7,500 research outputs found
Modeling Spacing Distribution of Queuing Vehicles in Front of a Signalized Junction Using Random-Matrix Theory
Modeling of headway/spacing between two consecutive vehicles has many
applications in traffic flow theory and transport practice. Most known
approaches only study the vehicles running on freeways. In this paper, we
propose a model to explain the spacing distribution of queuing vehicles in
front of a signalized junction based on random-matrix theory. We show that the
recently measured spacing distribution data well fit the spacing distribution
of a Gaussian symplectic ensemble (GSE). These results are also compared with
the spacing distribution observed for car parking problem. Why
vehicle-stationary-queuing and vehicle-parking have different spacing
distributions (GSE vs GUE) seems to lie in the difference of driving patterns
Many-body non-Hermitian skin effect under dynamic gauge coupling
We study an atom-cavity hybrid system where fermionic atoms in a
one-dimensional lattice are subject to a cavity-induced dynamic gauge
potential. The gauge coupling leads to highly-degenerate steady states in which
the fermions accumulate to one edge of the lattice under an open boundary
condition. Such a phenomenon originates from the many-body Liouvillian
superoperator of the system, which, being intrinsically non-Hermitian, is
unstable against boundary perturbations and manifests the non-Hermitian skin
effect. Contrary to the single-body case, the steady state of a multi-atom
system is approached much slower under the open boundary condition, as the
long-time damping of the cavity mode exhibits distinct rates at different
times. This stage-wise slowdown is attributed to the competition between
light-assisted hopping and the dynamic gauge coupling, which significantly
reduces the steady-state degeneracy under the open boundary condition, as
distinct hosts of quasi-steady states dominate the dynamics at different time
scales.Comment: 13 pages, 7 figure
Fully Scalable Massively Parallel Algorithms for Embedded Planar Graphs
We consider the massively parallel computation (MPC) model, which is a
theoretical abstraction of large-scale parallel processing models such as
MapReduce. In this model, assuming the widely believed 1-vs-2-cycles
conjecture, solving many basic graph problems in rounds with a strongly
sublinear memory size per machine is impossible. We improve on the recent work
of Holm and T\v{e}tek [SODA 2023] that bypass this barrier for problems when a
planar embedding of the graph is given. In the previous work, on graphs of size
with machines, the memory size per machine needs to be
at least , whereas we extend their work to the
fully scalable regime, where the memory size per machine can be for any constant . We give the first constant round
fully scalable algorithms for embedded planar graphs for the problems of (i)
connectivity and (ii) minimum spanning tree (MST). Moreover, we show that the
-emulator of Chang, Krauthgamer, and Tan [STOC 2022] can be
incorporated into our recursive framework to obtain constant-round
-approximation algorithms for the problems of computing (iii)
single source shortest path (SSSP), (iv) global min-cut, and (v) -max flow.
All previous results on cuts and flows required linear memory in the MPC model.
Furthermore, our results give new algorithms for problems that implicitly
involve embedded planar graphs. We give as corollaries constant round fully
scalable algorithms for (vi) 2D Euclidean MST using total memory and
(vii) -approximate weighted edit distance using
memory.
Our main technique is a recursive framework combined with novel graph drawing
algorithms to compute smaller embedded planar graphs in constant rounds in the
fully scalable setting.Comment: To appear in SODA24. 55 pages, 9 figures, 1 table. Added section on
weighted edit distance and shortened abstrac
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