Mathematics | Studies, essays, thesises » George Kampis - Dynamic Networks, Sex and Drugs and (not Rock and Roll)

Source: http://www.doksinet Dynamic  Networks:  Sex  and  Drugs   and  (not  Rock  and  Roll)   George  Kampis   Collegium  Budapest  and  Eötvös  University   gkampis@colbud.hu   Source: http://www.doksinet Sex  &  Drugs  &  Rock  &Roll   Source: http://www.doksinet Abstract:   • Network   science   offers   a   suggesKve   view   that   connects   many   domain   sciences   ranging   from   sociology   to   systems   biology.   Dynamic   networks   are   the  frontline  of  research  in  the  field,  studying  situaKons  where  the  nodes   (actors)   and   edges   (connecKons)   change   dynamically   due   to   network-­‐ internal   (and   someKmes   network-­‐external)   reasons.   The   research   of   dynamic   networks  

necessitates   new   techniques   and   concepts,   and   overwrites   much   of   our   intuiKon   and   what   we   have   learned   about   staKc   networks  so  far.   • For   example,   dynamic   human   contact   networks   invesKgated   from   a   causal   perspecKve,  such  as  required  when  studying  epidemics,  offer  radically  new   insights  and  suggesKons  for  disease  control.  Sexual  contact  networks  and   sexually   transmiSed   diseases   (such   as   AIDS)   provide   a   case   we   have   studied   extensively   using   modeling   techniques.   The   lecture   provides   an   overview   of   dynamic   networks   and   focuses   primarily   on   the   sexual   contacts   example,   to   meander   further

  to   crime   networks   and   ecological   evoluKon,   which   present   seemingly   different   problems   where,   nevertheless,  striking  parallels  can  be  drawn.   Source: http://www.doksinet          Today   • Sexual  contact  networks   • Crime  (e.g  Drug-­‐growing)  networks   • Evolving  ecosystems     Source: http://www.doksinet Networks   • A  network:  nodes  +  edges  (ie.  enKKes  and  relaKons)   • Networks  can  be  anything.   • Network  science  since  1735  ,  60-­‐70’s.  But  really  since  2000!   Source: http://www.doksinet Power  law  degree  distribuKon   Exponent  α   Source: http://www.doksinet Power  law  is  „everywhere”   • V.  Pareto:  wealth  distribuKon          

 G.K  Zipf:  word  freqency,  city  size   • Hungarian  publicaKon  and  citaKon  data  2000-­‐9   Source: http://www.doksinet Or  lognormal,  gamma?.  Long  tail!   2006   „the  new  marketplace”   Source: http://www.doksinet Average  and  STD  in  PL   • Normal  d.  vs  Powerlaw   Cf.  „average  income”,     „average  number  of  citaKons”  etc   If  α<2,  average  and  STD  diverge   If  2  <  α  <  3,  average  is  finite,  STD  diverges   Source: http://www.doksinet Betweenness  centrality   • BW:  number  of  shortest  paths  going  through  a  node   PL  networks:  hubs  (i.e  highest  degree  nodes)     are  highest  BW  nodes   Source: http://www.doksinet Networks  as  informaKon

 transmiSers   • ASack  PL  networks:  remove  hubs  (or  highest  BW)   Source: http://www.doksinet And  now.  To  sexual  networks!   Source: http://www.doksinet Sexual  networks.   hSp://www-­‐personal.umichedu/~mejn/networks/     Chains  of  AffecKon:  The  Structure  of  Adolescent  RomanKc  and   Sexual  Networks,  Peter  S.  Bearman,  James  Moody,  Katherine   Stovel,  AJS  Volume  110  Number  1  (July  2004):  44–91   An  MSM  network,  Wales  2007     Sex  Transm  Infect.  2008  Oct;84(5):377-­‐80   Epub  2008  Jul  2.InvesKgaKon  of  an   HIV  transmission  cluster  centred   in  South  Wales.Knapper  CM,  Roderick  J,  Smith   J,  Temple  M,  Birley  HD.   Source: http://www.doksinet .  are  PL  networks!  

(powerlaw  =  „scale  free”)   Network  of  Sexual  Contacts  and  Sexually   TransmiSed  HIV  InfecKon  in  Burkina  Faso,  V.   Latora  et  al.,  Journal  of  Medical  Virology  78   (2006)  724     Source: http://www.doksinet InformaKon  propagaKon:  Epidemics  on  SF  networks   Epidemic  Spreading  in  Scale-­‐Free  Networks,  Romualdo  Pastor-­‐Satorras  and  Alessandro   Vespignani  2001,  VOLUME  86,  NUMBER  14  PHYSICAL  REVIEW  LETTERS   The  spread  of  epidemic  disease  on  networks,  M.  E  J  Newman,  Phys  Rev  E  66,  016128  (2002)   Epidemic  threshold  refers  to  a  staKsKcal   statement  and  it  means  the  minimum  number   of  cases  that  need  to  be  infected  in  order  to

  assert  that  an  epidemic  (i.e  spreading)  is   taking  place.   If  2  <  α  <  3  in  an  SF  network,     the  epidemic  threshold     vanishes  as  STD  diverges   Ehm  but  we  are  sKll  here.  So   Either  not  SF,  or  some  other  conditon  is  not  met   (e.g  SIS  model  we  did  not  talk  about  yet),  or  both   Source: http://www.doksinet What  is  the  α  exponent  in  HIV?   Hamilton,  Deven  T.,  Mark  S   Handcock  and  MarKna  Morris   (2008).  Degree  distribuKons  in   sexual  networks:  A  framework   for  evaluaKng  evidence.  Sexually   Transmi=ed  Diseases,  Jan.  2008   Vol.  35  No  1   What  to  do?   • Remove  the  hubs.  Or  everybody  

