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The Travelling Salesperson Problem (TSP) is a nondeterministic-polynomial hard (NP-hard) combinatorial problem that occurs in a wide range of industrial domains, including logistics, route finding, and computer wiring. Interestingly, despite the problem's inherent computational difficulty, when presented in Euclidean space (ETSP), human participants can produce close-to-optimal solutions in near-linear time. However, when asked to compare and select the most optimum solution from a set of pre-defined competing solution options, participants can struggle. In this study we investigate this paradox by asking participants to compare four closed-loop Euclidean TSP solutions, in order to determine which solution they perceived to have the most optimal tour cost. We hypothesise that the extracted geometric properties have an effect on stimulus selection in a discrimination task (selection or no selection). Accordingly, we extracted four geometric properties from competing stimuli in order to create a perceptual activation function. Predictive analytics demonstrated that a classification model could identify the most optimal solution 97% of the time using the perceptual activation scores alone, yet human participants only correctly determined the most optimal solution 47% of the time. Mixed-effects models suggest that 'likelihood of stimulus selection' can be modelled as a function of the weighted coefficients of competing perceptual activation scores within each trial; however only a small amount of the variance is explained by these perceptual activation scores. Finally, a drift–diffusion model was used to create a theoretical framework of how likelihood of stimulus selection is influenced by competing perceptual activators. Our study highlights a novel way of extracting and analysing the importance of geometric properties that influence ETSP discrimination tasks, and links this analysis to human behaviour when discriminating between competing ETSP solutions. [ABSTRACT FROM AUTHOR]

The percolation behavior of composites comprising complex-shaped particles is a recurrent problem in materials science. Previous studies focused on the symmetric particles such as spheres, ellipsoids, spherocylinders, etc. The continuum percolation of a family of single axial asymmetric ovoids with tapering parameter T and aspect-ratio c / a is studied here. The geometrical properties and numerical contact detection algorithm of these ovoids are proposed firstly. Using the Monte Carlo finite-size-scaling method, the percolation threshold ϕ c of the systems comprising congruent overlapping ovoids is further determined. For a given T , ϕ c shows an initially increasing and then decreasing trend with the increasing c / a. Moreover, the value of ϕ c at the fixed c / a decreases with the increasing | T | and this trend will be more obvious with the decreasing c / a. Finally, an analytical formula is proposed to quantify the effect of ovoid's morphology, characterized by the dimensionless excluded volume of ovoid, on the percolation thresholds. (a) The system comprising random distributed overlapping asymmetric ovoids in cubic container. (b) The ovoids connected with the upper bound. (c) Percolation path in the system. Image 1 • The granular composite is assumed to be the system comprising congruent overlapping asymmetric ovoids. • A formula is proposed to calculate the volume of ovoid. • A new contact detection algorithm of inter-ovoid is developed. • The percolation thresholds of systems comprising randomly distributed overlapping ovoids are calculated. • An analytical formula is derived to predict the percolation threshold of ovoids. [ABSTRACT FROM AUTHOR]

The detection of structure centerlines from imaging data plays a crucial role in the understanding, application and further analysis of many diverse problems, such as road mapping, crack detection, medical imaging and biometric identification. In each of these cases, pixel-wise segmentation is not sufficient to understand and quantify overall graph structure and connectivity without further processing that can lead to compound error. We thus require a method for automatic extraction of graph representations of patterning. In this paper, we propose a novel Deep Orientated Distance-transform Network (DODN), which predicts the centerline map and an orientated distance map, comprising orientation and distance in relation to the centerline and allowing exploitation of its geometric properties. This is refined by jointly modeling the relationship between neighboring pixels and connectivity to further enhance the estimated centerline and produce a graph of the structure. The proposed approach is evaluated on a diverse range of problems, including crack detection, road mapping and superficial vein centerline detection from infrared/ color images, improving over the state-of-the-art by 2.1%, 10.9% and 17.3%/ 4.6% respectively in terms of quality, demonstrating its generalizability and performance in a wide range of mapping problems. • We present a novel multitask learning architecture for centerline detection. • We incorporate task uncertainty to simultaneously learn multiple losses. • A graph-cut based connectivity refinement approach is proposed. • Our proposed approach outperforms state-of-the-art methods on three datasets. [ABSTRACT FROM AUTHOR]

