Hierarchical Subdivision Research Articles

Integrated representation of technical systems with BIM and linked data: TUBES system ontology

Technical systems in the Architecture, Engineering, Construction, and Operations (AECO) industry are complex interconnected structures. To cope with this high complexity, large amounts of data must be processed and exchanged throughout the whole life cycle of these systems. Building Information Modeling (BIM) and Semantic Web Technologies (SWT) offer the possibility to structure and link this data as well as to define common terminology. Semantic Web ontologies describing HVAC systems in the AECO industry have been developed, but an ontology for an integrated representation based on general system theory is missing. Therefore, this study proposes the TUBES System Ontology (TSO) as a knowledge representation for an integrated, explicit representation of linked technical systems, their hierarchical subdivision, structural and functional interconnections, and relationships to spatial entities. The contribution is validated on two example models, and the results are critically discussed, pointing out corresponding limitations as well as the need for further research.

A fast multipole boundary element method for acoustics in viscothermal fluids

Standard numerical models in acoustics rely on the isentropic Helmholtz equation. Its derivation assumes adiabatic and reversible, i.e., dissipation-free, wave propagation. Sound waves in fluids are, however, subject to viscous and thermal losses. These losses originate from viscous friction and heat conduction, leading to the formation of acoustic boundary layers. Considering these effects becomes significant in setups with acoustic cavities of similar dimension as the boundary layers. Recently, boundary element methods (BEM) accounting for the viscothermal dissipation have been proposed. These methods limit the discretization to the surface of the fluid domain and require significantly fewer degrees of freedom than comparable finite element models. However, the BEM coefficient matrices are fully populated, resulting in high computational costs and storage requirements. This study develops a new BEM formulation for acoustics in viscothermal fluids that uses the fast multipole method - a low-rank approximation technique based on a hierarchical subdivision of the computational domain - to alleviate this shortcoming. It is shown that the fast viscothermal BEM improves the algorithmic complexity over the conventional formulation, reducing both the memory requirements and solution time. The results indicate good scalability of the method making it feasible for larger applications such as acoustic metamaterials.

Description of Divergence of Subpopulations in the Hierarchical System under the Analysis of Isonymy. II. Probabilities of Non-Isonymic Encounters

Metapopulations with typical for human populations hierarchical subdivision into parts (subpopulations) are considered, corresponding to classifications based on administrative-territorial division (say, village, village council, district, region, and so on) or on a genealogical approach based on ethnogenesis, as well as on other principles of biological classification. The purpose of this work is to analyze the general properties of the distribution of the surname concentration over subpopulations in their hierarchical structure. Attention is focused on the description of the surname divergence of subpopulations, as an indicator of which the total probability of two person with different surnames encounter is considered, which is understood as the probability of the encounter in a randomly chosen subpopulation, a unit of observation, from metapopulation with a hierarchical structure. Its decomposition by hierarchy levels is obtained, which generalizes the Wahlund effect in population genetics. The total probability of non-isonimic encounters in a hierarchically subdivided metapopulation is less than the probability of random encounters in it by the sum of the average surname concentration intragroup variances corresponding to separate levels. Such properties are purely statistical characteristics of the hierarchical structure, and not a feature of a particular population system, and are not derived from the regularities of one or another model of microevolution. They are computationally formulated in the same way for any hierarchical system, although in the general case they do not coincide quantitatively. The results obtained refer to rural and urban hierarchical metapopulations as separate components of the entire population.

Methodology for agile and iterative ontology development for toolmaking

Complex manufacturing processes and the absence of repeat effects characterize the toolmaking industry. German-speaking toolmaking companies are increasingly faced with the challenge of having to reach the limits of what is technically feasible and are confronted with an erosion of know-how, induced by demographic change. This applies in particular to know-how-intensive areas such as design, CAM-programming and work preparation. There is currently no comprehensive system support in these areas and the knowledge required for planning activities is often only available in the form of implicit technical and empirical knowledge. However, the use of heterogeneous manufacturing technologies requires a profound understanding of technology along the entire value chain. As a result of the very high semantic expressiveness of ontologies, they enable the representation of the most complex data models with logical relationships that go beyond hierarchical subdivision of content. This paper presents a novel agile methodology for the development of domain-specific ontologies in the environment of toolmaking. The methodology makes it possible to integrate the implicitly existing technical and experiential knowledge of employees at an early stage in the modelling process. In particular, the developed methodology extends conventional methods by the identified deficits in terms of knowledge acquisition, iteration and agility, as well as a separate consideration of the life cycle along the ontology of the use phase, taking into account agile methods from requirements engineering. Compliance with various guidelines and requirements is mandatory, such as the formulation of competence questions and the use of a standardised specification document. The iterative approach also ensures the needs-based integration of the characteristics of toolmaking. Furthermore, the methodology enables an early integration of IT structure and user interface for the needs-based design and use of the domain-specific ontology. The validation is based on an example in the mechanical production of a toolmaking company.

