Deployment and Mobility for Animal Social Life Monitoring Based on Preferential Attachment

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M. Ilhan Akbas

Education

1 Problem deﬁnition

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 2 / 22

1 Problem deﬁnition

2 System model

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 2 / 22

1 Problem deﬁnition

2 System model

3 Deployment and mobility

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 2 / 22

1 Problem deﬁnition

2 System model

3 Deployment and mobility

4 Simulation study

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 2 / 22

1 Problem deﬁnition

2 System model

3 Deployment and mobility

4 Simulation study

5 Conclusion

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 2 / 22

Problem deﬁnition

Problem:
Eﬀort and time in wild life monitoring is intensive
Deployment of WSAN enables scalable sampling and data collection
Realistic mobility data is missing for various animal species
Objective
Deployment and mobility algorithms to model a complete system of an
animal swarm to be used for animal social life monitoring

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 4 / 22

System model

Apes equipped with sensor nodes
Actors on group leaders and speciﬁc points in the area

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 6 / 22

Gorilla social network

Complex, hierarchical social structure with speciﬁc roles

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 7 / 22

Preferential attachment based deployment (PABD)

Preferential attachment modiﬁed for ape society
P(i) = Probability of adding a link to node i

dn
 N if di < dmax
 i=1 di
P(i) =

 Pc if di ≥ dmax

Roles of nodes deﬁned after network formation

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 9 / 22

Preferential attachment based deployment (PABD)

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 10 / 22

Center of mass based deployment (CMBD)

Society is divided into subgroups
Subgroup’s COM is leader of higher level group
Can be extended easily for diﬀerent scenarios

N N
xi yi
xs = ys =
N N
i=1 i=1

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 11 / 22

Mobility

L´vy walk is observed in most animal foraging patterns
e
L´vy distribution is Fourier transformation of moving distance of a
e
single random walk

∞
1
fz,α (x) = e −izt φ(t)dt
2π −∞

Silverback moves according to L´vy walk
e

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 12 / 22

Preferential attachment based mobility (PABM)

A node moves in the same direction with highest degree neighbor
with Pm (i)

(ra ) − (di )
Pm (i) = + c1 + c2
ra

Troop moves with L´vy walk while providing possibilities for rare
e
behaviors

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 13 / 22

Center of mass based mobility (CMBM)

Subgroup leader’s neighbors move s.t. node’s position always at the
center of mass

Controlled mobile network since hierarchical structure always same

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 14 / 22

Network deployment
Deployment of 11 nodes

Degree 0 1 2 3 4 5 6 7 8 9
Pref. Att. 0 7.03 1.83 0.93 0.46 0.30 0.21 0.18 0.13 0.09
PABD 0.23 6.30 2.27 0.73 0.53 0.83 0 0 0 0

Deployment of 32 nodes

Degree 0 1 2 3 4 5 6 7 8 >8
Pref. Att. 0 20.33 5.97 2.11 1.20 0.60 0.47 0.33 0.20 0.79
PABD 0.66 17.45 5.17 2.93 2.03 3.03 0 0 0 0

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 16 / 22

Degree distribution (PABD vs Pref. Att.)

Power law linearization in log scale not observed in PABD

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 17 / 22

Percentages of roles vs. time (1)

Random walk - Most nodes depart from group

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 18 / 22

Percentages of roles vs. time (2)

PABM - Probablistic nature observed

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 19 / 22

Troop behavior (PABM vs. CMBM vs. RW)

Metric 1: Ratio of current roles to the stationary case
Metric 2: Ratio of solitary animals to all animals in the society.

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 20 / 22

Conclusion

Mode deployment and mobility algorithms to provide a complete
system of animal swarm model for animal social life monitoring

Simulation results show PABD and PABM match with the
characteristics of the animal swarm under consideration

Future steps include generalization of the algorithms for other social
systems and employment of ﬁeld data

Akbas, Brust, Ribeiro, Turgut (UCF,TIA) Deployment and Mobility December 4, 2011 22 / 22

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We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barabási and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent $\beta$ as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.

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