Related papers: A semi-algebraic model for automatic loop parallel…
Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…
In this paper we describe the mathematical foundations of a new approach to semi-supervised Machine Learning. Using techniques of Symbolic Computation and Computer Algebra, we apply the concept of persistent homology to obtain a new…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…
We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However,…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
The symbolic manipulation program FORM is specialized to handle very large algebraic expressions. Some specific features of its internal structure make FORM very well suited for parallelization. We have now two parallel versions of FORM,…
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…
Polyhedral compilers perform optimizations such as tiling and parallelization; when doing both, they usually generate code that executes "barrier-synchronized wavefronts" of tiles. We present a system to express and generate code for hybrid…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
We consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the first section. This problem is the generalization of the classical parallel machine scheduling problem, when the…
We study the computational complexity of the recently proposed nubot model of molecular-scale self-assembly. The model generalises asynchronous cellular automata to have non-local movement where large assemblies of molecules can be pushed…
Scheduling parallel sessions of an academic meeting is a complicated task. If each presentation is assigned to an appropriate session, an antiferromagnetic Potts model can be used for semi-automatic timetabling. The timetabling method…
We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical…
In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
Weighted automata are a generalization of nondeterministic automata that associate a weight drawn from a semiring $K$ with every transition and every state. Their behaviours can be formalized either as weighted language equivalence or…