Publications

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

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

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

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

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

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