313,896 research outputs found
A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy
We characterize the locally finite networks admitting non-constant harmonic
functions of finite energy. Our characterization unifies the necessary
existence criteria of Thomassen and of Lyons and Peres with the sufficient
criterion of Soardi. We also extend a necessary existence criterion for
non-elusive non-constant harmonic functions of finite energy due to
Georgakopoulos
On the stability of the Kuramoto model of coupled nonlinear oscillators
We provide an analysis of the classic Kuramoto model of coupled nonlinear
oscillators that goes beyond the existing results for all-to-all networks of
identical oscillators. Our work is applicable to oscillator networks of
arbitrary interconnection topology with uncertain natural frequencies. Using
tools from spectral graph theory and control theory, we prove that for
couplings above a critical value, the synchronized state is locally
asymptotically stable, resulting in convergence of all phase differences to a
constant value, both in the case of identical natural frequencies as well as
uncertain ones. We further explain the behavior of the system as the number of
oscillators grows to infinity.Comment: 8 Pages. An earlier version appeared in the proceedings of the
American Control Conference, Boston, MA, June 200
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Collagen microarchitecture mechanically controls myofibroblast differentiation.
Altered microarchitecture of collagen type I is a hallmark of wound healing and cancer that is commonly attributed to myofibroblasts. However, it remains unknown which effect collagen microarchitecture has on myofibroblast differentiation. Here, we combined experimental and computational approaches to investigate the hypothesis that the microarchitecture of fibrillar collagen networks mechanically regulates myofibroblast differentiation of adipose stromal cells (ASCs) independent of bulk stiffness. Collagen gels with controlled fiber thickness and pore size were microfabricated by adjusting the gelation temperature while keeping their concentration constant. Rheological characterization and simulation data indicated that networks with thicker fibers and larger pores exhibited increased strain-stiffening relative to networks with thinner fibers and smaller pores. Accordingly, ASCs cultured in scaffolds with thicker fibers were more contractile, expressed myofibroblast markers, and deposited more extended fibronectin fibers. Consistent with elevated myofibroblast differentiation, ASCs in scaffolds with thicker fibers exhibited a more proangiogenic phenotype that promoted endothelial sprouting in a contractility-dependent manner. Our findings suggest that changes of collagen microarchitecture regulate myofibroblast differentiation and fibrosis independent of collagen quantity and bulk stiffness by locally modulating cellular mechanosignaling. These findings have implications for regenerative medicine and anticancer treatments
Fundamental Limits of Caching with Secure Delivery
Caching is emerging as a vital tool for alleviating the severe capacity
crunch in modern content-centric wireless networks. The main idea behind
caching is to store parts of popular content in end-users' memory and leverage
the locally stored content to reduce peak data rates. By jointly designing
content placement and delivery mechanisms, recent works have shown order-wise
reduction in transmission rates in contrast to traditional methods. In this
work, we consider the secure caching problem with the additional goal of
minimizing information leakage to an external wiretapper. The fundamental cache
memory vs. transmission rate trade-off for the secure caching problem is
characterized. Rather surprisingly, these results show that security can be
introduced at a negligible cost, particularly for large number of files and
users. It is also shown that the rate achieved by the proposed caching scheme
with secure delivery is within a constant multiplicative factor from the
information-theoretic optimal rate for almost all parameter values of practical
interest
Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities
The effects of nonlocal and reflecting connectivity are investigated in
coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange
of electrical signals between neurons. Earlier investigations have demonstrated
that non-local and hierarchical network connectivity often induces complex
synchronization patterns and chimera states in systems of coupled oscillators.
In the LIF system we show that if the elements are non-locally linked with
positive diffusive coupling in a ring architecture the system splits into a
number of alternating domains. Half of these domains contain elements, whose
potential stays near the threshold, while they are interrupted by active
domains, where the elements perform regular LIF oscillations. The active
domains move around the ring with constant velocity, depending on the system
parameters. The idea of introducing reflecting non-local coupling in LIF
networks originates from signal exchange between neurons residing in the two
hemispheres in the brain. We show evidence that this connectivity induces novel
complex spatial and temporal structures: for relatively extensive ranges of
parameter values the system splits in two coexisting domains, one domain where
all elements stay near-threshold and one where incoherent states develop with
multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure
Making Self-Stabilizing any Locally Greedy Problem
We propose a way to transform synchronous distributed algorithms solving
locally greedy and mendable problems into self-stabilizing algorithms in
anonymous networks. Mendable problems are a generalization of greedy problems
where any partial solution may be transformed -- instead of completed -- into a
global solution: every time we extend the partial solution we are allowed to
change the previous partial solution up to a given distance. Locally here means
that to extend a solution for a node, we need to look at a constant distance
from it. In order to do this, we propose the first explicit self-stabilizing
algorithm computing a -ruling set (i.e. a "maximal independent set at
distance "). By combining multiple time this technique, we compute a
distance- coloring of the graph. With this coloring we can finally simulate
\local~model algorithms running in a constant number of rounds, using the
colors as unique identifiers. Our algorithms work under the Gouda daemon, which
is similar to the probabilistic daemon: if an event should eventually happen,
it will occur under this daemon
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