242 research outputs found
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
Probing topological invariants in the bulk of a non-Hermitian optical system
Topological insulators are insulating in the bulk but feature conducting
states on their surfaces. Standard methods for probing their topological
properties largely involve probing the surface, even though topological
invariants are defined via the bulk band structure. Here, we utilize
non-hermiticy to experimentally demonstrate a topological transition in an
optical system, using bulk behavior only, without recourse to surface
properties. This concept is relevant for a wide range of systems beyond optics,
where the surface physics is difficult to probe
Experimental realization of a topological Anderson insulator
We experimentally demonstrate that disorder can induce a topologically non-trivial phase. We implement this “Topological Anderson Insulator” in arrays of evanescently coupled waveguides and demonstrate its unique features
Convoluted -cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines
Convoluted -cosine functions and semigroups in a Banach space setting
extending the classes of fractionally integrated -cosine functions and
semigroups are systematically analyzed. Structural properties of such operator
families are obtained. Relations between convoluted -cosine functions and
analytic convoluted -semigroups, introduced and investigated in this paper
are given through the convoluted version of the abstract Weierstrass formula
which is also proved in the paper. Ultradistribution and hyperfunction sines
are connected with analytic convoluted semigroups and ultradistribution
semigroups. Several examples of operators generating convoluted cosine
functions, (analytic) convoluted semigroups as well as hyperfunction and
ultradistribution sines illustrate the abstract approach of the authors. As an
application, it is proved that the polyharmonic operator
acting on with appropriate boundary
conditions, generates an exponentially bounded -convoluted cosine
function, and consequently, an exponentially bounded analytic
-convoluted semigroup of angle for suitable
exponentially bounded kernels and $K_{n+1}.
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
Fractionation of parietal function in bistable perception probed with concurrent TMS-EEG
When visual input has conflicting interpretations, conscious perception can alternate spontaneously between these possible interpretations. This is called bistable perception. Previous neuroimaging studies have indicated the involvement of two right parietal areas in resolving perceptual ambiguity (ant-SPLr and post-SPLr). Transcranial magnetic stimulation (TMS) studies that selectively interfered with the normal function of these regions suggest that they play opposing roles in this type of perceptual switch. In the present study, we investigated this fractionation of parietal function by use of combined TMS with electroencephalography (EEG). Specifically, while participants viewed either a bistable stimulus, a replay stimulus, or resting-state fixation, we applied single pulse TMS to either location independently while simultaneously recording EEG. Combined with participant’s individual structural magnetic resonance imaging (MRI) scans, this dataset allows for complex analyses of the effect of TMS on neural time series data, which may further elucidate the causal role of the parietal cortex in ambiguous perception
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
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