ainl 2016: proncheva

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

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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

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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

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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

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Blue line– use mass-media Purple line– don’t use mass media

Two-steps information perception

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red line - the number of spreaders blue line - the number of pre-spreaders

Successive individuals transformation: ignorants→pre-spreaders→spreaders

Information dissemination without

warfare

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(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

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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

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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

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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)

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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

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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

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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

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• 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

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(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

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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:

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o 1 – party 2 wins

o 3 – draw

o 5 – party 1 wins

1 2b b

Homogeneous group

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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

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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

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1 2A b bP

a

0A CNQ

a

Case of a slowly polarizing society

Thank you for your attention!

Proncheva Olga

Olga.proncheva@gmail.com

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