Face Inverse Rendering via Hierarchical Decoupling.

Previous face inverse rendering methods often require synthetic data with ground truth and/or professional equipment like a lighting stage. However, a model trained on synthetic data or using pre-defined lighting priors is typically unable to generalize well for real-world situations, due to the gap between synthetic data/lighting priors and real data. Furthermore, for common users, the professional equipment and skill make the task expensive and complex. In this paper, we propose a deep learning framework to disentangle face images in the wild into their corresponding albedo, normal, and lighting components. Specifically, a decomposition network is built with a hierarchical subdivision strategy, which takes image pairs captured from arbitrary viewpoints as input. In this way, our approach can greatly mitigate the pressure from data preparation, and significantly broaden the applicability of face inverse rendering. Extensive experiments are conducted to demonstrate the efficacy of our design, and show its superior performance in face relighting over other state-of-the-art alternatives. Our code is available at https://github.com/AutoHDR/HD-Net.git.

An Accelerating Convergence Rate Method for Moving Morphable Components

In the structural topology optimization approaches, the Moving Morphable Components (MMC) is a new method to obtain the optimized structural topologies by optimizing shapes, sizes, and locations of components. However, the size of the mesh has a strong influence on the rate of which the component builds the initial topological configuration by moving. The influence may slow down the convergence rate. In this paper, a hierarchical mesh subdivision solution method that can accelerate the convergence rate for the MMC is developed. First, the coarse mesh is used as the starting point for the optimization problem, and the construction process of the initial topology structure is increased speed by accelerating the movement of components. Second, the optimized solution obtained by the coarse mesh is equivalently mapped to the same problem with a finer mesh and used to construct a good starting point for the next optimization. Finally, two-dimensional (2D) MBB beam example and three-dimensional (3D) short cantilever beam example are provided so as to validate that with the use of the proposed approach, demonstrating that this method can improve the convergence rate and the stability of the MMC method.

Numerical Integration Over Implicitly Defined Domains with Topological Guarantee

Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.

Research and application of Boolean operation for triangular mesh model of underground space engineering—Boolean operation for triangular mesh model

AbstractThis study is aiming at the problems of slow collision detection speed of bounding box, low efficiency of triangle intersection detection, and triangulation in regions where complex intersecting lines are segmented that exist in Boolean operation of triangular mesh model in underground space engineering. The orientation calculation method of underground space engineering is put forward, and the precise definition of bounding box is realized. A simple method to realize the fast intersection detection algorithm between triangles is presented, the process of transforming the projection of intersecting lines into scalar and then judging is eliminated, and the efficiency of triangle intersection detection is improved. On the basis of Delaunay triangulation robust algorithm, numbering method of intersection position is improved. Central axis region division method and hierarchical subdivision triangulation method are proposed, which can divide all the regions of mixed complex intersections in one traversal. A subdivision triangulation method by comparing the cosine value of internal tension angle is proposed, and the subdivision triangulation of polygon is optimized. The feasibility of the algorithm is verified by practical engineering application.

