603 research outputs found
Blocked All-Pairs Shortest Paths Algorithm on Intel Xeon Phi KNL Processor: A Case Study
Manycores are consolidating in HPC community as a way of improving
performance while keeping power efficiency. Knights Landing is the recently
released second generation of Intel Xeon Phi architecture. While optimizing
applications on CPUs, GPUs and first Xeon Phi's has been largely studied in the
last years, the new features in Knights Landing processors require the revision
of programming and optimization techniques for these devices. In this work, we
selected the Floyd-Warshall algorithm as a representative case study of graph
and memory-bound applications. Starting from the default serial version, we
show how data, thread and compiler level optimizations help the parallel
implementation to reach 338 GFLOPS.Comment: Computer Science - CACIC 2017. Springer Communications in Computer
and Information Science, vol 79
Degenerations of ideal hyperbolic triangulations
Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The
deformation variety D(T), a subset of which parameterises (incomplete)
hyperbolic structures obtained on M using T, is defined and compactified by
adding certain projective classes of transversely measured singular
codimension-one foliations of M. This leads to a combinatorial and geometric
variant of well-known constructions by Culler, Morgan and Shalen concerning the
character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische
Zeitschrif
Computing CMB Anisotropy in Compact Hyperbolic Spaces
The measurements of CMB anisotropy have opened up a window for probing the
global topology of the universe on length scales comparable to and beyond the
Hubble radius. For compact topologies, the two main effects on the CMB are: (1)
the breaking of statistical isotropy in characteristic patterns determined by
the photon geodesic structure of the manifold and (2) an infrared cutoff in the
power spectrum of perturbations imposed by the finite spatial extent. We
present a completely general scheme using the regularized method of images for
calculating CMB anisotropy in models with nontrivial topology, and apply it to
the computationally challenging compact hyperbolic topologies. This new
technique eliminates the need for the difficult task of spatial eigenmode
decomposition on these spaces. We estimate a Bayesian probability for a
selection of models by confronting the theoretical pixel-pixel temperature
correlation function with the COBE-DMR data. Our results demonstrate that
strong constraints on compactness arise: if the universe is small compared to
the `horizon' size, correlations appear in the maps that are irreconcilable
with the observations. If the universe is of comparable size, the likelihood
function is very dependent upon orientation of the manifold wrt the sky. While
most orientations may be strongly ruled out, it sometimes happens that for a
specific orientation the predicted correlation patterns are preferred over the
conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in
separate files. Minor revision to match the version accepted in Class.
Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper
can be also downloaded from
http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g
Dimension of the Torelli group for Out(F_n)
Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use
combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space
which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated
(n at least 3). In particular, this recovers the result of Krstic-McCool that
T_3 is not finitely presented. We also give a new proof of the fact, due to
Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure
Augmenting forearm crutches with wireless sensors for lower limb rehabilitation
Forearm crutches are frequently used in the rehabilitation of an injury to the lower limb. The recovery rate is improved if the patient correctly applies a certain fraction of their body weight (specified by a clinician) through the axis of the crutch, referred to as partial weight bearing (PWB). Incorrect weight bearing has been shown to result in an extended recovery period or even cause further damage to the limb. There is currently no minimally invasive tool for long-term monitoring of a patient's PWB in a home environment. This paper describes the research and development of an instrumented forearm crutch that has been developed to wirelessly and autonomously monitor a patient's weight bearing over the full period of their recovery, including its potential use in a home environment. A pair of standard forearm crutches are augmented with low-cost off-the-shelf wireless sensor nodes and electronic components to provide indicative measurements of the applied weight, crutch tilt and hand position on the grip. Data are wirelessly transmitted between crutches and to a remote computer (where they are processed and visualized in LabVIEW), and the patient receives biofeedback by means of an audible signal when they put too much or too little weight through the crutch. The initial results obtained highlight the capability of the instrumented crutch to support physiotherapists and patients in monitoring usage
Blocked All-Pairs Shortest Paths Algorithm on Intel Xeon Phi KNL Processor: A Case Study
Manycores are consolidating in HPC community as a way of improving performance while keeping power efficiency. Knights Landing is the recently released second generation of Intel Xeon Phi architec- ture.While optimizing applications on CPUs, GPUs and first Xeon Phi’s has been largely studied in the last years, the new features in Knights Landing processors require the revision of programming and optimization techniques for these devices. In this work, we selected the Floyd-Warshall algorithm as a representative case study of graph and memory-bound ap- plications. Starting from the default serial version, we show how data, thread and compiler level optimizations help the parallel implementation to reach 338 GFLOPS
Subset currents on free groups
We introduce and study the space of \emph{subset currents} on the free group
. A subset current on is a positive -invariant locally finite
Borel measure on the space of all closed subsets of consisting of at least two points. While ordinary geodesic currents
generalize conjugacy classes of nontrivial group elements, a subset current is
a measure-theoretic generalization of the conjugacy class of a nontrivial
finitely generated subgroup in , and, more generally, in a word-hyperbolic
group. The concept of a subset current is related to the notion of an
"invariant random subgroup" with respect to some conjugacy-invariant
probability measure on the space of closed subgroups of a topological group. If
we fix a free basis of , a subset current may also be viewed as an
-invariant measure on a "branching" analog of the geodesic flow space for
, whose elements are infinite subtrees (rather than just geodesic lines)
of the Cayley graph of with respect to .Comment: updated version; to appear in Geometriae Dedicat
Reshaping Curriculum to Enhance the Relevance of Literary Competence in Children's Education06
Twenty-first century learners face a multi-literacy landscape as they strive to acquire the cognitive skills needed for independent learning, apply linguistic skills to other knowledge base, and become computer literate. This article envisions a combination of skill sets and knowledge bases as the foundation of a literary competence-based curriculum. Such a curriculum would have the goal of enhancing young learners"critical thinking abilities; this would also help them take charge of the cognitive,linguistic, and sociocultural dimensions of written and spoken language in order to make learning transferable and applicable to the real world
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