1,862 research outputs found
Hypercube orientations with only two in-degrees
We consider the problem of orienting the edges of the -dimensional
hypercube so only two different in-degrees and occur. We show that this
can be done, for two specified in-degrees, if and only if an obvious necessary
condition holds. Namely, there exist non-negative integers and so that
and . This is connected to a question arising from
constructing a strategy for a "hat puzzle."Comment: 9 pages, 4 figure
Minimum Entropy Orientations
We study graph orientations that minimize the entropy of the in-degree
sequence. The problem of finding such an orientation is an interesting special
case of the minimum entropy set cover problem previously studied by Halperin
and Karp [Theoret. Comput. Sci., 2005] and by the current authors
[Algorithmica, to appear]. We prove that the minimum entropy orientation
problem is NP-hard even if the graph is planar, and that there exists a simple
linear-time algorithm that returns an approximate solution with an additive
error guarantee of 1 bit. This improves on the only previously known algorithm
which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).Comment: Referees' comments incorporate
CABE : a cloud-based acoustic beamforming emulator for FPGA-based sound source localization
Microphone arrays are gaining in popularity thanks to the availability of low-cost microphones. Applications including sonar, binaural hearing aid devices, acoustic indoor localization techniques and speech recognition are proposed by several research groups and companies. In most of the available implementations, the microphones utilized are assumed to offer an ideal response in a given frequency domain. Several toolboxes and software can be used to obtain a theoretical response of a microphone array with a given beamforming algorithm. However, a tool facilitating the design of a microphone array taking into account the non-ideal characteristics could not be found. Moreover, generating packages facilitating the implementation on Field Programmable Gate Arrays has, to our knowledge, not been carried out yet. Visualizing the responses in 2D and 3D also poses an engineering challenge. To alleviate these shortcomings, a scalable Cloud-based Acoustic Beamforming Emulator (CABE) is proposed. The non-ideal characteristics of microphones are considered during the computations and results are validated with acoustic data captured from microphones. It is also possible to generate hardware description language packages containing delay tables facilitating the implementation of Delay-and-Sum beamformers in embedded hardware. Truncation error analysis can also be carried out for fixed-point signal processing. The effects of disabling a given group of microphones within the microphone array can also be calculated. Results and packages can be visualized with a dedicated client application. Users can create and configure several parameters of an emulation, including sound source placement, the shape of the microphone array and the required signal processing flow. Depending on the user configuration, 2D and 3D graphs showing the beamforming results, waterfall diagrams and performance metrics can be generated by the client application. The emulations are also validated with captured data from existing microphone arrays.</jats:p
Impact of Dynamical Fermions on QCD Vacuum Structure
We examine how dynamical fermions affect both the UV and infrared structure
of the QCD vacuum. We consider large lattices from the MILC
collaboration, using a gluonic definition of the topological charge density,
founded on a new over-improved stout-link smearing algorithm. The algorithm
reproduces established results from the overlap formalism and is designed to
preserve nontrivial topological objects including instantons. At short
distances we focus on the topological charge correlator, , where
negative values at small $x$ reveal a sign-alternating layered structure to the
topological-charge density of the QCD vacuum. We find that the magnitudes of
the negative dip in the correlator and the positive
contact term are both increased with the introduction of dynamical fermion
degrees of freedom. This is in accord with expectations based on charge
renormalization and the vanishing of the topological susceptibility in the
chiral limit. At large distances we examine the extent to which instanton-like
objects are found on the lattice, and how their distributions vary between
quenched and dynamical gauge fields. We show that dynamical gauge fields
contain more instanton-like objects with an average size greater than in the
quenched vacuum. Finally, we directly visualize the topological charge density
in order to investigate the effects of dynamical sea-quark degrees of freedom
on topology.Comment: 9 pages, 8 figure
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