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@MASTERSTHESIS{Bouss:889256,
      author       = {Bouss, Peter},
      othercontributors = {Stella, Alessandra and Grün, Sonja},
      title        = {{S}tatistical {E}valuation of {D}ithering {M}ethods for
                      {P}attern {D}etection},
      school       = {RWTH Aachen},
      type         = {Masterarbeit},
      address      = {Aachen},
      publisher    = {RWTH Aachen},
      reportid     = {FZJ-2021-00161},
      pages        = {114 p.},
      year         = {2020},
      note         = {Masterarbeit, RWTH Aachen, 2020},
      abstract     = {The study of neuronal activity patterns is one of the
                      high-interest topics in neurosci-entific research (Abeles
                      (2010)). It is hypothesized that highly interconnected
                      groupsof neurons, so-called cell assemblies, can be building
                      blocks for information processing(Hebb (1949); Abeles
                      (1991); Harris (2005)). One of the effects of these cell
                      assemblies’activation would be the formation of precisely
                      timed arrangements of spikes emitted bythe neurons
                      participating in an assembly (Bienenstock (1995); Izhikevich
                      (2006)). Ex-perimental evidence for millisecond precise
                      spiking activity is available for synchronypatterns (Riehle
                      et al. (1997); Kilavik et al. (2009); Torre et al. (2016))
                      and for patternswith temporal delays (Prut et al. (1998);
                      Villa and Abeles (1990); Russo and Durstewitz(2017)).One of
                      the algorithms developed in recent years to verify this
                      hypothesis is calledSPADE (Torre et al. (2013, 2016);
                      Quaglio et al. (2017); Quaglio (2019); Stella et al.(2019)),
                      which stands for Spike PAttern Detection and Evaluation.
                      This method com-pares electrophysiological data against a
                      null hypothesis. Due to the complexity of thespiking
                      recordings, this null hypothesis is not determined
                      analytically but obtained by aMonte Carlo approach, i.e., by
                      opportunely generated surrogates (Torre et al. (2013)).This
                      thesis aims to compare different surrogate methods,
                      specifically regarding theirapplication to form a
                      statistically robust null hypothesis. Thereby, we refer to a
                      sub-category of surrogate approaches called dithering
                      methods (Louis et al. (2010b)), whoseparticular feature is
                      that each spike is displaced individually within a small
                      window.We proceed in such a way that first, we summarize the
                      necessary neuroscientificbackground in chapter 1. After a
                      brief explanation of the composition of neurons, wewill
                      introduce action potentials, or spikes, that serve to
                      propagate information. Wecontrast the two standard
                      hypotheses for neural coding and provide the reasons
                      behindthe expectation to find spatio-temporal patterns.The
                      second chapter gives an overview of the theory of
                      statistical point processesused to model spike trains, i.e.,
                      sequences of spike times. We introduce the commonstatistical
                      measures used to describe electrophysiological recordings.
                      In particular, wefocus on renewal and Markov processes,
                      which allow simple modeling of stationary andnon-stationary
                      spike trains. Throughout the thesis, we consider mainly the
                      Poissonprocesses with refractoriness (PPR), an adaptation of
                      the Poisson processes, and theGamma processes. In detail, we
                      discuss their statistical properties. Furthermore, wepresent
                      a typical form of discretization of time (used in SPADE) and
                      point out the3significant implications of this approach.We
                      describe in the third chapter the particular complexity of
                      spike trains obtainedin electrophysiological recordings. As
                      an example, we refer to the reach-to-grasp dataset (Brochier
                      et al. (2018)), which was already used for analyses with
                      earlier versions ofSPADE (Torre et al. (2016)).SPADE is
                      presented explicitly in the fourth chapter. We do not only
                      provide anoverview of the entire workflow and how
                      spatio-temporal patterns are defined, but alsoexplain in
                      detail how the patterns are mined and statistically
                      evaluated.Chapter 5 presents the three dithering methods and
                      compares them against one an-other. We contrast the standard
                      approach of uniform dithering with a newly
                      introducedadaptation, which takes refractoriness into
                      account, and with the joint-ISI dithering. Foruniform
                      dithering, we analytically examine the generated surrogate
                      spike trains in termsof their statistical properties. The
                      same statistical properties are determined numeri-cally for
                      the other two methods, enabling us to compare the
                      performance of the threemethods.In the last chapter, we
                      develop a test case that allows a final assessment of
                      theperformances of the presented surrogate methods within
                      SPADE, by evaluating them interms of false positives and
                      false negatives. We can compare the results obtained by
                      thesurrogate methods against a ground truth since we
                      generate spike trains by employingthe processes presented in
                      the second chapter. Therefore, we discuss the reasons forthe
                      occurrences of false positives and false negatives.
                      Consequently, depending on thefiring rate, we recommend
                      which dithering method to use for statistically robust
                      patterndetection.In conclusion, we summarize the results of
                      this thesis and place them in the broadercontext of other
                      surrogate methods, including non-dithering methods. Finally,
                      we ad-dress the research questions raised by this thesis,
                      and we give an outlook concerningupcoming studies.},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {571 - Connectivity and Activity (POF3-571)},
      pid          = {G:(DE-HGF)POF3-571},
      typ          = {PUB:(DE-HGF)19},
      url          = {https://juser.fz-juelich.de/record/889256},
}