2. Bonneau - Complex Networks
Transcript of 2. Bonneau - Complex Networks
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Complex Networks
Dr. Robert J. Bonneau
Program Manager
AFOSR/RSL
Air Force Research Laboratory
AFOSR
Distribution A: Approved for public release; distribution is unlimited. 88ABW-2011-0774
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NAME: Robert Bonneau
Program: Complex Networks/Complex Networked Systems (DCT)
Goals:
• Preserve critical information structure and minimize latency over a heterogeneous mobile network• Ensure network robustness and stability under a diverse set of network resource constraints• Find invariant properties for a given network from a distributed set of observations and predict network behavior• Develop unifying mathematical approach to discovering fundamental principles of networks and use them in network design
Payoffs:
• Preserve information structures in a network rather than just delivering packets• Quantify likelihood of a given network management policy to support critical mission functions• Predict and manage network failure comprehensively
2011 AFOSR SPRING REVIEW2311NX PORTFOLIO OVERVIEW
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Complex networks uses the results of the mathematical quantification of critical
information delivery to assure, manage, predict, and design Air Force networks
Local Network Research: Coding that assures information delivery and security
Network Management Research: Network protocol to maximize information flow
Global Network Research: Predict network performance and design robustness
Complex Networks
Roadmap
Global Network
Research
Predict Network
Performance
Local Network
Research
Assure Critical
Information Delivery
Network
Management Research
Manage
Information Flow
Mathematical
Characterization of
Network
Raw Network
Data
Dynamic, Heterogeneous,
Air Force Network
Guaranteed Delivery
Of Time Critical
Information
Critical
Information
Diverse Types of
Networks
Communications
Networks
Unified Mission Assured
Design
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Complex Networks Trends
• Local Network Theory
– Geometric and non-binary information coding
– Coding information with network performance objectives
– Integration with verification and quantum methods
• Network Management
– Nonparametric strategies for assessing network performance
– Distributed strategies for measuring and assessing network information transfer
– Sparse network management
• Global Network Theory
– Invariant metrics for analysis of network performance
– Geometric flow analysis for prediction and management of network performance
– Global state space taxonomy and categorization
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Local Network Research: Preserving Information Structure
• Statistical geometric coding structures are used to transport diverse sets of information in a network
and preserve its critical structure
- Communication networks can often degrade or destroy information relationships
- Geometric structures can preserve critical information in the process of coding and
packetization so that protocol requirements can be relaxed
Information
Timescale t
Code Information
Distribution
Coding
Information Loss
With Interference
Coding
Information
Recovery
Less Latency/Computation/
Storage
More Information Loss
With Interference
Less Information Loss With
Interference
More Latency/Computation/
Storage
Recovered
Information
Information
Loss Distributed
Information Loss
Measurable
Information Loss
Significant
Information
Source
Deterministic/Minimal
Coding
(ex: Trellis Code)
Hybrid Code
(ex: Network Code)
Random Code
(ex: Rateless Code)t packetsRecover Using
Coding
Recover With
Code and Retransmit
Recover With
Retransmission
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PI: Bobby Kleinberg Institution: Cornell University
Index Coding in Networks
Approach: Index coding sets bits to indicate to receiver what statistical class
information to be decoded belongs to
- This allows different statistical classes to be prioritized differently in
in coding mechanism
Payoff: Different classes of information can be prioritized according to content as
it is packetized and transmitted between two points on a network without having
to specify complete destination address – reduces overhead
Message structure can give different
probability of decoding message for
different users
Network
CodingContent Prioritized
Network Coding
Statistical Algebraic
Decoded Output
Decoded Output
Error Bounds
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Geometric AdaptiveSubspace Coding
Olgiza Milenkovic, UIUC
Approach: Standard coding theory relies on fixed geometric statistical
assumptions for the encoder and decoder. This assumption can be changed by
using an adaptive decoding mechanism.
Payoff: Allows dynamic adaptation to large amounts of dropped packets and lost
information when specific classes of information must be recovered.
