---
_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: '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: '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: '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'
...