# Publications

# PAGE IS under construction

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## Preprints (submitted)

### Random graphs with node and block effects: models, goodness-of-fit tests, and applications to biological networks,

Elizabeth Gross, Sonja Petrović, and Despina Stasi.

### Threaded Gr\"obner Bases: a Macaulay2 package,

Sonja Petrović and Shahrzad Jamshidi Zelenberg.

### Exact tests for stochastic block models,

Vishesh Karwa, Debdeep Pati, Sonja Petrović, Liam Solus, Nikita Alexeev, Mateja Raič, Dane Wilburne, Robert Williams, Bowei Yan.

### DERGMs: Degeneracy-restricted exponential random graph models,

Vishesh Karwa, Sonja Petrović and Denis Bajić.

*Major* revision completed October 2018 (see arXiv v2). Minor revision in progress.

Supplementary material: on GitHub.

## published / accepted / in press

**Algebraic statistics, tables, and networks: The Fienberg advantage.**

Elizabeth Gross, Vishesh Karwa, Sonja Petrovi\'c.

To appear in the Springer volume Statistics in the public interest - in memory of Stephen E. Fienberg. arXiv:1910.01692.

**Algebraic Statistics in Practice: Applications to Networks,**

Marta Casanellas, Sonja Petrović and Caroline Uhler.

Annual Reviews of Statistics and its Applications 2020. 7:9.1–9.24.

arXiv:1906.09537. Published version https://doi.org/10.1146/annurev-statistics-031017-100053

**WHAT IS... a Markov basis?**

Sonja Petrović. Notices of the American Mathematical Society 2019, 66 (7), 1088—1092.

Read the full article here or on arXiv:1907.07320.

**“Old Wine in New Bottles,” and Some More New Wine – Stephen Fienberg’s Influence on Algebraic Statistics,**

Sonja Petrović, Aleksandra Slavkovic, and Ruriko Yoshida. Editorial piece for the Journal of Algebraic Statistics' Special Volume in honor of memory of S.E.Fienberg, 2019.

**Random Monomial Ideals: a Macaulay2 package**

Sonja Petrovic, Despina Stasi, Dane Wilburne.Journal of Software for Algebra and Geometry, 9 (2019), 65–70.

Code available in Macaulay2 as of version 1.11.

**Hypergraph encodings of arbitrary toric ideals,**

Sonja Petrović, Apostolos Thoma and Marius Vladoiu.

Journal of Combinatorial Theory, Series A 166 (2019) pp. 11-41.

**Bouquet algebra of toric ideals,**

Sonja Petrović, Apostolos Thoma and Marius Vladoiu.

Journal of Algebra 512 (2018) 493–525

arXiv:1507.02740. (Revised 2017.)

**Random Monomial Ideals,**

Jesus A. De Loera, Sonja Petrovic, Lily Silverstein, Despina Stasi, Dane Wilburne

Journal of Algebra, 519(1): 440--473, 2019.

arXiv:1701.07130. (Revised April 2018.)

**The multiple roots phenomenon in maximum likalihood estimation for factor analysis,**

Elizabeth Gross, Sonja Petrovic, Donald Richards, Despina Stasi.

Adv. Stud. Pure Math. 75 (2017).

**Statistical models for cores decomposition of an undirected random graph,**

Vishesh Karwa, Michael J. Pelsmajer, Sonja Petrović, Despina Stasi, and Dane Wilburne.

Electronic Journal of Statistics 2017, Vol. 11, No. 1, 1949-1982.

arXiv:1410.7357 (v3, Nov 2016); http://dx.doi.org/10.1214/17-EJS1235.

Supplementary material: R code on GitHub.

**Coauthorship and citation networks for statisticians: Comment**,

Vishesh Karwa and Sonja Petrovic. Invited comment on the paper `Coauthorship and citation networks for statisticians' by Jin and Ji.

Annals of Applied Statistics, 10 (2016), no. 4, 1827--1834. doi:10.1214/16-AOAS978.

**On the Geometry and Extremal Properties of the Edge-Degeneracy Model,**

Nicolas Kim, Dane Wilburne, Sonja Petrovic, Alessandro Rinaldo.

MNG 2016: The Third SDM Workshop on Mining Networks and Graphs: A Big Data Analytic Challenge.

**A survey of discrete methods in (algebraic) statistics for networks,** Contemporary Mathematics, vol. 685, 260-281, American Mathematical Society, 2017.

**Blow-up algebras, determinantal ideals, and Dedekind-Mertens-like formulas,** with Alberto Corso, Uwe Nagel, and Cornelia Yuen. (2016)

Forum Mathematicum, 29(4), pp. 799-830. DOI: 10.1515/forum-2016-0007.

**Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces,** Jesus A. De Loera, Sonja Petrovic, and Despina Stasi.

Journal of Symbolic Computation, 77 (2016) pp.1-15. 10.1016/j.jsc.2016.01.001. Link to article.