Adaptive Decoding Strategy for Different
Classes of InformationDynamic Information Sources
Bounds on Recovery for Different
Subspaces
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Managing on Degrees of Freedom –A Network Coding Approach
Muriel Medard, MIT
Approach: Sparse approximation can be used to decode different streams of
information
- Source coder can create different probability distributions of coded
information
Payoff: Different classes of content can be prioritized according to content and
packets prioritized accordingly
Sparse Approximation Coding and Recovery
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Less: Information Loss With
Disruption
More: Latency, Difficult to
Control
Less: Latency
More: Information Loss With
Disruption, Controllable
Information
Sources
Information
Timescale t
Protocol Information
Distribution
Protocol
Information Loss
With Interference
Protocol
Information
Recovery
Source 1
Source 2
Source 3
t groups of
packets
Deterministic
Routing
(ex: OSPF)
Hybrid Routing
(ex: OLSR)
Random Protocol
(ex: Flooding)
Recover With
Redundancy
and Retransmit
Recover With
Redundancy
Recover With
Retransmission
Information
Loss Distributed
Information Loss
Measurable
Information Loss
Significant
The state of information transfer on a network changes with network management policy and protocol
– Particularly important to the Air Force given its unique mobile infrastructure
The state of the network and its ability to transfer information in a network can be described at different
timescales and managed through coding and protocol design
Network Management Research:
Guaranteeing Information Transfer
Recovered
Information
Message 1
Message 2
Message 3
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PI: Prashant Metha, Sean Meyn Institution: UIUC
Approach: Use dynamic programming as an approach to estimate network state and manage
adaptively rather than having a fixed model for network behavior
Payoff: Will adapt to dynamic conditions of topology and structural information change
- Can handle non-Gaussian distributions of state variables more efficiently than
learning methods
Reinforcement Learning of
Complex Networks
Dynamic Stochastic Programming Mean Field Statistical Approaches Allow
Much Less Resource Utilization
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PIs: A. Goldsmith, Yonina Eldar, S. Boyd Stanford, V. Poor Princeton
Complex Network Information Exchange In
Random Wireless Environments
Sparse Sampling Architecture
Approach: Wireless propagation channels can be sparsely sampled and the
information recovery can still approximate the throughput with full sampling
- Allows low dimensional network traffic flow management
Payoff: Throughput in wireless channels can be increased in extremely low signal
to noise scenarios and correlated interference
Wireless Statistical Channel
Covariance Structure
Throughput Slightly Less Than Full Sampling
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Network Coding and Verification
With SheavesRob Ghrist, Michael Robinson UPenn
Approach: Network coding can be formalized through a sheaf theoretic framework to
represent maximum information flow regimes
- Sheaf theory enables detailed algebraic specification of different information classes
Payoff: Verification of information flows on the network can be accomplished over different
classes of information
Sheaf Formulation of Network Coding
Algebraic Information
Class
Verification of Information Flow
In Logical State Diagram
Information Flow
Class
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Less: Latency/Disruption
Tolerant
More: Controllable
Less: Information Loss Under
Disruption
More: Latency, Resource
Intensive
Information
Sources
Information
Timescale t
Network Information
Distribution
Network
Information Loss
With Interference
Network
Information
Recovery
Source 1
Source 2
Source 3
Recovered
Information
Message 1
Message 2
Message 3
t blocks of
information
Deterministic
Routing
(ex: Core/Backbone)
Hybrid Network
(Mesh)
Random Network
(ex: Mobile Ad Hoc)
Reroute Information
Reroute and Change
Distribution
Change Information
Distribution
Information
Loss Distributed
Information Loss
Measurable
Information Loss
Significant
• We wish to develop information invariants that can be used to assess network performance
- Describe statistical geometric invariant properties to characterize performance
of network in transporting information through algebraic and topological methods
- Use geometric flow analysis to predict and manage future network state
Global Network Research: Network
Performance Invariants and Prediction
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Geometric NetworkParameterization
Approach: Different classes of networks have different behavioral
properties according to their geometry
Payoff: Properties such as stability under resource constraints, security
properties and latency can be measured and characterized
