201 research outputs found
Stability analysis of coupled map lattices at locally unstable fixed points
Numerical simulations of coupled map lattices (CMLs) and other complex model
systems show an enormous phenomenological variety that is difficult to classify
and understand. It is therefore desirable to establish analytical tools for
exploring fundamental features of CMLs, such as their stability properties.
Since CMLs can be considered as graphs, we apply methods of spectral graph
theory to analyze their stability at locally unstable fixed points for
different updating rules, different coupling scenarios, and different types of
neighborhoods. Numerical studies are found to be in excellent agreement with
our theoretical results.Comment: 22 pages, 6 figures, accepted for publication in European Physical
Journal
Well-Posedness and Symmetries of Strongly Coupled Network Equations
We consider a diffusion process on the edges of a finite network and allow
for feedback effects between different, possibly non-adjacent edges. This
generalizes the setting that is common in the literature, where the only
considered interactions take place at the boundary, i. e., in the nodes of the
network. We discuss well-posedness of the associated initial value problem as
well as contractivity and positivity properties of its solutions. Finally, we
discuss qualitative properties that can be formulated in terms of invariance of
linear subspaces of the state space, i. e., of symmetries of the associated
physical system. Applications to a neurobiological model as well as to a system
of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change
Multiple dynamical time-scales in networks with hierarchically nested modular organization
Many natural and engineered complex networks have intricate mesoscopic
organization, e.g., the clustering of the constituent nodes into several
communities or modules. Often, such modularity is manifested at several
different hierarchical levels, where the clusters defined at one level appear
as elementary entities at the next higher level. Using a simple model of a
hierarchical modular network, we show that such a topological structure gives
rise to characteristic time-scale separation between dynamics occurring at
different levels of the hierarchy. This generalizes our earlier result for
simple modular networks, where fast intra-modular and slow inter-modular
processes were clearly distinguished. Investigating the process of
synchronization of oscillators in a hierarchical modular network, we show the
existence of as many distinct time-scales as there are hierarchical levels in
the system. This suggests a possible functional role of such mesoscopic
organization principle in natural systems, viz., in the dynamical separation of
events occurring at different spatial scales.Comment: 10 pages, 4 figure
Synchronization, Diversity, and Topology of Networks of Integrate and Fire Oscillators
We study synchronization dynamics of a population of pulse-coupled
oscillators. In particular, we focus our attention in the interplay between
networks topological disorder and its synchronization features. Firstly, we
analyze synchronization time in random networks, and find a scaling law
which relates to networks connectivity. Then, we carry on comparing
synchronization time for several other topological configurations,
characterized by a different degree of randomness. The analysis shows that
regular lattices perform better than any other disordered network. The fact can
be understood by considering the variability in the number of links between two
adjacent neighbors. This phenomenon is equivalent to have a non-random topology
with a distribution of interactions and it can be removed by an adequate local
normalization of the couplings.Comment: 6 pages, 8 figures, LaTeX 209, uses RevTe
Quantum ergodicity for graphs related to interval maps
We prove quantum ergodicity for a family of graphs that are obtained from
ergodic one-dimensional maps of an interval using a procedure introduced by
Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take
the L^2 functions on the interval. The proof is based on the periodic orbit
expansion of a majorant of the quantum variance. Specifically, given a
one-dimensional, Lebesgue-measure-preserving map of an interval, we consider an
increasingly refined sequence of partitions of the interval. To this sequence
we associate a sequence of graphs, whose directed edges correspond to elements
of the partitions and on which the classical dynamics approximates the
Perron-Frobenius operator corresponding to the map. We show that, except
possibly for subsequences of density 0, the eigenstates of the quantum graphs
equidistribute in the limit of large graphs. For a smaller class of observables
we also show that the Egorov property, a correspondence between classical and
quantum evolution in the semiclassical limit, holds for the quantum graphs in
question.Comment: 20 pages, 1 figur
Norms of public argumentation and the ideals of correctness and participation
Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme
Bistable Percepts in the Brain: fMRI Contrasts Monocular Pattern Rivalry and Binocular Rivalry
The neural correlates of binocular rivalry have been actively debated in recent years, and are of considerable interest as they may shed light on mechanisms of conscious awareness. In a related phenomenon, monocular rivalry, a composite image is shown to both eyes. The subject experiences perceptual alternations in which the two stimulus components alternate in clarity or salience. The experience is similar to perceptual alternations in binocular rivalry, although the reduction in visibility of the suppressed component is greater for binocular rivalry, especially at higher stimulus contrasts. We used fMRI at 3T to image activity in visual cortex while subjects perceived either monocular or binocular rivalry, or a matched non-rivalrous control condition. The stimulus patterns were left/right oblique gratings with the luminance contrast set at 9%, 18% or 36%. Compared to a blank screen, both binocular and monocular rivalry showed a U-shaped function of activation as a function of stimulus contrast, i.e. higher activity for most areas at 9% and 36%. The sites of cortical activation for monocular rivalry included occipital pole (V1, V2, V3), ventral temporal, and superior parietal cortex. The additional areas for binocular rivalry included lateral occipital regions, as well as inferior parietal cortex close to the temporoparietal junction (TPJ). In particular, higher-tier areas MT+ and V3A were more active for binocular than monocular rivalry for all contrasts. In comparison, activation in V2 and V3 was reduced for binocular compared to monocular rivalry at the higher contrasts that evoked stronger binocular perceptual suppression, indicating that the effects of suppression are not limited to interocular suppression in V1
Topological Photonics
Topology is revolutionizing photonics, bringing with it new theoretical
discoveries and a wealth of potential applications. This field was inspired by
the discovery of topological insulators, in which interfacial electrons
transport without dissipation even in the presence of impurities. Similarly,
new optical mirrors of different wave-vector space topologies have been
constructed to support new states of light propagating at their interfaces.
These novel waveguides allow light to flow around large imperfections without
back-reflection. The present review explains the underlying principles and
highlights the major findings in photonic crystals, coupled resonators,
metamaterials and quasicrystals.Comment: progress and review of an emerging field, 12 pages, 6 figures and 1
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