{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T18:45:32Z","timestamp":1781030732159,"version":"3.54.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T00:00:00Z","timestamp":1401408000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s10208-014-9205-0","type":"journal-article","created":{"date-parts":[[2014,5,29]],"date-time":"2014-05-29T18:36:15Z","timestamp":1401388575000},"page":"1079-1116","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hypersurfaces and Their Singularities in Partial Correlation Testing"],"prefix":"10.1007","volume":"14","author":[{"given":"Shaowei","family":"Lin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caroline","family":"Uhler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"B\u00fchlmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2014,5,30]]},"reference":[{"key":"9205_CR1","doi-asserted-by":"crossref","unstructured":"V. I. Arnol\u2019d, S. M. Guse\u012dn-Zade and A. N. Varchenko: Singularities of Differentiable Maps, Vol. II, Birkh\u00e4user, Boston, 1985.","DOI":"10.1007\/978-1-4612-5154-5"},{"key":"9205_CR2","unstructured":"S. Chaudhuri and T.S. Richardson: Using the structure of d-connecting paths as a qualitative measure of the strength of dependence, Proceedings of the Nineteenth Conference on Uncertainty in, Artificial Intelligence, pages 116\u2013123, 2003."},{"key":"9205_CR3","doi-asserted-by":"crossref","unstructured":"D. Cox, J. Little and D. O\u2019Shea: Ideals, Varieties and Algorithms, Springer Undergraduate Texts, Third edition, Springer Verlag, New York, 2007.","DOI":"10.1007\/978-0-387-35651-8"},{"key":"9205_CR4","unstructured":"W. Decker, G.-M. Greuel, G. Pfister, and H. Sch\u00f6nemann: SINGULAR 3-1-5 - A computer algebra system for polynomial computations, 2012, http:\/\/www.singular.uni-kl.de ."},{"key":"9205_CR5","unstructured":"D. Grayson and M. Stillman: MACAULAY 2, a software system for research in algebraic geometry, available at http:\/\/www.math.uiuc.edu\/Macaulay2\/ ."},{"key":"9205_CR6","doi-asserted-by":"crossref","unstructured":"M. Greenblatt: Oscillatory integral decay, sublevel set growth, and the Newton polyhedron, Math. Annalen\u00a0346, pages 857\u2013890, 2010.","DOI":"10.1007\/s00208-009-0424-7"},{"key":"9205_CR7","doi-asserted-by":"crossref","unstructured":"S. Greenland: Quantifying biases in causal models: classical confounding vs collider-stratification bias, Epidemiology\u00a014, pages 300\u2013306, 2003.","DOI":"10.1097\/01.EDE.0000042804.12056.6C"},{"key":"9205_CR8","doi-asserted-by":"crossref","unstructured":"S. Greenland and J. Pearl: Adjustments and their consequences: collapsibility analysis using graphical models, International Statistical Review\u00a079, pages 401\u2013426, 2011.","DOI":"10.1111\/j.1751-5823.2011.00158.x"},{"key":"9205_CR9","doi-asserted-by":"crossref","unstructured":"H. Hauser: The Hironaka theorem on resolution of singularities (or: a proof that we always wanted to understand), Bull. Amer. Math. Soc.\u00a040, pages 323\u2013403, 2003.","DOI":"10.1090\/S0273-0979-03-00982-0"},{"key":"9205_CR10","doi-asserted-by":"crossref","unstructured":"H. Hironaka: Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 79, pages 109\u2013326, 1964.","DOI":"10.2307\/1970486"},{"key":"9205_CR11","unstructured":"M. Kalisch and P. B\u00fchlmann: Estimating high-dimensional directed acyclic graphs with the PC-algorithm, Journal of Machine Learning Research\u00a08, pages 613\u2013636, 2007."},{"key":"9205_CR12","unstructured":"J. Koll\u00e1r: Lectures on Resolution of Singularities, Annals of Mathematics Studies 166, Princeton University Press, Princeton, NJ, 2007."},{"key":"9205_CR13","unstructured":"J. B. Lasserre: Level sets and non Gaussian integrals of positively homogeneous functions, International Game Theory Review.\u00a0 http:\/\/homepages.laas.fr\/lasserre\/forthcoming.html ."},{"key":"9205_CR14","unstructured":"S. Lin: Algebraic Methods for Evaluating Integrals in Bayesian Statistics, Ph.D. dissertation, University of California, Berkeley, May 2011."},{"key":"9205_CR15","doi-asserted-by":"crossref","unstructured":"M. Marshall: Positive Polynomials and Sums of Squares, Mathematical Surveys and Monographs\u00a0146, American Mathematical Society, Providence, RI, 2008.","DOI":"10.1090\/surv\/146"},{"key":"9205_CR16","doi-asserted-by":"crossref","unstructured":"P. Spirtes, C. Glymour and R. Scheines: Prediction and Search, MIT Press, second edition, 2001.","DOI":"10.7551\/mitpress\/1754.001.0001"},{"key":"9205_CR17","doi-asserted-by":"crossref","unstructured":"C. Uhler, G. Raskutti, P. B\u00fchlmann and B. Yu: Geometry of faithfulness assumption in causal inference, Annals of Statistics\u00a041, pages 436\u2013463, 2013.","DOI":"10.1214\/12-AOS1080"},{"key":"9205_CR18","doi-asserted-by":"crossref","unstructured":"S. Watanabe: Algebraic Geometry and Statistical Learning Theory, Monographs on Applied and Computational Mathematics 25, Cambridge University Press, 2009.","DOI":"10.1017\/CBO9780511800474"},{"key":"9205_CR19","unstructured":"J. Zhang and P. Spirtes: Strong faithfulness and uniform consistency in causal inference, Uncertainty in Artificial Intelligence (UAI), pages 632\u2013639, 2003."},{"key":"9205_CR20","doi-asserted-by":"crossref","unstructured":"J. Zhang and P. Spirtes: Detection of unfaithfulness and robust causal inference, Minds and Machines\u00a018, pages 239\u2013271, 2008.","DOI":"10.1007\/s11023-008-9096-4"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-014-9205-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-014-9205-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-014-9205-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,11]],"date-time":"2019-08-11T03:56:38Z","timestamp":1565495798000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-014-9205-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,30]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["9205"],"URL":"https:\/\/doi.org\/10.1007\/s10208-014-9205-0","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,30]]}}}