Narayan, Saniee, Barishnikov, Korotky, UC Santa Cruz/Lucent
Geometric and Statistical Network
CharacterizationNetwork Taxonomy
Space of Networks
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Multi-scale Network Measuresand Covers
Jones, Rokhlin, Yale, Ness, Bassu Telcordia
Approach: Measure theory can be applied to geometric properties of statistical
distributions learned from networks
Payoff: Affine multi-scale operator theoretic metric properties can characterize
geometric and statistical characteristics of the network such as likelihood for
information loss, security compromise, or failure due to resource constraints
Geometric and Statistical
Network PropertiesOperator Theoretic
Network Representation
Network Transactional
Behavior According to Each
Operator Class
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Sparse Approximation and PersistentHomology of Networks
Approach: Persistent Homology can be used to characterize statistical class of
network traffic data
Payoff: Different classes of network behavior can be statistical parameterized by
homology and the risk of information loss and system failure can be defined
Robert Calderbank, Duke, Rob Nowak, Laura Balzano, UWisc
Network Data vs. ModelsNetwork Risk as a Function
Of Homology
Outlier Characterizing
Information LossNormal Network
Behavior
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Geometric Classical and QuantumNetwork Analysis
Approach: Use distance preserving high to low dimensional transformations to reduce
network data dimensionality, characterize with homology, classify according to statistical
region with quantum statistical analog
Payoff: Comprehensive statistical characterization of network data at multiple scales that is
invariant to dimensionality reduction – characterized on real Rome Emulab data
Alsing,Ypez, AFRL/RI/VS, Warner Miller, Florida Atlantic University, ST Yau, Harvard University
1b # (1D) “loops” (S1)
in network (2-D holes)
2b # (2D) “cavities” (S2)
in network (3-D holes)
3b # (3D) “voids” (S3)
in network (4-D holes)
High to Low Dimensional
Distance Preserving
Transformation
Statistical Quantum Network
Analog
Deterministic Hybrid Random
Homology Determines
Statistical Class on
Rome Emulab
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Fundamental Network Principles
Units of information transfer do not have to be packets – generalizing this approach to other
scientific areas allows generalized network design and analysis within constraints
- Taking this approach allows network design principles in terms of multiple network functions
Deterministic
Protocol
Distribution
Time Evolution(Global
Properties)
Deterministic Heterogeneous Random
Content(local)
Network Policy/
Protocol(management)
Network
Structure(global)
Deterministic
Content
Heterogeneous
Network
Heterogeneous
Protocol
Deterministic
Network
(1/information
timescale)
FrequencyData
Network
Packet
Packet
Groups
Packet
Blocks
Wireless
Network
Modulation
Unit
Waveform
Signal
Array
Hardware/
Software
Register/
Variable
Ram/
Subroutine
Virtual
Mem./
Program
Social
Words
Phrases
News
Reports/
Blogs
Biological
DNA
Protein
Synth.
Cell
Function
Basic Information Unit Scales
Communications
Networks
General
Networks
Random
Protocol
Random
Content
Heterogeneous
Content
Random
Network
Network Design Principles
Not Resourced,
Not Stable,
Not Secure
Design
Excluded Properties
Resourced,
Stable,
Secure
Design
Included Properties
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Program Impact &Collaboration with Agencies
• DARPA Collaboration/joint program reviews
– InPho – Information in a photon/quantum network
– KECOM – Knowledge aided compressed measurement
– ITMANET – Joint program review
– TDA/Stomp – topological data analysis/sensor topology for minimal
planning
• NITRD – Large Scale Networks Working Group, Interagency Working Group
on Spectrum, High Confidence Software Systems
– complex systems initiative (with NIST/DOE/NSF)
• OSD – Complex Engineering Systems, Assured Software Systems,
Systems 20/20, Command and Control Working Group
• ARL/ARO Board of Advisors – Collaborative Network Science & Biology
Technology Alliance
• NSF Future Internet, Net-Sci, BECS (Building and Engineering Complex
Systems)
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Cyber Operations: New Joint University Center of Excellence:
“Secure Cloud Computing” with university and AFRL/RI
Physics and Materials: New Joint MURI Topic: “Large Scale Integrated
Hybrid Nanophotonics”
Socio-Cultural Analysis: Social Networks – Joint MURI Topic: “Stable
Metrics for Inference in Social Networks ” – UCLA/USC/ASU
Quantum: Interaction with quantum network and quantum estimation
processes through lab tasks
Information Fusion: Critical feature selection in sensor networks
Optimization: Competing optimization requirements.
Decision: Networks of neurons.
Biology: Systems biological processes as networks.
