Transcript The Bioterrorism Sensor Location Problem

The Bioterrorism Sensor
Location Problem
• Early warning is
critical
• This is a crucial
factor underlying
government’s plans
to place networks of
sensors/detectors to
warn of a bioterrorist
attack
The BASIS System
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.
Two Fundamental Problems
• Sensor Location
Problem (SLP):
– Choose an
appropriate mix of
sensors
– decide where to
locate them for
best protection and
early warning
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?
Two Fundamental Problems
• The SLP and PIP are ripe for:
– Precise formulation
– Mathematical modeling
– Algorithmic analysis
– Applications of powerful new statistical
methods
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
Types of Sensors
• There are many
types of sensors.
Portal shield
Bioparticulate
counter/detector
Dry filtration unt
(portable)
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.
The SLP: What is a Measure of
Success of a Solution?
• A modeling problem.
• Needs to be made precise.
• Many possible formulations.
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
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?
The SLP: What is a Measure of
Success of a Solution?
•It’s 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.
Modeling Issues: Types of
Sensors
• Sensor
technology is
changing rapidly.
• Methods we
develop should
not be
dependent upon
Much of present technology
today’s
depends upon hand-held rapid
technology.
PCR assay together with
software for BW agent
identification
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
Reporting of Sensor Data
• Do humans physically examine collection
devices?
Reporting of Sensor Data
• Is the data electronically reported?
• Reporting at discrete times?
• Reporting continuously?
Other Relevant Modeling Issues
• Probability of
Release at
Different Locations
• Geography
• Buildings
• Weather
• Population
Distribution
Algorithmic Approaches I :
Greedy Algorithms
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.
Algorithmic Approaches II :
Variants of Classic Location and
Clustering Methods
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).
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.
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 > x)?
• Approximation methods due to Chuzhoy,
Ostrovsky, and Rabani and to Guha, Tardos,
and Shmoys are relevant.
Algorithmic Approaches III :
Variants of Highway Sensor
Network Algorithms
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)
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.
Algorithmic Approaches IV :
Variants of Air Pollution
Monitoring Models
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
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.
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 counterterrorism applications by Pate-Cornell.
Algorithmic Approaches V :
Building on Equipment Placing
Algorithms
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.
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)
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.
The Pattern Interpretation
Problem
The Pattern Interpretation
Problem
• It will be up to the
Decision Maker to
decide how to
respond to an
alarm from the
sensor network.
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?
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.
Approaching the PIP: Minimizing
False Alarms
Approaching the PIP: Minimizing
False Alarms
• One approach:
Redundancy.
Require two or
more sensors to
make a detection
before an alarm is
considered
confirmed.
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.
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.
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.
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.
Approaching the PIP: Using
Decision Rules
• Prior work along
these lines in
missile detection
(Cherikh and
Kantor)
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.
Approaching the PIP: SpatioTemporal Mining of Sensor Data
Approaching the PIP: SpatioTemporal 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.
Approaching the PIP: SpatioTemporal 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.
Approaching the PIP: SpatioTemporal Mining of Sensor Data
Work on Cellular networks and IP
networks is relevant.
Approaching the PIP: SpatioTemporal 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.
Approaching the PIP: SpatioTemporal 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
Approaching the PIP: SpatioTemporal 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.
Approaching the PIP: SpatioTemporal 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”
Approaching the PIP: SpatioTemporal 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.
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?
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?
Approaching the PIP: Triggering
Other Methods of Surveillance
• Decreased threshold for alarm from
subway worker absenteeism levels?
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.
There are Remarkably Many
Challenges from this One
Problem!
Thanks to DIMACS SLP/PIP
Team:
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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
Thanks also to:
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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.