22,352 research outputs found
Transient localized wave patterns and their application to migraine
Transient dynamics is pervasive in the human brain and poses challenging
problems both in mathematical tractability and clinical observability. We
investigate statistical properties of transient cortical wave patterns with
characteristic forms (shape, size, duration) in a canonical reaction-diffusion
model with mean field inhibition. The patterns are formed by a ghost near a
saddle-node bifurcation in which a stable traveling wave (node) collides with
its critical nucleation mass (saddle). Similar patterns have been observed with
fMRI in migraine. Our results support the controversial idea that waves of
cortical spreading depression (SD) have a causal relationship with the headache
phase in migraine and therefore occur not only in migraine with aura (MA) but
also in migraine without aura (MO), i.e., in the two major migraine subforms.
We suggest a congruence between the prevalence of MO and MA with the
statistical properties of the traveling waves' forms, according to which (i)
activation of nociceptive mechanisms relevant for headache is dependent upon a
sufficiently large instantaneous affected cortical area anti-correlated to both
SD duration and total affected cortical area such that headache would be less
severe in MA than in MO (ii) the incidence of MA is reflected in the distance
to the saddle-node bifurcation, and (iii) the contested notion of MO attacks
with silent aura is resolved. We briefly discuss model-based control and means
by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure
Non-Markovian decoherence in the adiabatic quantum search algorithm
We consider an adiabatic quantum algorithm (Grover's search routine) weakly
coupled to a rather general environment, i.e., without using the Markov
approximation. Markovian errors generally require high-energy excitations (of
the reservoir) and tend to destroy the scalability of the adiabatic quantum
algorithm. We find that, under appropriate conditions (such as low
temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most
important. Hence the scalability of the adiabatic quantum algorithm depends on
the infra-red behavior of the environment: a reasonably small coupling to the
three-dimensional electromagnetic field does not destroy the scaling behavior,
whereas phonons or localized degrees of freedom can be problematic. PACS:
03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz
Synchrotron and Synchrotron Self-Compton Spectral Signatures and Blazar Emission Models
We find that energy losses due to synchrotron self-Compton (SSC) emission in
blazar jets can produce distinctive signatures in the time-averaged synchrotron
and SSC spectra of these objects. For a fairly broad range of particle
injection distributions, SSC-loss dominated synchrotron emission exhibits a
spectral dependence . The presence or absence of this
dependence in the optical and ultraviolet spectra of flat spectrum radio
quasars such as 3C~279 and in the soft X-ray spectra of high frequency BL Lac
objects such as Mrk 501 gives a robust measure of the importance of SSC losses.
Furthermore, for partially cooled particle distributions, spectral breaks of
varying sizes can appear in the synchrotron and SSC spectra and will be related
to the spectral indices of the emission below the break. These spectral
signatures place constraints on the size scale and the non-thermal particle
content of the emitting plasma as well as the observer orientation relative to
the jet axis.Comment: 4 pages, 1 figure, LaTeX2e, emulateapj5.sty, accepted for publication
in Ap
Decelerated spreading in degree-correlated networks
While degree correlations are known to play a crucial role for spreading
phenomena in networks, their impact on the propagation speed has hardly been
understood. Here we investigate a tunable spreading model on scale-free
networks and show that the propagation becomes slow in positively (negatively)
correlated networks if nodes with a high connectivity locally accelerate
(decelerate) the propagation. Examining the efficient paths offers a coherent
explanation for this result, while the -core decomposition reveals the
dependence of the nodal spreading efficiency on the correlation. Our findings
should open new pathways to delicately control real-world spreading processes
Numerical equilibrium analysis for structured consumer resource models
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for âDaphnia consuming algaeâ models in C-code. The results obtained by way of this implementation are shown in the form of graphs
Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk
We propose a new method to construct an isotropic cellular automaton
corresponding to a reaction-diffusion equation. The method consists of
replacing the diffusion term and the reaction term of the reaction-diffusion
equation with a random walk of microscopic particles and a discrete vector
field which defines the time evolution of the particles. The cellular automaton
thus obtained can retain isotropy and therefore reproduces the patterns found
in the numerical solutions of the reaction-diffusion equation. As a specific
example, we apply the method to the Belousov-Zhabotinsky reaction in excitable
media
- âŚ