16,266 research outputs found
The Transition Probability of the -TAZRP (-Bosons) with Inhomogeneous Jump Rates
In this paper we consider the -deformed totally asymmetric zero range
process (-TAZRP), also known as the -boson (stochastic) particle system,
on the lattice, such that the jump rate of a particle depends on
the site where it is on the lattice. We derive the transition probability for
an particle process in Bethe ansatz form as a sum of -fold contour
integrals. Our result generalizes the transition probability formula by
Korhonen and Lee for -TAZRP with a homogeneous lattice, and our method
follows the same approach as theirs
ANTENNA FOR WIRELESS UNDERGROUND COMMUNICATION
Systems and methods are disclosed for an underground antenna structure for radiating through a dissipative medium, the antenna structure. The antenna structure includes a dielectric substrate, a feeding structure disposed on the substrate, and one or more electrical conductors. The one or more electrical conductors are disposed on the substrate, oriented, and buried within the dissipative medium. The electrical conductors are also adapted to radiate signals at a frequency in half-space adjacent to the dissipative medium. The adaptation includes a beamwidth state for one or more of the electrical conductors based at least in part on the relative permittivity of the dissipative medium
Network Density of States
Spectral analysis connects graph structure to the eigenvalues and
eigenvectors of associated matrices. Much of spectral graph theory descends
directly from spectral geometry, the study of differentiable manifolds through
the spectra of associated differential operators. But the translation from
spectral geometry to spectral graph theory has largely focused on results
involving only a few extreme eigenvalues and their associated eigenvalues.
Unlike in geometry, the study of graphs through the overall distribution of
eigenvalues - the spectral density - is largely limited to simple random graph
models. The interior of the spectrum of real-world graphs remains largely
unexplored, difficult to compute and to interpret.
In this paper, we delve into the heart of spectral densities of real-world
graphs. We borrow tools developed in condensed matter physics, and add novel
adaptations to handle the spectral signatures of common graph motifs. The
resulting methods are highly efficient, as we illustrate by computing spectral
densities for graphs with over a billion edges on a single compute node. Beyond
providing visually compelling fingerprints of graphs, we show how the
estimation of spectral densities facilitates the computation of many common
centrality measures, and use spectral densities to estimate meaningful
information about graph structure that cannot be inferred from the extremal
eigenpairs alone.Comment: 10 pages, 7 figure
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