• To implement the prognostic and health management (PHM) for industrial processes, a dynamic-controlled principal component analysis (DCPCA) for pattern modelling is proposed, which can facilitate the detecting and automatic rectifying of faults. • Significantly, the geometric properties of DCPCA are analysed, revealing the spatial structure relationships of different variables and how the data space is transmitted and partitioned. • The model relationships in DCPCA are explored, including the dynamic characteristics of time-series variables and the algebraic relationships of static variables. • Statistics are derived for monitoring both the dynamic and static relationships, and if in abnormal circumstance, by diagnosing the deviations between the fault pattern and the setpoint, a regulator for automatic recovery is triggered. To effectively implement the prognostic and health management for industrial processes, a dynamic-controlled principal component analysis (DCPCA) for pattern extraction and deviation diagnosis is proposed under the framework of multivariate statistical modelling, which can accurately detect and automatically rectify the faults. Significantly, the geometric properties of DCPCA are analysed, revealing the spatial structure relationships of different variables and how the data space is partitioned. In addition, the model relationships in DCPCA are explored, including the dynamic characteristics of time-series variables and the algebraic ones of static variables. Based on these results, statistics are derived for monitoring both the dynamic and static relationships of the process, and under the abnormal circumstance, by diagnosing the deviations between the fault pattern and the setpoint, a fault regulator for automatic recovery is designed. The case study of prognostic and health management for an industrial distillation column illustrates the advantages of DCPCA in fully extracting the process dynamics into pattern, as well as fault detection and automatic recovery. [ABSTRACT FROM AUTHOR]

• Differences in sphericity, angularity and surface texture of aggregates with different materials are discussed. • Effects of sphericity, angularity and surface texture of aggregate on the workability of asphalt mixture are analyzed. • Influence of geometric characteristics of aggregate on the uniformity of asphalt film is determined. Workability of asphalt mixtures is considered as an essential factor in quality control of asphalt pavement construction. However, there are fewer studies related to the influence of geometric properties of aggregates on the workability of asphalt mixture. The main purpose of this paper is to explore the influence of aggregate sphericity, angularity and surface texture on the workability of asphalt mixture during the mixing process. Firstly, a self-developed workability equipment of asphalt mixture was used to analyze the differences in the asphalt mixture workability of three materials, namely, basalt, limestone and pebble. Next, using the Aggregate Image Measurement System (AIMS), the geometric characteristics of the aggregates were determined. Accordingly, the correlation between the geometric characteristics of the aggregates and the workability index was established through linear correlation analysis. Finally, investigating the distribution uniformity of asphalt film by scanning electron microscope (SEM), the influence of the geometric characteristics of the aggregates on the workability of the asphalt mixture was determined. The results demonstrated that, compared with limestone and pebble asphalt mixtures, a significantly greater workability value was observed for the basalt asphalt mixture. Moreover, the geometric characteristics of the aggregates were found to influence the change rule of workability in the following order: sphericity > surface texture > angularity. Furthermore, the geometric characteristics revealed to have a significant effect on the uniformity of the asphalt film. [ABSTRACT FROM AUTHOR]

