Publications

Article

Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)

By: Scott Duke Kominers and Zachary Abel

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1. View Details

Keywords: Mathematical Methods

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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2011
Working Paper

Price Competition under Multinomial Logit Demand Functions with Random Coefficients

In this paper, we postulate a general class of price competition models with Mixed Multinomial Logit demand functions under affine cost functions. We first characterize the equilibrium behavior of this class of models in the case where each product in the market is... View Details

Keywords: Customers; Income Characteristics; Price; Product Marketing; Mathematical Methods; Competition; Segmentation

October 2000 (Revised March 2004)
Background Note

Variance Analysis and Flexible Budgeting

By: Robert S. Kaplan

Facilitates the teaching of cases on variance analysis and flexible budgeting. Uses algebra, diagrams, and numerical examples to illustrate the calculation of price, quantity, and mix variances for revenues and costs, and a flexible budget for analyzing indirect and... View Details

Keywords: Cost; Price; Mathematical Methods; Revenue; Budgets and Budgeting

Teaching Interest

Digital Marketing Strategy

By: John A. Deighton

When the tools of marketing change, strategies change too. The focus of this course is on firms trying to navigate the transition from offline to online market-making and strategy development. Our concern is primarily with corporations that have products and... View Details

14 May 2013
First Look

First Look: May 14

Lady Gaga, and LeBron James? Which strategies give leaders in film, television, music, publishing, and sports an edge over their rivals? In this book, drawing on my case studies and other research on the worlds of media and sports, I... View Details

Keywords: Sean Silverthorne

July 2009 (Revised January 2012)
Case

Risk Management at Wellfleet Bank: All That Glitters Is Not Gold

By: Anette Mikes

This case motivates a debate on the role of staff functions, such as risk management: what does it mean for them to be independent, and at the same time, to partner the business lines? The case describes the risk assessment process in the corporate banking arm of... View Details

Keywords: Decision Choices and Conditions; Judgments; Credit; Banks and Banking; Governance Controls; Risk Management; Mathematical Methods

19 Nov 2007
Lessons from the Classroom

Teaching The Moral Leader

What are the benefits of this integration? A: One benefit derives from the literature itself. Through the novels, plays, short stories, and historical accounts students are brought much closer to life as it is really lived, certainly closer than in lecture learning and... View Details

Keywords: by Sarah Jane Gilbert; Education

September 1993 (Revised August 2011)
Exercise

ExtendSim® Simulation Exercises in Process Analysis (A)

By: Roy D. Shapiro

First set of exercises meant to be used with ExtendSim, a simulation system created by Imagine That, Inc. of San Jose, California. These exercises allow students to investigate the impact of variable processing times on the performance of simple in-line processes.... View Details

Keywords: Operations; Business Processes; Performance; Mathematical Methods

September 2010 (Revised January 2011)
Background Note

Using Regression Analysis to Estimate Time Equations

This note presents a simple way to estimate time equations using regression analysis in Excel. The note quickly outlines regression analysis, then presents a real-life case example from the natural gas industry that students can use to gain experience developing and... View Details

Keywords: Accounting; Activity Based Costing and Management; Mathematical Methods

28 Jun 2010
HBS Case

Cincinnati Children’s Hospital Medical Center

Technology and Operations Management course (TOM), the case offers valuable takeaways for future managers of any complex service organization. "It's a good TOM case in that it includes hard numbers and... View Details

Keywords: by Julia Hanna; Health

10 Nov 2015
First Look

November 10, 2015

Impact Evaluation Methods in Public Economics: A Brief Introduction to Randomized Evaluations and Comparison with Other Methods By: Pomeranz, Dina Abstract—Recent years have seen a large expansion in the use... View Details

Keywords: Sean Silverthorne

2022
Working Paper

A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure

By: Jesse M. Shapiro and Liyang Sun

Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in... View Details

Keywords: Econometric Models; Mathematical Methods

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January 2002 (Revised October 2007)
Case

Grantham, Mayo, Van Otterloo & Co., 2001

By: Joshua Musher and Andre F. Perold

Asset manager GMO underperforms the market during the 1996-2000 stock market bubble because of the focus on absolute risk. After suffering significant client withdrawals, performance again shines when the bubble collapses. Did they win the battle only to lose the war?... View Details

Keywords: Customers; Asset Management; Stocks; Investment; Price Bubble; Mathematical Methods; Risk and Uncertainty

05 Sep 2023
Book

Thriving After Failing: How to Turn Your Setbacks Into Triumphs

which is where reflection comes in. People who are best at learning from failure don’t wait until they fail to start reflecting. Rather, they keep a practice journal or another method to gather data during projects even when they are... View Details

Keywords: by Michael Blanding

December 1998
Case

Origins of National Income Accounting

By: David A. Moss and Joseph P Gownder

Set in the Great Depression, this case explores the origins of national income accounting in the United States. Highlights Senator La Follette's 1932 proposal for the federal government to begin collecting national income statistics. View Details

Keywords: Accounting; Financial Crisis; Analytics and Data Science; Mathematical Methods; United States