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      Mathematical MethodsRemove Mathematical Methods →

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      • Winter 2017
      • Article

      Why Big Data Isn't Enough

      By: Sen Chai and Willy C. Shih
      There is a growing belief that sophisticated algorithms can explore huge databases and find relationships independent of any preconceived hypotheses. But in businesses that involve scientific research and technological innovation, this approach is misguided and... View Details
      Keywords: Big Data; Science-based; Science; Scientific Research; Data Analytics; Data Science; Data-driven Management; Data Scientists; Technological Innovation; Analytics and Data Science; Mathematical Methods; Theory
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      Chai, Sen, and Willy C. Shih. "Why Big Data Isn't Enough." Art. 58227. MIT Sloan Management Review 58, no. 2 (Winter 2017): 57–61.
      • 18 Nov 2016
      • Conference Presentation

      Rawlsian Fairness for Machine Learning

      By: Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
      Motivated by concerns that automated decision-making procedures can unintentionally lead to discriminatory behavior, we study a technical definition of fairness modeled after John Rawls' notion of "fair equality of opportunity". In the context of a simple model of... View Details
      Keywords: Machine Learning; Algorithms; Fairness; Decision Making; Mathematical Methods
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      Joseph, Matthew, Michael J. Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Rawlsian Fairness for Machine Learning." Paper presented at the 3rd Workshop on Fairness, Accountability, and Transparency in Machine Learning, Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD), November 18, 2016.
      • 2016
      • Working Paper

      Refugee Resettlement

      By: David Delacretaz, Scott Duke Kominers and Alexander Teytelboym
      Over 100,000 refugees are permanently resettled from refugee camps to hosting countries every year. Nevertheless, refugee resettlement processes in most countries are ad hoc, accounting for neither the priorities of hosting communities nor the preferences of refugees... View Details
      Keywords: Refugees; Marketplace Matching; Mathematical Methods
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      Delacretaz, David, Scott Duke Kominers, and Alexander Teytelboym. "Refugee Resettlement." Working Paper, November 2016.
      • Article

      Crowdsourcing City Government: Using Tournaments to Improve Inspection Accuracy

      By: Edward Glaeser, Andrew Hillis, Scott Duke Kominers and Michael Luca
      The proliferation of big data makes it possible to better target city services like hygiene inspections, but city governments rarely have the in-house talent needed for developing prediction algorithms. Cities could hire consultants, but a cheaper alternative is to... View Details
      Keywords: User-generated Content; Operations; Tournaments; Policy-making; Machine Learning; Online Platforms; Analytics and Data Science; Mathematical Methods; City; Infrastructure; Business Processes; Government and Politics
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      Glaeser, Edward, Andrew Hillis, Scott Duke Kominers, and Michael Luca. "Crowdsourcing City Government: Using Tournaments to Improve Inspection Accuracy." American Economic Review: Papers and Proceedings 106, no. 5 (May 2016): 114–118.
      • 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
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      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.)
      • January 2016
      • Article

      Zooming In: A Practical Manual for Identifying Geographic Clusters

      By: Juan Alcacer and Minyuan Zhao
      This paper takes a close look at the reasons, procedures, and results of cluster identification methods. Despite being a popular research topic in strategy, economics, and sociology, geographic clusters are often studied with little consideration given to the... View Details
      Keywords: Mathematical Methods
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      Alcacer, Juan, and Minyuan Zhao. "Zooming In: A Practical Manual for Identifying Geographic Clusters." Strategic Management Journal 37, no. 1 (January 2016): 10–21.
      • Article

      Formal Measures in Informal Management: Can a Balanced Scorecard Change a Culture?

