4,598 research outputs found
Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs
We study the effects of nonzero time delays in stochastic synchronization
problems with linear couplings in an arbitrary network. Using the known exact
threshold value from the theory of differential equations with delays, we
provide the synchronizability threshold for an arbitrary network. Further, by
constructing the scaling theory of the underlying fluctuations, we establish
the absolute limit of synchronization efficiency in a noisy environment with
uniform time delays, i.e., the minimum attainable value of the width of the
synchronization landscape. Our results have also strong implications for
optimization and trade-offs in network synchronization with delays.Comment: 3 figure
Invisible pushdown languages
Context free languages allow one to express data with hierarchical structure,
at the cost of losing some of the useful properties of languages recognized by
finite automata on words. However, it is possible to restore some of these
properties by making the structure of the tree visible, such as is done by
visibly pushdown languages, or finite automata on trees. In this paper, we show
that the structure given by such approaches remains invisible when it is read
by a finite automaton (on word). In particular, we show that separability with
a regular language is undecidable for visibly pushdown languages, just as it is
undecidable for general context free languages
Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks
We study the vulnerability of dominating sets against random and targeted
node removals in complex networks. While small, cost-efficient dominating sets
play a significant role in controllability and observability of these networks,
a fixed and intact network structure is always implicitly assumed. We find that
cost-efficiency of dominating sets optimized for small size alone comes at a
price of being vulnerable to damage; domination in the remaining network can be
severely disrupted, even if a small fraction of dominator nodes are lost. We
develop two new methods for finding flexible dominating sets, allowing either
adjustable overall resilience, or dominating set size, while maximizing the
dominated fraction of the remaining network after the attack. We analyze the
efficiency of each method on synthetic scale-free networks, as well as real
complex networks
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