VIRUSES structure and classification ppt by Dr.Prince C P
Network Science: Theory, Modeling and Applications
1. Network
Science:
Theory,
Modeling
and
Applications
Madhav
V.
Marathe
Dept.
of
Computer
Science
&
Network
Dynamics
and
Simulation
Science
Laboratory
Virginia
Bioinformatics
Institute
Virginia
Tech
NDSSL
TR-10-148
Supported by Grants from NIH MIDAS, NSF HSD, NSF CNS, CDC COE, and DoD.
2. Network Dynamics & Simulation Science Laboratory
Where:
LLNL,
Livermore,
Dates:
December
1st
to
December
15th
2010
Hosts:
Dr.
David
Brown
and
Dr.
Celeste
Matarazzo
Time:
10.00
am
to
11.30
am
(OfMice
hours
as
needed
afterwards)
Lecturer:
Madhav
Marathe,
Virginia
Tech
(mmarathe@vbi.vt.edu)
Guest
Lectures:
Christopher
Kuhlman
(VT),
Goran
Konjevod
(Staff
Scientist,
LLNL),
Anil
Vullikanti
(Asst
Prof.
VT
and
DOE
Career
award
recipient)
3. Network Dynamics & Simulation Science Laboratory
Complex
Networks
are
pervasive
in
our
society.
Realistic
biological,
information,
social
and
technical
networks
share
a
number
of
unique
features
that
distinguish
them
from
physical
networks.
Examples
of
such
features
include:
irregularity,
time-‐varying
structure,
heterogeneity
among
individual
components,
and
selMish/
cooperative
game-‐like
behavior
by
individual
components
and
co-‐evolution.
The
size
and
heterogeneity
of
these
networks,
their
co-‐evolving
nature
and
the
technical
difMiculties
in
applying
dimension
reduction
techniques
commonly
used
to
analyze
physical
systems
makes
reasoning,
prediction
and
controlling
of
these
networks
even
more
challenging.
Recent
quantitative
changes
in
high
performance
and
pervasive
computing
including
faster
machines,
distributed
sensors
and
service-‐oriented
software
have
created
new
opportunities
for
collecting,
integrating,
analyzing
and
accessing
information
related
to
such
large
complex
networks.
The
advances
in
network
and
information
science
that
build
on
this
new
capability
provide
entirely
new
ways
for
reasoning
and
controlling
these
networks.
Together,
they
enhance
our
ability
to
formulate,
analyze
and
realize
novel
public
policies
pertaining
to
these
complex
networks.
The
course
will
cover
the
mathematical
and
computational
aspects
of
Network
Science.
It
will
provide
a
broad
overview
of
the
area
and
then
will
focus
on
• Mathematical
aspects,
including
structure
theorems,
existence
proofs,
• Computational
aspects,
including,
provable
lower
as
well
as
upper
bounds
on
the
computational
resources,
efMicient
algorithms
for
computing
the
structure
and
dynamics
over
complex
networks,
• Developing
high
performance
computing
based
computational
models
and
modeling
environments
for
supporting
Network
Science.
Practical
applications
arising
in
the
context
of
infrastructure
planning,
energy
systems,
national
security
and
integrated
communication
systems
will
be
used
to
illustrate
the
applicability
of
the
concepts.
Course Synopsis
4. Network Dynamics & Simulation Science Laboratory
Work
funded
in
part
by
NIGMS,
NIH
MIDAS
program,
CDC,
Center
of
Excellence
in
Medical
Informatics,
DTRA
CNIMS,
NSF,
NeTs,
NECO
and
OCI
program,
VT
Foundation.
5. Network Dynamics & Simulation Science Laboratory
•
Lada
Adamic:
For
graciously
sharing
her
course
notes
•
NDSSL
Laboratory
members
who
are
in
reality
coauthors
of
this.
•
Other
places
that
I
have
borrowed
the
material
includes:
• Tim
Roughgarden’s
lectures
on
Games
• David
Kempe’s
Lectures
on
Networks
• Henning
Mortveit’s
lectures
on
SDS
• Bogdan
Oporowski’s
lecture
on
Graph
theory
• Michael
Kearns
lectures
on
Networks
and
Games
• …
and
many
more
• Books
• Fernando
Vega-‐Redondo,
Complex
Social
Networks,
Econometric
Society
Monographs,
,
Cambridge
University
Press,
2007
• D.
