ainl 2016: proncheva
TRANSCRIPT
A. Mikhailov1
A. Petrov1
O. Proncheva1,2 1Keldysh Institute of Applied Mathematics (RAS)
2Moscow Institute of Physics and Technology (SU)
Mathematical modeling of information processes
AINL FRUCT: Artificial Intelligence and Natural Language
Conference
The weapon of criticism cannot, of course, replace criticism of the weapon, material force must be overthrown by material force; but theory also becomes a material force as soon as it has gripped the masses.
Marx, A Contribution to the Critique of Hegel’s Philosophy of Right (1844)
A newspaper is not only a collective propagandist and collective agitator, but also a collective organiser.
Lenin, Where To Begin (1901)
2
Information
3
Information is not entropy, information is not
uncertainty!
Thomas D. Schneider
Information is a measure of the decrease of
uncertainty.
Claude Shannon
Information is information, not matter or energy.
Norbert Wiener
Society in the information field
4
The vertical
(centralized)
flows of
information
influence
Horizontal
(interpersonal,
networking)
flows of
information
influence
The combination of these flows determines the dynamics of
information dissemination in society
Conceptual framework
Sociological argument about information
dissemination through mass-media and
interpersonal communication
5
The Rwandan genocide, known officially as the genocide against the Tutsi, was a genocidal mass slaughter of Tutsi in Rwanda by members of the Hutu majority government.
Empirical facts: The broadcasts increased militia violence not only directly by
influencing behavior in villages with radio reception, but also indirectly by increasing participation in neighboring villages.
Spillovers are estimated to have caused more militia violence than the direct effects.
(D. Yanagizawa-Drott,
Propaganda and conflict: evidence from the Rwandan Genocide» (2014))
Basic model of information attack
- the number of spreaders - external persuasion - internal persuasion - size of a group
Information dissemination without
warfare
0
dNN N N
dt
(Mikhailov A.P., Klusov N.V., 2002)
00N N
00
0 0
exp
exp
N tN N
N t N
6
0N
( )N t
Maximum agiotage: 0
1
2gN N
Information dissemination without
warfare
7
adoption of the information with forgetting 0
dXX N X X
dt
incomplete coverage of society by the media
two-steps information perception
1
2
dXX Y N X
dt
dYX Y N Y
dt
0 2dx
X N X xdt
dXx X
dt
Adoption of the information with
forgetting
8
2
0 0 04
2
sN N N
N
Steady state:
The condition for maximum agiotage 0
0 , gN N N
Incomplete coverage of society by
the media
9
Blue line– use mass-media Purple line– don’t use mass media
Two-steps information perception
10
red line - the number of spreaders blue line - the number of pre-spreaders
Successive individuals transformation: ignorants→pre-spreaders→spreaders
Information dissemination without
warfare
11
(Mikhailov A.P., Petrov A.P., Marevtseva N.A., Tretiakova I.V., 2014)
11 2 1 1 1 1 1
21 2 2 2 2 2 2
11 1 2 1
21 2 2 2
2
2
dxX X N X x x X
dt
dxX X N X x x X
dt
dXx X X X
dt
dXX X x X
dt
Information dissemination under
warfare
The necessary and sufficient condition of the victory I1
over I2
12
1 2
1 0 2 0
1 2
ln(1 ) ln(1 )2 2
N N
1 1 0
2 2 0
dXX N X Y
dt
dYY N X Y
dt
0N
X Y
1 1, 2 2,
(Mikhailov A.P., Marevtseva N.A., 2011)
The model of information warfare
with three additional factors
13
21 2 1 2 1 2
dXx X X X
dt
11 2 2 1 2 2 1
dYy Y Y Y
dt
22 2 1 2 2 2
dYy Y Y Y
dt
11 1 1 2 1 1 1 1 1 1 1 1 12
dxX X N X Y x y X x
dt
21 1 2 2 2 2 2 2 1 2 1 22
dxX X N X Y x y X x
dt
12 2 1 2 1 1 1 1 1 2 1 2 12
dyY Y N X Y x y Y x
dt
22 1 2 2 2 2 2 2 2 2 2 22
dyY Y N X Y x y Y y
dt
11 1 1 1 2 1 1
dXx X X X
dt
14
Group 1 (accessible for mass-media ) Group 2 (inaccessible for mass-media)
Strong propaganda VS virality
Intensity of forgetting γ is small
0 1 2 3 4 50
20
40
60
80
100
X1
(t),
Y1(t
)
t0 1 2 3 4 5
0
10
20
30
40
X2
(t),
Y2(t
)
t
Blue line - information source 1 (propaganda) Red line - information source 2 (virality)
Group 1 (accessible for mass-media ) Group 2 (inaccessible for mass-media)
15
Intensity of forgetting γ is large
Blue line - information source 1 (propaganda) Red line - information source 2 (virality)
0 20 40 60 80 1000
20
40
60
80
100
X1
(t),
Y1(t
)
t
0 5 10 15 200
10
20
30
40
50
X2
(t),
Y2(t
)
t
Strong propaganda VS virality
16
1
2
dXt X N X Y
dt
dYY N X Y
dt
*
1
1 *
1
, ;, 0,1,2,3...
, ;
sw
sw
t iT iT ti
h t iT t iT T
Periodic destabilizing effect on
information warfare
0 5 10 150
20
40
60
Y,X
t
Periodic destabilizing effect on information warfare
17
1
2
dXt X N X Y X
dt
dYY N X Y Y
dt
*
1
1 *
1
, ;, 0,1,2,3...
, ;
sw
sw
t iT iT ti
h t iT t iT T
(Mikhailov A.P., Petrov A.P., Proncheva O.G., Pronchev G.B.., Marevtseva N.A., 2016)
Rashevsky's neurological scheme
18
• L,B - feed braking elements
• S – external incentives
• R - reaction
• ε, j – generated incentives
• w - internal incentives
(Rashevsky N., 1933)
A model of making choices by
individuals during information warfare
in a society
19
(Petrov A.P., Maslov A.I., Tsaplin N.A., 2015)
X(t) – the number of first party
ϕ – internal propensity for response selection
N(ϕ) – distribution of individuals
N0 – size of society
ψ - shift of incentives (defined social environment) toward
the first party support
b1 и b2 - propaganda first and second party, respectively
0 1 2
0
2 , 0
t
dA C N d N b b a X N d
dt
t
X t N d
Effect of Social Polarization
20
0
0,
,4
0,
d h
NN d h d h
h
d h
Sociological sense: •society is divided into two groups, each of which has
a propensity to support "their" party
•d parameter characterizes the degree of social
polarization (how radical is each group)
•h parameter characterizes the degree of
fragmentation of each group
Equilibrium states
Consider a case
There are from 1 to 5 equilibrium states
(depending on initial conditions)
Stable equilibrium states:
21
o 1 – party 2 wins
o 3 – draw
o 5 – party 1 wins
1 2b b
Homogeneous group
22
Case of a slowly polarizing society
0 2
02
Q d h hP
h Q
0 2
02
Q d h hP
h Q
1 2A b bP
a
0A CNQ
a
Medium group
23
0 2
02
Q d h hP
h Q
1 2A b bP
a
0A CNQ
a
0 2
02
Q d h hP
h Q
Case of a slowly polarizing society
Heterogeneous group
24
1 2A b bP
a
0A CNQ
a
Case of a slowly polarizing society
