arXiv (Cornell University),
Год журнала:
2023,
Номер
unknown
Опубликована: Янв. 1, 2023
These
are
exciting
times
for
quantum
physics
as
new
technologies
expected
to
soon
transform
computing
at
an
unprecedented
level.
Simultaneously
network
science
is
flourishing
proving
ideal
mathematical
and
computational
framework
capture
the
complexity
of
large
interacting
systems.
Here
we
provide
a
comprehensive
timely
review
rising
field
complex
networks.
On
one
side,
this
subject
key
harness
potential
networks
in
order
design
principles
boost
enhance
algorithms
technologies.
other
side
can
generation
infer
significant
properties.
The
features
fundamental
research
questions
diverse
designing
shape
Hamiltonians
their
corresponding
phase
diagram,
taming
many-body
systems
with
theory,
revealing
how
predict
novel
properties
transitions,
studying
interplay
between
architecture,
topology
performance
communication
Our
covers
all
these
multifaceted
aspects
self-contained
presentation
aimed
both
network-curious
physicists
quantum-curious
theorists.
We
that
unifies
along
four
main
lines:
network-generalized,
quantum-applied,
quantum-generalized
quantum-enhanced.
Finally
draw
attention
connections
lines,
which
lead
opportunities
discoveries
interface
science.
Journal of Physics A Mathematical and Theoretical,
Год журнала:
2024,
Номер
57(23), С. 233001 - 233001
Опубликована: Апрель 22, 2024
Abstract
These
are
exciting
times
for
quantum
physics
as
new
technologies
expected
to
soon
transform
computing
at
an
unprecedented
level.
Simultaneously
network
science
is
flourishing
proving
ideal
mathematical
and
computational
framework
capture
the
complexity
of
large
interacting
systems.
Here
we
provide
a
comprehensive
timely
review
rising
field
complex
networks.
On
one
side,
this
subject
key
harness
potential
networks
in
order
design
principles
boost
enhance
algorithms
technologies.
other
side
can
generation
infer
significant
properties.
The
features
fundamental
research
questions
diverse
designing
shape
Hamiltonians
their
corresponding
phase
diagram,
taming
many-body
systems
with
theory,
revealing
how
predict
novel
properties
transitions,
studying
interplay
between
architecture,
topology
performance
communication
Our
covers
all
these
multifaceted
aspects
self-contained
presentation
aimed
both
network-curious
physicists
quantum-curious
theorists.
We
that
unifies
along
four
main
lines:
network-generalized,
quantum-applied,
quantum-generalized
quantum-enhanced.
Finally
draw
attention
connections
lines,
which
lead
opportunities
discoveries
interface
science.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(5)
Опубликована: Май 1, 2024
Simplicial
Kuramoto
models
have
emerged
as
a
diverse
and
intriguing
class
of
describing
oscillators
on
simplices
rather
than
nodes.
In
this
paper,
we
present
unified
framework
to
describe
different
variants
these
models,
categorized
into
three
main
groups:
“simple”
“Hodge-coupled”
“order-coupled”
(Dirac)
models.
Our
is
based
topology
discrete
differential
geometry,
well
gradient
systems
frustrations,
permits
systematic
analysis
their
properties.
We
establish
an
equivalence
between
the
simple
simplicial
model
standard
pairwise
networks
under
condition
manifoldness
complex.
Then,
starting
from
notion
synchronization
derive
bounds
coupling
strength
necessary
or
sufficient
for
achieving
it.
For
some
variants,
generalize
results
provide
new
ones,
such
controllability
equilibrium
solutions.
Finally,
explore
potential
application
in
reconstruction
brain
functional
connectivity
structural
connectomes
find
that
edge-based
perform
competitively
even
outperform
complex
extensions
node-based
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2023,
Номер
33(3)
Опубликована: Март 1, 2023
We
propose
Local
Dirac
Synchronization
that
uses
the
operator
to
capture
dynamics
of
coupled
nodes
and
link
signals
on
an
arbitrary
network.
In
Synchronization,
harmonic
modes
oscillate
freely
while
other
are
interacting
non-linearly,
leading
a
collectively
synchronized
state
when
coupling
constant
model
is
increased.
characterized
by
discontinuous
transitions
emergence
rhythmic
coherent
phase.
this
phase,
one
two
complex
order
parameters
oscillates
in
plane
at
slow
frequency
(called
emergent
frequency)
frame
which
intrinsic
frequencies
have
zero
average.
Our
theoretical
results
obtained
within
annealed
approximation
validated
extensive
numerical
fully
connected
networks
sparse
Poisson
scale-free
networks.
both
random
real
networks,
such
as
connectome
Caenorhabditis
Elegans,
reveals
interplay
between
topology
(Betti
numbers
modes)
non-linear
dynamics.
This
unveils
how
might
play
role
onset
brain
rhythms.
Scientific Reports,
Год журнала:
2023,
Номер
13(1)
Опубликована: Июль 11, 2023
Molecular
representations
are
of
fundamental
importance
for
the
modeling
and
analysing
molecular
systems.
The
successes
in
drug
design
materials
discovery
have
been
greatly
contributed
by
representation
models.
