate Analysis 143 (2016) 440–452.
date_created: 2018-12-11T11:54:15Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:53:30Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.jmva.2015.10.005
intvolume: ' 143'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1501.00600
month: '01'
oa: 1
oa_version: Preprint
page: 440 - 452
publication: Journal of Multivariate Analysis
publication_status: published
publisher: Elsevier
publist_id: '5270'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the closure of relational models
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 143
year: '2016'
...
---
_id: '1480'
abstract:
- lang: eng
text: 'Exponential varieties arise from exponential families in statistics. These
real algebraic varieties have strong positivity and convexity properties, familiar
from toric varieties and their moment maps. Among them are varieties of inverses
of symmetric matrices satisfying linear constraints. This class includes Gaussian
graphical models. We develop a general theory of exponential varieties. These
are derived from hyperbolic polynomials and their integral representations. We
compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. '
author:
- first_name: Mateusz
full_name: Michałek, Mateusz
last_name: Michałek
- first_name: Bernd
full_name: Sturmfels, Bernd
last_name: Sturmfels
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Piotr
full_name: Zwiernik, Piotr
last_name: Zwiernik
citation:
ama: Michałek M, Sturmfels B, Uhler C, Zwiernik P. Exponential varieties. Proceedings
of the London Mathematical Society. 2016;112(1):27-56. doi:10.1112/plms/pdv066
apa: Michałek, M., Sturmfels, B., Uhler, C., & Zwiernik, P. (2016). Exponential
varieties. Proceedings of the London Mathematical Society. Oxford University
Press. https://doi.org/10.1112/plms/pdv066
chicago: Michałek, Mateusz, Bernd Sturmfels, Caroline Uhler, and Piotr Zwiernik.
“Exponential Varieties.” Proceedings of the London Mathematical Society.
Oxford University Press, 2016. https://doi.org/10.1112/plms/pdv066.
ieee: M. Michałek, B. Sturmfels, C. Uhler, and P. Zwiernik, “Exponential varieties,”
Proceedings of the London Mathematical Society, vol. 112, no. 1. Oxford
University Press, pp. 27–56, 2016.
ista: Michałek M, Sturmfels B, Uhler C, Zwiernik P. 2016. Exponential varieties.
Proceedings of the London Mathematical Society. 112(1), 27–56.
mla: Michałek, Mateusz, et al. “Exponential Varieties.” Proceedings of the London
Mathematical Society, vol. 112, no. 1, Oxford University Press, 2016, pp.
27–56, doi:10.1112/plms/pdv066.
short: M. Michałek, B. Sturmfels, C. Uhler, P. Zwiernik, Proceedings of the London
Mathematical Society 112 (2016) 27–56.
date_created: 2018-12-11T11:52:16Z
date_published: 2016-01-07T00:00:00Z
date_updated: 2021-01-12T06:51:02Z
day: '07'
department:
- _id: CaUh
doi: 10.1112/plms/pdv066
intvolume: ' 112'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1412.6185
month: '01'
oa: 1
oa_version: Preprint
page: 27 - 56
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: Oxford University Press
publist_id: '5714'
quality_controlled: '1'
scopus_import: 1
status: public
title: Exponential varieties
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2016'
...
---
_id: '1293'
abstract:
- lang: eng
text: For a graph G with p vertices the closed convex cone S⪰0(G) consists of all
real positive semidefinite p×p matrices whose sparsity pattern is given by G,
that is, those matrices with zeros in the off-diagonal entries corresponding to
nonedges of G. The extremal rays of this cone and their associated ranks have
applications to matrix completion problems, maximum likelihood estimation in Gaussian
graphical models in statistics, and Gauss elimination for sparse matrices. While
the maximum rank of an extremal ray in S⪰0(G), known as the sparsity order of
G, has been characterized for different classes of graphs, we here study all possible
extremal ranks of S⪰0(G). We investigate when the geometry of the (±1)-cut polytope
of G yields a polyhedral characterization of the set of extremal ranks of S⪰0(G).
For a graph G without K5 minors, we show that appropriately chosen normal vectors
to the facets of the (±1)-cut polytope of G specify the off-diagonal entries of
extremal matrices in S⪰0(G). We also prove that for appropriately chosen scalars
the constant term of the linear equation of each facet-supporting hyperplane is
the rank of its corresponding extremal matrix in S⪰0(G). Furthermore, we show
that if G is series-parallel then this gives a complete characterization of all
possible extremal ranks of S⪰0(G). Consequently, the sparsity order problem for
series-parallel graphs can be solved in terms of polyhedral geometry.
acknowledgement: We wish to thank Alexander Engström and Bernd Sturmfels for various
valuable discussions and insights. We also thank the two anonymous referees for
their thoughtful feedback on the paper. CU was partially supported by the Austrian
Science Fund (FWF) Y 903-N35.
author:
- first_name: Liam T
full_name: Solus, Liam T
id: 2AADA620-F248-11E8-B48F-1D18A9856A87
last_name: Solus
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Ruriko
full_name: Yoshida, Ruriko
last_name: Yoshida
citation:
ama: Solus LT, Uhler C, Yoshida R. Extremal positive semidefinite matrices whose
sparsity pattern is given by graphs without K5 minors. Linear Algebra and Its
Applications. 2016;509:247-275. doi:10.1016/j.laa.2016.07.026
apa: Solus, L. T., Uhler, C., & Yoshida, R. (2016). Extremal positive semidefinite
matrices whose sparsity pattern is given by graphs without K5 minors. Linear
Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2016.07.026
chicago: Solus, Liam T, Caroline Uhler, and Ruriko Yoshida. “Extremal Positive Semidefinite
Matrices Whose Sparsity Pattern Is given by Graphs without K5 Minors.” Linear
Algebra and Its Applications. Elsevier, 2016. https://doi.org/10.1016/j.laa.2016.07.026.
