Publications

November 1993
Article

Stable Matchings, Optimal Assignments, and Linear Programming

By: A. E. Roth, U. G. Rothblum and J. H. Vande Vate

Keywords: Mathematical Methods

November 2021
Article

Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data

By: William Herlands, Edward McFowland III, Andrew Gordon Wilson and Daniel B. Neill

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle,... View Details

Keywords: Pattern Detection; Subset Scanning; Gaussian Processes; Mathematical Methods

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

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