Easley,
J.
Kleinberg.
Networks,
Crowds,
and
Markets:
reasoning
about
a
Highly
Connected
World,
Cambridge
University
Press,
2010.
• J.
Kleinberg,
E.
Tardos.
Algorithm
Design.
Addison
Wesley,
2005.
Matthew
Jackson,
Social
and
Economic
Networks,
Princeton
University
Press,
2010
• …
and
many
more
Acknowledgements for Course Material
6. What
is
a
Network?
History,
Broad
Research
Questions,
Illustrative
Applications
7. Network Dynamics & Simulation Science Laboratory
What
is
a
network
?
Although
no
formal
accepted
deMinition,
there
appears
to
be
a
consensus
that
all
network
comprise
of
the
following
attributes:
A
set
of
agents
(entities):
agents
can
be
simple,
game
like,
adaptive
…
Interaction
among
the
entities
governed
by
a
graph
(binary
or
in
general
k-‐ary
relationship)
Graph
itself
can
change,
co-‐evolve
with
the
entities
Entities
modify
their
local
states
and
behavior
by
interacting
with
their
neighbors
Blogosphere
(datamining.typepad.com)
points lines
vertices edges, arcs math
nodes links computer science
sites bonds physics
actors ties, relations sociology
node
edge
9. Network Dynamics & Simulation Science Laboratory
Social
Networks:
Facebook
has
over
500Million
individuals!
http://www.smrfoundation.org/category/industry/companies/facebook/
10. Network Dynamics & Simulation Science Laboratory
High
School
Dating
Network
(Discovery
Magazine
2007)
11. Network Dynamics & Simulation Science Laboratory
Router-level
network
based
on
ISPs
14. Network Dynamics & Simulation Science Laboratory
Biological
Networks
Institute of biology and technology - Saclay (iBiTec-S)/ Unités/
Department of Integrative Biology and Molecular Genetics (SBiGeM)/
Integrative biology laboratory (LBI)/ Dynamics of Biological Network (J. Labarre)
http://djpowell.wordpress.com/
http://www.leonelmoura.com/tree.html
15. Network Dynamics & Simulation Science Laboratory
In
real
world
Networks
are
layered
and
coupled
16. Network Dynamics & Simulation Science Laboratory
Growth
of
network
science
as
measured
by
publications
#papers
with
“complex
networks”
in
the
title
[National
Academy
of
Science
Report,
2007]
Journal
special
issues
on
Network
Science
17. Network Dynamics & Simulation Science Laboratory
Even
appears
in
main
stream
publications
YESTERDAY
!
18. Network Dynamics & Simulation Science Laboratory
The
Emerging
Network
Science?
Newman,
Barabasi,
Watts:
The
Structure
and
Dynamics
of
Networks:
“We
argue
that
the
science
of
networks
that
has
been
taking
shape
over
the
last
few
years
is
distinguished
from
preceding
work
on
networks
in
three
important
ways:
(1)
by
focusing
on
the
properties
of
real-‐world
networks,
it
is
concerned
with
empirical
as
well
as
theoretical
questions;
(2)
it
frequently
takes
the
view
that
networks
are
not
static,
but
evolve
in
time
according
to
various
dynamical
rules;
and
(3)
it
aims,
ultimately
at
least,
to
understand
networks
not
just
as
topological
objects,
but
also
as
the
framework
upon
which
distributed
dynamical
systems
are
built.”
Kearns:
An
Emerging
Science:
Examine
apparent
similarities
(and
differences)
between
many
social,
economic,
information,
biological
and
technological
networks
Importance
of
network
effects
in
such
systems
How
things
are
connected
matters
greatly
Details
of
interaction
matter
greatly
Qualitative
and
quantitative;
can
be
very
subtle
A
revolution
of
measurement,
theory,
and
breadth
of
vision
19. Network Dynamics & Simulation Science Laboratory
Science
of
Networks:
A
personal
(and
likely
biased)
viewpoint
1:
Real
World
Networks:
Extremely
important
but
..
