163 research outputs found
FooPar: A Functional Object Oriented Parallel Framework in Scala
We present FooPar, an extension for highly efficient Parallel Computing in
the multi-paradigm programming language Scala. Scala offers concise and clean
syntax and integrates functional programming features. Our framework FooPar
combines these features with parallel computing techniques. FooPar is designed
modular and supports easy access to different communication backends for
distributed memory architectures as well as high performance math libraries. In
this article we use it to parallelize matrix matrix multiplication and show its
scalability by a isoefficiency analysis. In addition, results based on a
empirical analysis on two supercomputers are given. We achieve close-to-optimal
performance wrt. theoretical peak performance. Based on this result we conclude
that FooPar allows to fully access Scala's design features without suffering
from performance drops when compared to implementations purely based on C and
MPI
Scalable Parallel Numerical Constraint Solver Using Global Load Balancing
We present a scalable parallel solver for numerical constraint satisfaction
problems (NCSPs). Our parallelization scheme consists of homogeneous worker
solvers, each of which runs on an available core and communicates with others
via the global load balancing (GLB) method. The parallel solver is implemented
with X10 that provides an implementation of GLB as a library. In experiments,
several NCSPs from the literature were solved and attained up to 516-fold
speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho
The Petersen--Wilhelm conjecture on principal bundles
This paper studies Cheeger deformations on
principal bundles to obtain conditions for positive sectional curvature
submersion metrics. We conclude, in particular, a stronger version of the
Petersen--Wilhelm fiber dimension conjecture to the class of principal bundles.
We prove any principal bundle over a positively curved base admits a metric
of positive sectional curvature if, and only if, the submersion is fat, in
particular, . The proof combines the concept of ``good triples''
due to Munteanu and Tapp \cite{tappmunteanu2}, with a Chaves--Derdzisnki--Rigas
type condition to nonnegative curvature. Additionally, the conjecture is
verified for other classes of submersions.Comment: v4. follows anonymous referee suggestions to improve the exposition
significantly. Proofs were revised and simplified, and further results were
added. Comments are welcom
Fast But Not Furious. When Sped Up Bit Rate of Information Drives Rule Induction
The language abilities of young and adult learners range from memorizing specific items to finding statistical regularities between them (item-bound generalization) and generalizing rules to novel instances (category-based generalization). Both external factors, such as input variability, and internal factors, such as cognitive limitations, have been shown to drive these abilities. However, the exact dynamics between these factors and circumstances under which rule induction emerges remain largely underspecified. Here, we extend our information-theoretic model (Radulescu et al., 2019), based on Shannonâs noisy-channel coding theory, which adds into the âformulaâ for rule induction the crucial dimension of time: the rate of encoding information by a time-sensitive mechanism. The goal of this study is to test the channel capacity-based hypothesis of our model: if the input entropy per second is higher than the maximum rate of information transmission (bits/second), which is determined by the channel capacity, the encoding method moves gradually from item-bound generalization to a more efficient category-based generalization, so as to avoid exceeding the channel capacity. We ran two artificial grammar experiments with adults, in which we sped up the bit rate of information transmission, crucially not by an arbitrary amount but by a factor calculated using the channel capacity formula on previous data. We found that increased bit rate of information transmission in a repetition-based XXY grammar drove the tendency of learners toward category-based generalization, as predicted by our model. Conversely, we found that increased bit rate of information transmission in complex non-adjacent dependency aXb grammar impeded the item-bound generalization of the specific a_b frames, and led to poorer learning, at least judging by our accuracy assessment method. This finding could show that, since increasing the bit rate of information precipitates a change from item-bound to category-based generalization, it impedes the item-bound generalization of the specific a_b frames, and that it facilitates category-based generalization both for the intervening Xs and possibly for a/b categories. Thus, sped up bit rate does not mean that an unrestrainedly increasing bit rate drives rule induction in any context, or grammar. Rather, it is the specific dynamics between the input entropy and the maximum rate of information transmission
The complete dynamics description of positively curved metrics in the Wallach flag manifold
The family of invariant Riemannian manifolds in the Wallach flag manifold
is described by three parameters of
positive real numbers. By restricting such a family of metrics in the
\emph{tetrahedron} , in this paper, we describe all
regions admitting metrics with curvature properties
varying from positive sectional curvature to positive scalar curvature,
including positive intermediate curvature notion's. We study the dynamics of
such regions under the \emph{projected Ricci flow} in the plane ,
concluding sign curvature maintenance and escaping. In addition, we obtain some
results for positive intermediate Ricci curvature for a path of metrics on
fiber bundles over , further studying its
evolution under the Ricci flow on the base.Comment: 15 pages, 12 figures. arXiv admin note: text overlap with
arXiv:2305.0611
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