41 research outputs found
Amplitude chimeras and bump states with and without frequency entanglement: a toy model
When chaotic oscillators are coupled in complex networks a number of
interesting synchronization phenomena emerge. Notable examples are the
frequency and amplitude chimeras, chimera death states, solitary states as well
as combinations of these. In a previous study [Journal of Physics: Complexity,
2020, 1(2), 025006], a toy model was introduced addressing possible mechanisms
behind the formation of frequency chimera states. In the present study a
variation of the toy model is proposed to address the formation of amplitude
chimeras. The proposed oscillatory model is now equipped with an additional 3rd
order equation modulating the amplitude of the network oscillators. This way,
the single oscillators are constructed as bistable in amplitude and depending
on the initial conditions their amplitude may result in one of the two stable
fixed points. Numerical simulations demonstrate that when these oscillators are
nonlocally coupled in networks, they organize in domains with alternating
amplitudes (related to the two fixed points), naturally forming amplitude
chimeras. A second extension of this model incorporates nonlinear terms merging
amplitude together with frequency, and this extension allows for the
spontaneous production of composite amplitude-and-frequency chimeras occurring
simultaneously in the network. Moreover the extended model allows to understand
the emergence of bump states via the continuous passage from chimera states,
when both fixed point amplitudes are positive, to bump states when one of the
two fixed points vanishes. The proposed mechanisms of creating domains with
variable amplitudes and/or frequencies provide a generic scenario for
understanding the formation of the complex synchronization phenomena observed
in networks of coupled nonlinear and chaotic oscillators.Comment: 16 pages, 12 figures: Fig.1 (4 panels); Fig.2 (3 panels); Fig.3 (3
panels); Fig.4 (3 panels); Fig.5 (3 panels); Fig.6 (1 panel); Fig.7 (2
panels); Fig.8 (3 panels); Fig.9 (3 panels); Fig.10 (1 panel); Fig.11 (3
panels); Fig.12 (3 panels
Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab
PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from
metastatic melanoma have been analysed using fractal and multifractal analysis
to assess the impact of monoclonal antibody ipilimumab treatment with respect
to therapy outcome. Our analysis shows that the fractal dimensions which
describe the tracer dispersion in the body decrease consistently with the
deterioration of the patient therapeutic outcome condition. In 20 out-of 24
cases the fractal analysis results match those of the medical records, while 7
cases are considered as special cases because the patients have non-tumour
related medical conditions or side effects which affect the results. The
decrease in the fractal dimensions with the deterioration of the patient
conditions (in terms of disease progression) are attributed to the hierarchical
localisation of the tracer which accumulates in the affected lesions and does
not spread homogeneously throughout the body. Fractality emerges as a result of
the migration patterns which the malignant cells follow for propagating within
the body (circulatory system, lymphatic system). Analysis of the multifractal
spectrum complements and supports the results of the fractal analysis. In the
kinetic Monte Carlo modelling of the metastatic process a small number of
malignant cells diffuse throughout a fractal medium representing the blood
circulatory network. Along their way the malignant cells engender random
metastases (colonies) with a small probability and, as a result, fractal
spatial distributions of the metastases are formed similar to the ones observed
in the PET/CT images. In conclusion, we propose that fractal and multifractal
analysis has potential application in the quantification of the evaluation of
PET/CT images to monitor the disease evolution as well as the response to
different medical treatments.Comment: 38 pages, 9 figure
Coupled Intermittent Maps Modelling the Statistics of Genomic Sequences: A Network Approach
The dynamics of coupled intermittent maps is used to model the correlated
structure of genomic sequences. The use of intermittent maps, as opposed to
other simple chaotic maps, is particularly suited for the production of long
range correlation features which are observed in the genomic sequences of
higher eucaryotes. A weighted network approach to symbolic sequences is
introduced and it is shown that coupled intermittent polynomial maps produce
degree and link size distributions with power law exponents similar to the ones
observed in real genomes. The proposed network approach to symbolic sequences
is generic and can be applied to any symbol sequence (artificial or natural)
Ecological Complex Systems
Main aim of this topical issue is to report recent advances in noisy
nonequilibrium processes useful to describe the dynamics of ecological systems
and to address the mechanisms of spatio-temporal pattern formation in ecology
both from the experimental and theoretical points of view. This is in order to
understand the dynamical behaviour of ecological complex systems through the
interplay between nonlinearity, noise, random and periodic environmental
interactions. Discovering the microscopic rules and the local interactions
which lead to the emergence of specific global patterns or global dynamical
behaviour and the noises role in the nonlinear dynamics is an important, key
aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System
to appear in EPJ B, Vol. 65 (2008