Related papers: A mathematical formalization of data parallel oper…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
We suggest that the canonical parallel operation of processes is composition in a well-supported compact closed category of spans of reflexive graphs. We present the parallel operations of classical process algebras as derived operations…
Parallel batched data structures are designed to process synchronized batches of operations in a parallel computing model. In this paper, we propose parallel combining, a technique that implements a concurrent data structure from a parallel…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
We present GraSSP, a novel approach to perform automated parallelization relying on recent advances in formal verification and synthesis. GraSSP augments an existing sequential program with an additional functionality to decompose data…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We consider parallel computation for Gaussian process calculations to overcome computational and memory constraints on the size of datasets that can be analyzed. Using a hybrid parallelization approach that uses both threading (shared…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…
The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the…
New trends towards multiple core processors imply using standard programming models to develop efficient, reliable and portable programs for distributed memory multiprocessors and workstation PC clusters. Message passing using MPI is widely…
The ability to express a program as a hierarchical composition of parts is an essential tool in managing the complexity of software and a key abstraction this provides is to separate the representation of data from the computation. Many…
As ML applications are becoming ever more pervasive, fully-trained systems are made increasingly available to a wide public, allowing end-users to submit queries with their own data, and to efficiently retrieve results. With increasingly…
We introduce an object-oriented framework for parallel programming, which is based on the observation that programming objects can be naturally interpreted as processes. A parallel program consists of a collection of persistent processes…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…