---
_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'
acknowledgement: Code
author:
- first_name: Anna
full_name: Anna Klimova
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*. The Comprehensive R Archive Network; 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,p.'
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, GIPFrm: Generalized Iterative Proportional Fitting
for Relational Models, The Comprehensive R Archive Network, 2014.'
date_created: 2018-12-11T11:55:10Z
date_published: 2014-03-20T00:00:00Z
date_updated: 2019-01-24T13:05:59Z
day: '20'
department:
- _id: CaUh
extern: 0
main_file_link:
- open_access: '1'
url: 'https://CRAN.R-project.org/package=gIPFrm '
month: '03'
oa: 1
publication_status: published
publisher: The Comprehensive R Archive Network
publist_id: '5069'
quality_controlled: 0
status: public
title: 'gIPFrm: Generalized iterative proportional fitting for relational models'
type: other_academic_publication
year: '2014'
...