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SUMMARY:Dr Ginestra Bianconi: Simplicial complexes and emergent network geo
metry.
DESCRIPTION:Abstract: Simplicial complexes are generalized network structu
res able to encode interactions occurring between more than two nodes. Sim
plicial complex describe a large variety of complex interacting systems ra
nging from brain networks\, to social and collaboration networks. Addition
ally simplicial complexes have a geometrical interpretation and for this r
easons they have been widely used in quantum gravity. Simplicial complexes
are the ideal structures to characterize emergent network geometry [1-3]
in which geometrical properties of the networks emerge spontaneously from
their dynamics. Here we propose a general model for growing simplicial com
plexes called network geometry with flavor (NGF) [4]. This model deepens o
ur understanding of growing complex networks and reveals the important eff
ect that the dimensionality of growing simplicial complexes have on their
evolution. The NGF can generate discrete geometries of different nature\,
ranging from chains and higher dimensional manifolds to scale-free network
s with small-world properties\, scale-free degree distribution and non-tri
vial community structure. We find that\, for NGF with dimension greater th
an one\, scale-free topologies emerge also without including an explicit p
referential attachment because and efficient preferential attachment mecha
nism naturally emerges from the dynamical rules. Interestingly the NGF wit
h fitness of the nodes reveals relevant relations with quantum statistics.
In fact the faces of the NGF have generalized degrees that follow either
the Fermi-Dirac\, Boltzmann or Bose-Einstein statistics depending on their
flavor and on their dimensionality. Specifically\, NGFs with flavor s=-1\
, when constructed in dimension d=3 gluing tetrahedra along their triangul
ar faces\, have the generalized degrees of the triangular faces\, of the l
inks\, and of the nodes following respectively the Fermi-Dirac\, the Boltz
mann or the Bose-Einstein distribution.We will characterize the emergent
geometry of NGF as hyperbolic [5] and describe its properties in any di
mension.\n[1] G. Bianconi\, Interdisciplinary and physics challenges in ne
twork theory\, EPL 111\, 56001 (2015).[2] Z. Wu\, G. Menichetti C. Rahmede
G. Bianconi\, Emergent Complex Network Geometry\, Scientific Reports 5\,
10073 (2015).[3] G. Bianconi and C. Rahmede\, Complex Quantum Network Mani
folds are Scale-Free in d>2\, Scientific Reports 5\, 13979 (2015)[4] G. Bi
anconi and C. Rahmede\, Network geometry with flavor: from complexity to q
uantum geometry\, Physical Review E\, 93\, 032315. (2016).[5] G. Biancon
i and C. Rahmede\, Emergent hyperbolic network geometry Scientific Reports
7\, 41974 (2017).
URL:https://www.imperial.ac.uk/events/99886/dr-ginestra-bianconi-simplicial
-complexes-and-emergent-network-geometry/
DTSTART;TZID=Europe/London:20171010T130000
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LOCATION:United Kingdom
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