Publications

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

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

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

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

Educators

1994
Chapter

Industry Analysis

By: D. J. Collis and P. Ghemawat

Keywords: Mathematical Methods

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

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

March 2022
Article

Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models

By: Fiammetta Menchetti and Iavor Bojinov

Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details

Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods

2021
Working Paper

Population Interference in Panel Experiments

By: Iavor I Bojinov, Kevin Wu Han and Guillaume Basse

The phenomenon of population interference, where a treatment assigned to one experimental unit affects another experimental unit's outcome, has received considerable attention in standard randomized experiments. The complications produced by population interference in... View Details

Keywords: Finite Population; Potential Outcomes; Dynamic Causal Effects; Mathematical Methods

SSRN

September 2021
Article

Oh's 8-Universality Criterion Is Unique

By: Scott Duke Kominers

Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh’s 8-universality criterion as an... View Details

Keywords: N-universal Lattice; 8-universal Lattice; Universality Criteria; Quadratic Forms; Additively Indecomposable; Mathematical Methods

2021
Article

Prisoners, Rooms, and Lightswitches

By: Daniel M. Kane and Scott Duke Kominers

We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his n prisoners in and out of r rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The... View Details

Keywords: Mathematical Methods

2019
Article

Configurations of Extremal Type II Codes via Harmonic Weight Enumerators

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

2019
Article

Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading

By: Iavor I Bojinov and Neil Shephard

We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal... View Details

Keywords: Causality; Nonparametric; Potential Outcomes; Trading Costs; Mathematical Methods

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Article

A New Proof of Serre's Homological Characterization of Regular Local Rings

By: Ravi Jagadeesan and Aaron Landesman

We give a new proof of Serre’s result that a Noetherian local ring is regular if and only if it has finite global dimension. Our proof avoids the explicit construction of a Koszul complex. View Details

Keywords: Mathematical Methods

October 2015
Article

A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants

By: Ravi Jagadeesan

We study the action of Gal(ℚ^⎯/ℚ) on the category of Belyĭ functions (finite étale covers of ℙ^1_(ℚ^⎯) \ {0,1,∞}. We describe a new combinatorial Gal(ℚ^⎯/ℚ)‐invariant for Belyĭ functions whose monodromy cycle types above 0 and ∞ are the same. We use a version of our... View Details

Keywords: Mathematical Methods

2014
Article

Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations

By: Ravi Jagadeesan

We investigate pattern avoidance in alternating permutations and an alternating analogue of Young diagrams. In particular, using an extension of Babson and West’s notion of shape-Wilf equivalence described in our recent paper (with N. Gowravaram), we generalize results... View Details

Keywords: Pattern Avoidance; Alternating Permutations; Shape-Wilf Equivalence; Mathematical Methods

2018
Working Paper

Semi-Parametric Estimation of Dynamic Discrete Choice Models

By: David Hao Zhang

I develop a new method for estimating counterfactuals in dynamic discrete choice models, a widely used set of models in economics, without requiring a distributional assumption on utility shocks. Applying my method to the canonical Rust (1987) setting, I find that the... View Details

Keywords: Semiparametrics; Dynamic Discrete Choice; Consumer Choice; Mathematical Methods