Folks
in
social
sciences,
transportation,
electrical
systems,
VLSI,
…
all
have
been
studying
real
world
networks
We
need
to
seriously
revisit
the
use
of
simple
random
graph
models
as
a
way
to
explain
a
phenomenon:
the
mathematics
is
elegant
but
often
means
very
little
in
the
real
world
Real
world
networks
are
dynamic,
coupled
and
co-‐evolve
Ability
to
collect
data
that
is
diverse
(spatially,
demographically),
process
it,
store
it
and
reason
about
it
very
fast
New
data
should
be
utilized
in
developing
network
models
New
and
realistic
models
of
real
world
networks.
Models
should
represent
coupling
and
co-evolution
20. Network Dynamics & Simulation Science Laboratory
Accessibility
of
Network
Science:
Pervasive
Computing
Environment
High
performance
computing
(larger
machines,
data
intensive
systems,
distributed
systems
…)
Software
as
a
service;
delivering
results
to
specialist
who
is
not
interested
in
becoming
a
computer
scientist
Ability
to
collect
data
that
is
diverse
(spatially,
demographically),
process
it,
store
it
and
reason
about
it
very
fast
Develop
Pervasive
computing
technology
to
deliver
Network
Science
technology
to
domain
specialists
and
others
who
are
not
computing
experts
21. Network Dynamics & Simulation Science Laboratory
Science
of
Networks:
Centrality
of
Computing
and
Information
Science
From
analytical
results
to
algorithmic
viewpoint:
this
is
the
essence
of
new
science
in
my
opinion
if
one
has
to
do
deal
with
real
networks
Questions
that
become
important
are:
How
can
we
design
certain
networks
How
can
we
measure
distributed
networks
What
is
a
certain
set
of
distributed
agents
computing:
interaction
based
computing
and
social
cognition
Models
are
not
monolithic
or
federated
anymore
but
really
a
way
to
synthesize
information
by
interacting
with
various
components
–
Milner’s
in_luential
idea
on
interactionism
Algorithmic
Viewpoint
provide
the
foundational
basis
HPC
computing
provide
the
underlying
technology
22. Network Dynamics & Simulation Science Laboratory
Inter
and
intra-discipline
interactions
–
Emergence
of
a
Giant
Component
!
We
have
reached
critical
point
wherein
researchers
from
diverse
disciplines
are
starting
to
share
their
ideas
and
interact
(Gladwell’s
Tipping
point)
Beautiful
convergence
of
ideas
and
view
points
in
CS,
Engineering,
Economics,
Mathematics,
Physics,
Social
Science,
Biology….
(convergence
of
several
events,
world
becoming
smaller,
funding
agencies
pushing
to
do
joint
work!,
global
problems,
problems
that
were
being
solved
by
disciplinary
viewpoints)
Economic
drivers:
Information
economy,
distributed
logisitics,
global
markets,
mobile
labor
force,
funding
shortfalls
Measurement
technologies
and
technologies
for
developing
and
sustaining
diverse
organizations
and
ecosystems
have
taken
hold
Multi-disciplinary
view
important:
from
real
research
social
networks
!
23. Network Dynamics & Simulation Science Laboratory
Culmination
of
diverse
_ields:
Viewpoints
are
different
and
interesting
Engineers
• Understand
how
infrastructure
networks
work
• Design
and
control
of
these
networks
Computer
Scientists
• Understand
and
design
complex,
distributed
networks
•
algorithmic
view:
design
of
a
system
and
inferring
its
semantics
Social
Scientists,
Behavioral
Psychologists,
Economists
• Understand
human
behavior
in
“simple”
settings
• Revised
views
of
economic
rationality
in
humans
Biologists
• Neural
networks,
gene
regulatory
networks,…
• Understanding
the
evolution
of
networks
Physicists
and
Mathematicians
• Interest
and
methods
in
complex
systems
• Theories
of
macroscopic
behavior
(phase
transitions)
Scientists forming
co-evolving
networks World
24. Network Dynamics & Simulation Science Laboratory
Proposed
Components
of
a
Research
Program
in
Network
Science
and
Engineering
Structural
Analysis
of
Complex
Networks
Dynamics
on
Complex
Networks
Co-‐evolution
of
dynamics,
network
and
individual
behavior
Measurement
and
Inference
Networks
Science in Real
World
25. Network Dynamics & Simulation Science Laboratory
Key
Research
Challenges
(NA
report
on
Network
Science)
1. Dynamics:
Better
understanding
between
structure
and
function
2. Modeling
and
Analysis
of
large
networks:
Tools,
abstractions,
approximations
3. Design
and
Synthesis
of
Networks
4. Increasing
level
of
rigor
and
mathematical
structure
5. Abstracting
common
concepts
across
Mields
6. Better
experiments
and
measurements
of
network
structure
7. Robustness
and
Security
27. Network Dynamics & Simulation Science Laboratory
Application
1
(1736):
First
Use
of
Graphs
Seven
Bridges
of
Königsberg
Seven
Bridges
of
Königsberg
–
one
of
the
Mirst
problems
in
graph
theory
Is
there
a
route
that
crosses
each
bridge
only
once
and
returns
to
the
starting
point?