      By: Robert Gibbons and Robert S. Kaplan
      Agency theorists, historically, have analyzed what kinds of performance measures should be used in formal incentive contracts. For example, after Kaplan-Norton proposed a balanced scorecard of both financial and non-financial measures, some envisioned its role only in... View Details
      Keywords: Relational Contracts; Performance Measurement; Informal Management; Balanced Scorecard; Economics; Mathematical Methods
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      Gibbons, Robert, and Robert S. Kaplan. "Formal Measures in Informal Management: Can a Balanced Scorecard Change a Culture?" American Economic Review: Papers and Proceedings 105, no. 5 (May 2015).
      • 2015
      • Working Paper

      Configurations of Extremal Type II Codes

      By: Noam D. Elkies and Scott Duke Kominers
      We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
      Keywords: Mathematical Methods
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      Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes." Working Paper, March 2015.
      • 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
      Keywords: Brane Tiling; Del Pezzo 3 Lattice; Dimer Model; Mathematical Methods
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      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).
      • 2014
      • Working Paper

      Non-Adherence in Health Care: A Positive and Normative Analysis

      By: Mark Egan and Tomas J. Philipson
      Non-adherence in health care results when a patient does not initiate or continue care that a provider has recommended. Previous research identifies non-adherence as a major source of waste in US health care, totaling approximately 2.3% of GDP, and have proposed a... View Details
      Keywords: Health Care and Treatment; Behavior; Economics; Analysis; Mathematical Methods
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      Egan, Mark, and Tomas J. Philipson. "Non-Adherence in Health Care: A Positive and Normative Analysis." NBER Working Paper Series, No. 20330, July 2014. (Previously titled, "Health Care Adherence and Personalized Medicine.")
      • Article

      Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

      By: Daniel M. Kane and Scott Duke Kominers
      For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details
      Keywords: Mathematical Methods
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      Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
      • October 2013
      • Article

      How Much to Make and How Much to Buy? An Analysis of Optimal Plural Sourcing Strategies

      By: Phanish Puranam, Ranjay Gulati and Sourav Bhattacharya
      While many theories of the firm seek to explain when firms make rather than buy, in practice, firms often make and buy the same input—they engage in plural sourcing. We argue that explaining the mix of external procurement and internal sourcing for the same input... View Details
      Keywords: Supply Chain; Forecasting and Prediction; Framework; Prejudice and Bias; Mathematical Methods
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      Puranam, Phanish, Ranjay Gulati, and Sourav Bhattacharya. "How Much to Make and How Much to Buy? An Analysis of Optimal Plural Sourcing Strategies." Strategic Management Journal 34, no. 10 (October 2013): 1145–1161.
      • 2013
      • Working Paper

      Applying Random Coefficient Models to Strategy Research: Testing for Firm Heterogeneity, Predicting Firm-Specific Coefficients, and Estimating Strategy Trade-Offs

      By: Juan Alcacer, Wilbur Chung, Ashton Hawk and Goncalo Pacheco-de-Almeida
      Although Strategy research aims to understand how firm actions have differential effects on performance, most empirical research estimates the average effects of these actions across firms. This paper promotes Random Coefficients Models (RCMs) as an ideal empirical... View Details
      Keywords: Strategy; Mathematical Methods
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      Alcacer, Juan, Wilbur Chung, Ashton Hawk, and Goncalo Pacheco-de-Almeida. "Applying Random Coefficient Models to Strategy Research: Testing for Firm Heterogeneity, Predicting Firm-Specific Coefficients, and Estimating Strategy Trade-Offs." Harvard Business School Working Paper, No. 14-022, September 2013.
      • 2013
      • Working Paper

      Where do the Most Active Customers Originate and How Can Firms Keep Them Engaged?

      By: Clarence Lee, E. Ofek and Thomas Steenburgh
      In this paper, we study how firms offering Web services can acquire and develop an active customer base. We focus on two basic questions. First, how does the method of customer acquisition affect the way customers use the service to meet their own needs and to interact... View Details
      Keywords: Customer Engagement; Adoption Routes; Hidden Markov Models; Search; Word-of-Mouth; Digital Media; Customer Relationship Management; Internet and the Web; Mathematical Methods; Consumer Behavior; Entrepreneurship; Marketing Reference Programs; Web Services Industry
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      Lee, Clarence, E. Ofek, and Thomas Steenburgh. "Where do the Most Active Customers Originate and How Can Firms Keep Them Engaged?" Working Paper, 2013. (Revise and Resubmit at Management Science.)
      • June 2013 (Revised November 2022)
      • Exercise

