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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.

35

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*()

12

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

41

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.

42

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

44

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

45

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

46

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

47

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

48

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

49

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

52

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

53

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