We
will
see
how
this
problem
can
be
solved
by
modeling
it
as
a
graph
theory
problem
later
28. Network Dynamics & Simulation Science Laboratory
Application
2
(1850s):
Cholera
Pandemic:
John
Snow
First
Cholera
Pandemic
Second
Cholera
Pandemic
During
this
time
germ
theory
of
diseases
was
not
widely
accepted.
During
John
Snow's
life
time
there
were
three
pandemics
of
Asiatic
cholera
(1817-‐23,
1826-‐37
and
1846-‐63),
two
of
which
reached
the
British
isles.
The
epidemic
in
1848
to
1849,
killed
between
50,000
and
70,000
in
England
and
Wales.
A
third
outbreak
in
1854
left
over
30,000
people
dead
in
London
alone.
Vibrio
cholerae:
Toxin
alters
sodium
pump
in
intestinal
cells
Mluid
loss
Entry:
oral
Colonization:
small
intestine
Symptoms:
nausea,
diarrhea,
muscle
cramps,
shock
http://www.ph.ucla.edu/epi/snow.html
29. Network Dynamics & Simulation Science Laboratory
Application
3
(1950-60)
Segregation
(Schelling):
Micromotives
to
Macrobehavior
Duncan
and
Duncan’s
(1957)
study
of
Chicago
1940-‐1950
Census
tracts,
mixed
neighborhoods
all
segregate
Placed
pennies
and
dimes
on
a
chess
board
and
moved
them
around
according
to
various
rules.
Board
=
city,
Square
=
Housing
lot,
agent:
at
a
location
Pennies
and
dimes
=
agents
representing
two
groups
in
society,
e.g.
boys
and
girls,
smokers
and
non-‐smokers,
etc.
Neighborhood
=adjacent
locations
on
the
board
Happy
if
(neighbors
of
same
type
>
threshold)
If
Unhappy
then
move
to
a
random
location
that
is
happy
Result:
Many
basic
conMigurations
produce
segregation
relate
decisions
about
where
to
live
(micro)
to
patterns
of
segregation
(macro)
No
obvious
relationship
between
individual
behavior
and
aggregate
outcomes.
Behavior
is
interdependent.
Individuals’
behaviors
depend
on
social
context
(micro)
Individual
behaviors
collectively
change
social
context
(long
term,
macro)
http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/
30. Network Dynamics & Simulation Science Laboratory
Application
4:
Power
grids
and
cascading
failures
Vast
system
of
electricity
generation,
transmission
&
distribution
is
essentially
a
single
network
Power
Mlows
through
all
paths
from
source
to
sink
(Mlow
calculations
are
important
for
other
networks,
even
social
ones)
All
AC
lines
within
an
interconnect
must
be
in
sync
If
frequency
varies
too
much
(as
line
approaches
capacity),
a
circuit
breaker
takes
the
generator
out
of
the
system
Larger
Mlows
are
sent
to
neighboring
parts
of
the
grid
–
triggering
a
cascading
failure
31. Network Dynamics & Simulation Science Laboratory
Application
4:
Blackout
of
2003:
Electrical
Infrastructure
Affected
Area
of
50
million
people
in
eight
US
states
and
two
provinces
in
Canada
Approximately61,800Megawatts
(MW)oMload
Most
cascaded
happen
extremely
rapidly
from
4.10
pm
to
4.13
pm
Human
and
information
system
error
also
contributed
to
the
cascade
Other
Infrastructures
including
water,
communication,
and
most
notably
transportation
(rail,
road
and
air)
were
affected
TV
and
radio
stations
also
affected
32. Network Dynamics & Simulation Science Laboratory
Timeline
for
2003
Blackout:
Need
for
Multi-level
networks
The
2003
blackout
wasn't
just
about
fallen
trees
and
broken
transmission
lines.
