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Show Results For
- All HBS Web
(1,959)
- People (2)
- News (215)
- Research (1,360)
- Events (15)
- Multimedia (13)
- Faculty Publications (906)
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- Article
Aztec Castles and the dP3 Quiver
By: Megan Leoni, Gregg Musiker, Seth Neel and Paxton Turner
Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 (dP3) quiver and geometric properties of its corresponding brane tiling. In... View Details
Leoni, Megan, Gregg Musiker, Seth Neel, and Paxton Turner. "Aztec Castles and the dP3 Quiver." Journal of Physics A: Mathematical and Theoretical 47, no. 47 (November 28, 2014).
- 1990
- Chapter
Refinement of Nash Equilibrium: The Main Ideas
By: E. Kohlberg
Keywords: Mathematical Methods
Kohlberg, E. "Refinement of Nash Equilibrium: The Main Ideas." In Game Theory and Applications, edited by T. Ichiishi, A. Neyman, and Y. Tauman. San Diego: Academic Press, 1990.
- Article
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80
By: Noam D. Elkies and Scott Duke Kominers
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80." Proceedings of the American Mathematical Society 138, no. 1 (January 2010): 105–108.
- February 2006
- Teaching Note
Cost-Volume-Profit Models (TN)
By: David F. Hawkins, V.G. Narayanan, Michele Jurgens and Jacob Cohen
Keywords: Mathematical Methods
- August 2005 (Revised April 2008)
- Teaching Note
Store24 (A): Statistics Review with Data Desk (TN)
By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
- 2006
- Chapter
Advanced Regression Models
By: Raghuram Iyengar and Sunil Gupta
Keywords: Mathematical Methods
- 1978
- Chapter
Matrix-Weighted Averages: Computation and Presentation
By: Dutch Leonard
Keywords: Mathematical Methods
Leonard, Dutch. "Matrix-Weighted Averages: Computation and Presentation." In Proceedings of the Eleventh Symposium on the Interface of Computers and Statistics, edited by Ronald A. Gallant and Thomas Michael Gerig. Raleigh, NC: North Carolina State University, Institute of Statistics, 1978.
- July 1982 (Revised March 1984)
- Background Note
Worked Examples in Dynamic Programming
By: David E. Bell
Keywords: Mathematical Methods
Bell, David E. "Worked Examples in Dynamic Programming." Harvard Business School Background Note 183-028, July 1982. (Revised March 1984.)
- 22 Oct 2020
- Working Paper Summaries
Estimating Causal Effects in the Presence of Partial Interference Using Multivariate Bayesian Structural Time Series Models
Keywords: by Fiammetta Menchetti and Iavor Bojinov
- Article
The Shapley Value as a von Neumann-Morgenstern Utility
By: A. E. Roth
Roth, A. E. "The Shapley Value as a von Neumann-Morgenstern Utility." Econometrica 45, no. 3 (April 1977): 657–664.
- June 1994
- Article
Influence of Mathematical Models in Finance on Practice: Past, Present and Future
By: Robert C. Merton
Merton, Robert C. "Influence of Mathematical Models in Finance on Practice: Past, Present and Future." Series A. Philosophical Transactions of the Royal Society of London, Series A, Physical Sciences and Engineering 347 (June 1994): 451–463. (Reprinted in Financial Practice and Education, spring 1995.)
- Article
Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns
By: Joel Goh, Kian Guan Lim, Melvyn Sim and Weina Zhang
We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using... View Details
Goh, Joel, Kian Guan Lim, Melvyn Sim, and Weina Zhang. "Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns." European Journal of Operational Research 221, no. 2 (September 1, 2012): 397–406.
- July 1985 (Revised March 1994)
- Background Note
Exposure and Hedging
By: David E. Bell
Describes the concept of exposure; the dependence of a goal on an uncertain external event. Describes in detail how hedges may be constructed to eliminate exposure, including the algebra of cross-hedging and hedge ratios. The relevance of regression analysis is... View Details
Bell, David E. "Exposure and Hedging." Harvard Business School Background Note 186-036, July 1985. (Revised March 1994.)
- 1976
- Book
Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America
Wheeler, Michael A. Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America. New York, NY: W. W. Norton & Company, 1976.
- 20 Nov 2006
- Research & Ideas
Open Source Science: A New Model for Innovation
scientific problem solving? Yes, and it comes from an unexpected and unrelated corner of the universe: open source software development. That's the view of Karim R. Lakhani, an assistant professor at Harvard Business School with an extensive View Details
Keywords: by Martha Lagace
- 2021
- Conference Presentation
An Algorithmic Framework for Fairness Elicitation
By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu
We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details
Jung, Christopher, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton, and Zhiwei Steven Wu. "An Algorithmic Framework for Fairness Elicitation." Paper presented at the 2nd Symposium on Foundations of Responsible Computing (FORC), 2021.
- March 1992 (Revised June 1992)
- Background Note
Strategic Industry Model: Emergent Technologies
By: Robert J. Dolan
Describes computer model and output from conjoint analysis and perceptual mapping for product line planning. View Details
Dolan, Robert J. "Strategic Industry Model: Emergent Technologies." Harvard Business School Background Note 592-086, March 1992. (Revised June 1992.)