Other Program Interactions
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Academia/Commercial Outreach
• Keynote Speaker: IEEE Mobile and Ad-Hoc Sensor SystemsNovember 2010
• Keynote Speaker: IDGA Military Radar Symposium, February 2011
• Invited Speaker: IEEE Information Theory and Applications, UCSDFebruary 2010, 2011
• Invited Speaker: IEEE Infocom, SanDiego, March 2010
• Invited Speaker: IEEE GlobeCom Dec 2010
• Panel Organizer: IEEE Milcom, Dec 2011
• Invited Speaker: IDGA RPA Payloads Conference
• Invited Speaker: Workshop on Algebraic and Random Topology, University of Chicago, April 2010
• Organizer: Cambridge University, Newton Institute Workshop on Network Mathematics, Cambridge England, June 2010
• Organizer: Workshop on Mathematics of Distributed Systems,Duke University 2010
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Transition Activities
• DCT
– AFRL/RI – Lab tasks/Joint Emulab research center AFRL/RI online January 2010
• Integration of MURI – “Information Dynamics in Networks” with AFRL Emulab through Princeton/UC Irvine
• Transition of Yale diffusion map to AFRL/RI for network analysis
• Network management and coding interaction with ACC – Jim Lehnert Purdue/Len Cimini Delaware/Andrea Goldsmith-Stanford
– AFRL/RW – weapons tactical data links interaction – Chad Jenkins/Brown
– AFRL/RH – social network analysis interaction – Michael Mahoney/Stanford
– AFRL/RY - collaboration for transitions in network/software policy and management - Larry Carin - Duke
• STTR
– Transitions between STTR/AFRL/ESC/Boeing under STTR IAI activity –interactions with AFRL/RI
– STTR ANDRO Computational Research interaction with OSD/NII/NTIA/ARL CERDEC for spectrum planning research – interaction with AFRL/RI
– Interaction with Princeton/ASU with IAI for integration of STTR work
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Transition Activities
• Customer/Industry
– Collaboration with ACC/GCIC, Air Force Spectrum Management Agency on JALIN ICD
– Collaboration with Boeing, ESC, IAI for transition of coding and routing management protocols baseline CORE tools to Rome Lab for possible integration in CABLE JCTD
– Briefing to Space Command/Peterson for potential collaboration
– Interaction with Northrup Grumman/BACN airborne networking program for potential collaboration
• OSD
– Complex Systems Engineering and Systems 20/20 initiative
– Software Assurance and Security Initiative
– Robust Command and Control Intiative
• Commercial
– Interaction with ATT/Stanford on real time network information recovery
– New initiatives with Akamai for content distribution analysis
– Interaction with USFA/DHS/CISCO on router algorithm design
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Complex Networks TransitionOrganization
• Complex Networks has an integrated transition strategy
Integrated NetworkingApproach/Stable Under
Heterogeneous
Conditions
Complex NetworksAFRL In House/
AFRL/RI – Network Emulation
STTR
MURI
Customer Interaction
ACC/ASC/ESC/AMC
/Joint
Network Emulation Centers
Network Science OSD
Working GroupAirborne Networks
Requirements and
Capabilities Documents
AFOSR
Discovery
Challenges
AFRL Focused Long
Term Challenges
SBIR
OSD
Activitie
s
Cross Federal Collaboration
NITRD/NSF/DHS
Partnerships
DARPA
- OSD/COI Working Groups
- Industry Partnerships
- Commercial Interaction
Distribution
DARPA
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Backup
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• Basic research in networks:
– ARMY/ARL/ARO – Network Science/ITA/CTA/MURI – applying analytic
models to network problems and using to assess protocols on the basis of
similarity to model – some network statistical analysis
– Navy/ONR/NRL – MURI/6.1/6.2 - Statistical analysis of network
phenomenon – some protocol analysis
– DARPA – COGNETS/ITMANET – heavy emphasis on system
development – some work on information theory for cross layer design –
sensor planning
– NSF – Future Internet/NetSci/CDI/Portfolios – developmental work in
information theory – casting broad net to larger research community for
networking concepts
– DOE/NIST/NASA – Focused on large scale backbone network systems
and physics-based phenomenology
Other Agencies
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Complex Networked System
Design Principles
Units of information transfer do not have to be packets – generalizing this approach to
other scientific areas allows generalized network analyses
- Examples: Social Networks, Wireless Propagation, Software Performance, Biological
Architecture Design Principles
Not Resourced,
Not Stable,
Not Secure
Content(local)
System Policy/
Protocol(management)
System
Structure(global)
(1/information
timescale)
Deterministic
Protocol
Distribution
Time Evolution(Global
Properties)
Deterministic Heterogeneous Random
Deterministic
Content
Heterogeneous
Network
Heterogeneous
Protocol
Deterministic
Network
Frequency
Random
Protocol
Random
Content
Heterogeneous
Content
Random
Network
Resourced,
Stable,
Secure
Design
Excluded Properties
Design
Included Properties
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Complex Networks Approach
Goal: Develop unifying mathematical approach to discovering fundamental principles of networks rather than imposing
them
Air Force Communication
Networks Diverse Types of
Networks
“Fundamental Principles”
of Networks
Complex Networks
Theory
Hard Theoretical
Problems
Guarantee
Information
Transfer
Network
Management Research
Global Network
Research
Preserve
Information
Structure
Local Network
Research
Predict
Network
Performance
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Air Force Network Environment
The Air Force is unique among the DOD and civilian world in that it has a highly
heterogeneous set of users and must provide a mobile infrastructure
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What’s a Complex Network?
