The Bioterrorism Sensor Location Problem

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The Bioterrorism Sensor Location Problem
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• Early warning is critical
• This is a crucial factor underlying governments
  plans to place networks of sensors/detectors to
  warn of a bioterrorist attack

The BASIS System
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Locating Sensors is not Easy

• Networks of sensors are expensive
• Ways to locate them to maximize coverage and
  expedite an alarm are not easy to determine
• Approaches that improve upon existing, ad hoc
  location methods could save countless lives in
  the case of an attack and also money in capital
  and operational costs.

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Two Fundamental Problems

• Sensor Location Problem (SLP)
• Choose an appropriate mix of sensors
• decide where to locate them for best protection
  and early warning

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Two Fundamental Problems

• Pattern Interpretation Problem (PIP) When
  sensors set off an alarm, help public health
  decision makers decide
• Has an attack taken place?
• What additional monitoring is needed?
• What was its extent and location?
• What is an appropriate response?

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Two Fundamental Problems

• The SLP and PIP are ripe for
• Precise formulation
• Mathematical modeling
• Algorithmic analysis
• Applications of powerful new statistical methods

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Two Fundamental Problems

• Relevant tools include
• Network design
• Network analysis
• Location theory
• Reliability theory
• Data mining
• Fluid dynamic modeling
• Source-to-dose modeling
• Time series analysis

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Types of Sensors

• There are many types of sensors.

Portal shield
Dry filtration unt (portable)
Bioparticulate counter/detector
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The SLP

• Sensor technology is changing rapidly
• Sensors come with a variety of characteristics
• A good sensor location methodology should not be
  dependent upon particular sensor technologies.

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The SLP What is a Measure of Success of a
Solution?

• A modeling problem.
• Needs to be made precise.
• Many possible formulations.

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The SLP What is a Measure of Success of a
Solution?

• Identify and ameliorate false alarms.
• Defending against a worst case attack or an
  average case attack.
• Minimize time to first alarm? (Worst case?
  (Average case?)
• Maximize coverage of the area.
• Minimize geographical area not covered
• Minimize size of population not covered
• Minimize probability of missing an attack

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The SLP What is a Measure of Success of a
Solution?

• Cost Given a mix of available sensors and a
  fixed budget, what mix will best accomplish our
  other goals?

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The SLP What is a Measure of Success of a
Solution?

• Its hard to separate the goals.
• Even a small number of sensors might detect an
  attack if there is no constraint on time to
  alarm.
• Without budgetary restrictions, a lot more can be
  accomplished.

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Modeling Issues Types of Sensors

• Sensor technology is changing rapidly.
• Methods we develop should not be dependent upon
  todays technology.

Much of present technology depends upon hand-held
rapid PCR assay together with software for BW
agent identification
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Modeling Issues Types of Sensors

• Sensors differ as to
• Response
• Accuracy and reliability
• Stationarity vs. mobility
• Constraints on their location
• Cost
• How sensor data is reported

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Reporting of Sensor Data

• Do humans physically examine collection devices?

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Reporting of Sensor Data

• Is the data electronically reported?
• Reporting at discrete times?
• Reporting continuously?

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Other Relevant Modeling Issues

• Probability of Release at Different Locations
• Geography
• Buildings
• Weather
• Population Distribution

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Algorithmic Approaches I Greedy Algorithms
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Greedy Algorithms

• Find the most important location first and locate
  a sensor there.
• Find second-most important location.
• Etc.
• Builds on earlier work at IDA (Grotte, Platt)
• Steepest ascent approach.
• No guarantee of optimality.
• In practice, peak of objective function is rather
  flat, so not hard to get close to optima.

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Algorithmic Approaches II Variants of Classic
Location and Clustering Methods
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Algorithmic Approaches II Variants of Classic
Location and Clustering Methods

• Location theory locate facilities (sensors) to
  be used by users located in a region.
• Cluster analysis Given points in a metric space,
  partition them into groups or clusters so points
  within clusters are relatively close.
• Clusters correspond to points covered by a
  facility (sensor).

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Variants of Classic Location and Clustering
Methods

• k-median clustering Given k sensors, place them
  so each point in the city is within x feet of a
  sensor.
• Complications More dimensions location affects
  sensitivity, wind strength enters, sensors have
  different characteristics, etc.
• This higher-dimensional k-median clustering
  problem is hard! Best-known algorithms are due to
  Rafail Ostrovsky.

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Variants of Classic Location and Clustering
Methods

• Further complications make this even more
  challenging
• Different costs of different sensors
• Restrictions on where we can place different
  sensors
• Is it better to have every point within x feet of
  some sensor or every point within y feet of at
  least three sensors (y gt x)?

