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(838)
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- Faculty Publications (632)
Show Results For
- All HBS Web
(838)
- News (79)
- Research (640)
- Events (14)
- Multimedia (4)
- Faculty Publications (632)
- 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.
- 01 Mar 2009
- News
The Case for Studying Financial History
guide than certain other disciplines that are sometimes regarded as more rigorous, like economics, for example. Economists with their more mathematical approach to social science conspicuously failed to anticipate this crisis, whereas a... View Details
- 1969
- Other Unpublished Work
An Empirical Investigation of the Samuelson Rational Warrant Pricing Theory
By: Robert C. Merton
- Web
Moritz Pail | MBA
Moritz Pail Computer Science / Mathematics Quincy 2025 Cohort 6 I am grateful for the opportunity to be a part of the HUTIF program, and I am excited to learn from and collaborate with other talented individuals who are committed to using... View Details
- Web
Bibliography - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections
the American Mathematical Society , no. 4. New York, N.Y.: American Mathematical Society, 1951. * Samuelson, Paul A. Foundations of Economic Analysis . Cambridge, Mass.: Harvard University Press, 1947. *... 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.
- 1972
- Chapter
Random Walks and Technical Theories: Some Additional Evidence
By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
Benington, George A., and Michael C. Jensen. "Random Walks and Technical Theories: Some Additional Evidence." In Security Evaluation and Portfolio Analysis, edited by E. Elton and M. Gruber. Prentice Hall, 1972. (Also published in Journal of Finance (May 1970) and Investment Management: Some Readings, J. Lorie and R. Brealey, Editors (Praeger Publishers, 1972).)
- 1979
- Article
An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem
By: C. Blair and A. E. Roth
Keywords: Mathematical Methods
Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.