--- _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' ...