ieee: L. T. Solus, C. Uhler, and R. Yoshida, “Extremal positive semidefinite matrices
whose sparsity pattern is given by graphs without K5 minors,” Linear Algebra
and Its Applications, vol. 509. Elsevier, pp. 247–275, 2016.
ista: Solus LT, Uhler C, Yoshida R. 2016. Extremal positive semidefinite matrices
whose sparsity pattern is given by graphs without K5 minors. Linear Algebra and
Its Applications. 509, 247–275.
mla: Solus, Liam T., et al. “Extremal Positive Semidefinite Matrices Whose Sparsity
Pattern Is given by Graphs without K5 Minors.” Linear Algebra and Its Applications,
vol. 509, Elsevier, 2016, pp. 247–75, doi:10.1016/j.laa.2016.07.026.
short: L.T. Solus, C. Uhler, R. Yoshida, Linear Algebra and Its Applications 509
(2016) 247–275.
date_created: 2018-12-11T11:51:11Z
date_published: 2016-11-15T00:00:00Z
date_updated: 2021-01-12T06:49:40Z
day: '15'
department:
- _id: CaUh
doi: 10.1016/j.laa.2016.07.026
intvolume: ' 509'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1506.06702.pdf
month: '11'
oa: 1
oa_version: Preprint
page: 247 - 275
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Linear Algebra and Its Applications
publication_status: published
publisher: Elsevier
publist_id: '6024'
quality_controlled: '1'
scopus_import: 1
status: public
title: Extremal positive semidefinite matrices whose sparsity pattern is given by
graphs without K5 minors
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 509
year: '2016'
...
---
_id: '1997'
abstract:
- lang: eng
text: We prove that the three-state toric homogeneous Markov chain model has Markov
degree two. In algebraic terminology this means, that a certain class of toric
ideals is generated by quadratic binomials. This was conjectured by Haws, Martin
del Campo, Takemura and Yoshida, who proved that they are generated by degree
six binomials.
author:
- first_name: Patrik
full_name: Noren, Patrik
id: 46870C74-F248-11E8-B48F-1D18A9856A87
last_name: Noren
citation:
ama: Noren P. The three-state toric homogeneous Markov chain model has Markov degree
two. Journal of Symbolic Computation. 2015;68/Part 2(May-June):285-296.
doi:10.1016/j.jsc.2014.09.014
apa: Noren, P. (2015). The three-state toric homogeneous Markov chain model has
Markov degree two. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/j.jsc.2014.09.014
chicago: Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has
Markov Degree Two.” Journal of Symbolic Computation. Elsevier, 2015. https://doi.org/10.1016/j.jsc.2014.09.014.
ieee: P. Noren, “The three-state toric homogeneous Markov chain model has Markov
degree two,” Journal of Symbolic Computation, vol. 68/Part 2, no. May-June.
Elsevier, pp. 285–296, 2015.
ista: Noren P. 2015. The three-state toric homogeneous Markov chain model has Markov
degree two. Journal of Symbolic Computation. 68/Part 2(May-June), 285–296.
mla: Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has Markov
Degree Two.” Journal of Symbolic Computation, vol. 68/Part 2, no. May-June,
Elsevier, 2015, pp. 285–96, doi:10.1016/j.jsc.2014.09.014.
short: P. Noren, Journal of Symbolic Computation 68/Part 2 (2015) 285–296.
date_created: 2018-12-11T11:55:07Z
date_published: 2015-05-01T00:00:00Z
date_updated: 2021-01-12T06:54:35Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.jsc.2014.09.014
issue: May-June
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1207.0077
month: '05'
oa: 1
oa_version: Preprint
page: 285 - 296
publication: Journal of Symbolic Computation
publication_status: published
publisher: Elsevier
publist_id: '5082'
quality_controlled: '1'
scopus_import: 1
status: public
title: The three-state toric homogeneous Markov chain model has Markov degree two
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68/Part 2
year: '2015'
...
---
_id: '2006'
abstract:
- lang: eng
text: 'The monotone secant conjecture posits a rich class of polynomial systems,
all of whose solutions are real. These systems come from the Schubert calculus
on flag manifolds, and the monotone secant conjecture is a compelling generalization
of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko).
We present some theoretical evidence for this conjecture, as well as computational
evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of
the phenomena we observed in our data. '
article_processing_charge: No
author:
- first_name: Nicolas
full_name: Hein, Nicolas
last_name: Hein
- first_name: Christopher
full_name: Hillar, Christopher
last_name: Hillar
- first_name: Abraham
full_name: Martin Del Campo Sanchez, Abraham
id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87
last_name: Martin Del Campo Sanchez
- first_name: Frank
full_name: Sottile, Frank
last_name: Sottile
- first_name: Zach
full_name: Teitler, Zach
last_name: Teitler
citation:
ama: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone
secant conjecture in the real Schubert calculus. Experimental Mathematics.
2015;24(3):261-269. doi:10.1080/10586458.2014.980044
apa: Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., & Teitler,
Z. (2015). The monotone secant conjecture in the real Schubert calculus. Experimental
Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2014.980044
chicago: Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank
Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert
Calculus.” Experimental Mathematics. Taylor & Francis, 2015. https://doi.org/10.1080/10586458.2014.980044.
ieee: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler,
“The monotone secant conjecture in the real Schubert calculus,” Experimental
Mathematics, vol. 24, no. 3. Taylor & Francis, pp. 261–269, 2015.
ista: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015.
The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics.
24(3), 261–269.
mla: Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert
Calculus.” Experimental Mathematics, vol. 24, no. 3, Taylor & Francis,
2015, pp. 261–69, doi:10.1080/10586458.2014.980044.
short: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, Z. Teitler,
Experimental Mathematics 24 (2015) 261–269.
date_created: 2018-12-11T11:55:10Z
date_published: 2015-06-23T00:00:00Z
date_updated: 2021-01-12T06:54:40Z
day: '23'
department:
- _id: CaUh
doi: 10.1080/10586458.2014.980044
intvolume: ' 24'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.3436
month: '06'
oa: 1
oa_version: Preprint
page: 261 - 269
publication: Experimental Mathematics
publication_status: published
publisher: Taylor & Francis
publist_id: '5070'
quality_controlled: '1'
scopus_import: 1
status: public
title: The monotone secant conjecture in the real Schubert calculus
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2015'
...