As
this
timeline
from
the
Department
of
Energy
report
shows,
it
resulted
from
a
combination
of
many
grid
events,
computer
glitches,
and
human
interaction.
33. Network Dynamics & Simulation Science Laboratory
Blackout
of
2003:Time
Line
–
The
Initial
Phase
12:15
p.m.
Incorrect
telemetry
data
renders
inoperative
the
state
estimator,
a
power
Mlow
monitoring
tool
operated
by
the
Indiana-‐based
Midwest
Independent
Transmission
System
Operator
(MISO).
An
operator
corrects
the
telemetry
problem
but
forgets
to
restart
the
monitoring
tool.
1:31
p.m.
The
Eastlake,
Ohio
generating
plant
shuts
down.
The
plant
is
owned
by
FirstEnergy,
an
Akron,
Ohio-‐based
company
that
had
experienced
extensive
recent
maintenance
problems.
2:02
p.m.
The
Mirst
of
several
345
kV
overhead
transmission
lines
in
northeast
Ohio
fails
due
to
contact
with
a
tree
in
Walton
Hills,
Ohio.
2:14
p.m.
An
alarm
system
fails
at
FirstEnergy's
control
room
and
is
not
repaired.
3:05
p.m.
A
345
kV
transmission
line
known
as
the
Chamberlain-‐Harding
line
fails
in
Parma,
south
of
Cleveland,
due
to
a
tree.
3:17
p.m.
Voltage
dips
temporarily
on
the
Ohio
portion
of
the
grid.
Controllers
take
no
action.
3:32
p.m.
Power
shifted
by
the
Mirst
failure
onto
another
345
kV
power
line,
the
Hanna-‐Juniper
interconnection,
causes
it
to
sag
into
a
tree,
bringing
it
ofMline
as
well.
While
MISO
and
FirstEnergy
controllers
concentrate
on
understanding
the
failures,
they
fail
to
inform
system
controllers
in
nearby
states.
3:39
p.m.
A
FirstEnergy
138
kV
line
fails
in
northern
Ohio.
3:41
p.m.
A
circuit
breaker
connecting
FirstEnergy's
grid
with
that
of
American
Electric
Power
is
tripped
as
a
345
kV
power
line
(Star-‐South
Canton
interconnection)
and
Mifteen
138
kV
lines
fail
in
rapid
succession
in
northern
Ohio.
http://en.wikipedia.org/wiki/Northeast_Blackout_of_2003
34. Network Dynamics & Simulation Science Laboratory
Blackout
of
2003:
Timeline
--
the
cascade
begins
3:46
p.m.
A
Mifth
345
kV
line,
the
Tidd-‐Canton
Central
line,
trips
ofMline.
4:05:57
p.m.
The
Sammis-‐Star
345
kV
line
trips
due
to
undervoltage
and
overcurrent
interpreted
as
a
short
circuit.
Later
analysis
suggests
that
the
blackout
could
have
been
averted
prior
to
this
failure
by
cutting
1.5
GW
of
load
in
the
Cleveland–Akron
area.
4:06–4:08
p.m.
Sustained
power
surge
north
toward
Cleveland
overloads
3
138
kV
lines.
4:09:02
p.m.
Voltage
sags
deeply
as
Ohio
draws
2
GW
of
power
from
Michigan,
creating
simultaneous
undervoltage
and
overcurrent
conditions
as
power
attempts
to
Mlow
in
such
a
way
as
to
rebalance
the
system's
voltage.
4:10:34
p.m.
Many
transmission
lines
trip
out,
Mirst
in
Michigan
and
then
in
Ohio,
blocking
the
eastward
Mlow
of
power
around
the
south
shore
of
Lake
Erie.
Suddenly
bereft
of
demand,
generating
stations
go
ofMline,
creating
a
huge
power
deMicit.
In
seconds,
power
surges
in
from
the
east,
overloading
east-‐coast
power
plants
whose
generators
go
ofMline
as
a
protective
measure,
and
the
blackout
is
on.
