@misc{2007,
author = {Anna Klimova and Rudas, Tamás},
publisher = {The Comprehensive R Archive Network},
title = {{gIPFrm: Generalized iterative proportional fitting for relational models}},
year = {2014},
}
@article{1911,
abstract = {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.},
author = {Engström, Alexander and Noren, Patrik},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {207 -- 220},
publisher = {Springer},
title = {{Tverberg's Theorem and Graph Coloring}},
doi = {10.1007/s00454-013-9556-3},
volume = {51},
year = {2014},
}
@article{2178,
abstract = {We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time T, the size of the design matrix is 6 × 3 · 2T-1 and the convex hull of its columns is the model polytope. We study the behavior of this polytope for T ≥ 3 and we show that it is defined by 24 facets for all T ≥ 5. Moreover, we give a complete description of these facets. From this, we deduce that the toric ideal associated with the design matrix is generated by binomials of degree at most 6. Our proof is based on a result due to Sturmfels, who gave a bound on the degree of the generators of a toric ideal, provided the normality of the corresponding toric variety. In our setting, we established the normality of the toric variety associated to the THMC model by studying the geometric properties of the model polytope.},
author = {Haws, David and Martin Del Campo Sanchez, Abraham and Takemura, Akimichi and Yoshida, Ruriko},
journal = {Beitrage zur Algebra und Geometrie},
number = {1},
pages = {161 -- 188},
publisher = {Springer},
title = {{Markov degree of the three-state toric homogeneous Markov chain model}},
doi = {10.1007/s13366-013-0178-y},
volume = {55},
year = {2014},
}
@article{2011,
abstract = {The protection of privacy of individual-level information in genome-wide association study (GWAS) databases has been a major concern of researchers following the publication of “an attack” on GWAS data by Homer et al. (2008). Traditional statistical methods for confidentiality and privacy protection of statistical databases do not scale well to deal with GWAS data, especially in terms of guarantees regarding protection from linkage to external information. The more recent concept of differential privacy, introduced by the cryptographic community, is an approach that provides a rigorous definition of privacy with meaningful privacy guarantees in the presence of arbitrary external information, although the guarantees may come at a serious price in terms of data utility. Building on such notions, Uhler et al. (2013) proposed new methods to release aggregate GWAS data without compromising an individual’s privacy. We extend the methods developed in Uhler et al. (2013) for releasing differentially-private χ2χ2-statistics by allowing for arbitrary number of cases and controls, and for releasing differentially-private allelic test statistics. We also provide a new interpretation by assuming the controls’ data are known, which is a realistic assumption because some GWAS use publicly available data as controls. We assess the performance of the proposed methods through a risk-utility analysis on a real data set consisting of DNA samples collected by the Wellcome Trust Case Control Consortium and compare the methods with the differentially-private release mechanism proposed by Johnson and Shmatikov (2013).},
author = {Yu, Fei and Fienberg, Stephen and Slaković, Alexandra and Uhler, Caroline},
journal = {Journal of Biomedical Informatics},
pages = {133 -- 141},
publisher = {Elsevier},
title = {{Scalable privacy-preserving data sharing methodology for genome-wide association studies}},
doi = {10.1016/j.jbi.2014.01.008},
volume = {50},
year = {2014},
}
@inproceedings{2047,
abstract = {Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems with convex penalty functions and selecting the penalty parameters by cross-validation. In particular, we focus on penalized logistic regression with elastic-net regularization, a method widely used to in GWAS analyses to identify disease-causing genes. We show how a differentially private procedure for penalized logistic regression with elastic-net regularization can be applied to the analysis of GWAS data and evaluate our method’s performance.},
author = {Yu, Fei and Rybar, Michal and Uhler, Caroline and Fienberg, Stephen},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Domingo Ferrer, Josep},
location = {Ibiza, Spain},
pages = {170 -- 184},
publisher = {Springer},
title = {{Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases}},
doi = {10.1007/978-3-319-11257-2_14},
volume = {8744},
year = {2014},
}