Parallelizing RRT on distributed-memory architectures

This paper addresses the problem of improving the performance of the Rapidly-exploring Random Tree (RRT) algorithm by parallelizing it. For scalability reasons we do so on a distributed-memory architecture, using the message-passing paradigm. We present three parallel versions of RRT along with the technicalities involved in their implementation. We also evaluate the algorithms and study how they behave on different motion planning problems

Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories

The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for effective decision procedures, called Satisfiability Modulo Theory solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories, that applies to the Delayed Theory Combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state of the art algorithms for Satisfiability Modulo Theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for this application, a cube of 4096^3 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the FFT algorithm as numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the TSUBAME-2.0 system). The FFT-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the FFT algorithm. The calculation time for one time step was 108 seconds for the vortex method and 154 seconds for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex method calculations to date

The spatial prediction sandbox - Investigating the use of spatially-explicit modelling and cross-validation strategies in spatial interpolation machine learning problems

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesMachine Learning (ML) methods are increasingly used for spatial interpolation and di erent strategies have been proposed to introduce space into the modelling and validation phases. Nevertheless, a comparison of these methods under di erent landscape autocorrelation ranges and sampling designs is still missing. This Master Thesis investigates under which scenarios spatially-explicit ML modelling and validation strategies are appropriate for spatial interpolation problems. We designed a framework that allowed us to simulate predictor and outcome spatial elds with di erent autocorrelation ranges, as well as samples with di erent number of points and distributions. With these data, we tested di erent non-spatial and spatially-explicit (coordinates, EDF, RFsp) Random Forest ML models and evaluated them using the simulated surfaces as well as di erent standard (Leave-One- Out, LOO) and spatially-explicit (spatial bu er LOO, sbLOO) Cross-Validation (CV) strategies. We developed a new method called Nearest Distance Matching (NDM) to estimate the appropriate radius for sbLOO CV for spatial interpolation based on sample distribution and landscape range, and compared it to state-of-the art methods for radius search, only based on range. While for short ranges non-spatial models were superior to spatially-explicit models regardless of the sample size and distribution; for long ranges, spatial models performed better under regular and random sampling designs, but not clustered and non-uniform. CV results indicated that although LOO correctly estimated model performance under random designs, it yielded overestimated errors for regular samples and underestimated errors for clustered and non-uniform designs under long ranges. Results of sbLOO combined with NDM correctly addressed error underestimation of LOO in clustered and non-uniform samples, whereas sbLOO based solely on the range resulted in error overestimation for all designs under long ranges. This Master Thesis provides important insights to the eld of predictive mapping: it elucidates in which cases spatially-explicit methods may be preferred, and establishes that state-of-the-art approaches for spatial CV designed to assess model transferability are not suited for spatial interpolation and proposes an alternative

Context-Specific Preference Learning of One Dimensional Quantitative Geospatial Attributes Using a Neuro-Fuzzy Approach

Change detection is a topic of great importance for modern geospatial information systems. Digital aerial imagery provides an excellent medium to capture geospatial information. Rapidly evolving environments, and the availability of increasing amounts of diverse, multiresolutional imagery bring forward the need for frequent updates of these datasets. Analysis and query of spatial data using potentially outdated data may yield results that are sometimes invalid. Due to measurement errors (systematic, random) and incomplete knowledge of information (uncertainty) it is ambiguous if a change in a spatial dataset has really occurred. Therefore we need to develop reliable, fast, and automated procedures that will effectively report, based on information from a new image, if a change has actually occurred or this change is simply the result of uncertainty. This thesis introduces a novel methodology for change detection in spatial objects using aerial digital imagery. The uncertainty of the extraction is used as a quality estimate in order to determine whether change has occurred. For this goal, we develop a fuzzy-logic system to estimate uncertainty values fiom the results of automated object extraction using active contour models (a.k.a. snakes). The differential snakes change detection algorithm is an extension of traditional snakes that incorporates previous information (i.e., shape of object and uncertainty of extraction) as energy functionals. This process is followed by a procedure in which we examine the improvement of the uncertainty at the absence of change (versioning). Also, we introduce a post-extraction method for improving the object extraction accuracy. In addition to linear objects, in this thesis we extend differential snakes to track deformations of areal objects (e.g., lake flooding, oil spills). From the polygonal description of a spatial object we can track its trajectory and areal changes. Differential snakes can also be used as the basis for similarity indices for areal objects. These indices are based on areal moments that are invariant under general affine transformation. Experimental results of the differential snakes change detection algorithm demonstrate their performance. More specifically, we show that the differential snakes minimize the false positives in change detection and track reliably object deformations