We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks. Since normal neural networks are data intensive and cannot provide predictive uncertainty, we propose ...

We investigate the long term dynamics for a predation model of Plankton community with indirect effects, under fluctuating environments. A random version and a stochastic version with multiplicative noise of the model are discussed and compared. We prove that the solutions to both versions are non-negative and bounded given any non-negative positive initial conditions. We also prove that both t...

We present a new partial order planner called PSIPLAN, which builds on SNLP. We drop the closed world assumption, add sensing actions, add a class of propositions about the agent’s knowledge, and add a class of universally quantified propositions. This latter class of propositions, which we call ψ-forms, distinguishes this research. ψ-forms represent partially closed worlds, such as “Block A is...

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the EXA-DUNE project, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on t...

Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is “fundamental” and deterministic or “phenomenological” and stochastic, all changes are described relative to an external time. Here we show that once we define what we are talking about, namely, the system, its states and a criterion to distinguish among them, there is a single, unique, and natur...

We present conditions to obtain the asymptotic normality of the maximum likelihood estimator of a loss process presented in [2]. We shall use the notations of [2], write ‖ · ‖q for the standard L norm on an arbitrary space R, d ≥ 1, and let D φ denote the k−th order di erentiation with respect to φ. Let us introduce the following hypotheses: (A4) For all i ∈ {1, . . . , r}, λi(Φ0) > 0. (A5) For...

Hit-and-Run is a well-known class of Markov chain algorithms for sampling from essentially arbitrary distributions over bounded regions of the Euclidean space. We present a class of Small World network models constructed using Hit-and-Run in a Euclidean ball. We prove that there is a unique scale invariant model in this class that admits efficient search by a decentralized algorithm. This resea...

Cochlear implants (CI) are used to treat severe hearing loss by surgically inserting an electrode array into the cochlea. Since current electrodes are designed with various insertion depth, ENT surgeons must choose the implant that will maximise the insertion depth without causing any trauma based on preoperative CT images. In this paper, we propose a novel framework for estimating the insertio...

We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we show that the total mass of the process grows exponentially in time whenever it survives. More precisely, we prove that there exists an open path, oriented ...

In this paper, techniques are proposed for limiting state explosion in the context of resource allocation problems. It is shown that given any system organized into a — possibly irregular — network of — possibly heterogeneous — processes, model checking over that system can be reduced by an efficient, fully automatic and exact method to model checking over a certain small system. These results ...