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Show Results For
- All HBS Web
(1,919)
- People (2)
- News (212)
- Research (1,369)
- Events (15)
- Multimedia (13)
- Faculty Publications (905)
- 2010
- Article
On the Classification of Type II Codes of Length 24
By: Noam D. Elkies and Scott Duke Kominers
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "On the Classification of Type II Codes of Length 24." SIAM Journal on Discrete Mathematics 23, no. 4 (2010).
- March 2010
- Article
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Shaofang Hong and Scott Duke Kominers
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >=... View Details
Keywords: Mathematical Methods
Hong, Shaofang, and Scott Duke Kominers. "Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Proceedings of the American Mathematical Society 138, no. 3 (March 2010): 809–813.
- August 2005 (Revised April 2008)
- Teaching Note
GuestFirst Hotel (B): Statistics Review with Data Desk (TN)
By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
- March 2004
- Teaching Note
Variance Analysis Tutorial (Instructor Guide)
By: David F. Hawkins
Instructor Guide to (9-104-709). View Details
Keywords: Mathematical Methods
- October 1979 (Revised March 1995)
- Background Note
Note on the Management of Queues
Contains four sections: 1) measuring the performance of queuing systems; 2) types of queuing systems; 3) the behavior of simple systems (elementary queuing theory); and 4) the management of queues (including a discussion of their psychology). View Details
Keywords: Mathematical Methods
Maister, David H. "Note on the Management of Queues." Harvard Business School Background Note 680-053, October 1979. (Revised March 1995.)
- 1997
- Chapter
On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios
By: Robert C. Merton
Keywords: Mathematical Methods
Merton, Robert C. "On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios." In The Legacy of Norbert Wiener: A Centennial Symposium. Vol. 60, edited by D. Jerison, I. M. Singer, and D. W. Stroock. Proceedings of Symposia in Pure Mathematics . Providence, RI: American Mathematical Society, 1997.
- 19 Oct 2017
- Working Paper Summaries
Games of Threats
- 09 Jul 2019
- Blog Post
Solving the Complexities of the Biotechnology Industry
method implements. The unique case method at HBS is the result of decades of thinking critically about how to build the ability to react quickly and thoughtfully to situations. Providing someone with a... View Details
- July 2023
- Article
Design and Analysis of Switchback Experiments
By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted... View Details
Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Management Science 69, no. 7 (July 2023): 3759–3777.
- January 1997
- Background Note
Simulation as a Decision Aid
By: Roy D. Shapiro
A brief introduction to simulation--what it is, why it's used, etc. Meant to set context for a first class on simulation. A rewritten version of an earlier note. View Details
Shapiro, Roy D. "Simulation as a Decision Aid." Harvard Business School Background Note 697-062, January 1997.
- Article
Games of Threats
By: Elon Kohlberg and Abraham Neyman
A game of threats on a finite set of players, N, is a function d that assigns a real number to any coalition, S ⊆ N, such that d(S) = -d(N\S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(Ø) = 0. We show that analogs... View Details
Kohlberg, Elon, and Abraham Neyman. "Games of Threats." Games and Economic Behavior 108 (March 2018): 139–145.
- November 1977
- Article
On the Pricing of Contingent Claims and the Modigliani-Miller Theorem
By: Robert C. Merton
Merton, Robert C. "On the Pricing of Contingent Claims and the Modigliani-Miller Theorem." Journal of Financial Economics 5 (November 1977): 241–249. (Chapter 13 in Continuous-Time Finance.)
- August 1970
- Case
Hawthorne Plastics
An "imperfect tester" problem involving the decision of how to produce batches of plastic strapping, given uncertainty about the length of the molecular chain in the raw material. A decision on whether to test the raw material and a choice of production process must be... View Details
Hammond, John S. "Hawthorne Plastics." Harvard Business School Case 171-004, August 1970.
- 2021
- Article
Fair Algorithms for Infinite and Contextual Bandits
By: Matthew Joseph, Michael J Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions... View Details
Joseph, Matthew, Michael J Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Fair Algorithms for Infinite and Contextual Bandits." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society 4th (2021).
- Other Unpublished Work
The Role of Inventory in Empowered Work Settings: Model and Empirical Analysis
By: S. Datar, M. Alles and R. Sarkar
- 1987
- Chapter
Money in the Utility Function: An Empirical Implementation
By: Julio J. Rotemberg and James Poterba
Rotemberg, Julio J., and James Poterba. "Money in the Utility Function: An Empirical Implementation." In New Approaches to Monetary Economics, edited by W. Barnett and K. Singleton, 219–240. Cambridge University Press, 1987.
- Article
Scale Economies in Statistical Analyses of Market Power
By: R. E. Caves, J. Khalizadeh-Shirazi and M. E. Porter
Caves, R. E., J. Khalizadeh-Shirazi, and M. E. Porter. "Scale Economies in Statistical Analyses of Market Power." Review of Economics and Statistics 57, no. 2 (May 1975): 133–140.
- 1976
- Other Unpublished Work
Simulation of the Market Effects of Housing Allowance
By: Dutch Leonard, Gregory K. Ingram and Robert Schafer
- 1969
- Other Unpublished Work
An Empirical Investigation of the Samuelson Rational Warrant Pricing Theory
By: Robert C. Merton