Hexagonal Convolutional Neural Networks for Hexagonal Grids

Hexagonal grids use a hierarchical subdivision tessellation to cover the entire plane or sphere. Due to the 6-fold rotational symmetry, hexagonal grids have some advantages (e.g. isoperimetry, equidistant neighbors, and uniform connectivity) over quadrangular and triangular girds, which makes them suitable to tackle tasks of geospatial information processing and intelligent decision-making. In this paper, we first introduce some applications based on the hexagonal grids. Then, we introduce the planer and spherical hexagonal grids and analyze the group representations for them, we review geometric deep learning, some Convolutional Neural Networks (CNNs) for hexagonal grids, and group-based equivariant convolution. Next in importance, we propose the HexagonNet for hexagonal grids, and define a new convolution operator and pooling operator. Finally, in order to evaluate the effectiveness of the proposed HexagonNet, we perform experiments on two tasks: aerial scene classification on the aerial image dataset (AID), and 3D shape classification on the ModelNet40 dataset. The experimental results verify the practical applicability of the HexagonNet given some fixed parameter budgets.

Force field driven skeleton extraction method for point cloud trees

A key step in processing natural trees from point cloud data is to reconstruct the trees’ skeleton, which plays an important role in forest investigation and monitoring. Although the techniques for general objects skeletonizing based on point clouds have made a large stride, there are few efficient and simple studies on the natural trees, which have complex topologies. In this paper, we propose a novel method to reconstruct tree skeletons based on the point cloud data, named as the force field driven tree skeleton extracting method, which consists of the following steps. Specifically, to make the point cloud tree a little bit cleaner, the hierarchical subdivision to the original point cloud space is firstly proposed. Then the split-level of the trees’ applied space is considered in each layers, and a simplified representation of the feature points for the tree model is then established under the neighbor relationships. After that, the feature points in the peripheral are connected by the geodesic distance. To get the initial skeleton, the surface geodesic lines are compressed into the tree model by applying a visible repulsive force field. Finally, the final skeleton is acquired by polishing the initial skeleton according to a threshold setting. The experimental results on two kinds of representative naturally growing trees, which are the Cherry and Michelia, indicate that this method can provide a satisfactory performance.

The microstructural origin of work hardening stages

The strain evolution of the flow stress and work hardening rate in stages III and IV is explored by utilizing a fully described deformation microstructure. Extensive measurements by transmission electron microscopy reveal a hierarchical subdivision of grains by low angle incidental dislocation boundaries (IDBs) and medium to high angle geometrically necessary boundaries (GNBs). This universal evolution is demonstrated for nickel, copper, and aluminum deformed by cold rolling from strains of 0.05–5.5. Microstructural morphology evolves with increasing strain through a transition resulting in a lamellar cell-block structure aligned with the deformation. This transition is caused by the emergence of new slip systems and a stable texture. Four parameters describe the microstructure, the misorientation angle across each boundary type and their respective spacing. Universal scaling characterizes the normalized distributions of three separate parameters. A new scaling law connects the strain evolution of two strength parameters: the dislocation density of IDBs and the spacing between GNBs. Strengthening mechanisms and strength contributions for those two parameters are expressed respectively as a linear addition of the classical Taylor and Hall-Petch formulations. Model predictions agree closely with experimental values of flow stress and work hardening rate in stages III and IV. Strong connections between the evolutionary stages of the deformation microstructure and work hardening rates create a new (modern) basis for the classic problem of work hardening in metals and alloys. These connections lead the way for the future development of ultra high strength ductile metals produced via plastic deformation.

THE STATUS OF STRATIGRAPHY IN THE 21ST CENTURY

The 21st century geological time scale (GTS) will comprise an internationally agreed chronologic hierarchy. Correlation of events into the GTS will be undertaken using a wide variety of methods, including numeric dating, fossil occurrence, physical and chemical properties, tephrochronology and astrochronologic retrodictions. Chronostratigraphic subdivision of the sedimentary rock record should proceed in a bottom up hierarchical manner with lower units defining the boundaries of stratigraphically higher units. A moderate amount of work is required to improve the basis of the hierarchical subdivision of some Cenozoic series boundary subdivisions and to bring them in line with recommendations by the Stratigraphic Guide and recommendations by the International Committee of Stratigraphy (ICS).

