2,144 research outputs found
Delayed feedback as a means of control of noise-induced motion
Time--delayed feedback is exploited for controlling noise--induced motion in
coherence resonance oscillators. Namely, under the proper choice of time delay,
one can either increase or decrease the regularity of motion. It is shown that
in an excitable system, delayed feedback can stabilize the frequency of
oscillations against variation of noise strength. Also, for fixed noise
intensity, the phenomenon of entrainment of the basic oscillation period by the
delayed feedback occurs. This allows one to steer the timescales of
noise-induced motion by changing the time delay.Comment: 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d)
were amended. The reason is numerical error found, that affected the
quantitative estimates of correlation time, but did not affect the main
messag
Monotone graph limits and quasimonotone graphs
The recent theory of graph limits gives a powerful framework for
understanding the properties of suitable (convergent) sequences of
graphs in terms of a limiting object which may be represented by a symmetric
function on , i.e., a kernel or graphon. In this context it is
natural to wish to relate specific properties of the sequence to specific
properties of the kernel. Here we show that the kernel is monotone (i.e.,
increasing in both variables) if and only if the sequence satisfies a
`quasi-monotonicity' property defined by a certain functional tending to zero.
As a tool we prove an inequality relating the cut and norms of kernels of
the form with and monotone that may be of interest in its
own right; no such inequality holds for general kernels.Comment: 38 page
Consequences of critical interchain couplings and anisotropy on a Haldane chain
Effects of interchain couplings and anisotropy on a Haldane chain have been
investigated by single crystal inelastic neutron scattering and density
functional theory (DFT) calculations on the model compound SrNiVO.
Significant effects on low energy excitation spectra are found where the
Haldane gap (; where is the intrachain exchange
interaction) is replaced by three energy minima at different antiferromagnetic
zone centers due to the complex interchain couplings. Further, the triplet
states are split into two branches by single-ion anisotropy. Quantitative
information on the intrachain and interchain interactions as well as on the
single-ion anisotropy are obtained from the analyses of the neutron scattering
spectra by the random phase approximation (RPA) method. The presence of
multiple competing interchain interactions is found from the analysis of the
experimental spectra and is also confirmed by the DFT calculations. The
interchain interactions are two orders of magnitude weaker than the
nearest-neighbour intrachain interaction = 8.7~meV. The DFT calculations
reveal that the dominant intrachain nearest-neighbor interaction occurs via
nontrivial extended superexchange pathways Ni--O--V--O--Ni involving the empty
orbital of V ions. The present single crystal study also allows us to
correctly position SrNiVO in the theoretical - phase
diagram [T. Sakai and M. Takahashi, Phys. Rev. B 42, 4537 (1990)] showing where
it lies within the spin-liquid phase.Comment: 12 pages, 12 figures, 3 tables PRB (accepted). in Phys. Rev. B (2015
Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.
A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles’ behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived
Degree distributions of growing networks
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each immediately attach to a pre-existing node, and (ii) creation of new links between pre-existing nodes. This process naturally generates correlated in- and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained
Distance distribution in random graphs and application to networks exploration
We consider the problem of determining the proportion of edges that are
discovered in an Erdos-Renyi graph when one constructs all shortest paths from
a given source node to all other nodes. This problem is equivalent to the one
of determining the proportion of edges connecting nodes that are at identical
distance from the source node. The evolution of this quantity with the
probability of existence of the edges exhibits intriguing oscillatory behavior.
In order to perform our analysis, we introduce a new way of computing the
distribution of distances between nodes. Our method outperforms previous
similar analyses and leads to estimates that coincide remarkably well with
numerical simulations. It allows us to characterize the phase transitions
appearing when the connectivity probability varies.Comment: 12 pages, 8 figures (18 .eps files
The cut metric, random graphs, and branching processes
In this paper we study the component structure of random graphs with
independence between the edges. Under mild assumptions, we determine whether
there is a giant component, and find its asymptotic size when it exists. We
assume that the sequence of matrices of edge probabilities converges to an
appropriate limit object (a kernel), but only in a very weak sense, namely in
the cut metric. Our results thus generalize previous results on the phase
transition in the already very general inhomogeneous random graph model we
introduced recently, as well as related results of Bollob\'as, Borgs, Chayes
and Riordan, all of which involve considerably stronger assumptions. We also
prove corresponding results for random hypergraphs; these generalize our
results on the phase transition in inhomogeneous random graphs with clustering.Comment: 53 pages; minor edits and references update
Dynamic scaling regimes of collective decision making
We investigate a social system of agents faced with a binary choice. We
assume there is a correct, or beneficial, outcome of this choice. Furthermore,
we assume agents are influenced by others in making their decision, and that
the agents can obtain information that may guide them towards making a correct
decision. The dynamic model we propose is of nonequilibrium type, converging to
a final decision. We run it on random graphs and scale-free networks. On random
graphs, we find two distinct regions in terms of the "finalizing time" -- the
time until all agents have finalized their decisions. On scale-free networks on
the other hand, there does not seem to be any such distinct scaling regions
- …