---
_id: '2008'
abstract:
- lang: eng
text: The paper describes a generalized iterative proportional fitting procedure
that can be used for maximum likelihood estimation in a special class of the general
log-linear model. The models in this class, called relational, apply to multivariate
discrete sample spaces that do not necessarily have a Cartesian product structure
and may not contain an overall effect. When applied to the cell probabilities,
the models without the overall effect are curved exponential families and the
values of the sufficient statistics are reproduced by the MLE only up to a constant
of proportionality. The paper shows that Iterative Proportional Fitting, Generalized
Iterative Scaling, and Improved Iterative Scaling fail to work for such models.
The algorithm proposed here is based on iterated Bregman projections. As a by-product,
estimates of the multiplicative parameters are also obtained. An implementation
of the algorithm is available as an R-package.
acknowledgement: Part of the material presented here was contained in the PhD thesis
of the first author to which the second author and Thomas Richardson were advisers.
The authors wish to thank him for several comments and suggestions. We also thank
the reviewers and the Associate Editor for helpful comments. The proof of Proposition 1
uses the idea of Olga Klimova, to whom the authors are also indebted. The second
author was supported in part by Grant K-106154 from the Hungarian National Scientific
Research Fund (OTKA).
author:
- first_name: Anna
full_name: Klimova, Anna
id: 31934120-F248-11E8-B48F-1D18A9856A87
last_name: Klimova
- first_name: Tamás
full_name: Rudas, Tamás
last_name: Rudas
citation:
ama: Klimova A, Rudas T. Iterative scaling in curved exponential families. Scandinavian
Journal of Statistics. 2015;42(3):832-847. doi:10.1111/sjos.12139
apa: Klimova, A., & Rudas, T. (2015). Iterative scaling in curved exponential
families. Scandinavian Journal of Statistics. Wiley. https://doi.org/10.1111/sjos.12139
chicago: Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential
Families.” Scandinavian Journal of Statistics. Wiley, 2015. https://doi.org/10.1111/sjos.12139.
ieee: A. Klimova and T. Rudas, “Iterative scaling in curved exponential families,”
Scandinavian Journal of Statistics, vol. 42, no. 3. Wiley, pp. 832–847,
2015.
ista: Klimova A, Rudas T. 2015. Iterative scaling in curved exponential families.
Scandinavian Journal of Statistics. 42(3), 832–847.
mla: Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.”
Scandinavian Journal of Statistics, vol. 42, no. 3, Wiley, 2015, pp. 832–47,
doi:10.1111/sjos.12139.
short: A. Klimova, T. Rudas, Scandinavian Journal of Statistics 42 (2015) 832–847.
date_created: 2018-12-11T11:55:11Z
date_published: 2015-09-01T00:00:00Z
date_updated: 2021-01-12T06:54:41Z
day: '01'
department:
- _id: CaUh
doi: 10.1111/sjos.12139
intvolume: ' 42'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.3282
month: '09'
oa: 1
oa_version: Preprint
page: 832 - 847
publication: Scandinavian Journal of Statistics
publication_status: published
publisher: Wiley
publist_id: '5068'
quality_controlled: '1'
scopus_import: 1
status: public
title: Iterative scaling in curved exponential families
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2015'
...
---
_id: '2014'
abstract:
- lang: eng
text: The concepts of faithfulness and strong-faithfulness are important for statistical
learning of graphical models. Graphs are not sufficient for describing the association
structure of a discrete distribution. Hypergraphs representing hierarchical log-linear
models are considered instead, and the concept of parametric (strong-) faithfulness
with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence
of uniformly consistent parameter estimators and enables building uniformly consistent
procedures for a hypergraph search. The strength of association in a discrete
distribution can be quantified with various measures, leading to different concepts
of strong-faithfulness. Lower and upper bounds for the proportions of distributions
that do not satisfy strong-faithfulness are computed for different parameterizations
and measures of association.
author:
- first_name: Anna
full_name: Klimova, Anna
id: 31934120-F248-11E8-B48F-1D18A9856A87
last_name: Klimova
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Tamás
full_name: Rudas, Tamás
last_name: Rudas
citation:
ama: Klimova A, Uhler C, Rudas T. Faithfulness and learning hypergraphs from discrete
distributions. Computational Statistics & Data Analysis. 2015;87(7):57-72.
doi:10.1016/j.csda.2015.01.017
apa: Klimova, A., Uhler, C., & Rudas, T. (2015). Faithfulness and learning hypergraphs
from discrete distributions. Computational Statistics & Data Analysis.
Elsevier. https://doi.org/10.1016/j.csda.2015.01.017
chicago: Klimova, Anna, Caroline Uhler, and Tamás Rudas. “Faithfulness and Learning
Hypergraphs from Discrete Distributions.” Computational Statistics & Data
Analysis. Elsevier, 2015. https://doi.org/10.1016/j.csda.2015.01.017.
ieee: A. Klimova, C. Uhler, and T. Rudas, “Faithfulness and learning hypergraphs
from discrete distributions,” Computational Statistics & Data Analysis,
vol. 87, no. 7. Elsevier, pp. 57–72, 2015.
ista: Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from
discrete distributions. Computational Statistics & Data Analysis. 87(7), 57–72.
mla: Klimova, Anna, et al. “Faithfulness and Learning Hypergraphs from Discrete
Distributions.” Computational Statistics & Data Analysis, vol. 87,
no. 7, Elsevier, 2015, pp. 57–72, doi:10.1016/j.csda.2015.01.017.
short: A. Klimova, C. Uhler, T. Rudas, Computational Statistics & Data Analysis
87 (2015) 57–72.
date_created: 2018-12-11T11:55:13Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:54:43Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.csda.2015.01.017
intvolume: ' 87'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1404.6617
month: '07'
oa: 1
oa_version: Preprint
page: 57 - 72
publication: Computational Statistics & Data Analysis
publication_status: published
publisher: Elsevier
publist_id: '5062'
quality_controlled: '1'
scopus_import: 1
status: public
title: Faithfulness and learning hypergraphs from discrete distributions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 87
year: '2015'
...