Open architecture RDBMS and GIS as tools for analysing the Etruscan presence in the Po Plain: towards a model of the urban/non urban landscape

The Po Valley was occupied by the Etruscans starting in the 9th century BC. This presence experienced a significant transformation from the mid-6th century BC, when the territory underwent a widespread colonisation process, which brought about a new pattern in the organization of the landscape. A network of farms and secondary settlements appeared and expanded around both old and new cities. Through the structuring power and the analytical potential of GIS, this research develops new perspectives on the reconstruction of the ancient landscape. In addition to cultural aspects closely related to Etruscan society, in this study we have taken into consideration the role played by the resources of the territory itself, both from economic and the transport network points of view. First, we briefly present the conceptual and physical structure of the GIS. It includes an archive of all the known sites N of the Apennines (541), dating to between the 6th and 4th century BC (managed in a relational database), and a set of geographic and thematic data of general interest, recorded in the same cartographic reference system, handled with GIS software. Second, on the basis of certain distinctive characteristics of settlements such as the size of the occupied area, the internal organization and the building techniques employed, a possible hierarchical subdivision of the settlements is identified. Further, the optimal pathways between major cities are hypothesised considering factors such as slope and the presence of rivers or streams, and a possible road network is calculated using the MADO model (optimal accumulation model of movement from a given origin). The final aim is to propose a settlement model that can then be compared to the reality of the current archaeological record.

Total variation for the analysis of event-related potentials

BackgroundEvent-related potential waveforms are often analysed in the time-domain for changes of striking morphological features, like amplitudes or latencies of extrema, at the expense of missing less obvious changes in overall morphology. New methodThe measure of total variation can capture a variety of changes in curve morphology. We show analytical examples, and the application to two sets of EEG data (n1=41, n2=19) difficult to analyse with more traditional methods. ResultsTotal variation can be used to identify the effects of experimental manipulations on event-related potential waveforms, and can additionally be used to identify the respective time windows by means of hierarchical subdivision of longer signals. Comparison with existing methodsThe ANOVA of total variation provided additional insights into effects already hinted at by the ANOVA of global field power in the first experiment, and identified a number of interactions missed by an ANOVA of amplitude as well as a topographic ANOVA in the second one. ConclusionsThe analysis of total variation can be an interesting complement to more traditional analyses, especially when changes are hard to assess with traditional methods, e.g. in the absence of pronounced extrema, or the presence of noise or large interindividual variations of latency.

A stabilised immersed boundary method on hierarchical b-spline grids

In this work, an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b-spline grid and employs the non-symmetric and penalty-free version of Nitsche’s method to enforce the boundary conditions. The strategy allows for h- and p-refinement and employs a so-called ghost penalty term to stabilise the cut cells. An effective procedure based on hierarchical subdivision and sub-cell merging, which avoids excessive numbers of quadrature points, is used for the integration of the cut cells. A basic Laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty-free Nitsche method as well as their impact on accuracy. The methodology is also applied to the incompressible Navier–Stokes equations, where the SUPG/PSPG stabilisation is employed. Simulations of the lid-driven cavity flow and the flow around a cylinder at low Reynolds number show the good performance of the methodology. Excessive ill-conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field.

Location Privacy with Randomness Consistency

Abstract Location-Based Social Network (LBSN) applications that support geo-location-based posting and queries to provide location-relevant information to mobile users are increasingly popular, but pose a location-privacy risk to posts. We investigated existing LBSNs and location privacy mechanisms, and found a powerful potential attack that can accurately locate users with relatively few queries, even when location data is well secured and location noise is applied. Our technique defeats previously proposed solutions including fake-location detection and query rate limits. To protect systems from this attack, we propose a simple, scalable, yet effective defense that quantizes the map into squares using hierarchical subdivision, consistently returns the same random result to multiple queries from the same square for posts from the same user, and responds to queries with different distance thresholds in a correlated manner, limiting the information gained by attackers, and ensuring that an attacker can never accurately know the quantized square containing a user. Finally, we verify the performance of our defense and analyze the trade-offs through comprehensive simulation in realistic settings. Surprisingly, our results show that in many environments, privacy level and user accuracy can be tuned using two independent parameters; in the remaining environments, a single parameter adjusts the tradeoff between privacy level and user accuracy. We also thoroughly explore the parameter space to provide guidance for actual deployments.