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Approach: Use geometric lattice theory as a mechanism for code design such that
an information capacity of the code is increased as packets dropped & corrupted
Payoff: Coding can be performed to preserve information content in transmission
during severe network interference and may potentially take toward coding over
integers
Sriram Vishwanath, UT Austin
Coding for Interference Networks
Lattice structures enable robust preservation of information structure during packetization through regular lattice a potential to code over non binary number sequences
Probability of
information lost
rigorously
bounded
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Geometric Coding for Networks
Approach: Coding theory that exploits both network routing state and
information structure across packets to guarantee information transfer
Payoff: Ability to guarantee transfer of information at coding level
without significant packet retransmission
Geometric Coding Result Improved Performance With Routing
Information Embedded
Lizhong Zheng, MIT
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Managing on Degrees of Freedom –A Network Coding Approach
Muriel Medard, MIT
Approach: Specific routing path configuration of networks can allow superior
throughput of information based on a geometrically structured code
Payoff: Information transfer becomes more independent of network protocol
performance
• We would like to move away from a depth one network and from restrictive conditions on the inputs/function
• We consider a somewhat different version of graph entropy
• We are able to remove the restrictive conditions
• Our approach also allows us to consider a more general topology - trees
Configure code/packet structure using algebraic geometry do induce maximum information transfer for a given network architecture
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Approach: Analysis of geometric strategy to bound information loss and instability due to conflicts between coding, packetization, and routing
Payoff: Define what part of network management approach destabilizes networks and destroys information transfer
Management of Complex NetworksJohn Doyle, Caltech
Network Protocol
Information vs. RoutingDestabilizing Behavior
(Information Flow Disruption)
(1,1,1)
S
d2d1
(1,1,1) (1,1,1)
(1,0,1)
(1,0,1) (1,1,0)
(1,1,0) (1,0,1)
(1,1,0)
),,( 21
,,,
d
ji
d
jiji ggf
Information
Coding/Routing
Structure
(with Geometric Bound)
2 2min
xkp x dt p x
x kp
Geometric coding method can potentially
bound disruption.
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Approach: Characterize information capacity of wireless network as thermo-
dynamic process and use to guide management of network protocol selection
Payoff: Reliable statistical and queuing methods to govern and predict network
behavior
D. Tse, Berkeley, P. Gupta, Alcatel Lucent, D. Shah, MIT
Thermodynamics of Large-Scale
Heterogeneous Wireless Networks
Multiple Input/Output (MIMO)
Fully Connected Network
e*()
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1
2 3
Multihop
Hierarchical MIMO
Fully Connected
Network
Information
Capacity
Throughput Capacity
In Phase Transition
Using MIMO
Multihop Network
Wireless multiple input/output protocol allow network to reach maximum information throughput.
Information Throughput
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Approach: Use estimation theory to measure the state of information transfer on a
network from multiple distributed measurements (network tomography)
Payoff: Map the current state of any network from distributed measurements and
allow management of future network state based on coding and/or timing
Rob Nowak, University of Wisc. Madison
Learning, Inference, and Coding
in Complex Networks
Current Estimated Network State
Estimation of Local Information Throughput Estimation of Global Information Throughput
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Topological Features ofNetwork Geometry
Approach: Develop techniques to measure curvature as parameter in real
networks to determine if there are quantifiable properties of topological
network invariance
Payoff: Curvature key indicator of stability of network performance after
mapping graph onto manifold
Curvature is a characteristic of a manifold
K=0
K<0K>0
Narayan, Saniee, Barishnikov, Korotky, UC Santa Cruz/Lucent
Results from Communications Networks
CurvatureAnalysis
Network Graph
RealNetworks
Experimental FiberSize
#node – #links
Diameter-
d*
Radius Average
geodesic
3447 - 18780 11 - 2 2.9 5.0
TopologicallyInvariant?