---
_id: '1547'
abstract:
- lang: eng
text: Let G be a graph on the vertex set V(G) = {x1,…,xn} with the edge set E(G),
and let R = K[x1,…, xn] be the polynomial ring over a field K. Two monomial ideals
are associated to G, the edge ideal I(G) generated by all monomials xixj with
{xi,xj} ∈ E(G), and the vertex cover ideal IG generated by monomials ∏xi∈Cxi for
all minimal vertex covers C of G. A minimal vertex cover of G is a subset C ⊂
V(G) such that each edge has at least one vertex in C and no proper subset of
C has the same property. Indeed, the vertex cover ideal of G is the Alexander
dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we
consider the lattice of vertex covers LG and we explicitly describe the minimal
free resolution of the ideal associated to LG which is exactly the vertex cover
ideal of G. Then we compute depth, projective dimension, regularity and extremal
Betti numbers of R/I(G) in terms of the associated lattice.
author:
- first_name: Fatemeh
full_name: Mohammadi, Fatemeh
id: 2C29581E-F248-11E8-B48F-1D18A9856A87
last_name: Mohammadi
- first_name: Somayeh
full_name: Moradi, Somayeh
last_name: Moradi
citation:
ama: Mohammadi F, Moradi S. Resolution of unmixed bipartite graphs. Bulletin
of the Korean Mathematical Society. 2015;52(3):977-986. doi:10.4134/BKMS.2015.52.3.977
apa: Mohammadi, F., & Moradi, S. (2015). Resolution of unmixed bipartite graphs.
Bulletin of the Korean Mathematical Society. Korean Mathematical Society.
https://doi.org/10.4134/BKMS.2015.52.3.977
chicago: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite
Graphs.” Bulletin of the Korean Mathematical Society. Korean Mathematical
Society, 2015. https://doi.org/10.4134/BKMS.2015.52.3.977.
ieee: F. Mohammadi and S. Moradi, “Resolution of unmixed bipartite graphs,” Bulletin
of the Korean Mathematical Society, vol. 52, no. 3. Korean Mathematical Society,
pp. 977–986, 2015.
ista: Mohammadi F, Moradi S. 2015. Resolution of unmixed bipartite graphs. Bulletin
of the Korean Mathematical Society. 52(3), 977–986.
mla: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite Graphs.”
Bulletin of the Korean Mathematical Society, vol. 52, no. 3, Korean Mathematical
Society, 2015, pp. 977–86, doi:10.4134/BKMS.2015.52.3.977.
short: F. Mohammadi, S. Moradi, Bulletin of the Korean Mathematical Society 52 (2015)
977–986.
date_created: 2018-12-11T11:52:39Z
date_published: 2015-05-31T00:00:00Z
date_updated: 2021-01-12T06:51:31Z
day: '31'
department:
- _id: CaUh
doi: 10.4134/BKMS.2015.52.3.977
intvolume: ' 52'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0901.3015
month: '05'
oa: 1
oa_version: Preprint
page: 977 - 986
publication: Bulletin of the Korean Mathematical Society
publication_identifier:
eissn:
- 2234-3016
publication_status: published
publisher: Korean Mathematical Society
publist_id: '5624'
quality_controlled: '1'
scopus_import: 1
status: public
title: Resolution of unmixed bipartite graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2015'
...
---
_id: '1579'
abstract:
- lang: eng
text: We show that the Galois group of any Schubert problem involving lines in projective
space contains the alternating group. This constitutes the largest family of enumerative
problems whose Galois groups have been largely determined. Using a criterion of
Vakil and a special position argument due to Schubert, our result follows from
a particular inequality among Kostka numbers of two-rowed tableaux. In most cases,
a combinatorial injection proves the inequality. For the remaining cases, we use
the Weyl integral formulas to obtain an integral formula for these Kostka numbers.
This rewrites the inequality as an integral, which we estimate to establish the
inequality.
acknowledgement: "This research was supported in part by NSF grant DMS-915211 and
the Institut Mittag-Leffler.\r\n"
article_processing_charge: No
author:
- first_name: Christopher
full_name: Brooks, Christopher
last_name: Brooks
- first_name: Abraham
full_name: Martin Del Campo Sanchez, Abraham
id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87
last_name: Martin Del Campo Sanchez
- first_name: Frank
full_name: Sottile, Frank
last_name: Sottile
citation:
ama: Brooks C, Martin del Campo Sanchez A, Sottile F. Galois groups of Schubert
problems of lines are at least alternating. Transactions of the American Mathematical
Society. 2015;367(6):4183-4206. doi:10.1090/S0002-9947-2014-06192-8
apa: Brooks, C., Martin del Campo Sanchez, A., & Sottile, F. (2015). Galois
groups of Schubert problems of lines are at least alternating. Transactions
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0002-9947-2014-06192-8
chicago: Brooks, Christopher, Abraham Martin del Campo Sanchez, and Frank Sottile.
“Galois Groups of Schubert Problems of Lines Are at Least Alternating.” Transactions
of the American Mathematical Society. American Mathematical Society, 2015.
https://doi.org/10.1090/S0002-9947-2014-06192-8.
ieee: C. Brooks, A. Martin del Campo Sanchez, and F. Sottile, “Galois groups of
Schubert problems of lines are at least alternating,” Transactions of the American
Mathematical Society, vol. 367, no. 6. American Mathematical Society, pp.
