[{"publisher":"Elsevier","year":"2015","title":"Faithfulness and learning hypergraphs from discrete distributions","date_updated":"2021-01-12T06:54:43Z","language":[{"iso":"eng"}],"citation":{"short":"A. Klimova, C. Uhler, T. Rudas, Computational Statistics & Data Analysis 87 (2015) 57–72.","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.","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.","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","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.","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"},"date_created":"2018-12-11T11:55:13Z","scopus_import":1,"month":"07","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"57 - 72","oa_version":"Preprint","day":"01","oa":1,"publication_status":"published","publist_id":"5062","intvolume":" 87","status":"public","doi":"10.1016/j.csda.2015.01.017","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1404.6617"}],"author":[{"first_name":"Anna","last_name":"Klimova","id":"31934120-F248-11E8-B48F-1D18A9856A87","full_name":"Klimova, Anna"},{"first_name":"Caroline","last_name":"Uhler","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","full_name":"Uhler, Caroline"},{"last_name":"Rudas","first_name":"Tamás","full_name":"Rudas, Tamás"}],"department":[{"_id":"CaUh"}],"publication":"Computational Statistics & Data Analysis","_id":"2014","volume":87,"date_published":"2015-07-01T00:00:00Z","quality_controlled":"1","issue":"7","type":"journal_article"},{"publisher":"Korean Mathematical Society","scopus_import":1,"month":"05","page":"977 - 986","day":"31","publication_status":"published","publist_id":"5624","doi":"10.4134/BKMS.2015.52.3.977","_id":"1547","date_published":"2015-05-31T00:00:00Z","quality_controlled":"1","year":"2015","title":"Resolution of unmixed bipartite graphs","date_updated":"2021-01-12T06:51:31Z","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:52:39Z","citation":{"short":"F. Mohammadi, S. Moradi, Bulletin of the Korean Mathematical Society 52 (2015) 977–986.","ista":"Mohammadi F, Moradi S. 2015. Resolution of unmixed bipartite graphs. Bulletin of the Korean Mathematical Society. 52(3), 977–986.","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.","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.","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"oa_version":"Preprint","oa":1,"publication_identifier":{"eissn":["2234-3016"]},"intvolume":" 52","status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0901.3015"}],"author":[{"first_name":"Fatemeh","last_name":"Mohammadi","id":"2C29581E-F248-11E8-B48F-1D18A9856A87","full_name":"Mohammadi, Fatemeh"},{"last_name":"Moradi","first_name":"Somayeh","full_name":"Moradi, Somayeh"}],"department":[{"_id":"CaUh"}],"publication":"Bulletin of the Korean Mathematical Society","volume":52,"type":"journal_article","issue":"3"},{"_id":"1579","date_published":"2015-06-01T00:00:00Z","quality_controlled":"1","doi":"10.1090/S0002-9947-2014-06192-8","publist_id":"5592","publication_status":"published","month":"06","scopus_import":1,"day":"01","page":"4183 - 4206","publisher":"American Mathematical Society","acknowledgement":"This research was supported in part by NSF grant DMS-915211 and the Institut Mittag-Leffler.\r\n","volume":367,"department":[{"_id":"CaUh"}],"author":[{"last_name":"Brooks","first_name":"Christopher","full_name":"Brooks, Christopher"},{"last_name":"Martin Del Campo Sanchez","first_name":"Abraham","full_name":"Martin Del Campo Sanchez, Abraham","id":"4CF47F6A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sottile, Frank","first_name":"Frank","last_name":"Sottile"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.4280"}],"publication":"Transactions of the American Mathematical Society","type":"journal_article","issue":"6","oa":1,"status":"public","intvolume":" 367","article_processing_charge":"No","abstract":[{"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.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","year":"2015","title":"Galois groups of Schubert problems of lines are at least alternating","date_created":"2018-12-11T11:52:50Z","citation":{"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.","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","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","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.","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.","short":"C. Brooks, A. Martin del Campo Sanchez, F. Sottile, Transactions of the American Mathematical Society 367 (2015) 4183–4206."},"language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:51:43Z"},{"publisher":"Springer","title":"Tverberg's Theorem and Graph Coloring","year":"2014","acknowledgement":"Patrik Norén gratefully acknowledges support from the Wallenberg foundation","date_updated":"2021-01-12T06:54:01Z","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:54:40Z","citation":{"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.","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","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.","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","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.","short":"A. Engström, P. Noren, Discrete & Computational Geometry 51 (2014) 207–220."},"scopus_import":1,"month":"01","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."}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","page":"207 - 220","oa_version":"None","day":"01","publication_status":"published","intvolume":" 51","publist_id":"5183","status":"public","doi":"10.1007/s00454-013-9556-3","author":[{"first_name":"Alexander","last_name":"Engström","full_name":"Engström, Alexander"},{"full_name":"Noren, Patrik","id":"46870C74-F248-11E8-B48F-1D18A9856A87","last_name":"Noren","first_name":"Patrik"}],"publication":"Discrete & Computational Geometry","department":[{"_id":"CaUh"}],"volume":51,"_id":"1911","date_published":"2014-01-01T00:00:00Z","type":"journal_article","issue":"1"},{"date_updated":"2019-01-24T13:05:59Z","citation":{"short":"A. Klimova, 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.","ieee":"A. Klimova and T. Rudas, *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.","ama":"Klimova A, Rudas T. *GIPFrm: Generalized Iterative Proportional Fitting for Relational Models*. The Comprehensive R Archive Network; 2014.","mla":"Klimova, Anna, and Tamás Rudas. *GIPFrm: Generalized Iterative Proportional Fitting for Relational Models*. The Comprehensive R Archive Network, 2014.","chicago":"Klimova, Anna, and Tamás Rudas. *GIPFrm: Generalized Iterative Proportional Fitting for Relational Models*. The Comprehensive R Archive Network, 2014."},"date_created":"2018-12-11T11:55:10Z","acknowledgement":"Code","year":"2014","title":"gIPFrm: Generalized iterative proportional fitting for relational models","publisher":"The Comprehensive R Archive Network","day":"20","month":"03","publist_id":"5069","status":"public","publication_status":"published","extern":0,"oa":1,"type":"other_academic_publication","quality_controlled":0,"date_published":"2014-03-20T00:00:00Z","_id":"2007","department":[{"_id":"CaUh"}],"main_file_link":[{"url":"https://CRAN.R-project.org/package=gIPFrm ","open_access":"1"}],"author":[{"last_name":"Klimova","first_name":"Anna","full_name":"Anna Klimova","id":"31934120-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Rudas, Tamás","last_name":"Rudas","first_name":"Tamás"}]}]