Theoretical Network
Size
#node – #links
Diameter -
d*
Radius Average
geodesic
4,264-15,022 14 - 2 6.4 11.6
ExperimentalWireless
Size
#node – #links
Diameter -
d*
Radius Average
geodesic
2998 - 7612 12 - 2 3.1 5.53
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Geometric Network Analysis
Approach: Combine several methods of topological analysis to determine and
filter network information so invariant properties emerge consistently
Payoff: We have a consistent realization of when networks are connected and what
resources need to be managed to preserve stability
M. Mahoney, Stanford University
Distributed Geometric
Network Measurements
Measured Information
Features
Points From Distributed
Measurements
Invariant Network
Properties
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Approach: Apply Discrete Morse Theory to find probabilistic description
of the evolution of a global network into a particular state
Payoff: Global network state can have a precise probability of evolving to
a given condition
Databases for the Estimation Global State of
Multi-parameter Networks
Directed Network
Graph With Noise
Evolution of Network
To Particular State?
Estimate of Evolution
Of Topological
Structure
Multi-parameter
Database
Phase space
configuration
Konstatin Mischaikow, Rutgers University
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Mathematical
Physics
Percolation
(model)
Network Information Models
Approach: Characterize cascading network failure in terms of
percolation/thermodynamics model
Payoff: Transactions of information can be mapped to stability &
vulnerability of nodes
PI: Edmund Yeh Institution: Yale
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Topological & Geometric Tools for Complex Networks
Approach: Apply geometric flow analysis to topological network objects
to predict future global network behavior
Payoff: Global network structure can be rigorously analyzed and
predicted probabilistically
PIs: A. Jadbabaie, UPenn F. C. Graham, UCSD, STYau Harvard
• Laplacian flows : a neutrally
stable
– Converges an element in the kernel
– If ker(L1) {0}, then converges to a
non-zero element in the kernel for
almost all initial conditions.
• Algorithm:
• Run the local update for a random
initial condition.
• If non-zero, there exists at least one
coverage hole.
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Analysis and Geometry for Complex
Network ProcessingPI: Ronald Coifman Institution: Yale University
Approach: Use Diffusion Map geometric learning algorithm to
detect various network parameters
Payoff: Direct mapping between input feature vectors and network
anomaly detection.
Step1 Training -> Step 2 Network Analysis
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Coding Through Packet Timing
Approach: Understand dynamical behavior of codes on global
network performance
Payoff: Enables regulation of global behavior using local coding
method
PI: Todd Coleman Institution: University of Illinois
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Analysis of Network Policy andIts Effect on Spectrum Utilization
PI: Lehnert Institution: Purdue
0 0.2 0.4 0.6 0.8 110
0
101
102
System Load
Exp
ecte
d D
ela
y
Upper Bound
MWM
Lower Bound
Upper bound of spectrum load vs. network latency
Approach: Analyze global bounds of spectrum resource utilization as a
function of all network transaction cost
Payoff: Make wireless network exchange spectrum efficient and less
subject to instabilities introduced due to lack of available spectrum and
inefficient
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PI: Kannan Ramchandran Institution: UC Berkeley
Approach: Deterministic codes (MDS) are bandwidth intensive – random codes (repetition
coding) are storage and computationally intensive
- Trade the advantages of each using minimum storage regenerating (MSR)
vs. minimum bandwidth regenerating codes (MBR) using geometric cut set
analysis
Payoff: Provides the most robust and stable coding strategy that enables predictable recovery
of large sets of networked information with minimum amount of available resources
Codes for Distributed Storage Networks
lemma: for any (potentially infinite) graph G(α,β,d),
any data collector has flow at least
1
0},){()(
k
iidMiniDCMinCut
Graph of Information Flow
Minimum Bandwidth RegenerationInformation Recovery Trade Space
Criteria for Information Recovery
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p(x|w1,w2)
user 1
user 2
transmitter
(W1, W2)
Y1
Y2
X
stochastic encoder
Z1
Z2
H1
H2
dec W1
H(W2|Y1 )
dec W2
H(W1|Y2 )
n
n
PIs: A. Goldsmith, D. O’Niel, S. Boyd Stanford, V. Poor Princeton
Complex Network Information Exchange In
Random Wireless Environments
Approach: Networks at the physical layer generate a lot of extra protocol traffic
particularly when they transmit highly correlated information
- Using network coding at the physical layer can reduce overhead in high
signal to noise environments maximizing geometric flow of information
Payoff: Can combine correlated information at the multiple access layer to cut
down on protocol overhead, particularly in multicast scenarios.
