2,319 research outputs found
A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem
The Task Graph Cost-Optimal Scheduling Problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of Binate Covering Problems, hinged within a Bounded Model Checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to Minimum-Cost Satisfiability solvers or Pseudo-Boolean Optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the "circuit cofactoring" strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tool
Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension
In this paper, we establish lower and upper Gaussian bounds for the
probability density of the mild solution to the stochastic heat equation with
multiplicative noise and in any space dimension. The driving perturbation is a
Gaussian noise which is white in time with some spatially homogeneous
covariance. These estimates are obtained using tools of the Malliavin calculus.
The most challenging part is the lower bound, which is obtained by adapting a
general method developed by Kohatsu-Higa to the underlying spatially
homogeneous Gaussian setting. Both lower and upper estimates have the same
form: a Gaussian density with a variance which is equal to that of the mild
solution of the corresponding linear equation with additive noise
The 1-d stochastic wave equation driven by a fractional Brownian motion
In this paper, we develop a Young integration theory in dimension 2 which
will allow us to solve a non-linear one dimensional wave equation driven by an
arbitrary signal whose rectangular increments satisfy some H\"{o}lder
regularity conditions, for some H\"older exponent greater than 1/2. This result
will be applied to the infinite dimensional fractional Brownian motion.Comment: 37 pages, 3 figure
Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations
In this paper we establish lower and upper Gaussian bounds for the solutions
to the heat and wave equations driven by an additive Gaussian noise, using the
techniques of Malliavin calculus and recent density estimates obtained by
Nourdin and Viens. In particular, we deal with the one-dimensional stochastic
heat equation in driven by the space-time white noise, and the
stochastic heat and wave equations in ( and ,
respectively) driven by a Gaussian noise which is white in time and has a
general spatially homogeneous correlation
Existence of weak solutions for a class of semilinear stochastic wave equations
We prove existence of weak solutions (in the probabilistic sense) for a
general class of stochastic semilinear wave equations on bounded domains of
driven by a possibly discontinuous square integrable martingale.Comment: 21 pages, final versio
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