Quantitative Study of Innovation and Knowledge Building in Questions&Answers System with Math Tags
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Quantitative Study of Innovation and KnowledgeBuilding in Questions&Answers System with
Math Tags
Marija Mitrovic Dankulov, Bosiljka Tadic
Scientific Computing Laboratory, Institute of Physics Belgrade
University of Belgrade, Pregrevica 118, 11080 Belgrade
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Collective Knowledge Building
Socio-cultural process which takes place trough self-organizeddynamics of interactions among individualsConditions that support collective knowledge building:
(i) Problems as an attempt to understand world/field.
(ii) Improving coherence, quality and utility of ideas.
(iii) Interaction - participants negotiate fit between theirown ideas and of others.
(iv) All participants must contribute.
(v) Knowledge-building discourse, more than knowledgesharing;. participants engage in constructing, refining andtransforming knowledge.
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Questions & Answers Sites
Rich repositories for studying dynamics of collective knowledgebuilding
On Q&A sites:
Participants ask, answer and vote for questions.
Comment and engage in discussion aboutquestions/answers.
All participants contribute trough different type of actions:posting and voting for questions, answers, comments. Theyconstruct (ask/answer), refine (comment/vote) andtransform knowledge.
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Data: Stack Exchange
Stack Exchange: where expert answers to your questions!Network of 130 Q&A sites where participants answers toinformational and factual questions.Mathematics:
Data for four year period: since the beginning (July 2010)until April 2014.
Rich dataset: 77895 Users posted 269819 Questions,400511 Answers and 1265445 Comments.
High temporal resolution.
Tags - list of up to 5 tags is assigned to each question.Overall 1040 tags: calculus, linear algebra, complexanalysis, application, . . .
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Quantitative study of knowledge building:methods
Tools and methods from statistical physics and complexnetwork theory.
Complex networks - topological structure.
Entropy measures of user activity and activity ondifferent tags.
Time series analysis - power spectrum, avalanches,fluctuations.
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Network mapping
Weighted bipartite network
Two partitions: Users andQuestions.
Link weight: number ofanswers/comments.
Structural properties ofbipartite network and it’sprojections to Question andUser partitions.
[M. Mitrovic et al., EPJB 73,
293-301, (2010).]
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Topology
Broad distributions of degree for both partitions stable overtime and tags.
100 101 102
s10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
P(s
)
1st year2nd year3rd year4th year
100 101 102 103 104
s10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
P(s
)
Users1st year2nd year3rd year4th year
100 101
q10-6
10-5
10-4
10-3
10-2
10-1
100
101
P(q
)
homeworkcalculusreal-analysislinear-algebra
100 101 102 103
q10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
P(q
)
homeworkcalculusreal-analysislinear-algebra
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Community structure
2 week activity network.Community detectionmethod - Louvainmethod. [V. D. Blondel,
JSTAT 2008 (10), P100,
(2008).]
Communities are formedaround few very activeexperts.
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Focus and expertise of users
0 1 2 3 4 5 6 7 8
H
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
number of users
Questions
0 1 2 3 4 5 6 7 8 9
H
0.00
0.05
0.10
0.15
0.20
0.25
numberofusers
Answers+Comments
User activity on separatetags - Xi = n1, . . . , nmax;Total activity Σi =
∑l ni
User’s entropy -Hi = −
∑lnlΣi
Lower Hi higher focus.
[Adamic et al., Proceedings
of WWW’08, (2008).]
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Zipf’s and Heap’s law
Heap’s law
100 101 102 103 104 105 106 107
N
100
101
102
103
104
105
D(N
)
TagsCombination of Tags
D(N) ∼ N−β ; β < 1 sublinear
growth (β = 0.27 (Tags) &
β = 0.92 (Combination of Tags)
Zipfs’s law
100 101 102 103 104 105
R
100
101
102
103
104
105
106
f(R)
TagsCombination of Tags
f(R) ∼ R−α; α = 1.47 (Tags) &
α = 1 (Combination of Tags)
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Entropy of events associated to Tag
100 101 102 103 104 105 106
K
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
S/log
(K)
datareshuffle
K - number of occurrence ofTag.
Ψ - sequence of eventsdivide into K equalintervals; fl is the numberof occurrence of Tag ininterval l;
S = −∑K
l=1flK log( flK )
S = 0 all events are in oneinterval; Smax = log(K)events are equallydistributed.
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Power spectrum
Power spectrum is of type 1f for small frequencies - long term
correlations.
100 101 102 103 104
s10-1100101102103104105106107108109
P(s
)
p(t)
binned
100 101 102 103 104
s100101102103104105106107108109
10101011
P(s
)
Na(t)
binned
100 101 102 103 104
q10-1100101102103104105106107108109
P(q
)
homeworkbinned
100 101 102 103 104
q10-1100101102103104105106107108
P(q
)
calculusbinned
0 10000 20000 30000 40000 50000 60000
t[10min]
0
5
10
15
20
25
p(t
)
New users
0 10000 20000 30000 40000 50000 60000
t[10min]
0
5
10
15
20
25
Na(t
)
all
0 10000 20000 30000 40000 50000 60000
t[10min]
0
5
10
15
20
25
N(t
)
homework
0 10000 20000 30000 40000 50000 60000
t[10min]
0
5
10
15
20
25
N(t
)
calculus
[M. Mitrovic et al., JSTAT 2011, P02005, (2011).]
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Avalanche distribution
Time series of events N(t) ⇒ time series of avalanches Si.
100 101 102 103
S
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
P(S
)
allhomeworkcalculus
100 101 102
T
10-6
10-5
10-4
10-3
10-2
10-1
100
101
P(T
)allhomeworkcalculus
78000 78500 79000 79500 80000
t
2
4
6
8
10
12
14
N(t)
time series of events
Broad distributions of avalanche sizes and duration ⇒self-organized criticality (SOC).
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Avalanche size returns
−20 −15 −10 −5 0 5 10 15 20d/σ
10-6
10-5
10-4
10-3
10-2
10-1
100
P(d
)
homeworkcalculus
Return di=Si+1 − Si+∆
P (d) = P0(1− (1− q)( dσ )2)1
1−q
SOC ⇒ peaked distributionwith fat tail.
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INSTITUTE OF PHYSICS
BELGRADEIntroduction
Network topologyEntropy measuresTemporal patterns
Summary
Summary
Collective knowledge building can be studied by applyingmethods of complex networks and statistical physics:
Complex networks - Q&A sites can be used for studyingof dynamics of collective knowledge building process.
Entropy measures - most of the users focus on fewcategories (expertise); tag specific dynamics is highlycooperative process.
Time series analysis - self-organized criticalitymechanism with long-range correlations is at the origin ofcollective knowledge building.
KnowEscape 2014| M. Mitrovic Dankulov: Quantitative study of knowledge building