Additive domain decomposition operator splittings -- convergence analyses in a dissipative framework

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction implicit schemes and additive splitting schemes of first and second order. For the standard first-order additive splitting scheme we also extend the error analysis to semilinear evolution equations, which may only have mild solutions.Comment: Please refer to the published article for the final version which also contains numerical experiments. Version 3 and 4: Only comments added. Version 2, page 2: Clarified statement on stability issues for ADI schemes with more than two operator

Quarks, gluons, colour: Facts or fiction?

A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the spatio--temporal scale. Particles which are confined to small scales, i.e., do not appear in the physical spectrum, can be uncovered in this way without taking recourse to gauge fields or indefinite metric spaces. In this way notions such as quark, gluon, colour symmetry and confinement acquire a new and intrinsic meaning which is stable under gauge or duality transformations. The method is illustrated by the example of the Schwinger model.Comment: 22 pages, ams-latex; the article had to be replaced because of tex problems, there are no changes in the tex

Multi-scale statistics of turbulence motorized by active matter

A number of micro-scale biological flows are characterized by spatio-temporal chaos. These include dense suspensions of swimming bacteria, microtubule bundles driven by motor proteins, and dividing and migrating confluent layers of cells. A characteristic common to all of these systems is that they are laden with active matter, which transforms free energy in the fluid into kinetic energy. Because of collective effects, the active matter induces multi-scale flow motions that bear strong visual resemblance to turbulence. In this study, multi-scale statistical tools are employed to analyze direct numerical simulations (DNS) of periodic two- (2D) and three-dimensional (3D) active flows and compare them to classic turbulent flows. Statistical descriptions of the flows and their variations with activity levels are provided in physical and spectral spaces. A scale-dependent intermittency analysis is performed using wavelets. The results demonstrate fundamental differences between active and high-Reynolds number turbulence; for instance, the intermittency is smaller and less energetic in active flows, and the work of the active stress is spectrally exerted near the integral scales and dissipated mostly locally by viscosity, with convection playing a minor role in momentum transport across scales.Comment: Accepted in Journal of Fluid Mechanics (2017

Dynamic gesture recognition using PCA with multi-scale theory and HMM

In this paper, a dynamic gesture recognition system is presented which requires no special hardware other than a Webcam. The system is based on a novel method combining Principal Component Analysis (PCA) with hierarchical multi-scale theory and Discrete Hidden Markov Models (DHMM). We use a hierarchical decision tree based on multiscale theory. Firstly we convolve all members of the training data with a Gaussian kernel, which blurs differences between images and reduces their separation in feature space. This reduces the number of eigenvectors needed to describe the data. A principal component space is computed from the convolved data. We divide the data in this space into two clusters using the k-means algorithm. Then the level of blurring is reduced and PCA is applied to each of the clusters separately. A new principal component space is formed from each cluster. Each of these spaces is then divided into two and the process is repeated. We thus produce a binary tree of principal component spaces where each level of the tree represents a different degree of blurring. The search time is then proportional to the depth of the tree, which makes it possible to search hundreds of gestures in real time. The output of the decision tree is then input into DHMM to recognize temporal information

NeMO-Net The Neural Multi-Modal Observation & Training Network for Global Coral Reef Assessment

We present NeMO-Net, the Srst open-source deep convolutional neural network (CNN) and interactive learning and training software aimed at assessing the present and past dynamics of coral reef ecosystems through habitat mapping into 10 biological and physical classes. Shallow marine systems, particularly coral reefs, are under significant pressures due to climate change, ocean acidification, and other anthropogenic pressures, leading to rapid, often devastating changes, in these fragile and diverse ecosystems. Historically, remote sensing of shallow marine habitats has been limited to meter-scale imagery due to the optical effects of ocean wave distortion, refraction, and optical attenuation. NeMO-Net combines 3D cm-scale distortion-free imagery captured using NASA FluidCam and Fluid lensing remote sensing technology with low resolution airborne and spaceborne datasets of varying spatial resolutions, spectral spaces, calibrations, and temporal cadence in a supercomputer-based machine learning framework. NeMO-Net augments and improves the benthic habitat classification accuracy of low-resolution datasets across large geographic ad temporal scales using high-resolution training data from FluidCam.NeMO-Net uses fully convolutional networks based upon ResNet and ReSneNet to perform semantic segmentation of remote sensing imagery of shallow marine systems captured by drones, aircraft, and satellites, including WorldView and Sentinel. Deep Laplacian Pyramid Super-Resolution Networks (LapSRN) alongside Domain Adversarial Neural Networks (DANNs) are used to reconstruct high resolution information from low resolution imagery, and to recognize domain-invariant features across datasets from multiple platforms to achieve high classification accuracies, overcoming inter-sensor spatial, spectral and temporal variations.Finally, we share our online active learning and citizen science platform, which allows users to provide interactive training data for NeMO-Net in 2D and 3D, integrated within a deep learning framework. We present results from the PaciSc Islands including Fiji, Guam and Peros Banhos 1 1 2 1 3 1 where 24-class classification accuracy exceeds 91%

Learning Representations in Model-Free Hierarchical Reinforcement Learning

Common approaches to Reinforcement Learning (RL) are seriously challenged by large-scale applications involving huge state spaces and sparse delayed reward feedback. Hierarchical Reinforcement Learning (HRL) methods attempt to address this scalability issue by learning action selection policies at multiple levels of temporal abstraction. Abstraction can be had by identifying a relatively small set of states that are likely to be useful as subgoals, in concert with the learning of corresponding skill policies to achieve those subgoals. Many approaches to subgoal discovery in HRL depend on the analysis of a model of the environment, but the need to learn such a model introduces its own problems of scale. Once subgoals are identified, skills may be learned through intrinsic motivation, introducing an internal reward signal marking subgoal attainment. In this paper, we present a novel model-free method for subgoal discovery using incremental unsupervised learning over a small memory of the most recent experiences (trajectories) of the agent. When combined with an intrinsic motivation learning mechanism, this method learns both subgoals and skills, based on experiences in the environment. Thus, we offer an original approach to HRL that does not require the acquisition of a model of the environment, suitable for large-scale applications. We demonstrate the efficiency of our method on two RL problems with sparse delayed feedback: a variant of the rooms environment and the first screen of the ATARI 2600 Montezuma's Revenge game