4183–4206, 2015.
ista: Brooks C, Martin del Campo Sanchez A, Sottile F. 2015. Galois groups of Schubert
problems of lines are at least alternating. Transactions of the American Mathematical
Society. 367(6), 4183–4206.
mla: Brooks, Christopher, et al. “Galois Groups of Schubert Problems of Lines Are
at Least Alternating.” Transactions of the American Mathematical Society,
vol. 367, no. 6, American Mathematical Society, 2015, pp. 4183–206, doi:10.1090/S0002-9947-2014-06192-8.
short: C. Brooks, A. Martin del Campo Sanchez, F. Sottile, Transactions of the American
Mathematical Society 367 (2015) 4183–4206.
date_created: 2018-12-11T11:52:50Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2021-01-12T06:51:43Z
day: '01'
department:
- _id: CaUh
doi: 10.1090/S0002-9947-2014-06192-8
intvolume: ' 367'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1207.4280
month: '06'
oa: 1
oa_version: Preprint
page: 4183 - 4206
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5592'
quality_controlled: '1'
scopus_import: 1
status: public
title: Galois groups of Schubert problems of lines are at least alternating
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2015'
...
---
_id: '1911'
abstract:
- lang: eng
text: The topological Tverberg theorem has been generalized in several directions
by setting extra restrictions on the Tverberg partitions. Restricted Tverberg
partitions, defined by the idea that certain points cannot be in the same part,
are encoded with graphs. When two points are adjacent in the graph, they are not
in the same part. If the restrictions are too harsh, then the topological Tverberg
theorem fails. The colored Tverberg theorem corresponds to graphs constructed
as disjoint unions of small complete graphs. Hell studied the case of paths and
cycles. In graph theory these partitions are usually viewed as graph colorings.
As explored by Aharoni, Haxell, Meshulam and others there are fundamental connections
between several notions of graph colorings and topological combinatorics. For
ordinary graph colorings it is enough to require that the number of colors q satisfy
q>Δ, where Δ is the maximal degree of the graph. It was proven by the first
author using equivariant topology that if q>Δ 2 then the topological Tverberg
theorem still works. It is conjectured that q>KΔ is also enough for some constant
K, and in this paper we prove a fixed-parameter version of that conjecture. The
required topological connectivity results are proven with shellability, which
also strengthens some previous partial results where the topological connectivity
was proven with the nerve lemma.
acknowledgement: Patrik Norén gratefully acknowledges support from the Wallenberg
foundation
author:
- first_name: Alexander
full_name: Engström, Alexander
last_name: Engström
- first_name: Patrik
full_name: Noren, Patrik
id: 46870C74-F248-11E8-B48F-1D18A9856A87
last_name: Noren
citation:
ama: Engström A, Noren P. Tverberg’s Theorem and Graph Coloring. Discrete &
Computational Geometry. 2014;51(1):207-220. doi:10.1007/s00454-013-9556-3
apa: Engström, A., & Noren, P. (2014). Tverberg’s Theorem and Graph Coloring.
Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9556-3
chicago: Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.”
Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-013-9556-3.
ieee: A. Engström and P. Noren, “Tverberg’s Theorem and Graph Coloring,” Discrete
& Computational Geometry, vol. 51, no. 1. Springer, pp. 207–220, 2014.
ista: Engström A, Noren P. 2014. Tverberg’s Theorem and Graph Coloring. Discrete
& Computational Geometry. 51(1), 207–220.
mla: Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.”
Discrete & Computational Geometry, vol. 51, no. 1, Springer, 2014,
pp. 207–20, doi:10.1007/s00454-013-9556-3.
short: A. Engström, P. Noren, Discrete & Computational Geometry 51 (2014) 207–220.
date_created: 2018-12-11T11:54:40Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:01Z
day: '01'
department:
- _id: CaUh
doi: 10.1007/s00454-013-9556-3
intvolume: ' 51'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 207 - 220
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5183'
scopus_import: 1
status: public
title: Tverberg's Theorem and Graph Coloring
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2014'
...
---
_id: '2007'
abstract:
- lang: eng
text: Maximum likelihood estimation under relational models, with or without the
overall effect. For more information see the reference manual
article_processing_charge: No
author:
- first_name: Anna
full_name: Klimova, Anna
id: 31934120-F248-11E8-B48F-1D18A9856A87
last_name: Klimova
- first_name: Tamás
full_name: Rudas, Tamás
last_name: Rudas
citation:
ama: 'Klimova A, Rudas T. gIPFrm: Generalized iterative proportional fitting for
relational models. 2014.'
apa: 'Klimova, A., & Rudas, T. (2014). gIPFrm: Generalized iterative proportional
fitting for relational models. The Comprehensive R Archive Network.'
chicago: 'Klimova, Anna, and Tamás Rudas. “GIPFrm: Generalized Iterative Proportional
Fitting for Relational Models.” The Comprehensive R Archive Network, 2014.'
ieee: 'A. Klimova and T. Rudas, “gIPFrm: Generalized iterative proportional fitting
for relational models.” The Comprehensive R Archive Network, 2014.'
ista: 'Klimova A, Rudas T. 2014. gIPFrm: Generalized iterative proportional fitting
for relational models, The Comprehensive R Archive Network.'
mla: 'Klimova, Anna, and Tamás Rudas. GIPFrm: Generalized Iterative Proportional
Fitting for Relational Models. The Comprehensive R Archive Network, 2014.'
short: A. Klimova, T. Rudas, (2014).