gets  infected!   • (Is  this  really  the  best  advice?)   Source: http://www.doksinet Sexual  networks,  again   hSp://plaza.ufledu/garnerb/SexChartJPG     Source: http://www.doksinet So,  actually.   Aggregate  network  vs  „instant”  network   Spreading  of  an  SI  infecKon  (!),     hSp://csde.washingtonedu/~skyebend/betaMovies/10seed05take3mov     Source: http://www.doksinet The  importance  of  aggregaKon   windows   Whats  in  a  crowd?  Analysis  of  face-­‐to-­‐face  behavioral  networks,     L.  Isella  et  al  J  Theor  Biol  271  (2011)  166-­‐180   Kme-­‐evolving  degree  distribuKons   Source: http://www.doksinet InfecKousness  =  Viral  load   • HIV   • infecKon  window   0-­‐3  to  9-­‐12  weeks   • flu,  e.g

 H1N1   • infecKon  window   0  to  5-­‐6  days   Source: http://www.doksinet HIV  infecKon  along  a  causal  network   • Causal  network  =  aggregated  for  infecKon  window   Source: http://www.doksinet HIV  infecKon  along  a  causal  network   • Causal  network  =  aggregated  for  infecKon  window   AssortaKve  mixing   Source: http://www.doksinet HIV  infecKon  along  a  causal  network   • Causal  network  =  aggregated  for  infecKon  window   AssortaKve  mixing   Source: http://www.doksinet Aggregate  vs  causal  „SF”  network   • Looking  at  the  aggregate  network,  we  may  believe  it  is  impossible/ difficult  to  stop  epidemic.   • Now  in  the  causal  dynamics  network,  we  have  the  opposite

 problem:   how  to  get  a  sustained  infecKon  at  all  (such  as  in  reality)?   •  A  soluKon:  assortaKve  mixing   Source: http://www.doksinet Concurrency!   So,  to  stop/prevent  HIV  epidemics,  here  is  a  beSer  suggesKon:   -­‐  do  not  immunize/remove  the  hubs  /  high  BW  modes   -­‐  immunize/remove  the  highly  concurrent  nodes   (may  or  may  not  coincide:  a  different  parameter)   Source: http://www.doksinet A  sKll  beSer  suggesKon?  Dynamic  BW!   „classic”  betweenness  is  highly  unstable   Dynamic  (snapshot)  networks   Aggregate  network   Source: http://www.doksinet Source: http://www.doksinet Drug  networks!   Source: http://www.doksinet Terrorist  networks   Source: http://www.doksinet Crime

 networks   Source: http://www.doksinet Can  this  be  a  crime  network?   Network  diameter:  longest  path   Source: http://www.doksinet „Small  world”  networks   • Average  distance  (hence  diameter)  is  VERY   small  in  MOST  known  networks  (but  not  in   crime  networks!)     Source: http://www.doksinet Crime  networks  have  a  large  diameter   Source: http://www.doksinet Who  to  arrest  to  maximize  damage?   • Usually,  many  nodes  are  on  a  „criKcal  path”   • Again,  highest  BW  seems  to  be  a  good  candidate   Source: http://www.doksinet Dynamics  of  social  (e.g  crime  networks):   every  social  network  is  a  subnetwork   Dynamic  subnetwork  reorganizaKon:   A   B   C   Dynamic

 subnetwork  reorganizaKon:   B   C   Dynamic  subnetwork  reorganizaKon:   B   C   How  does  knowledge  of  the   embedding  network  help  idenKfying   the  nodes  to  be  removed?   • They  nodes  of  the  embedding  network  are  not  members  of  the  crime  network   (yet),  so  they  cannot  be  arrested  .   • SelecKng  the  „most  influenKal  node”  of  the  original  crime  network  (to  be   removed)  must  also  reflect  the  reorganizaKon  possibiliKes   • Removing  the  one  making  the  largest  damage,  the  possible  reorganizaKons   taken  into  account.   • A  „most  influenKal  node”  is  not  (or  not  only)  on  a  criKcal  path  (as  A)  but  on  a  

criKcal  path  to  „suitable  others”  (as  B)   • A  new  problem:  there  can  be  waaay  too  many  of  the  laSer.   • Huge  embedding  network,  shool,  prison,  workplace,  gym.   Dynamic  subnetwork  reorganizaKon  II:   A   B   C   Dynamic  subnetwork  reorganizaKon  II:   A   C   C  may  never  be  able  to  become  part     of  the  network  any  more   „Workflow”  model  of  crime:     drug  growing  (cannabis)*   Worker   Master Mind   Land   Owner   Electrician   Agronomist   Worker   Worker   Worker   *folks,  don’t  try  this  at  home     Driver   ElaboraKng  the  workflow   Worker   Master Mind   Land   Owner   Electrician   Agronomist   Worker   Worker   Worker

  Driver   Workflow  based  crime  prevenKon   E   D   A   B   C   Workflow  based  crime  prevenKon   E   D   A   B   C   Summary  and  conclusion   Dynamics,  when  taken  into  account,  may   enKrely  change  the  way  we  thing  about   networks,  e.g   – InfecKon  networks,  such  as  HIV   – Crime  networks,  such  as  drug  growing   Thank  you!