**Goodness of fit for log-linear network models: Dynamic Markov bases using hypergraphs,** with Elizabeth Gross and Despina Stasi.

Annals of the Institute of Statistical Mathematics (2017) 69: 673. DOI: 10.1007/s10463-016-0560-2

**Beta models for random hypergraphs with a given degree sequence,** Despina Stasi, Kayvan Sadeghi, Alessandro Rinaldo, Sonja Petrovic, and Stephen Fienberg. Proceedings of 21st International Conference on Computational Statistics (2014).

**Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases, **with Aleksandra B. Slavkovic and Xiaotian Zhu. Annals of the Institute of Statistical Mathematics, August 2015, Volume 67, Issue 4, pp 621-648. DOI: 10.1007/s10463-014-0471-z.

arXiv:1401.1397. Published online: June 2014.

**Toric algebra of hypergraphs,** with Despina Stasi,

Journal of Algebraic Combinatorics, February 2014, Volume 39, Issue 1, pp 187-208.

**A combinatorial degree bound for toric ideals of hypergraphs**, with Elizabeth Gross, International Journal of Algebra and Computation, Volume 23, Issue 06, pp. 1503-1520, September 2013. DOI.

arXiv:1206.2512 (previous title: "Markov complexity of hypergraphs").

**PHCpack in Macaulay2, **with Elizabeth Gross and Jan Verschelde,

Journal of Software for Algebra and Geometry, Volume 5, 2013; certified code also available with Macaulay2 release 1.6.

arXiv:1105.4881 (see the Software page for more information).

**GraphicalModels in Macaulay2**, with Seth Sullivant. and Luis Garcia-Puente.

Journal of Software for Algebra and Geometry, Volume 5, 2013; certified code also available with Macaulay2 release 1.5.

arXiv:1208.6550. (see the Software page for more information).

**Maximum Likelihood Estimation in the Beta model, **with Alessandro Rinaldo and Stephen E. Fienberg.

Annals of Statistics 2013, Vol. 41, No. 3, 1085-1110.

arXiv:1105.6145. ( DOI)

**Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees, **with Erik Stokes.

Journal of Algebraic Combinatorics, Volume 37, Issue 4 (2013), Page 667-682.

**How Does Maximum Likelihood Estima- tion for the p1 Model Scale for Large Sparse Networks?**, Rinaldo, A., Petrovíc, S. and Fienberg, S.E. (2012).

NIPS 2012 workshop on Algorithmic and Statistical Approaches for Large Social Network Data Sets.

**Equality of Graver and Universal Gröbner bases of colored partition identities, **with Tristram Bogart and Raymond Hemmecke.

Experimental Mathematics 2012, Vol. 21 (4), 395-401.

**Maximum likelihood degree of variance component models, **with Elizabeth Gross and Mathias Drton.

Electronic Journal of Statistics 2012, Vol. 6, No. 0, 993-1016.

**Algebraic Statistics, **with Aleksandra Slavkovic.

In M. Lovric, editor, International Encyclopedia of Statistical Science, Part 1, 29-32, Springer. (2011) (DOI: 10.1007/978-3-642-04898-2_112)

**Identifiability of two-tree mixtures under group-based models, **with Elizabeth Allman, John Rhodes, and Seth Sullivant.

IEEE/ACM Transactions in Computational Biology and Bioinformatics, 8 no. 3 (2011) 710-722.

arXiv:0909.1854; Supplementary material.

**Algebraic statistics for a directed random graph model with reciprocation,** with Alessandro Rinaldo and Stephen E. Fienberg.

In: Algebraic Methods in Statistics and Probability II, M. Viana and H. Wynn (editors). CONM, vol 516. AMS.

**Algebraic statistics for p_1 random graph models: Markov bases and their uses, **with Alessandro Rinaldo and Stephen E. Fienberg.

*Book chapter* in S. Sinharay and N. J. Dorans, editors, Papers in Honor of Paul W. Holland. ETS. (2010) Springer

**Properties of cut ideals of ring graphs,** with Uwe Nagel.

J. Commut. Algebra 1 (2009), no. 3, 547--565.

**Universal Gröbner bases of varieties of minimal degree.**

Math. Res. Lett. 15 (2008), no. 6, 1211--1221.

**Toric ideals of phylogenetic invariants for the general group-based model on claw trees, **with Julia Chifman, in Proceedings of the Second international conference on Algebraic Biology, (eds. H.Anai, K. Horimoto and T. Kutsia),

Springer LNCS 454 (2007), 307--321.

**A nonlinear Sturm-Picone comparison theorem for dynamic equations on time scales, **with Boris Belinskiy and John Graef.

Int. J. Difference Equ. 2 (2007), no. 1, 25--35. (pdf)