date_created: 2018-12-11T11:55:10Z
date_published: 2014-03-20T00:00:00Z
date_updated: 2022-08-26T08:12:12Z
day: '20'
department:
- _id: CaUh
main_file_link:
- open_access: '1'
url: 'https://CRAN.R-project.org/package=gIPFrm '
month: '03'
oa: 1
oa_version: Published Version
publisher: The Comprehensive R Archive Network
publist_id: '5069'
status: public
title: 'gIPFrm: Generalized iterative proportional fitting for relational models'
type: research_data_reference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2011'
abstract:
- lang: eng
text: The protection of privacy of individual-level information in genome-wide association
study (GWAS) databases has been a major concern of researchers following the publication
of “an attack” on GWAS data by Homer et al. (2008). Traditional statistical methods
for confidentiality and privacy protection of statistical databases do not scale
well to deal with GWAS data, especially in terms of guarantees regarding protection
from linkage to external information. The more recent concept of differential
privacy, introduced by the cryptographic community, is an approach that provides
a rigorous definition of privacy with meaningful privacy guarantees in the presence
of arbitrary external information, although the guarantees may come at a serious
price in terms of data utility. Building on such notions, Uhler et al. (2013)
proposed new methods to release aggregate GWAS data without compromising an individual’s
privacy. We extend the methods developed in Uhler et al. (2013) for releasing
differentially-private χ2χ2-statistics by allowing for arbitrary number of cases
and controls, and for releasing differentially-private allelic test statistics.
We also provide a new interpretation by assuming the controls’ data are known,
which is a realistic assumption because some GWAS use publicly available data
as controls. We assess the performance of the proposed methods through a risk-utility
analysis on a real data set consisting of DNA samples collected by the Wellcome
Trust Case Control Consortium and compare the methods with the differentially-private
release mechanism proposed by Johnson and Shmatikov (2013).
acknowledgement: This research was partially supported by NSF Awards EMSW21-RTG and
BCS-0941518 to the Department of Statistics at Carnegie Mellon University, and by
NSF Grant BCS-0941553 to the Department of Statistics at Pennsylvania State University.
This work was also supported in part by the National Center for Research Resources,
Grant UL1 RR033184, and is now at the National Center for Advancing Translational
Sciences, Grant UL1 TR000127 to Pennsylvania State University. The content is solely
the responsibility of the authors and does not necessarily represent the official
views of the NSF and NIH.
author:
- first_name: Fei
full_name: Yu, Fei
last_name: Yu
- first_name: Stephen
full_name: Fienberg, Stephen
last_name: Fienberg
- first_name: Alexandra
full_name: Slaković, Alexandra
last_name: Slaković
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: Yu F, Fienberg S, Slaković A, Uhler C. Scalable privacy-preserving data sharing
methodology for genome-wide association studies. Journal of Biomedical Informatics.
2014;50:133-141. doi:10.1016/j.jbi.2014.01.008
apa: Yu, F., Fienberg, S., Slaković, A., & Uhler, C. (2014). Scalable privacy-preserving
data sharing methodology for genome-wide association studies. Journal of Biomedical
Informatics. Elsevier. https://doi.org/10.1016/j.jbi.2014.01.008
chicago: Yu, Fei, Stephen Fienberg, Alexandra Slaković, and Caroline Uhler. “Scalable
Privacy-Preserving Data Sharing Methodology for Genome-Wide Association Studies.”
Journal of Biomedical Informatics. Elsevier, 2014. https://doi.org/10.1016/j.jbi.2014.01.008.
ieee: F. Yu, S. Fienberg, A. Slaković, and C. Uhler, “Scalable privacy-preserving
data sharing methodology for genome-wide association studies,” Journal of Biomedical
Informatics, vol. 50. Elsevier, pp. 133–141, 2014.
ista: Yu F, Fienberg S, Slaković A, Uhler C. 2014. Scalable privacy-preserving data
sharing methodology for genome-wide association studies. Journal of Biomedical
Informatics. 50, 133–141.
mla: Yu, Fei, et al. “Scalable Privacy-Preserving Data Sharing Methodology for Genome-Wide
Association Studies.” Journal of Biomedical Informatics, vol. 50, Elsevier,
2014, pp. 133–41, doi:10.1016/j.jbi.2014.01.008.
short: F. Yu, S. Fienberg, A. Slaković, C. Uhler, Journal of Biomedical Informatics
50 (2014) 133–141.
date_created: 2018-12-11T11:55:12Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2021-01-12T06:54:42Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.jbi.2014.01.008
intvolume: ' 50'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1401.5193
month: '08'
oa: 1
oa_version: Submitted Version
page: 133 - 141
publication: Journal of Biomedical Informatics
publication_status: published
publisher: Elsevier
publist_id: '5065'
quality_controlled: '1'
scopus_import: 1
status: public
title: Scalable privacy-preserving data sharing methodology for genome-wide association
studies
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2014'
...
---
_id: '2012'
abstract:
- lang: eng
text: The classical sphere packing problem asks for the best (infinite) arrangement
of non-overlapping unit balls which cover as much space as possible. We define
a generalized version of the problem, where we allow each ball a limited amount
of overlap with other balls. We study two natural choices of overlap measures
and obtain the optimal lattice packings in a parameterized family of lattices
which contains the FCC, BCC, and integer lattice.
acknowledgement: We thank Herbert Edelsbrunner for his valuable discussions and ideas
on the topic of this paper. The second author has been supported by the Max Planck
Center for Visual Computing and Communication
article_number: '1401.0468'
article_processing_charge: No
arxiv: 1
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv.
doi:10.48550/arXiv.1401.0468
apa: Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited
overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468
chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing
with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.
ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,”
arXiv. .
ista: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv,
1401.0468.
mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv,
1401.0468, doi:10.48550/arXiv.1401.0468.
short: M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).
date_created: 2018-12-11T11:55:12Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2023-10-18T08:06:45Z
day: '01'
department:
- _id: HeEd
- _id: CaUh
doi: 10.48550/arXiv.1401.0468
external_id:
arxiv:
- '1401.0468'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://cccg.ca/proceedings/2014/papers/paper23.pdf
month: '01'
oa: 1
oa_version: Submitted Version
publication: arXiv
publication_status: submitted
publist_id: '5064'
status: public
title: Sphere packing with limited overlap
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2013'
abstract:
- lang: eng
text: "An asymptotic theory is developed for computing volumes of regions in the
parameter space of a directed Gaussian graphical model that are obtained by bounding
partial correlations. We study these volumes using the method of real log canonical
thresholds from algebraic geometry. Our analysis involves the computation of the
singular loci of correlation hypersurfaces. Statistical applications include the
strong-faithfulness assumption for the PC algorithm and the quantification of
confounder bias in causal inference. A detailed analysis is presented for trees,
bow ties, tripartite graphs, and complete graphs.\r\n"
acknowledgement: This work was supported in part by the US National Science Foundation
(DMS-0968882) and the Defense Advanced Research Projects Agency (DARPA) Deep Learning
program (FA8650-10-C-7020).
author:
- first_name: Shaowei
full_name: Lin, Shaowei
last_name: Lin
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Bernd
full_name: Sturmfels, Bernd
last_name: Sturmfels
- first_name: Peter
full_name: Bühlmann, Peter
last_name: Bühlmann
citation:
ama: Lin S, Uhler C, Sturmfels B, Bühlmann P. Hypersurfaces and their singularities
in partial correlation testing. Foundations of Computational Mathematics.
2014;14(5):1079-1116. doi:10.1007/s10208-014-9205-0
apa: Lin, S., Uhler, C., Sturmfels, B., & Bühlmann, P. (2014). Hypersurfaces
and their singularities in partial correlation testing. Foundations of Computational
Mathematics. Springer. https://doi.org/10.1007/s10208-014-9205-0
chicago: Lin, Shaowei, Caroline Uhler, Bernd Sturmfels, and Peter Bühlmann. “Hypersurfaces
and Their Singularities in Partial Correlation Testing.” Foundations of Computational
Mathematics. Springer, 2014. https://doi.org/10.1007/s10208-014-9205-0.
ieee: S. Lin, C. Uhler, B. Sturmfels, and P. Bühlmann, “Hypersurfaces and their
singularities in partial correlation testing,” Foundations of Computational
Mathematics, vol. 14, no. 5. Springer, pp. 1079–1116, 2014.
ista: Lin S, Uhler C, Sturmfels B, Bühlmann P. 2014. Hypersurfaces and their singularities
in partial correlation testing. Foundations of Computational Mathematics. 14(5),
1079–1116.
mla: Lin, Shaowei, et al. “Hypersurfaces and Their Singularities in Partial Correlation
Testing.” Foundations of Computational Mathematics, vol. 14, no. 5, Springer,
2014, pp. 1079–116, doi:10.1007/s10208-014-9205-0.
short: S. Lin, C. Uhler, B. Sturmfels, P. Bühlmann, Foundations of Computational
Mathematics 14 (2014) 1079–1116.
date_created: 2018-12-11T11:55:12Z
date_published: 2014-10-10T00:00:00Z
date_updated: 2021-01-12T06:54:43Z
day: '10'
department:
- _id: CaUh
doi: 10.1007/s10208-014-9205-0
intvolume: ' 14'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1209.0285
month: '10'
oa: 1
oa_version: Submitted Version
page: 1079 - 1116
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '5063'
quality_controlled: '1'
scopus_import: 1
status: public
title: Hypersurfaces and their singularities in partial correlation testing
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '2047'
abstract:
- lang: eng
text: Following the publication of an attack on genome-wide association studies
(GWAS) data proposed by Homer et al., considerable attention has been given to
developing methods for releasing GWAS data in a privacy-preserving way. Here,
we develop an end-to-end differentially private method for solving regression
problems with convex penalty functions and selecting the penalty parameters by
cross-validation. In particular, we focus on penalized logistic regression with
elastic-net regularization, a method widely used to in GWAS analyses to identify
disease-causing genes. We show how a differentially private procedure for penalized
logistic regression with elastic-net regularization can be applied to the analysis
of GWAS data and evaluate our method’s performance.
acknowledgement: This research was partially supported by BCS- 0941518 to the Department
of Statistics at Carnegie Mellon University.
alternative_title:
- LNCS
arxiv: 1
author:
- first_name: Fei
full_name: Yu, Fei
last_name: Yu
- first_name: Michal
full_name: Rybar, Michal
id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87
last_name: Rybar
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Stephen
full_name: Fienberg, Stephen
last_name: Fienberg
citation:
ama: 'Yu F, Rybar M, Uhler C, Fienberg S. Differentially-private logistic regression
for detecting multiple-SNP association in GWAS databases. In: Domingo Ferrer J,
ed. Lecture Notes in Computer Science (Including Subseries Lecture Notes in
Artificial Intelligence and Lecture Notes in Bioinformatics). Vol 8744. Springer;
2014:170-184. doi:10.1007/978-3-319-11257-2_14'
apa: 'Yu, F., Rybar, M., Uhler, C., & Fienberg, S. (2014). Differentially-private
logistic regression for detecting multiple-SNP association in GWAS databases.
In J. Domingo Ferrer (Ed.), Lecture Notes in Computer Science (including subseries
Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
(Vol. 8744, pp. 170–184). Ibiza, Spain: Springer. https://doi.org/10.1007/978-3-319-11257-2_14'
chicago: Yu, Fei, Michal Rybar, Caroline Uhler, and Stephen Fienberg. “Differentially-Private
Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases.”
