11,064 research outputs found
Some new results on the Chu duality of discrete groups
This paper deals mainly with the Chu duality of discrete groups. Among other
results, we give sufficient conditions for an group to satisfy Chu duality
and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a
group coincide. As a consequence, it follows that when is a weak sum of
a family of finite simple groups, if the exponent of the groups in the family
is bounded then satisfies Chu duality; on the other hand, if the exponent
of the groups goes to infinite then the Chu quasi-dual of coincide with its
Takahashi quasi-dual. We also present examples of discrete groups whose Chu
quasi-duals are not locally compact and examples of discrete Chu reflexive
groups which contain non-trivial sequences converging in the Bohr topology of
the groups. Our results systematize some previous work and answer some open
questions in the subject
GraphMP: An Efficient Semi-External-Memory Big Graph Processing System on a Single Machine
Recent studies showed that single-machine graph processing systems can be as
highly competitive as cluster-based approaches on large-scale problems. While
several out-of-core graph processing systems and computation models have been
proposed, the high disk I/O overhead could significantly reduce performance in
many practical cases. In this paper, we propose GraphMP to tackle big graph
analytics on a single machine. GraphMP achieves low disk I/O overhead with
three techniques. First, we design a vertex-centric sliding window (VSW)
computation model to avoid reading and writing vertices on disk. Second, we
propose a selective scheduling method to skip loading and processing
unnecessary edge shards on disk. Third, we use a compressed edge cache
mechanism to fully utilize the available memory of a machine to reduce the
amount of disk accesses for edges. Extensive evaluations have shown that
GraphMP could outperform state-of-the-art systems such as GraphChi, X-Stream
and GridGraph by 31.6x, 54.5x and 23.1x respectively, when running popular
graph applications on a billion-vertex graph
GraphH: High Performance Big Graph Analytics in Small Clusters
It is common for real-world applications to analyze big graphs using
distributed graph processing systems. Popular in-memory systems require an
enormous amount of resources to handle big graphs. While several out-of-core
approaches have been proposed for processing big graphs on disk, the high disk
I/O overhead could significantly reduce performance. In this paper, we propose
GraphH to enable high-performance big graph analytics in small clusters.
Specifically, we design a two-stage graph partition scheme to evenly divide the
input graph into partitions, and propose a GAB (Gather-Apply-Broadcast)
computation model to make each worker process a partition in memory at a time.
We use an edge cache mechanism to reduce the disk I/O overhead, and design a
hybrid strategy to improve the communication performance. GraphH can
efficiently process big graphs in small clusters or even a single commodity
server. Extensive evaluations have shown that GraphH could be up to 7.8x faster
compared to popular in-memory systems, such as Pregel+ and PowerGraph when
processing generic graphs, and more than 100x faster than recently proposed
out-of-core systems, such as GraphD and Chaos when processing big graphs
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Long-term stability studies of a semiconductor photoelectrode in three-electrode configuration
Improving the stability of semiconductor materials is one of the major challenges for sustainable and economic photoelectrochemical water splitting. N-terminated GaN nanostructures have emerged as a practical protective layer for conventional high efficiency but unstable Si and III-V photoelectrodes due to their near-perfect conduction band-alignment, which enables efficient extraction of photo-generated electrons, and N-terminated surfaces, which protects against chemical and photo-corrosion. Here, we demonstrate that Pt-decorated GaN nanostructures on an n+-p Si photocathode can exhibit an ultrahigh stability of 3000 h (i.e., over 500 days for usable sunlight ∼5.5 h per day) at a large photocurrent density (>35 mA cm-2) in three-electrode configuration under AM 1.5G one-sun illumination. The measured applied bias photon-to-current efficiency of 11.9%, with an excellent onset potential of ∼0.56 V vs. RHE, is one of the highest values reported for a Si photocathode under AM 1.5G one-sun illumination. This study provides a paradigm shift for the design and development of semiconductor photoelectrodes for PEC water splitting: stability is no longer limited by the light absorber, but rather by co-catalyst particles
On a discrete nonlinear boundary value problem
AbstractThe nonlinear eigenvalue problem Δ2uk−1+λ|uk|γ=0,k=1,2,…,n under the Dirichlet boundary conditions u0=0=un+1 is studied. An existence and uniqueness theorem is proved. Qualitative properties of solutions are also given
Infection and inflammation stimulate expansion of a CD74+ Paneth cell subset to regulate disease progression
Paneth cells (PCs), a specialized secretory cell type in the small intestine, are increasingly recognized as having an essential role in host responses to microbiome and environmental stresses. Whether and how commensal and pathogenic microbes modify PC composition to modulate inflammation remain unclear. Using newly developed PC-reporter mice under conventional and gnotobiotic conditions, we determined PC transcriptomic heterogeneity in response to commensal and invasive microbes at single cell level. Infection expands the pool of CD7
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