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

Gromoll--Meyer's actions and the geometry of (exotic) spacetimes

Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a smooth structure assumption different from some classical known models could produce different physical meanings. In this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll--Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers.Comment: Accepted paper. To appear in Differential Geometry and its Application

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 $\mathrm{S}^3, \mathrm{SO}(3)$ 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 $\pi: \mathrm{SO}(3), \mathrm{S}^3 \hookrightarrow \cal P \rightarrow B$ principal bundle over a positively curved base admits a metric of positive sectional curvature if, and only if, the submersion is fat, in particular, $\dim B \geq 4$. 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 Shannon’s noisy-channel coding theory, which adds into the “formula” 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