In Lecture Notes in Computer Science (Including Subseries Lecture Notes in
Artificial Intelligence and Lecture Notes in Bioinformatics), edited by Josep
Domingo Ferrer, 8744:170–84. Springer, 2014. https://doi.org/10.1007/978-3-319-11257-2_14.
ieee: F. Yu, M. Rybar, C. Uhler, and S. Fienberg, “Differentially-private logistic
regression for detecting multiple-SNP association in GWAS databases,” in Lecture
Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence
and Lecture Notes in Bioinformatics), Ibiza, Spain, 2014, vol. 8744, pp. 170–184.
ista: 'Yu F, Rybar M, Uhler C, Fienberg S. 2014. Differentially-private logistic
regression for detecting multiple-SNP association in GWAS databases. Lecture Notes
in Computer Science (including subseries Lecture Notes in Artificial Intelligence
and Lecture Notes in Bioinformatics). PSD: Privacy in Statistical Databases, LNCS,
vol. 8744, 170–184.'
mla: Yu, Fei, et al. “Differentially-Private Logistic Regression for Detecting Multiple-SNP
Association in GWAS Databases.” Lecture Notes in Computer Science (Including
Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),
edited by Josep Domingo Ferrer, vol. 8744, Springer, 2014, pp. 170–84, doi:10.1007/978-3-319-11257-2_14.
short: F. Yu, M. Rybar, C. Uhler, S. Fienberg, in:, J. Domingo Ferrer (Ed.), Lecture
Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence
and Lecture Notes in Bioinformatics), Springer, 2014, pp. 170–184.
conference:
end_date: 2014-09-19
location: Ibiza, Spain
name: 'PSD: Privacy in Statistical Databases'
start_date: 2014-09-17
date_created: 2018-12-11T11:55:24Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:57Z
day: '01'
department:
- _id: KrPi
- _id: CaUh
doi: 10.1007/978-3-319-11257-2_14
editor:
- first_name: Josep
full_name: Domingo Ferrer, Josep
last_name: Domingo Ferrer
external_id:
arxiv:
- '1407.8067'
intvolume: ' 8744'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1407.8067
month: '01'
oa: 1
oa_version: Submitted Version
page: 170 - 184
project:
- _id: 25636330-B435-11E9-9278-68D0E5697425
grant_number: 11-NSF-1070
name: ROOTS Genome-wide Analysis of Root Traits
publication: Lecture Notes in Computer Science (including subseries Lecture Notes
in Artificial Intelligence and Lecture Notes in Bioinformatics)
publication_status: published
publisher: Springer
publist_id: '5004'
quality_controlled: '1'
scopus_import: 1
status: public
title: Differentially-private logistic regression for detecting multiple-SNP association
in GWAS databases
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8744
year: '2014'
...
---
_id: '2178'
abstract:
- lang: eng
text: We consider the three-state toric homogeneous Markov chain model (THMC) without
loops and initial parameters. At time T, the size of the design matrix is 6 ×
3 · 2T-1 and the convex hull of its columns is the model polytope. We study the
behavior of this polytope for T ≥ 3 and we show that it is defined by 24 facets
for all T ≥ 5. Moreover, we give a complete description of these facets. From
this, we deduce that the toric ideal associated with the design matrix is generated
by binomials of degree at most 6. Our proof is based on a result due to Sturmfels,
who gave a bound on the degree of the generators of a toric ideal, provided the
normality of the corresponding toric variety. In our setting, we established the
normality of the toric variety associated to the THMC model by studying the geometric
properties of the model polytope.
acknowledgement: Research of Martín del Campo supported in part by NSF Grant DMS-915211.
author:
- first_name: David
full_name: Haws, David
last_name: Haws
- first_name: Abraham
full_name: Martin Del Campo Sanchez, Abraham
id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87
last_name: Martin Del Campo Sanchez
- first_name: Akimichi
full_name: Takemura, Akimichi
last_name: Takemura
- first_name: Ruriko
full_name: Yoshida, Ruriko
last_name: Yoshida
citation:
ama: Haws D, Martin del Campo Sanchez A, Takemura A, Yoshida R. Markov degree of
the three-state toric homogeneous Markov chain model. Beitrage zur Algebra
und Geometrie. 2014;55(1):161-188. doi:10.1007/s13366-013-0178-y
apa: Haws, D., Martin del Campo Sanchez, A., Takemura, A., & Yoshida, R. (2014).
Markov degree of the three-state toric homogeneous Markov chain model. Beitrage
Zur Algebra Und Geometrie. Springer. https://doi.org/10.1007/s13366-013-0178-y
chicago: Haws, David, Abraham Martin del Campo Sanchez, Akimichi Takemura, and Ruriko
Yoshida. “Markov Degree of the Three-State Toric Homogeneous Markov Chain Model.”
Beitrage Zur Algebra Und Geometrie. Springer, 2014. https://doi.org/10.1007/s13366-013-0178-y.
ieee: D. Haws, A. Martin del Campo Sanchez, A. Takemura, and R. Yoshida, “Markov
degree of the three-state toric homogeneous Markov chain model,” Beitrage zur
Algebra und Geometrie, vol. 55, no. 1. Springer, pp. 161–188, 2014.
ista: Haws D, Martin del Campo Sanchez A, Takemura A, Yoshida R. 2014. Markov degree
of the three-state toric homogeneous Markov chain model. Beitrage zur Algebra
und Geometrie. 55(1), 161–188.
mla: Haws, David, et al. “Markov Degree of the Three-State Toric Homogeneous Markov
Chain Model.” Beitrage Zur Algebra Und Geometrie, vol. 55, no. 1, Springer,
2014, pp. 161–88, doi:10.1007/s13366-013-0178-y.
short: D. Haws, A. Martin del Campo Sanchez, A. Takemura, R. Yoshida, Beitrage Zur
Algebra Und Geometrie 55 (2014) 161–188.
date_created: 2018-12-11T11:56:10Z
date_published: 2014-03-01T00:00:00Z
date_updated: 2021-01-12T06:55:48Z
day: '01'
department:
- _id: CaUh
doi: 10.1007/s13366-013-0178-y
intvolume: ' 55'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1204.3070
month: '03'
oa: 1
oa_version: Submitted Version
page: 161 - 188
publication: Beitrage zur Algebra und Geometrie
publication_status: published
publisher: Springer
publist_id: '4804'
quality_controlled: '1'
scopus_import: 1
status: public
title: Markov degree of the three-state toric homogeneous Markov chain model
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2014'
...