Shared phylogeographical breaks in a Caribbean coral reef sponge and its invertebrate commensals

AbstractAimTo test whether phylogeographical barriers in the brooding sponge Callyspongia vaginalis match breaks previously identified in the Caribbean. We also compared patterns of subdivision in the sponge to those of three of its commensals, the broadcast spawning brittle star Ophiothrix suensonii and the brooding amphipods Leucothoe ashleyae and L. kensleyi, and tested whether any shared breaks arose simultaneously.LocationFlorida, Bahamas and the Caribbean.MethodsSubdivision of C. vaginalis populations was inferred from one mitochondrial (COI) and six nuclear loci using clustering analyses. We identified phylogeographical breaks in the sponge and its invertebrate commensals by determining geographical patterns of genetic variation and tested simultaneous population divergence across barriers shared among taxa using hierarchical approximate Bayesian computation.ResultsSponge populations were partitioned into western and eastern groups across the Caribbean, with hierarchical subdivision within regions. The sponge and its commensals shared barriers across their ranges despite differences in dispersal strategy: C. vaginalis, L. ashleyae and O. suensonii populations in Central America were isolated from the remainder of the Caribbean, and all four taxa shared a break between Florida and the Bahamas, although simultaneous population divergence could not be inferred with statistical certainty. Our results also suggest cryptic speciation within C. vaginalis.Main conclusionsPhylogeographical patterns in C. vaginalis largely matched barriers previously identified at the Florida Straits, Mona Passage and Bay of Honduras in other Caribbean taxa. Oceanographic features such as deep water between locations, strong currents, and eddies are likely mechanisms responsible for these breaks.

STRUCTURELESS BUNDLE ADJUSTMENT WITH SELF-CALIBRATION USING ACCUMULATED CONSTRAINTS

Abstract. Bundle adjustment based on collinearity is the most widely used optimization method within image based scene reconstruction. It incorporates observed image coordinates, exterior and intrinsic camera parameters as well as object space coordinates of the observed points. The latter dominate the resulting nonlinear system, in terms of the number of unknowns which need to be estimated. In order to reduce the size of the problem regarding memory footprint and computational effort, several approaches have been developed to make the process more efficient, e.g. by exploitation of sparsity or hierarchical subdivision. Some recent developments express the bundle problem through epipolar geometry and scale consistency constraints which are free of object space coordinates. These approaches are usually referred to as structureless bundle adjustment. The number of unknowns in the resulting system is drastically reduced. However, most work in this field is focused on optimization towards speed and considers calibrated cameras, only. We present our work on structureless bundle adjustment, focusing on precision issues as camera calibration and residual weighting. We further investigate accumulation of constraint residuals as an approach to decrease the number of rows of the Jacobian matrix.

STRUCTURELESS BUNDLE ADJUSTMENT WITH SELF-CALIBRATION USING ACCUMULATED CONSTRAINTS

Bundle adjustment based on collinearity is the most widely used optimization method within image based scene reconstruction. It incorporates observed image coordinates, exterior and intrinsic camera parameters as well as object space coordinates of the observed points. The latter dominate the resulting nonlinear system, in terms of the number of unknowns which need to be estimated. In order to reduce the size of the problem regarding memory footprint and computational effort, several approaches have been developed to make the process more efficient, e.g. by exploitation of sparsity or hierarchical subdivision. Some recent developments express the bundle problem through epipolar geometry and scale consistency constraints which are free of object space coordinates. These approaches are usually referred to as structureless bundle adjustment. The number of unknowns in the resulting system is drastically reduced. However, most work in this field is focused on optimization towards speed and considers calibrated cameras, only. We present our work on structureless bundle adjustment, focusing on precision issues as camera calibration and residual weighting. We further investigate accumulation of constraint residuals as an approach to decrease the number of rows of the Jacobian matrix.

On the linear independence of truncated hierarchical generating systems

Motivated by the necessity to perform adaptive refinement in geometric design and numerical simulation, the construction of hierarchical splines from generating systems spanning nested spaces has been recently studied in several publications. Linear independence can be guaranteed with the help of the local linear independence of the spline basis at each level. The present paper extends this framework in several ways. Firstly, we consider spline functions that are defined on domain manifolds, while the existing constructions are limited to domains that are open subsets of Rd. Secondly, we generalize the approach to generating systems containing functions which are not necessarily non-negative. Thirdly, we present a more general approach to guarantee linear independence and present a refinement algorithm that maintains this property. The three extensions of the framework are then used in several relevant applications: doubly hierarchical B-splines, hierarchical Zwart-Powell elements, and three different types of hierarchical subdivision splines.