3D interactive topology optimization on hand-held devices

This educational paper describes the implementation aspects, user interface design considerations and workflow potential of the recently published TopOpt 3D App. The app solves the standard minimum compliance problem in 3D and allows the user to change design settings interactively at any point in time during the optimization. Apart from its educational nature, the app may point towards future ways of performing industrial design. Instead of the usual geometrize, then model and optimize approach, the geometry now automatically adapts to the varying boundary and loading conditions. The app is freely available for iOS at Apple’s App Store and at http://www.topopt.dtu.dk/TopOpt3D for Windows and OSX.     

Mixing matrix estimation using discriminative clustering for blind source separation

Mixing matrix estimation in instantaneous blind source separation (BSS) can be performed by exploiting the sparsity and disjoint orthogonality of source signals. As a result, approaches for estimating the unknown mixing process typically employ clustering algorithms on the mixtures in a parametric domain, where the signals can be sparsely represented. In this paper, we propose two algorithms to perform discriminative clustering of the mixture signals for estimating the mixing matrix. For the case of overdetermined BSS, we develop an algorithm to perform linear discriminant analysis based on similarity measures and combine it with K-hyperline clustering. Furthermore, we propose to perform discriminative clustering in a high-dimensional feature space obtained by an implicit mapping, using the kernel trick, for the case of underdetermined source separation. Using simulations on synthetic data, we demonstrate the improvements in mixing matrix estimation performance obtained using the proposed algorithms in comparison to other clustering methods. Finally we perform mixing matrix estimation from speech mixtures, by clustering single source points in the time-frequency domain, and show that the proposed algorithms achieve higher signal to interference ratio when compared to other baseline algorithms.     

Generic visual analysis for multi- and hyperspectral image data

Multi- and hyperspectral imaging and data analysis has been investigated in the last decades in the context of various fields of application like remote sensing or microscopic spectroscopy. However, recent developments in sensor technology and a growing number of application areas require a more generic view on data analysis, that clearly expands the current, domain-specific approaches. In this context, we address the problem of interactive exploration of multi- and hyperspectral data, consisting of (semi-)automatic data analysis and scientific visualization in a comprehensive fashion. In this paper, we propose an approach that enables a generic interactive exploration and easy segmentation of multi- and hyperspectral data, based on characterizing spectra of an individual dataset, the so-called endmembers. Using the concepts of existing endmember extraction algorithms, we derive a visual analysis system, where the characteristic spectra initially identified serve as input to interactively tailor a problem-specific visual analysis by means of visual exploration. An optional outlier detection improves the robustness of the endmember detection and analysis. An adequate system feedback of the costly unmixing procedure for the spectral data with respect to the current set of endmembers is ensured by a novel technique for progressive unmixing and view update which is applied at user modification. The progressive unmixing is based on an efficient prediction scheme applied to previous unmixing results. We present a detailed evaluation of our system in terms of confocal Raman microscopy, common multispectral imaging and remote sensing.     

Spatial inverse query processing

Traditional spatial queries return, for a given query object q, all database objects that satisfy a given predicate, such as epsilon range and k-nearest neighbors. This paper defines and studies inverse spatial queries, which, given a subset of database objects Q and a query predicate, return all objects which, if used as query objects with the predicate, contain Q in their result. We first show a straightforward solution for answering inverse spatial queries for any query predicate. Then, we propose a filter-and-refinement framework that can be used to improve efficiency. We show how to apply this framework on a variety of inverse queries, using appropriate space pruning strategies. In particular, we propose solutions for inverse epsilon range queries, inverse k-nearest neighbor queries, and inverse skyline queries. Furthermore, we show how to relax the definition of inverse queries in order to ensure non-empty result sets. Our experiments show that our framework is significantly more efficient than naive approaches.     

