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Consortium for Mathematics and its Applications

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Some Limitations of Financial Models

Abstract This paper is motivated by the essays of N.N. Taleb [2001; 2007; 2008] on randomness in the real world. In particular, we are interested in the "rare" event, one residing in the tail of some distribution. We begin with Taleb's mythical...

Randomness in Cryptography

Introduction This article is about randomness, in particular about random binary strings, and, even more particularly, about the use of randomness in cryptography. • What do we mean by the word "random," • why do we need randomness, and • are there...

Oracles and Signatures

Introduction Digital signatures are all around us (though barely noticeable by the average person), especially in electronic (digital) financial transactions. Like its paper-and-pen ancestor, a signature has as its purposes guaranteeing the integrity...

A Method for Ranking Teams Based on Simple Paths

Abstract Rankings play an important role in sports, as well as in the evaluation of proposals and the operation of search engines. How are such rankings obtained? We outline several linear algebra approaches used in sports ranking methods and then...

Executive Summary

In the Interdisciplinary Contest in Mathematics (ICM) and Mathematical Contest in Modeling (MCM), a team provides a one-page executive summary as the first page of their submission. Despite the guidance in the paragraph below (from the MCM/ICM Contest...

The Cutoff Paradox in the Kansas Presidential Caucuses

Abstract The Kansas Republican Party uses an apportionment method of its own invention to apportion delegates to candidates in its presidential caucus. This method includes a threshold that eliminates candidates (and their votes) who receive less than...

Change-Point Models: What Are They and Why Do We Need Them?

Introduction So what is a "change point"? Formally, a change point is a point at which the statistical properties of a model change. But what does that actually mean? Suppose that we are trying to fit a linear model to the data shown in Figure 1a,...

Mr. Markov Plays Goose Solitaire

Introduction The Game of the Goose (hereafter simply "Goose") is an early modern board game, existing as early as 1463 [Seville 2019]. Goose is a race game similar to Chutes and Ladders, with landing on some positions sending a player forward or...

The Variational Principle and Einstein's Gravity

Introduction In Isaac Newton's theory, gravity is a force between masses. You are probably familiar with the equation, F = Gm1m2/r2, where F is the force, G is the gravitational constant,m1 andm2 are masses, and r is the distance between the masses....

When Should Your Parents Take Social Security?

Introduction The U.S. Social Security Administration offers and administers retirement income to workers who have paid Social Security taxes on their working income generally for at least 10 years. A worker has the option of deciding when to retire and...

Mathematical Modeling of Patch Transdermal Drug Delivery Systems

Abstract We detail two different mathematical solution techniques for a system of first-order differential equations used to model the diffusion of a drug in a transdermal drug delivery system. We include derivation of the mathematical model from first...

Data Detectives: Homicides in Chicago

Introduction Woodlawn, Chicago In Fall 2019, my wife and I undertook a residency to learn the stark realities of life faced by disadvantaged black communities, living in an apartment in theWoodlawn neighborhood on Chicago's South side. Woodlawn is a...

Teaching Modeling: Tell Us How!

By the time students begin their post-secondary education, most have been preconditioned to expect a structured environment full of objectively-right and -wrong answers when they cross the threshold of a mathematics classroom. They have come to expect...

Magic: The Gathering, Integer Linear Programming and Arbitrage

Context and Motivation Magic: The Gathering® is a collectible card game created in 1993, and iswidely regarded as the first trading card game ever produced. To this day,it remains wildly popular, with millions of players and billions of cardsprinted....

Why Monday Never Wins: An Instance of the Secretary Problem

Abstract We analyze statistics of the German TV show "Das Perfekte Dinner" (The Perfect Dinner), a cooking competition in which contestants assign scores to rate one another. We find a strong dependency of winning on the order of performing....

Minimodule and Model Reality Check Sustaining Fisheries

Introduction Consider a stock of fish. If there is no harvest, the stock will tend to renew itself with births and deaths: It will arrive at more or less the same level of biomass each year-with variation due to climate and weather variability, and...

The Dogbone is the Unique Auto-Reversing Track Configuration

Introduction Motivated by one author's grandsons play with Fisher-Price® Thomas & FriendsTM TrackmasterTM, a battery-operated train and its tracks, we became interested in track configurations that allow the train to traverse the track completely in...

Data Detectives: ShotSpotter in Chicago

Introduction ShotSpotter is a technology to detect, locate, and report gunshots to police. Its deployment in Chicago has led to claims of saving lives and apprehending violent offenders, but also activists objecting that it is ineffective in reducing...