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Show Results For
- All HBS Web
(853)
- News (77)
- Research (638)
- Events (12)
- Multimedia (4)
- Faculty Publications (635)
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- 2016
- Article
Penalized Fast Subset Scanning
By: Skyler Speakman, Sriram Somanchi, Edward McFowland III and Daniel B. Neill
We present the penalized fast subset scan (PFSS), a new and general framework for scalable and accurate pattern detection. PFSS enables exact and efficient identification of the most anomalous subsets of the data, as measured by a likelihood ratio scan statistic.... View Details
Keywords: Disease Surveillance; Likelihood Ratio Statistic; Pattern Detection; Scan Statistic; Mathematical Methods
Speakman, Skyler, Sriram Somanchi, Edward McFowland III, and Daniel B. Neill. "Penalized Fast Subset Scanning." Journal of Computational and Graphical Statistics 25, no. 2 (2016): 382–404. (Selected for “Best of JCGS” invited session by the journal’s editor in chief.)
- 2013
- Article
Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux
By: Nihal Gowravaram and Ravi Jagadeesan
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West’s notion of shape-Wilf equivalence to apply to alternating... View Details
Keywords: Pattern Avoidance; Alternating Permutations; Descent Type Permutations; Wilf Equivalence; Shape-Wilf Equivalence; Mathematical Methods
Gowravaram, Nihal, and Ravi Jagadeesan. "Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux." #P17. Electronic Journal of Combinatorics 20, no. 4 (2013).
- Article
Hinged Dissections Exist
By: Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine and Scott Duke Kominers
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form... View Details
Abbott, Timothy G., Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Duke Kominers. "Hinged Dissections Exist." Discrete & Computational Geometry 47, no. 1 (January 2012): 150–186.
- 2009
- Article
On Universal Binary Hermitian Forms
Earnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms... View Details
Keywords: Mathematical Methods
Kominers, Scott Duke. "On Universal Binary Hermitian Forms." A02. INTEGERS: Electronic Journal of Combinatorial Number Theory 9 (2009): 9–15.
- May 2009
- Article
Configurations of Extremal Even Unimodular Lattices
We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. View Details
Keywords: Mathematical Methods
Kominers, Scott Duke. "Configurations of Extremal Even Unimodular Lattices." International Journal of Number Theory 5, no. 3 (May 2009): 457–464.
- 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.
- 1980
- Chapter
Tests of Capital Market Theory and Implications of the Evidence
By: Michael Jensen
Jensen, Michael. "Tests of Capital Market Theory and Implications of the Evidence." In Handbook of Financial Economics, edited by J. L. Bicksler. North-Holland Publishing Company, 1980. (Originally published in Is Financial Analysis Useless? Proceedings of a Seminar on the Efficient Market and Random Walk Hypotheses (The Financial Analysts Research Foundation, 1975).)
- Article
Value of Information with Sequential Futures Markets
By: Jerry R. Green
The effects of an improvement in information on the efficiency of risk-bearing are studied under various systems of incomplete markets. With sequential futures markets for uncontingent delivery, the welfare effects are indeterminate in sign, except under special... View Details
Green, Jerry R. "Value of Information with Sequential Futures Markets." Econometrica 49, no. 2 (March 1981): 335–358.
- March 2010
- Article
Matching with Preferences over Colleagues Solves Classical Matching
In this note, we demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues." We give an explicit reduction... View Details
Kominers, Scott Duke. "Matching with Preferences over Colleagues Solves Classical Matching." Games and Economic Behavior 68, no. 2 (March 2010): 773–780.
- July–August 2023
- Article
Demand Learning and Pricing for Varying Assortments
By: Kris Ferreira and Emily Mower
Problem Definition: We consider the problem of demand learning and pricing for retailers who offer assortments of substitutable products that change frequently, e.g., due to limited inventory, perishable or time-sensitive products, or the retailer’s desire to... View Details
Keywords: Experiments; Pricing And Revenue Management; Retailing; Demand Estimation; Pricing Algorithm; Marketing; Price; Demand and Consumers; Mathematical Methods
Ferreira, Kris, and Emily Mower. "Demand Learning and Pricing for Varying Assortments." Manufacturing & Service Operations Management 25, no. 4 (July–August 2023): 1227–1244. (Finalist, Practice-Based Research Competition, MSOM (2021) and Finalist, Revenue Management & Pricing Section Practice Award, INFORMS (2019).)
- July 1990
- Background Note
Perceptual Mapping: A Manager's Guide
By: Robert J. Dolan
Describes the perceptual mapping technique in a non-technical fashion. The procedure is useful for the depiction of the structure of the market. Discusses alternative methods, presents examples of each, and shows how the maps can be used in marketing decision making. View Details
Dolan, Robert J. "Perceptual Mapping: A Manager's Guide." Harvard Business School Background Note 590-121, July 1990.
- 1999
- Other Unpublished Work
Estimating Industry Multiples
By: Malcolm Baker and R. S. Ruback
We analyze industry multiples for the S&P 500 in 1995. We use Gibbs sampling to estimate simultaneously the error specification and small sample minimum variance multiples for 22 industries. In addition, we consider the performance of four common multiples: the simple... View Details
Baker, Malcolm, and R. S. Ruback. "Estimating Industry Multiples." 1999.
- 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.)