22,583 research outputs found
Faster 3-Periodic Merging Networks
We consider the problem of merging two sorted sequences on a comparator
network that is used repeatedly, that is, if the output is not sorted, the
network is applied again using the output as input. The challenging task is to
construct such networks of small depth. The first constructions of merging
networks with a constant period were given by Kuty{\l}owski, Lory\'s and
Oesterdikhoff. They have given -periodic network that merges two sorted
sequences of numbers in time and a similar network of period
that works in . We present a new family of such networks that are
based on Canfield and Williamson periodic sorter. Our -periodic merging
networks work in time upper-bounded by . The construction can be
easily generalized to larger constant periods with decreasing running time, for
example, to -periodic ones that work in time upper-bounded by .
Moreover, to obtain the facts we have introduced a new proof technique
Dynamic Time-Dependent Route Planning in Road Networks with User Preferences
There has been tremendous progress in algorithmic methods for computing
driving directions on road networks. Most of that work focuses on
time-independent route planning, where it is assumed that the cost on each arc
is constant per query. In practice, the current traffic situation significantly
influences the travel time on large parts of the road network, and it changes
over the day. One can distinguish between traffic congestion that can be
predicted using historical traffic data, and congestion due to unpredictable
events, e.g., accidents. In this work, we study the \emph{dynamic and
time-dependent} route planning problem, which takes both prediction (based on
historical data) and live traffic into account. To this end, we propose a
practical algorithm that, while robust to user preferences, is able to
integrate global changes of the time-dependent metric~(e.g., due to traffic
updates or user restrictions) faster than previous approaches, while allowing
subsequent queries that enable interactive applications
Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
We consider systems of many spatially distributed phase oscillators that
interact with their neighbors. Each oscillator is allowed to have a different
natural frequency, as well as a different response time to the signals it
receives from other oscillators in its neighborhood. Using the ansatz of Ott
and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed
in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic
dynamics of these systems to a macroscopic partial-differential-equation
description. Using this macroscopic formulation, we numerically find that
finite oscillator response time leads to interesting spatio-temporal dynamical
behaviors including propagating fronts, spots, target patterns, chimerae,
spiral waves, etc., and we study interactions and evolutionary behaviors of
these spatio-temporal patterns
Individual and Collective Behavior of Small Vibrating Motors Interacting Through a Resonant Plate
We report on experiments of many small motors -- cell phone vibrators --
glued to and interacting through a resonant plate. We find that individual
motors interacting with the plate demonstrate hysteresis in their steady-state
frequency due to interactions with plate resonances. For multiple motors
running simultaneously, the degree of synchronization between motors increases
when the motors' frequencies are near a resonance of the plate, and the
frequency at which the motors synchronize shows a history dependence.Comment: 7 pages, 8 figure
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