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### The Mathematics of Homeland Security

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 Getting early warning of the outbreak of a disease or a biological attack Dona Schneider To help us identify new disease outbreaks either in our backyard or in remote areas of the world, government agencies are making use of many, and highly unusual, sources of information, such as emergency room visits, prescription drug purchases, "hits" on medical advice websites, etc. How do we combine all of this information to get an early indication of a potential outbreak? The field is coming to be known as "syndromic surveillance" and we will describe data mining methods of syndromic surveillance. Using mathematics modeling of the spread of diseases to identify preventive strategies and best responses to bioterrorism Fred Roberts Our society faces threats from newly emerging diseases such as bird flu and from diseases such as smallpox or anthrax that might be introduced by bioterrorists. How can mathematics help us identify the best strategies to prevent the spread of disease and respond to outbreaks? Mathematical modeling of infectious disease goes back to Bernoulli's work on smallpox in 1760 and is widely used today by government agencies such as the Centers for Disease Control and Prevention (CDC). We will explore how simple models based on vertex-edge graphs can be used to explore strategies like vaccination and quarantine. Locating sensors to detect chemical, biological, or nuclear threats Fred Roberts Early warning of a terrorist event is critical in preventing or minimizing damages. Sensors are being heavily used on bridges, tunnels, subways, buildings, etc. as an aid in helping us get early warnings of possible "attacks". How do we locate a set of sensors and then how do we "read" a set of sensor alarms to determine if there really was an "attack" and where it took place? The problem will be formulated in the context of attacks on networks and investigated using vertex-edge graphs. Identifying the author of a document David Madigan How can we tell if two messages really come from the same person? More generally, how do we identify the author of a document? This could help us in identifying terrorists and finding the "bad guys". Mathematics can play an important role here. We can use data about a person's writing to create a "signature" that identifies the person's style. Similar problems have arisen historically in determining who wrote plays attributed to Shakespeare and whether an accused criminal actually wrote a confession. Mathematical methods of machine learning such as those used to analyze text data are being used to solve this problem and will be described here. Searching data for evidence of conspiracies Bill Pottenger The U.S. homeland security effort requires monitoring huge amounts of data to gain early warning of a potential terrorist event. The huge amount of data that comes in is in many forms: blog postings, financial transactions, travel records, facial images, fingerprints, voice data, etc. We will look at the problem of searching through a large number of text documents like blog postings, to see if there is a pattern of a new "topic" being "discussed". The methods will involve identifying "features" from large amounts of text, summarizing a document in terms of its feature vector, and using "machine learning" algorithms to classify documents and find new classes of documents that seem to imply a new topic of concern is being discussed. Inspecting containers at ports Fred Roberts At the present time, we are inspecting fewer than 6% of all containers that come through U.S. ports of entry for weapons of mass destruction. Mathematical methods using "decision trees" are being developed to aid in finding more efficient testing strategies so that we can explore more containers without backing up commerce at ports and within a reasonable budget. We will explore "sequential decision making" and describe the use of decision trees in planning more efficient inspection protocols.