Robustness of an aerobic metabolically vinyl chloride degrading bacterial enrichment culture

Degradation of the lower chlorinated ethenes is crucial to the application of natural attenuation or in situ bioremediation on chlorinated ethene contaminated sites. Recently, within mixtures of several chloroethenes as they can occur in contaminated groundwater inhibiting effects on aerobic chloroethene degradation have been shown. The current study demonstrated that metabolic vinyl chloride (VC) degradation by an enrichment culture originating from groundwater was not affected by an equimolar concentration (50 μM) of cis-1,2-dichloroethene (cDCE). Only cDCE concentrations at a ratio of 2.4:1 (initial cDCE to VC concentration) caused minor inhibition of VC degradation. Furthermore, the degradation of VC was not affected by the presence of trans-1,2-dichloroethene (tDCE), 1,1-dichloroethene (1,1-DCE), trichloroethene (TCE), and tetrachloroethene (PCE) in equimolar concentrations (50 μM). Only cDCE and tDCE were cometabolically degraded in small amounts. The VC-degrading culture demonstrated a broad pH tolerance from 5 to 9 with an optimum between 6 and 7. Results also showed that the culture could degrade VC concentrations up to 1,800 μM (110 mg/L).     

Examining the dimensionality of genuine multipartite entanglement

Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite states by the number of degrees of freedom being entangled. In this regard, we derive computable and experimentally friendly criteria for arbitrary multipartite qudit systems that enable to examine in how many degrees of freedom a mixed state is genuine multipartite entangled.     

Processing and interactive editing of huge point clouds from 3D scanners

This paper describes a new out-of-core multi-resolution data structure for real-time visualization, interactive editing and externally efficient processing of large point clouds. We describe an editing system that makes use of the novel data structure to provide interactive editing and preprocessing tools for large scanner data sets. Using the new data structure, we provide a complete tool chain for 3D scanner data processing, from data preprocessing and filtering to manual touch-up and real-time visualization. In particular, we describe an out-of-core outlier removal and bilateral geometry filtering algorithm, a toolset for interactive selection, painting, transformation, and filtering of huge out-of-core point-cloud data sets and a real-time rendering algorithm, which all use the same data structure as storage backend. The interactive tools work in real-time for small model modifications. For large scale editing operations, we employ a two-resolution approach where editing is planned in real-time and executed in an externally efficient offline computation afterwards. We evaluate our implementation on example data sets of sizes up to 63 GB, demonstrating that the proposed technique can be used effectively in real-world applications.     

Particle Level Set Advection for the Interactive Visualization of Unsteady 3D Flow

Typically, flow volumes are visualized by defining their boundary as iso‐surface of a level set function. Grid‐based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particle‐based methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advantages of both approaches by interchanging the information between the grid and the particles. Our work demonstrates that the PLS technique can be adapted to volumetric dye advection via streak volumes, and to the visualization by time surfaces and path volumes. We achieve this with a modified and extended PLS, including a model for dye injection. A new algorithmic interpretation of PLS is introduced to exploit the efficiency of the GPU, leading to interactive visualization. Finally, we demonstrate the high quality and usefulness of PLS flow visualization by providing quantitative results on volume preservation and by discussing typical applications of 3D flow visualization.     

Automatic Construction and Verification of Isotopy Invariants

We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques. The author’s work was supported by EPSRC MathFIT grant GR/S31099.     

Multi-block Poisson grid generator for cascade simulations

High quality computational grids can greatly enhance the accuracy of turbine and compressor cascade simulations especially when time-dependent results are sought where vortical structures are convected through the computational domain. A technique for generating periodic structured grids for cascade simulations based on the Poisson equations is described. To allow for more complex geometries, the grid can be divided into individual zones or blocks. The grids are generated simultaneously in all blocks, assuring continuity of the grid lines and their slopes across the zonal boundaries. Simple geometric rules can be employed for enforcing orthogonality at block boundaries. The method results in grids with low grid distortion by allowing both, block boundaries and grid points on physical boundaries, to move freely. Results are presented for a linear turbine and a linear compressor cascade.