4:10:37
p.m.
The
eastern
and
western
Michigan
power
grids
disconnect
from
each
other.
Two
345
kV
lines
in
Michigan
trip.
A
line
that
runs
from
Grand
Ledge
to
Ann
Arbor
known
as
the
Oneida-‐Majestic
interconnection
trips.
A
short
time
later,
a
line
running
from
Bay
City
south
to
Flint
in
Consumers
Energy's
system
known
as
the
Hampton-‐Thetford
line
also
trips.
4:10:38
p.m.
Cleveland
separates
from
the
Pennsylvania
grid.
35. Network Dynamics & Simulation Science Laboratory
Blackout
of
2003:
Timeline
--
Crescendo
4:10:39
p.m.
3.7
GW
power
Mlows
from
the
east
along
the
north
shore
of
Lake
Erie,
through
Ontario
to
southern
Michigan
and
northern
Ohio,
a
Mlow
more
than
ten
times
greater
than
the
condition
30
seconds
earlier,
causing
a
voltage
drop
across
the
system.
4:10:40
p.m.
Flow
Mlips
to
2
GW
eastward
from
Michigan
through
Ontario
(a
net
reversal
of
5.7
GW
of
power),
then
reverses
back
westward
again
within
a
half
second.
4:10:40
p.m.
Flow
Mlips
to
2
GW
eastward
from
Michigan
through
Ontario
(a
net
reversal
of
5.7
GW
of
power),
then
reverses
back
westward
again
within
a
half
second.
4:10:43
p.m.
International
connections
between
the
United
States
and
Canada
begin
failing.
4:10:45
p.m.
Northwestern
Ontario
separates
from
the
east
when
the
Wawa-‐Marathon
230
kV
line
north
of
Lake
Superior
disconnects.
The
Mirst
Ontario
power
plants
go
ofMline
in
response
to
the
unstable
voltage
and
current
demand
on
the
system.
4:10:46
p.m.
New
York
separates
from
the
New
England
grid.
4:10:50
p.m.
Ontario
separates
from
the
western
New
York
grid.
4:11:57
p.m.
The
Keith-‐Waterman,
Bunce
Creek-‐Scott
230
kV
lines
and
the
St.
Clair-‐Lambton
#1
230
kV
line
and
#2
345
kV
line
between
Michigan
and
Ontario
fail.
4:12:03
p.m.
Windsor,
Ontario
and
surrounding
areas
drop
off
the
grid.
4:12:58
p.m.
Northern
New
Jersey
separates
its
power-‐grids
from
New
York
and
the
Philadelphia
area,
causing
a
cascade
of
failing
secondary
generator
plants
along
the
Jersey
coast
and
throughout
the
inland
west.
4:13
p.m.
End
of
cascading
failure.
256
power
plants
are
off-‐line,
85%
of
which
went
ofMline
after
the
grid
separations
occurred,
most
due
to
the
action
of
automatic
protective
controls.
36. Network Dynamics & Simulation Science Laboratory
Milgram’s
Small
World
Experiment
Travers
&
Milgram
1969:
classic
early
social
network
study
destination:
a
Boston
stockbroker;
lived
in
Sharon,
MA
sources:
Nebraska
stockowners;
forward
letter
to
a
Mirst-‐name
acquaintance
“closer”
to
target
Information
provided:
name,
address,
occupation,
Mirm,
college,
wife’s
name
and
hometown
navigational
value?
Basic
Mindings:
64
of
296
chains
reached
the
target
20%
of
senders
reached
target.
average
chain
length
=
6.5:
“Six
degrees
of
separation”
average
length
of
completed
chains:
5.2
interaction
of
chain
length
and
navigational
difMiculties
main
approach
routes:
home
(6.1)
and
work
(4.6)
Boston
sources
(4.4)
faster
than
Nebraska
(5.5)
no
advantage
for
Nebraska
stockowners
NE
MA
37. Network Dynamics & Simulation Science Laboratory
Recent
small
world
experiment
Setup
Email
experiment
Dodds,
Muhamad,
Watts,
Science
301,
(2003)
18
targets,
13
different
countries
60,000+
participants
a
professor
at
an
Ivy
League
university,
an
archival
inspector
in
Estonia,
a
technology
consultant
in
India,
a
policeman
in
Australia,
a
veterinarian
in
the
Norwegian
army.
