19,297 research outputs found
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
Reconfiguration on sparse graphs
A vertex-subset graph problem Q defines which subsets of the vertices of an
input graph are feasible solutions. A reconfiguration variant of a
vertex-subset problem asks, given two feasible solutions S and T of size k,
whether it is possible to transform S into T by a sequence of vertex additions
and deletions such that each intermediate set is also a feasible solution of
size bounded by k. We study reconfiguration variants of two classical
vertex-subset problems, namely Independent Set and Dominating Set. We denote
the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete
on graphs of bounded bandwidth and W[1]-hard parameterized by k on general
graphs. We show that ISR is fixed-parameter tractable parameterized by k when
the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we
answer positively an open question concerning the parameterized complexity of
the problem on graphs of bounded treewidth. Moreover, our techniques generalize
recent results showing that ISR is fixed-parameter tractable on planar graphs
and graphs of bounded degree. For DSR, we show the problem fixed-parameter
tractable parameterized by k when the input graph does not contain large
bicliques, a class of graphs which includes graphs of bounded degeneracy and
nowhere-dense graphs
Reconfiguring Independent Sets in Claw-Free Graphs
We present a polynomial-time algorithm that, given two independent sets in a
claw-free graph , decides whether one can be transformed into the other by a
sequence of elementary steps. Each elementary step is to remove a vertex
from the current independent set and to add a new vertex (not in )
such that the result is again an independent set. We also consider the more
restricted model where and have to be adjacent
Short-time Critical Dynamics of the 3-Dimensional Ising Model
Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are
reported for the three-dimensional Ising model at criticality. Besides the
exponent of the critical initial increase and the dynamic exponent
, the static critical exponents and as well as the critical
temperature are determined from the power-law scaling behaviour of observables
at the beginning of the time evolution. States of very high temperature as well
as of zero temperature are used as initial states for the simulations.Comment: 8 pages with 7 figure
Perceptions of Multicultural Training in Predoctoral Internship Programs: A Survey of Interns and Training Directors
Multicultural training at internship sites is a critical component in the preparation of doctoral-level psychologists, so the quality of this training is of the utmost importance. In the following study, the authors examine multicultural training from the perspective of predoctoral interns and training directors at counseling center sites that offer a major or minor rotation in multicultural therapy. Results suggest that perspectives vary between interns and training directors and that there is a great difference in the type of criteria used by each site as evidence of a major or minor rotation. The need for more standardized criteria to define major and minor rotations and suggestions for the Association of Psychology Postdoctoral and Internship Centers, internship training directors, and prospective interns are discussed
Optimized coupling of cold atoms into a fiber using a blue-detuned hollow-beam funnel
We theoretically investigate the process of coupling cold atoms into the core
of a hollow-core photonic-crystal optical fiber using a blue-detuned
Laguerre-Gaussian beam. In contrast to the use of a red-detuned Gaussian beam
to couple the atoms, the blue-detuned hollow-beam can confine cold atoms to the
darkest regions of the beam thereby minimizing shifts in the internal states
and making the guide highly robust to heating effects. This single optical beam
is used as both a funnel and guide to maximize the number of atoms into the
fiber. In the proposed experiment, Rb atoms are loaded into a magneto-optical
trap (MOT) above a vertically-oriented optical fiber. We observe a
gravito-optical trapping effect for atoms with high orbital momentum around the
trap axis, which prevents atoms from coupling to the fiber: these atoms lack
the kinetic energy to escape the potential and are thus trapped in the laser
funnel indefinitely. We find that by reducing the dipolar force to the point at
which the trapping effect just vanishes, it is possible to optimize the
coupling of atoms into the fiber. Our simulations predict that by using a
low-power (2.5 mW) and far-detuned (300 GHz) Laguerre-Gaussian beam with a
20-{\mu}m radius core hollow-fiber it is possible to couple 11% of the atoms
from a MOT 9 mm away from the fiber. When MOT is positioned further away,
coupling efficiencies over 50% can be achieved with larger core fibers.Comment: 11 pages, 12 figures, 1 tabl
On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
We investigate supergroups with Grassmann parameters replaced by odd Clifford
parameters. The connection with non-anticommutative supersymmetry is discussed.
A Berezin-like calculus for odd Clifford variables is introduced. Fermionic
covariant derivatives for supergroups with odd Clifford variables are derived.
Applications to supersymmetric quantum mechanics are made. Deformations of the
original supersymmetric theories are encountered when the fermionic covariant
derivatives do not obey the graded Leibniz property. The simplest non-trivial
example is given by the N=2 SQM with a real multiplet and a cubic
potential. The action is real. Depending on the overall sign ("Euclidean" or
"Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian
hamiltonian is encountered when solving the equation of motion of the auxiliary
field. A possible connection of our framework with the Drinfeld twist
deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page
Independent Set Reconfiguration in Cographs
We study the following independent set reconfiguration problem, called
TAR-Reachability: given two independent sets and of a graph , both
of size at least , is it possible to transform into by adding and
removing vertices one-by-one, while maintaining an independent set of size at
least throughout? This problem is known to be PSPACE-hard in general. For
the case that is a cograph (i.e. -free graph) on vertices, we show
that it can be solved in time , and that the length of a shortest
reconfiguration sequence from to is bounded by , if such a
sequence exists.
More generally, we show that if is a graph class for which (i)
TAR-Reachability can be solved efficiently, (ii) maximum independent sets can
be computed efficiently, and which satisfies a certain additional property,
then the problem can be solved efficiently for any graph that can be obtained
from a collection of graphs in using disjoint union and complete join
operations. Chordal graphs are given as an example of such a class
The Engagement Model of Person-Environment Interaction
This article focuses on growth-promoting aspects in the environment, and the authors propose a strength-based, dynamic model of person-environment interaction. The authors begin by briefly discussing the typical recognition of contextual variables in models that rely on the concept of person-environment fit. This is followed by a review of recent approaches to incorporating positive environmental factors in conceptualizations of human functioning. These approaches lead to an alternative model of person-environment interaction in which the engagement construct (i.e., the quality of a person-environment relationship determined by the extent to which negotiation, participation, and evaluation processes occur during the interaction) replaces the static notion of fit. Finally, the authors outline recommendations for overcoming environmental neglect in research, practice, and training
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