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Publications

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  • All HBS Web  (837)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)

Show Results For

  • All HBS Web  (837)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
← Page 14 of 837 Results →
  • 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
Keywords: Folding; Reconfiguration; Hinge; Plygon; Refinement; Mathematical Methods
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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

By: Scott Duke Kominers
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
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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

By: Scott Duke Kominers
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
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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
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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
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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
Keywords: Mathematical Methods; Accommodations Industry
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Frei, Frances X. "GuestFirst Hotel (B): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-039, August 2005. (Revised April 2008.)
  • March 2004
  • Teaching Note

Variance Analysis Tutorial (Instructor Guide)

By: David F. Hawkins
Instructor Guide to (9-104-709). View Details
Keywords: Mathematical Methods
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Hawkins, David F. "Variance Analysis Tutorial (Instructor Guide)." Harvard Business School Teaching Note 104-077, March 2004.
  • 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
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Maister, David H. "Note on the Management of Queues." Harvard Business School Background Note 680-053, October 1979. (Revised March 1995.)
  • 1994
  • Chapter

Industry Analysis

By: D. J. Collis and P. Ghemawat
Keywords: Mathematical Methods
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Collis, D. J., and P. Ghemawat. "Industry Analysis." In The Portable MBA in Strategy, edited by Liam Fahey and Robert M. Randall. New York: John Wiley & Sons, 1994.
  • 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
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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.
  • January 2024
  • Article

Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics

By: Rui Cao, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector and Tianzhong Yang
Multi-trait analysis has been shown to have greater statistical power than single-trait analysis. Most of the existing multi-trait analysis methods only work with a limited number of traits and usually prioritize high statistical power over identifying relevant traits,... View Details
Keywords: Mathematical Methods; Health Disorders
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Cao, Rui, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector, and Tianzhong Yang. "Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics." Bioinformatics 40, no. 1 (January 2024).
  • 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
Keywords: Mathematical Methods; Product Marketing
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Dolan, Robert J. "Strategic Industry Model: Emergent Technologies." Harvard Business School Background Note 592-086, March 1992. (Revised June 1992.)
  • 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

    Parker Treacy

    Competition in 2016, becoming the first Latin American startup to receive the award. In 2019, Cobli was elected by LinkedIn as one of the top ten startups in Brazil. Previously, Parker founded First Help Financial, the tenth largest independent vehicle finance company... View Details
    Keywords: Insurance;#64;#Software/App;#68;#Transportation & Logistics
    • 01 Dec 1997
    • News

    Merton's Economics Research Wins Nobel Prize

    evaluation began when he was a graduate student in applied mathematics at the California Institute of Technology and intensified in the late 1960s, when he went to MIT to study economics under Nobel Laureate Paul Samuelson. At MIT, he... View Details
    • 2024
    • Article

    A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time

    By: Zachary Abel, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman and Frederick Stock
    In the modular robot reconfiguration problem we are given n cube-shaped modules (or "robots") as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules... View Details
    Keywords: Robots; Mathematical Methods
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    Abel, Zachary, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman, and Frederick Stock. "A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time." Proceedings of the International Symposium on Computational Geometry (SoCG) 40th (2024): 1:1–1:14.
    • 2023
    • Working Paper

    Causal Interpretation of Structural IV Estimands

    By: Isaiah Andrews, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan and Jesse M. Shapiro
    We study the causal interpretation of instrumental variables (IV) estimands of nonlinear, multivariate structural models with respect to rich forms of model misspecification. We focus on guaranteeing that the researcher's estimator is sharp zero consistent, meaning... View Details
    Keywords: Mathematical Methods
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    Andrews, Isaiah, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan, and Jesse M. Shapiro. "Causal Interpretation of Structural IV Estimands." NBER Working Paper Series, No. 31799, October 2023.
    • Article

    Learning Models for Actionable Recourse

    By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
    As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations provide individuals adversely... View Details
    Keywords: Machine Learning Models; Recourse; Algorithm; Mathematical Methods
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    Ross, Alexis, Himabindu Lakkaraju, and Osbert Bastani. "Learning Models for Actionable Recourse." Advances in Neural Information Processing Systems (NeurIPS) 34 (2021).
    • Mar 2020
    • Conference Presentation

    A New Analysis of Differential Privacy's Generalization Guarantees

    By: Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi and Moshe Shenfeld
    We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and... View Details
    Keywords: Machine Learning; Transfer Theorem; Mathematical Methods
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    Jung, Christopher, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, and Moshe Shenfeld. "A New Analysis of Differential Privacy's Generalization Guarantees." Paper presented at the 11th Innovations in Theoretical Computer Science Conference, Seattle, March 2020.
    • Article

    Active World Model Learning with Progress Curiosity

    By: Kuno Kim, Megumi Sano, Julian De Freitas, Nick Haber and Daniel Yamins
    World models are self-supervised predictive models of how the world evolves. Humans learn world models by curiously exploring their environment, in the process acquiring compact abstractions of high bandwidth sensory inputs, the ability to plan across long temporal... View Details
    Keywords: World Models; Mathematical Methods
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    Kim, Kuno, Megumi Sano, Julian De Freitas, Nick Haber, and Daniel Yamins. "Active World Model Learning with Progress Curiosity." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
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