      Competition Simulator Exercise

      By: Eric J. Van den Steen
      In the Competition Simulator Exercise, students explore through trial and error some important economic foundations of competitive strategy and managerial economics. In particular, the nine simulator exercises let students explore horizontal differentiation with and... View Details
      Keywords: Competition; Economics; Game Theory; Competitive Strategy; Learning; Mathematical Methods; Analysis
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      Van den Steen, Eric J. "Competition Simulator Exercise." Harvard Business School Exercise 713-804, June 2013. (Revised November 2022.)
      • April 2013
      • Case

      Managing with Analytics at Procter & Gamble

      By: Thomas H. Davenport, Marco Iansiti and Alain Serels
      Senior management at P&G has put a strong emphasis on using data to make "better, smarter, real-time business decisions." The Global Business Services (GBS) organization has developed tools, systems and processes to provide managers throughout P&G with direct access to... View Details
      Keywords: Analytics; Data Management; Forecasting; Shared Services; Procter & Gamble; Laundry Detergent; Information Management; Forecasting and Prediction; Information Technology; Mathematical Methods; Consumer Products Industry; North America
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      Davenport, Thomas H., Marco Iansiti, and Alain Serels. "Managing with Analytics at Procter & Gamble." Harvard Business School Case 613-045, April 2013.
      • 2013
      • Chapter

      Weighted Generating Functions for Type II Lattices and Codes

      By: Noam D. Elkies and Scott Duke Kominers
      We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we... View Details
      Keywords: Mathematical Methods
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      Elkies, Noam D., and Scott Duke Kominers. "Weighted Generating Functions for Type II Lattices and Codes." In Quadratic and Higher Degree Forms. Vol. 31, edited by Alladi Krishnaswami, Manjul Bhargava, David Savitt, and Pham Huu Tiep, 63–108. Developments in Mathematics. Springer, 2013.
      • Article

      Assent-maximizing Social Choice

      By: Katherine A. Baldiga and Jerry R. Green
      We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population's preferences and on the probability... View Details
      Keywords: Decision Choices and Conditions; Theory; Measurement and Metrics; Mathematical Methods; Society
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      Baldiga, Katherine A., and Jerry R. Green. "Assent-maximizing Social Choice." Social Choice and Welfare 40, no. 2 (February 2013): 439–460.
      • December 2012
      • Case

      Delwarca Software Remote Support Unit

      By: Roy D. Shapiro and Paul E. Morrison
      Delwarca Software provides business software to large corporate clients around the world. The firm serves customers who prefer to assemble corporate solutions using a combination of software programs from various suppliers rather than implementing a single enterprise... View Details
      Keywords: Service Operations; Service Delivery; Mathematical Methods; Applications and Software; Problems and Challenges; Customer Satisfaction; Information Technology Industry
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      Shapiro, Roy D., and Paul E. Morrison. "Delwarca Software Remote Support Unit." Harvard Business School Brief Case 913-541, December 2012.
      • 2014
      • Working Paper

      Search-Based Peer Firms: Aggregating Investor Perceptions Through Internet Co-Searches

      By: Charles M.C. Lee, Paul Ma and Charles C.Y. Wang
      Applying a "co-search" algorithm to Internet traffic at the SEC's EDGAR web-site, we develop a novel method for identifying economically-related peer firms and for measuring their relative importance. Our results show that firms appearing in chronologically adjacent... View Details
      Keywords: Peer Firm; EDGAR Search Traffic; Revealed Preference; Co-search; Industry Classification; Analytics and Data Science; Internet and the Web; Mathematical Methods; Corporate Finance
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      Lee, Charles M.C., Paul Ma, and Charles C.Y. Wang. "Search-Based Peer Firms: Aggregating Investor Perceptions Through Internet Co-Searches." Harvard Business School Working Paper, No. 13-048, November 2012. (Revised September 2013, March 2014, June 2014, July 2014.)
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