Question: Are Columbia University and Cornell University both private institutions?
Context: The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States.  The conference name is also commonly used to refer to those eight schools as a group beyond the sports context.  The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University.  The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism. The Weill Cornell Graduate School of Medical Sciences (WCGS) (formerly known as the Cornell University Graduate School of Medical Sciences) is a graduate college of Cornell University that was founded in 1952 as an academic partnership between two major medical institutions in New York City: the Weill Cornell Medical College and the Sloan-Kettering Institute.  Cornell is involved in the Tri-Institutional MD-PhD Program with Rockefeller University and the Sloan-Kettering Institute; each of these three institutions is part of a large biomedical center extending along York Avenue between 65th and 72nd Streets on the Upper East Side of Manhattan. There are a large variety of campus types and programs in the SUNY system; each site overlaps somewhat in specialties.  SUNY divides its campuses into four categories: university centers / doctoral-granting institutions, comprehensive colleges, technology colleges, and community colleges.  SUNY also has a unique relationship with its statutory colleges, which embed state-owned, state-funded colleges within other institutions such as Cornell University and Alfred University.  Students at the statutory colleges pay tuition at a state-subsidized rate and are considered students of the private institutions in which the state-funded colleges are embedded. The Commonwealth System of Higher Education is a statutory designation by the Commonwealth of Pennsylvania that confers "state-related" status on four universities located within the state.  The designation establishes the schools as an "instrumentality of the commonwealth" and provides each university with annual, non-preferred financial appropriations in exchange offering tuition discounts to students that are residents of Pennsylvania and a minority state-representation on each school's board of trustees.  Legally, however, the universities remain separate and private entities, operating under their own charters, governed by independent boards of trustees, and with its assets under their own ownership and control thereby retaining much of the freedom and individuality of private institutions, both administratively and academically.  It is the only public-private hybrid system of higher education in the United States that is so construed, although Cornell University, the University of Delaware, and Rutgers University represent alternative types of public-private university hybrids. The Cornell University School of Nursing was founded in 1877 as the New York Hospital Training School for Nurses, in New York City.  As a part of New York Hospital, the school began its connection with Cornell University when Cornell's Medical College affiliated with New York Hospital in 1927.  In 1932, the school moved to the joint campus on the upper east side of New York when both institutions co-located.  The school became affiliated with Cornell and renamed as the Cornell University-New York Hospital School of Nursing in 1942. Paul L. Houston is Professor of Chemistry and Biochemistry at The Georgia Institute of Technology.  Most recently, he was Dean of the College of Sciences at Georgia Tech (from 2007-2013).  He started his professorial career at Cornell University in 1975 following undergraduate study at Yale, doctoral work at MIT, and postdoctoral research at the University of California at Berkeley.  He was formerly Chair of the Cornell Department of Chemistry and Chemical Biology (1997–2001), Senior Associate Dean of the College of Arts and Sciences (2002–2005), and the Peter J. W. Debye Professor of Chemistry.  He was a member of the Cornell Center for Materials Research, the Kavli Institute at Cornell for Nanoscale Science, and the Graduate Field of Applied Physics.  Dr. Houston has held visiting positions at the Max Planck Institute for Quantum Optics (1982), Columbia University (1986, 1987), the Institute for Molecular Science, Okazaki, Japan (1989), the University of California at Berkeley (2003), and the University of Rome La Sapienza (2001, 2006).  He has been an Alfred P. Sloan Research Fellow (1979–81), a Camille and Henry Dreyfus Teacher Scholar (1980), and a John Simon Guggenheim Fellow (1986–87).  He served as a Senior Editor of the Journal of Physical Chemistry (1991–97), as Chair of the American Physical Society Division of Laser Chemistry (1997–98), and as a member of the Science and Technology Steering Committee of Brookhaven National Laboratories (1998–2005).  Houston has authored or co-authored over 160 publications in the field of physical chemistry and a textbook on chemical kinetics.  In 2001 he shared with David W. Chandler the Herbert P. Broida Prize of the American Physical Society for work on product imaging in chemical dynamics.  He was elected a fellow of the American Academy of Arts and Sciences in 2005. The President of Cornell University is the chief administrator of Cornell University, an Ivy League institution located in Ithaca, New York and New York City.  Included in the list below are all Presidents of Cornell University, from the first President Andrew Dickson White and through the current President, Martha E. Pollack.  There have been 14 Presidents of Cornell University, not including three interregnum presidencies during university presidential transitions. Columbia University (Columbia; officially Columbia University in the City of New York), established in 1754, is a private Ivy League research university in Upper Manhattan, New York City, often cited as one of the world's most prestigious universities. Cornell University ( ) is a private and statutory Ivy League research university located in Ithaca, New York.  Founded in 1865 by Ezra Cornell and Andrew Dickson White, the university was intended to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied.  These ideals, unconventional for the time, are captured in Cornell's motto, a popular 1865 Ezra Cornell quotation: "I would found an institution where any person can find instruction in any study." This list of Cornell University alumni includes notable graduates, non-graduate former students, and current students of Cornell University, an Ivy League university located in Ithaca, New York.  Cornell counted 245,027 living alumni as of August 2008.  Its alumni constitute 25 recipients of National Medal of Science and National Medal of Technology and Innovation combined, 32 MacArthur Fellows, 34 Marshall Scholars and 31 Rhodes Scholars, and Cornell is the only university with three female winners of unshared Nobel Prizes among its graduates (Pearl S. Buck, Barbara McClintock, and Toni Morrison).  Many alumni maintain university ties through Homecoming's reunion weekend, through "Cornell Magazine", and through the Cornell Club of New York.  In 2005, Cornell ranked #3 nationwide for gifts and bequests from alumni.  Alumni are known as "Cornellians".
Answer: yes