• Approximation methods due to Chuzhoy,
  Ostrovsky, and Rabani and to Guha, Tardos, and
  Shmoys are relevant.

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Algorithmic Approaches III Variants of Highway
Sensor Network Algorithms
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Variants of Highway Sensor Network Algorithms

• Sensors located along highways and nearby
  pathways measure atmospheric and road conditions.
• Muthukrishnan, et al. have developed very
  efficient algorithms for sensor location.
• Based on bichromatic clustering and
  bichromatic facility location (color nodes
  corresponding to sensors red, nodes corresponding
  to sensor messages blue)

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Variants of Highway Sensor Network Algorithms

• These algorithms apply to situations with many
  more sensors than the bioterrorism sensor
  location problem.
• As BT sensor technology changes, we can envision
  a myriad of miniature sensors distributed around
  a city, making this work all the more relevant.

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Algorithmic Approaches IV Variants of Air
Pollution Monitoring Models
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Variants of Air Pollution Monitoring Models

• Long history of using models to locate air
  pollution monitors.
• MENTOR Modeling Environment for Total Risk
  developed by team at Rutgers and R.W.J. Medical
  School (Panos Georgopoulos, Paul Lioy) at Center
  for Exposure and Risk Modeling

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Variants of Air Pollution Monitoring Models

• MENTOR builds on
• personal exposures
• Source-to-dose modeling
• Environmental conditions
• Weather
• MENTOR is a powerful computational tool.
• However, the models it uses are not nearly as
  large or as complex as those traditionally used
  in nuclear weapons research at Los Alamos and
  elsewhere.

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Variants of Air Pollution Monitoring Models

• Combine air pollution monitor placement modeling
  tools like MENTOR with iteration/simulation
  tools.
• Piecewise heuristic approach developed by Tom
  Boucher, David Coit, E. Elsayed
• Based on initial simulation results, divide
  problem into subproblems and repeat local
  optimization algorithms
• Method recently applied to counter-terrorism
  applications by Pate-Cornell.

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Algorithmic Approaches V Building on Equipment
Placing Algorithms
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Building on Equipment Placing Algorithms

• The Node Placement Problem is problem of
  determining locations or nodes to install certain
  types of networking equipment.
• Coverage and cost are a major consideration.
• Researchers at Telcordia Technologies have
  studied variations of this problem arising from
  broadband access technologies.

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The Broadband Access Node Placement Problem

• There are inherent range limitations that drive
  placement.
• E.g. customer for DSL service must be within xx
  feet of an assigned multiplexer.
• Multiplexer sensor.
• Problem solved using dynamic programming
  algorithms.
• (Tamra Carpenter, Martin Eiger,David Shallcross,
  Paul Seymour)

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The Broadband Access Node Placement Problem
Complications

• Restrictions on types of equipment that can be
  placed at a given node.
• Constraints on how far a signal from a given
  piece of equipment can travel.
• Cost and profit maximization considerations.
• Relevance of work on general integer programming,
  the knapsack cover problem, and local access
  network expansion problems.

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The Pattern Interpretation Problem
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The Pattern Interpretation Problem

• It will be up to the Decision Maker to decide how
  to respond to an alarm from the sensor network.

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The Pattern Interpretation Problem

• Little has been done to develop analytical models
  for rapid evaluation of a positive alarm or
  pattern of alarms from a sensor network.
• How can this pattern be used to minimize false
  alarms?
• Given an alarm, what other surveillance measures
  can be used to confirm an attack, locate areas of
  major threat, and guide public health
  interventions?

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The Pattern Interpretation Problem (PIP)

• Close connection to the SLP.
• How we interpret a pattern of alarms will affect
  how we place the sensors.
• The same simulation models used to place the
  sensors can help us in tracing back from an alarm
  to a triggering attack.

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Approaching the PIP Minimizing False Alarms
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Approaching the PIP Minimizing False Alarms

• One approach Redundancy. Require two or more
  sensors to make a detection before an alarm is
  considered confirmed.

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Approaching the PIP Minimizing False Alarms

• Portal Shield requires two positives for the
  same agent during a specific time period.
• Redundancy II Place two or more sensors at or
  near the same location. Require two proximate
  sensors to give off an alarm before we consider
  it confirmed.
• Redundancy drawbacks cost, delay in confirming
  an alarm.

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Approaching the PIP Using Decision Rules

• Existing sensors come with a sensitivity level
  specified and sound an alarm when the number of
  particles collected is sufficiently high above
  threshold.

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Approaching the PIP Using Decision Rules

• Alternative decision rule alarm if two sensors
  reach 90 of threshold, three reach 75 of
  threshold, etc.
• One approach use clustering algorithms for
  sounding an alarm based on a given distribution
  of clusters of sensors reaching a percentage of
  threshold.

