752 research outputs found
Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
We study the collective dynamics of noise-driven excitable elements,
so-called active rotators. Crucially here, the natural frequencies and the
individual coupling strengths are drawn from some joint probability
distribution. Combining a mean-field treatment with a Gaussian approximation
allows us to find examples where the infinite-dimensional system is reduced to
a few ordinary differential equations. Our focus lies in the cooperative
behavior in a population consisting of two parts, where one is composed of
excitable elements, while the other one contains only self-oscillatory units.
Surprisingly, excitable behavior in the whole system sets in only if the
excitable elements have a smaller coupling strength than the self-oscillating
units. In this way positive local correlations between natural frequencies and
couplings shape the global behavior of mixed populations of excitable and
oscillatory elements.Comment: 10 pages, 6 figures, published in Eur. Phys. J.
G/G Models and W_N strings
We derive the BRST cohomology of the G/G topological model for the case of
A^{(1)}_{N-1} . It is shown that at level k={p/q}-N the latter describes the
(p,q) W_N minimal model coupled to gravity (plus some extra ``topological
sectors").Comment: 17 page
Excitable elements controlled by noise and network structure
We study collective dynamics of complex networks of stochastic excitable
elements, active rotators. In the thermodynamic limit of infinite number of
elements, we apply a mean-field theory for the network and then use a Gaussian
approximation to obtain a closed set of deterministic differential equations.
These equations govern the order parameters of the network. We find that a
uniform decrease in the number of connections per element in a homogeneous
network merely shifts the bifurcation thresholds without producing qualitative
changes in the network dynamics. In contrast, heterogeneity in the number of
connections leads to bifurcations in the excitable regime. In particular we
show that a critical value of noise intensity for the saddle-node bifurcation
decreases with growing connectivity variance. The corresponding critical values
for the onset of global oscillations (Hopf bifurcation) show a non-monotone
dependency on the structural heterogeneity, displaying a minimum at moderate
connectivity variances.Comment: 13 pages, 6 figure
Networks of noisy oscillators with correlated degree and frequency dispersion
We investigate how correlations between the diversity of the connectivity of
networks and the dynamics at their nodes affect the macroscopic behavior. In
particular, we study the synchronization transition of coupled stochastic phase
oscillators that represent the node dynamics. Crucially in our work, the
variability in the number of connections of the nodes is correlated with the
width of the frequency distribution of the oscillators. By numerical
simulations on Erd\"os-R\'enyi networks, where the frequencies of the
oscillators are Gaussian distributed, we make the counterintuitive observation
that an increase in the strength of the correlation is accompanied by an
increase in the critical coupling strength for the onset of synchronization. We
further observe that the critical coupling can solely depend on the average
number of connections or even completely lose its dependence on the network
connectivity. Only beyond this state, a weighted mean-field approximation
breaks down. If noise is present, the correlations have to be stronger to yield
similar observations.Comment: 6 pages, 2 figure
Physical States in G/G Models and 2d Gravity
An analysis of the BRST cohomology of the G/G topological models is performed
for the case of . Invoking a special free field parametrization of
the various currents, the cohomology on the corresponding Fock space is
extracted. We employ the singular vector structure and fusion rules to
translate the latter into the cohomology on the space of irreducible
representations. Using the physical states we calculate the characters and
partition function, and verify the index interpretation. We twist the
energy-momentum tensor to establish an intriguing correspondence between the
model with level and models
coupled to gravity.Comment: 42 page
c=1 String Theory as a Topological G/G Model
The physical states on the free field Fock space of the {SL(2,R)\over
SL(2,R) model at any level are computed. Using a similarity transformation on
, the cohomology of the latter is mapped into a direct sum of simpler
cohomologies. We show a one to one correspondence between the states of the
model and those of the string model. A full equivalence between
the {SL(2,R)\over SL(2,R) and {SL(2,R)\over U(1) models at the level of
their Fock space cohomologies is found.Comment: 19
Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories
We study the low-energy effective theory in N=2 super Yang-Mills theories by
microscopic and exact approaches. We calculate the one-instanton correction to
the prepotential for any simple Lie group from the microscopic approach. We
also study the Picard-Fuchs equations and their solutions in the semi-
classical regime for classical gauge groups with rank r \leq 3. We find that
for gauge groups G=A_r, B_r, C_r (r \leq 3) the microscopic results agree with
those from the exact solutions.Comment: 34 pages, LaTe
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