Dynamic Physical Network
Analog Network Coding (ANC) Strategy
Rate Throughput as A Function of Power
Rate/Capacity Through as a Function of Transmit Power
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PI: Olgica Milenkovic Institution: U. Illinois
Approach: Information in a network can be recovered by using sparse approximation theory for
specific classes of geometric information to recover large sets of structural information
- We can recover large sets of structural information with a specified probability even if large
numbers of packets are dropped
Payoff: Overhead in protocol significantly reduced and a specific probability of recovery can be
computed for large classes of information.
Coding for Complex Networks
Information Recovery as a Function of Packets
Sparse Approximation Criteria Geometric Functional Approximation
Recovery for Geometric Barriers
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PI: Mehran Mesbahi Inst: University of Washington
Approach: Robust network management can be achieved using controllability,
observability criteria can be used to assess how networks can be managed and
subject to compromise
- Eigenvalues of correlations of groups of packets can be used to assess
which nodes have the most influence over network behavior
Payoff: Design criteria for more robust, disruption tolerant, and secure network
management can be developed
Robust Network Management
Robust Network Management
Vulnerability Nodes to Disruption
Network Performance Using Eigen-spectra Eigen-spectra
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PI: Sean Meyn Institution: UIUC
Approach: Use reinforcement learning methods as an approach to estimate network state and
manage dynamically rather than having a fixed model for network behavior
Payoff: Will adapt to dynamic conditions of topology and structural information change
Reinforcement Learning of
Complex Networks
Feedback Process for Reinforcement Learning
Stochastic Process Approximation of System
Convergence to Solution
Robust Solution Space
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MURI: Complex Network ManagementPI: Robert Calderbank, Princeton, Emmanuel Candes, Stanford, Joel Tropp Caltech,
Athena Markopoulou, UC Irvine, Suhas Diggavi, UCLA, Robert Ghrist, UPenn (& more)
Approach: Integrate network information flow, network and structural information
estimation, and sparse approximation and information recovery
One computationally efficient strategy for integrated approach for network
management and information recovery of a dynamic network
Payoff: Predictable recovery of information in a dynamic network with many
resource constraintsSparsely Approximate Lost Information
Manage Network Information Flow
Estimation Information/Network Structure
Integrate
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PIs: Amit Singer, Ingrid Daubechies: Princeton
Rigidity Theory in Networks
Approach: Given local sampling of information in a network, use rigidity theory
to globally approximate information/network structure given some finite number of
local measurements in noise
Payoff: Assessment of global properties of information/network structure without
large amounts of overhead or accurate measurements in the network
Network Data Actual Network
Reconstruction from with
10% NoiseReconstruction from
20% Noise
H a set of sparse network measurements
Network
Reconstruction
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ST Yau, Harvard, Fan Chung Graham, UCSD, Ali Jadbabaie, UPenn
Geometric Curvature and Flow in Networks
Approach: Use Ricci flow and Ricci curvature as a means to shape information
flow in networks using greedy routing
Payoff: Dynamically shape network traffic to maximize information flow, decrease
the dimensionality of the routing problem, and minimize the possibility of network
instability and information loss
Target curvature Current curvature
Geometric Representation
Of Network
Deformation
Using Discrete
Ricci Flow
3d-2d Deformation With
Target CurvatureDiscrete Ricci Flow
Maximizes Information
Flow For Routing
Process
(New Greedy Routing
Strategy)
Arbitrary
Deformation
Creates Possible
Instability/Poor
Information Flow
Can Target Deformation
To Preserve Scaling Properties
Across Information Scales
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Ergodic vs. Nonergodic Coding
Approach: Advanced network coding method that uses estimation theory
together with ergodic/nonergodic model to determine best network
combination coding approach
Payoff: Significant in reducing network bandwidth of transferred data over
lossless Slepian Wolfe network coding
PI: Aaron Wagner Institution: Cornell University