Jonathan David Farley

Breaking Al Qaeda Cells: A Mathematical Analysis of Counterterrorism Operations (A Guide for Risk Assessment and Decision Making)

How can we tell if an Al Qaeda cell has been broken? That enough members have been captured or killed so that there is a high likelihood they will be unable to carry out a new attack, and military resources can be redirected away from them and toward more immediate threats? This article uses order theory to quantify the degree to which a terrorist network is still able to function. This tool will help law enforcement know when a battle against Al Qaeda has been won, thus saving the publics money without unduly risking the publics safety.‐

Mathematical Methods in Counterterrorism

The present work presents the most current research from mathematicians and computer scientists from around the world to develop strategies for counterterrorism and homeland security to the broader public. New mathematical and computational technique concepts are applied to counterterrorism and computer security problems. Topics covered include strategies for disrupting terrorist cells, border penetration and security, terrorist cell formation and growth, data analysis of terrorist activity, terrorism deterrence strategies, information security, emergency response and planning. Since 2001, tremendous amounts of information have been gathered regarding terrorist cells and individuals potentially planning future attacks. This book addresses this need to develop new countermeasures. Interested readers include researchers, policy makers, politicians, and the members of intelligence and law enforcement agencies.

Evolutionary Dynamics of the Insurgency in Iraq: A Mathematical Model of the Battle for Hearts and Minds

Individuals are not electrons. But in some situations, they behave very much alike. When it comes to many social and political questions, individuals’ complex attitudes and beliefs must be boiled down to a simple yea (“spin up”) or nay (“spin down”). Although human societies, like physical materials, are very complex, some of their properties can be determined by understanding the interactions that occur between individuals (“atoms”). In particular, the spread of a particular political opinion throughout a society can be modeled as the macroscopic manifestation of the myriad exchanges occurring at the local level between individuals and their neighbors. This model can be used to gain a qualitative foothold on the evolution of public opinion in Iraq for or against the U.S.-led occupation. It can also provide a mathematical instantiation of the “oil-spot” strategy proposed by Krepinevich (2005), which in turn could lead to a practical tool for commanders needing to allocate public relations resources in Iraq.

The uniqueness of the core

Simple proofs are given for two theorems of Duffus and Rival: If a finite poset is dismantled by irreducibles as much as possible, the subposet one finally obtains is unique up to isomorphism. If one dismantles by doubly irreducibles, the subposet is unique.

Posets that locally resemble distributive lattices

Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.

The number of order-preserving maps between fences and crowns

We compute the number of order-preserving and -reversing maps between posets in the class of fences (zig-zags) and crowns (cycles).

The Fixed Point Property for Posets of Small Width

The fixed point property for finite posets of width 3 and 4 is studied in terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4 are determined explicitly. The ranked forbidden retracts for the width 3 case that are linearly indecomposable are examined to see which are minimal automorphic. Part of a problem of Niederle from 1989 is thus solved.

Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge

Throughout the years mathematics has served as the most basic and fundamental tool employed by scientists and researchers to study and describe a wide variety of fields and phenomena. One of the most important practical application areas of mathematics has been for national defense and security purposes. For example, during the Second World War, the mathematical principles underlying game theory and cryptography played a very important role in military planning. Since that time, it has become clear that mathematics has an important role to play in securing victory in any global conflict, including the struggle faced by national security and law enforcement officials in the fight against those engaged in terrorism and other illicit activities. Recent events of the past decade have produced an increased interest in and focus upon the area of counterterrorism by a broad range of scholars, including mathematicians. At the same time, government decision makers have often been skeptical about mathematics and statistics, even while faced with the considerable challenges of sifting through enormous amounts of data that might hold critically important clues. Realizing that policy makers were not always receptive, the mathematical

The Torturer's Dilemma: A Theoretical Analysis of the Societal Consequences of Torturing Terrorist Suspects

Terrorism today is one of the main threats to Western civilization. Almost as dire a threat is the fight against terrorism itself. A broad spectrum of antiterrorism measures may significantly change the nature of society by destroying those forms of cooperative activity that underlie Western culture. This threat becomes obvious with an analysis of mathematical models of human moral behavior.

Perfect sequences of chain-complete posets

Abstract The formation of a perfect sequence for a chain-complete poset generalizes the process of dismantling a finite poset by irreducibles. In the finite case, according to a theorem of Duffus and Rival, the end result, or ‘core’, is unique up to isomorphism, no matter how the poset is dismantled. For chain-complete posets with no infinite antichains, the core is unique up to isomorphism, finite, and every perfect sequence has finite length, by an important and difficult theorem of Li and Milner. Li has asked if cores of chain-complete posets with no one-way infinite fence Fω and no tower are all isomorphic. He has also asked if the number of steps in the dismantling process, the length of the perfect sequence, is uniquely determined. The following results are obtained. (1) An example refuting the length conjecture is presented. (2) If at least one perfect sequence of a chain-complete poset has length λ ω 2 , then they all have length less than λ + ω , and their cores are isomorphic. (3) Both the isomorphism class of the core and the length of a perfect sequence are unique for posets with no F ω and no infinite chains; at every step of a perfect sequence, the corresponding poset is unique up to isomorphism. (4) A new, quick proof, perhaps yielding new insights, is presented of the theorem of Li and Milner.