In
this
paper,
we
present
a
computational
framework
that
is
mathematically
rigorous
based
on
persistent
Dirac
operator.
properties
discrete
weighted
unweighted
matrix
systematically
discussed,
biological
meanings
both
homological
non-homological
eigenvectors
studied.
We
also
evaluate
impact
various
weighting
schemes
matrix.
Additionally,
set
physical
attributes
characterize
persistence
variation
spectrum
matrices
during
filtration
process
proposed
to
be
fingerprints.
Our
used
classify
configurations
nine
different
types
organic-inorganic
halide
perovskites.
combination
with
gradient
boosting
tree
model
has
achieved
great
success
solvation
free
energy
prediction.
results
show
our
effective
characterizing
structures,
demonstrating
power
featurization
approach.
Physical Review Research,
Год журнала:
2024,
Номер
6(1)
Опубликована: Янв. 12, 2024
In
this
paper,
we
develop
a
bipartite
network
framework
to
study
the
robustness
of
interdependent
hypergraphs.
From
such
perspective,
nodes
and
hyperedges
hypergraph
are
equivalent
each
other,
property
that
largely
simplifies
their
mathematical
treatment.
We
general
percolation
theory
based
on
representation
apply
it
hypergraphs
against
random
damage,
which
verify
with
numerical
simulations.
analyze
variety
interacting
patterns,
from
heterogeneous
correlated
hyperstructures,
full-
partial-dependency
couplings
between
an
arbitrary
number
hypergraphs,
characterize
structural
stability
via
phase
diagrams.
Given
its
generality,
expect
our
will
provide
useful
insights
for
development
more
realistic
venues
cascading
failures
in
higher-order
systems.
Published
by
American
Physical
Society
2024
Foundations of Data Science,
Год журнала:
2024,
Номер
6(2), С. 124 - 153
Опубликована: Янв. 1, 2024
This
work
introduces
the
development
of
path
Dirac
and
hypergraph
operators,
along
with
an
exploration
their
persistence.
These
operators
excel
in
distinguishing
between
harmonic
non-harmonic
spectra,
offering
valuable
insights
into
subcomplexes
within
these
structures.
The
paper
showcases
functionality
through
a
series
examples
various
contexts.
An
essential
facet
this
research
involves
examining
operators'
sensitivity
to
filtration,
emphasizing
capacity
adapt
topological
changes.
also
explores
significant
application
persistent
molecular
science,
specifically
analyzing
study
strict
preorders
derived
from
structures,
which
generate
graphs
digraphs
intricate
depth
information
complexes
reflects
complexity
different
preorder
classes
influenced
by
characteristic
underscores
effectiveness
tools
realm
data
analysis.
Journal of Physics A Mathematical and Theoretical,
Год журнала:
2023,
Номер
57(1), С. 015001 - 015001
Опубликована: Ноя. 24, 2023
Abstract
We
propose
a
theoretical
framework
that
explains
how
the
mass
of
simple
and
higher-order
networks
emerges
from
their
topology
geometry.
use
discrete
topological
Dirac
operator
to
define
an
action
for
massless
self-interacting
field
inspired
by
Nambu–Jona-Lasinio
model.
The
network
is
strictly
speaking
this
defined
on
network;
it
results
chiral
symmetry
breaking
model
satisfies
self-consistent
gap
equation.
Interestingly,
shown
depends
its
spectral
properties,
topology,
Due
matter–antimatter
observed
harmonic
modes
operator,
two
possible
definitions
can
be
given.
For
both
definitions,
comes
equation
with
difference
among
encoded
in
value
bare
mass.
Indeed,
determined
either
Betti
number
β
0
or
1
network.
provide
numerical
different
networks,
including
random
graphs,
scale-free,
real
weighted
collaboration
networks.
also
discuss
generalization
these
defining
simplicial
complexes.
dependence
considered
geometry
could
lead
interesting
physics
scenario
which
coupled
dynamical
evolution
underlying
structure.
Chaos Solitons & Fractals,
Год журнала:
2023,
Номер
177, С. 114296 - 114296
Опубликована: Ноя. 22, 2023
Higher-order
networks
are
gaining
significant
scientific
attention
due
to
their
ability
encode
the
many-body
interactions
present
in
complex
systems.
However,
higher-order
have
limitation
that
they
only
capture
of
same
type.
To
address
this
limitation,
we
a
mathematical
framework
determines
topology
multiplex
and
illustrates
interplay
between
dynamics.
Specifically,
examine
diffusion
topological
signals
associated
not
nodes
but
also
links
higher-dimensional
simplices
simplicial
complexes.
We
leverage
on
ubiquitous
presence
overlap
couple
dynamics
among
layers,
introducing
definition
Hodge
Laplacians
Dirac
operators.
show
spectral
properties
these
operators
determine
Betti
numbers.
Our
numerical
investigation
synthetic
real
(connectome,
microbiome)
complexes
indicates
coupling
layers
can
either
speed
up
or
slow
down
signals.
This
is
very
general
be
applied
study
generic
systems
with
multiple
types.
In
particular,
results
might
find
applications
brain
which
understood
both
multilayer
higher-order.