Basic
Analysis
Approximate
37%
participation
rate
approximately
.
Probability
of
a
chain
of
length
10
getting
through:
.3710
~
5
x
10-‐5
so
only
one
out
of
20,000
chains
would
make
it
actual
#
of
completed
chains:
384
(1.6%
of
all
chains).
Average
path
length:
4,
median:
7
Small
changes
in
attrition
rates
lead
to
large
changes
in
completion
rates
e.g.,
a
15%
decrease
in
attrition
rate
would
lead
to
a
800%
increase
in
completion
rate
38. Network Dynamics & Simulation Science Laboratory
Estimating
‘recovered’
chain
lengths
for
uncompleted
chains
<L>
=
4.05
for
all
completed
chains
L*
=
Estimated
`true'
median
chain
length
Intra-‐country
chains:
L*
=
5
Inter-‐country
chains:
L*
=
7
All
chains:
L*
=
7
Milgram:
L
*
~
8-‐9
hops
39. Network Dynamics & Simulation Science Laboratory
Attrition
rate
stays
approx.
constant
throughout
rL
–
probability
of
not
passing
on
the
message
at
distance
L
from
the
source
average
95 % confidence interval
41. Network Dynamics & Simulation Science Laboratory
Small
world
experiment
at
Columbia
Successful
chains
disproportionately
used
weak
ties
(Granovetter)
professional
ties
(34%
vs.
13%)
ties
originating
at
work/college
target's
work
(65%
vs.
40%)
.
.
.
and
disproportionately
avoided
hubs
(8%
vs.
1%)
(+
no
evidence
of
funnels)
family/friendship
ties
(60%
vs.
83%)
Strategy:
Geography
-‐>
Work
42. Network Dynamics & Simulation Science Laboratory
How
many
hops
actually
separate
any
two
individuals
in
the
world?
Participants
are
not
perfect
in
routing
messages
They
use
only
local
information
“The
accuracy
of
small
world
chains
in
social
networks”
Peter
D.
Killworth,
Chris
McCarty
,
H.
Russell
Bernard&
Mark
House:
Analyze
10920
shortest
path
connections
between
105
members
of
an
interviewing
bureau,
together
with
the
equivalent
conceptual,
or
‘small
world’
routes,
which
use
individuals’
selections
of
intermediaries.
This
permits
the
Mirst
study
of
the
impact
of
accuracy
within
small
world
chains.
The
mean
small
world
path
length
(3.23)
is
40%
longer
than
the
mean
of
the
actual
shortest
paths
(2.30)
Model
suggests
that
people
make
a
less
than
optimal
small
world
choice
more
than
half
the
time.
43. Network Dynamics & Simulation Science Laboratory
Tentative
Schedule
Week
1
–
Module
1.
December
1-‐2
(Wednesday,
&
Thursday)
Wednesday(1st
December):
Introduction
to
Network
Science
Thursday(2nd
December):
SDS
and
Diffusion
on
Networks,
Friday
(Extra
Class
if
interest):
EpiCure
–
modeling
environment
for
studying
malware
propagation
in
wireless
networks.
Week
2
–
Module
2
December
7-‐9
(Monday,
Tuesday,
Thursday)
Monday
(6th
December):
Control
and
InMluence
maximization
Tuesday
(7th
December):
Branching
process
result,
proof
of
Fastdiffuse.
Introduction
to
various
diffusion
style
modeling
environments
Wednesday
(Extra
class
if
interest):
Population
and
Network
Synthesis.
Introduction
to
graph
analysis
Thursday
(9th
December):
SIMDEMICS
and
related
modeling
environments.
Week
3
–
Module
3
and
Module
4
(December
13-‐16)
Monday
(13th
December):
Markets,
Games,
Mechanism
Design
and
SIGMA:
a
modeling
environment
to
study
commodity
markets
on
networks,
Tuesday
(14th
December):
Shortest
Paths,
Formal
language
constrained
paths,
Greedy
routing,
routing
in
small
world
networks,
Introduction
to
TRANSIMS.
Thursday
(15th
December):
Concluding
remarks,
Brief
discussion
of
uncovered
topics,
Open
Problems,
Directions
for
Future
Work.