**6. Acknowledgement**

The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the excellence initiative.

**System Configurations Literature**

A Technique to Compensate Fiber Dispersion and Non-Linear Impairments

10Gbit/s to 40Gbit/s i) E. Ip et al.: IEEE JLT 2008.

<sup>45</sup> Digital Backward Propagation:

> 40Gbit/s till < 100Gbit/s i) D.S Millar et al.: ECOC 2009.

> 100Gbit/s i) O.S Tanimura et al.: OFC 2009.

WDM (25GHz channel spacing) i) P. Poggiolini et al.: IEEE PTL 2011.

WDM (50GHz channel spacing) i) P. Poggiolini et al.: IEEE PTL 2011.

WDM (100GHz channel spacing) i) P. Poggiolini et al.: IEEE PTL 2011.

Table 3. Summary of the literature of DBP based on system configurations

**Algorithm Complexity Literature**

Sub-span step size i) E. Ip et al.: IEEE/LEOS 2008.

Per-span step size i) E. Ip et al.: IEEE JLT 2008.

Multi-span step size i) L. Li et al.: OFC 2011.

Table 4. Summary of the literature of DBP based on algorithm complexity

ii) C-Y Lin et al.: ECOC 2010. iii) L. Du et al.: Opt Express 2010.

ii) C-Y Lin et al.: ECOC 2010. iii) L. Du et al.: Opt Express 2010.

v) R. Asif et al.: ICTON 2011.

ii) R. Asif et al.: ICTON 2011. iii) S. Savory et al.: IEEE PTL 2010.

ii) R. Asif et al.: ICTON 2011. iii) S. Savory et al.: IEEE PTL 2010. iv) E. Mateo et al.: Opt Express 2011.

ii) G. Li: Adv Opt Photon 2009.

iii) S. Savory et al.: IEEE PTL 2010.

ii) D. Rafique et al.: Opt Express 2011. iii) L. Du et .: Opt Express 2011. iv) C-Y Lin et al.: ECOC 2010.

ii) E. Ip et al.: OFC 2011.

iii) E. Mateo et al.: Opt Express 2011. iv) D. Rafique et al.: Opt Express 2011.

ii) D. Rafique et al.: Opt Express 2011.

ii) E. Ip et al.: OFC 2011.

#### **7. Appendix A**


Table 1. Summary of the literature of DBP based on implementation methods.


Table 2. Summary of the literature of DBP based on modulation formats.

20 Will-be-set-by-IN-TECH

ii) C-Y Lin et al.: ECOC 2010. iii) E. Mateo et al.: Opt Express 2010.

ii) C-Y Lin et al.: ECOC 2010. iii) D.S Millar et al.: ECOC 2009.

ii) Du et al.: Opt Express 2010. iii) Asif et al.: Photonics North 2011.

ii) Rafique et al.: Opt Express 2011.

**Method of Implementation Literature**

Symmetric split-step Fourier method (S-SSFM) i) E. Ip et al.: IEEE JLT 2010.

Asymmetric split-step Fourier method (A-SSFM) i) E. Ip et al.: IEEE JLT 2008.

Modified split-step Fourier method (M-SSFM) i) C.Y Lin et al.: ECOC 2010.

Filtered split-step Fourier method (F-SSFM) i) L. Du et al.: Opt Express 2010.

Correlated backward propagation (CBP) i) L. Li et al.: OFC 2011.

Table 1. Summary of the literature of DBP based on implementation methods.

**Modulation Formats Literature**

DPSK, DQPSK and QPSK i) E. Ip et al.: IEEE JLT 2010.

QAM (4,16,64,256) i) D. Rafique et al.: Opt Express 2011.

POLMUX and WDM (QPSK, QAM) i) F. Yaman et al.: IEEE J.Phot 2010.

OFDM i) E. Ip et al.: IEEE JLT 2010.

Table 2. Summary of the literature of DBP based on modulation formats.

ii) C-Y Lin et al.: ECOC 2010. iii) E. Mateo et al.: App Optics 2009.

ii) S. Makovejs et al.: Opt Express 2010. iii) E. Mateo et al.: Opt Express 2011.

ii) E. Mateo et al.: Opt Express 2010. iii) R. Asif et al.: Photonics North 2011.

iii) L. Du et al.: Opt Express 2010.

ii) E. Ip et al.: OFC 2011.

Logarithmic split-step Fourier method (L-SSFM) i) R. Asif et al.: ICTON Conference 2011.

**7. Appendix A**


Table 3. Summary of the literature of DBP based on system configurations



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Nikolai Nefedov *Nokia Research Center*

*Switzerland*

**3**

*ISI Lab, Swiss Federal Institute of Technology Zurich (ETHZ)*

The recent progress in wireless technology and growing spread of smart phones equipped with various sensors make it possible to record real-world rich-content data and compliment it with on-line processing. Depending on the application, mobile data processing could help people to enrich their social interactions and improve environmental and personal health awareness. At the same time, mobile sensing data could help service providers to understand better human behavior and its dynamics, identify complex patterns of users' mobility, and to develop various service-centric and user-centric mobile applications and services on-demand. One of the first steps in analysis of rich-content mobile datasets is to find an underlying structure of users' interactions and its dynamics by clustering data according

**Multiple-Membership Communities Detection** 

**and Its Applications for Mobile Networks** 

Classification and clustering (finding groups of similar elements in data) are well-known problems which arise in many fields of sciences, e.g., (Albert & Barabási, 2002; Flake et al, 2002; Wasserman & Faust, 1994). In cases when objects are characterized by vectors of attributes, a number of efficient algorithms to find groups of similar objects based on a metric between the attribute vectors are developed. On the other hand, if data are given in the relational format (causality or dependency relations), e.g., as a network consisting of *N* nodes and *E* edges representing some relation between the nodes, then the problem of finding similar elements corresponds to detection of communities, i.e., groups of nodes which are

The growing interest to the problem of community detection was triggered by the introduction of a new clustering measure called modularity (Girvan & Newman, 2002; 2004). The modularity maximization is known as the NP-problem and currently a number of different sub-optimal algorithms are proposed, e.g., see (Fortunato, 2011) and references within. However, most of these methods address network partitions into disjoint communities. On the other hand, in practice communities are often overlapping. It is especially visible in social networks, where only limited information is available and people are affiliated to different groups, depending on professional activities, family status, hobbies, and etc. Furthermore, social interactions are reflected in multiple dimensions, such as users activities, local proximities, geo-locations and etc. These multi-dimensional traces may be presented as multi-layer graphs. It raises the problem of overlapping communities detection at different

interconnected more densely among themselves than with the rest of the network.

**1. Introduction**

to some similarity measures.

Yamazaki, E., Sano, A., Kobayashi, T., Yoshida, E. & Miyamoto, Y. (2011). Mitigation of non-linearities in optical transmission systems. *Conference on Optical Fiber communication/National Fiber Optic Engineers Conference (OFC/NFOEC) 2011*, paper OThF1, Los Angeles USA, March 2011.