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Approaching the PIP Using Decision Rules

• When sensors are to be used jointly, the rules
  for tuning each sensor should be optimized to
  take advantage of the fact that each is part of a
  network.
• The optimal tuning depends on the decision rule
  applied to reach an overall decision given the
  sensor inputs.

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Approaching the PIP Using Decision Rules

• Prior work along these lines in missile detection
  (Cherikh and Kantor)

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Approaching the PIP Using Decision Rules

• Most work has concentrated on the case of
  stochastic independence of information available
  at two sensors clearly violated in BT sensor
  location problems.
• Even with stochastic independence, finding
  optimal decision rules is nontrivial.
• Recent promising approaches of Paul Kantor study
  fusion of multiple methods for monitoring message
  streams.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data
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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Sensors provide observations of the state of the
  world localized in space and time.
• Finding trends in data from individual sensors
  time series data mining.
• PIP detecting general correlations in multiple
  time series of observations.
• This has been studied in statistics, database
  theory, knowledge discovery, data mining.
• Complications proximity relationships based on
  geography complex chronological effects.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Sensor technology is evolving rapidly.
• It makes sense to consider idealized settings
  where data are collected continuously and
  communicated instantly.
• Then, modern methods of spatio-temporal data
  mining due to Muthukrishnan and others are
  relevant.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Work on Cellular networks and IP networks is
  relevant.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• There is relevant work of Muthukrishnan on
  cellular and IP networks
• Time-of-day effects in traffic calls across the
  country
• Geographic patterns in users mobility
• Correlations between IP router time series data.

• New challenges heterogeneous capabilities of
  nodes in telecommunications, most nodes have
  similar capabilities.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Promising Statistical Methods
• Still in idealized setting continuous sensor
  data collection.
• Building on the Bayesian approach to modeling
  spatio-temporal data.

Thomas Bayes 1702-1761
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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Promising Statistical Methods
• Bayesian approaches take advantage of recent
  dramatic advances in simulation technology
  (Markov chain Monte Carlo)
• Limitations of existing methods dependence on
  batch analysis arrival of new data means start
  from scratch.

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Promising Statistical Methods
• There is need for online or sequential
  methods that update models as data comes in.
• Relevance of recent work of Ridgeway and Madigan
  on sequential Monte Carlo methods using particle
  filters

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Approaching the PIP Spatio-Temporal Mining of
Sensor Data

• Additional Promising Statistical Methods
• Methods for visualizing the data will help human
  decision makers.
• Methods of statistical process control are
  relevant to finding the most effective ways to
  aggregate data across sensors to detect
  anomalies.

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Approaching the PIP Triggering Other Methods of
Surveillance

• One type of BT surveillance cannot be considered
  in isolation.
• Relevant work in talks of Madigan/Rolka, Pagano,
  and Zelicoff
• Question How can the pattern of sensor warnings
  guide other biosurveilance methods?

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Approaching the PIP Triggering Other Methods of
Surveillance

• Increased syndromic surveillance?
• Change threshold for alarm in syndromic
  surveillance?
• Increased attention to E.R. visits in a certain
  region?

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Approaching the PIP Triggering Other Methods of
Surveillance

• Decreased threshold for alarm from subway worker
  absenteeism levels?

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Approaching the PIP Triggering Other Methods of
Surveillance

• If there is an initial alarm, each sensor may be
  read more often.
• How do we pick the sensors to read more
  frequently?
• This is adaptive biosensor engagement.
• Methods of bichromatic combinatorial optimization
  may be relevant.
• As for the SLP, sensors get one color, sensor
  messages another.
• Relevance of work of Muthukrishnan.

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There are Remarkably Many Challenges from this
One Problem!
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Thanks to DIMACS SLP/PIP Team

• Benjamin Avi-Itzhak
• Thomas Boucher
• Tamra Carpenter
• David Coit
• Elsayed Elsayed
• Panos Georgopoulos
• Mel Janowitz
• Paul Kantor

• Howard Karloff
• Jon Kettenring
• Paul Lioy
• David Madigan
• S. Muthukrishnan
• Rafail Ostrovsky
• Michael Rothkopf
• Yehuda Vardi

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Thanks also to

• Jeff Grotte, Institute for Defense Analyses
• Farzad Mostashari, NYC Dept. of Health
• Dennis Nash, NYC Dept.of Health
• Nathan Platt, Institute for Defense Analyses
• Al Rhodes, Defense Threat Reduction Agency
• Jay Spingarn, DefenseThreat Reduction Agency
• Fred Steinberg, MITRE Corp.

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