An approach was proposed to automatically measure the discontinuity geometric properties from a point cloud acquired using Light Detection and Ranging (LiDAR). The procedure primarily includes the following features: (Assali et al., 2016) Grid data from the point cloud was created to enhance computational efficiency for data processing and retrieval; (Barton & Choubey, 1977) A modified region growing (MRG) algorithm, which is characterized by more efficient grow criterion, was used to recognize discontinuities from the point cloud; (Cao et al., 2017) Four geometric properties from identified discontinuities were calculated based on analytic geometry; (Chen et al., 2016) Influence of threshold T on the identified results was investigated through sensitivity analysis, and threshold T was suggested to be less than the minimum normal difference among all joints and larger than 0°. Two cases (regular polyhedrons and a tunnel in the Rumei hydropower station) were taken as case studies to validate the developed approach, and calculation results have good agreement with real situations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compute all the Frenet apparatus of non-transversal intersection curves (hyper-curves) of three implicit hypersurfaces in Euclidean 4-space. The tangential direction at a transversal intersection point can be computed easily, but at a non-transversal intersection point, it is difficult to calculate even the tangent vector. If three normal vectors are parallel at a point, the intersection is “tangential intersection”; and if three normal vectors are not parallel but are linearly dependent at a point, we have “almost tangential” intersection at the intersection point. We give algorithms for each case to find the Frenet vectors ( t , n , b 1 , b 2 ) and the curvatures ( k 1 , k 2 , k 3 ) of the non-transversal intersection curve. [ABSTRACT FROM AUTHOR]

Abstract: The performance of the Proton Exchange Membrane Fuel Cell (PEMFC) is greatly influenced by the various operating parameters and geometric properties. This paper deals with optimization of both operating and design parameters namely cell temperature, back pressure, anode and cathode inlet velocities, Gas Diffusion Layer (GDL) porosity and thickness, cathode water mass fraction, flow channel dimensions, rib width and porous electrode thickness. The Numerical model of single channel PEM fuel cell was developed and analyzed by using COMSOL Multiphysics 4.2 software package. The optimization of design and operating parameters in software was carried out in two stages using standard orthogonal array of Taguchi method. From the first stage of analysis, it was inferred that back pressure had maximum effect and rib width had least effect on fuel cell performance. In the second stage of analysis, fine tuned optimization was performed on selected factors which caused for 3% increase in power density and the results were also validated using COMSOL Multiphysics 4.2. [Copyright &y& Elsevier]

Abstract: We present algorithms for computing the differential geometry properties of Frenet apparatus of intersection curves of implicit–parametric–parametric and implicit–implicit–parametric hypersurfaces in , for transversal intersection. Some examples are given and plotted. [Copyright &y& Elsevier]

Abstract: Accurate geometric properties estimation from discrete curves is an important problem in many application domains, such as computer vision, pattern recognition, image processing, and geometric modeling. In this paper, we propose a novel method for estimating the geometric properties from discrete curves based on derivative estimation. We develop derivative estimation by defining the derivative of a discrete function at a point, which will be called the discrete derivative. Similarly, the second and higher order discrete derivatives at that point are also defined, and their convergence is demonstrated by theory analysis. These definitions of the different order discrete derivatives provide a simple and reliable way to estimate the derivatives from discrete curves. Based on the discrete derivatives, classical differential geometry can be discretized, and the geometric properties are estimated from discrete curves by using differential geometry theory. The proposed method is independent of any analytic curve and estimates the geometric properties directly from discrete data points, which makes it robust to the geometric shapes of discrete curves. Another advantage of the proposed method is the robustness to noise because of the calculation characteristics of the discrete derivatives. The proposed method is evaluated and compared with other existing methods in the experiments with both synthetic and real discrete curves. The test results show that the proposed method has good performance, and is robust to noise and suitable for different curve shapes. [Copyright &y& Elsevier]

Abstract: We present algorithms for computing the differential geometry properties of intersection curves of three implicit surfaces in , using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive vectors and curvatures () for transversal intersections of the intersection problem. [Copyright &y& Elsevier]

• The inertial dependence of the non-Darcy coefficient was disclosed. • The influence of fluid inertial effect on the non-Darcy coefficient was quantified. • The quantitative model of the non-Darcy coefficient was improved. • A new critical Reynolds number prediction model was obtained. This study experimentally and numerically investigated the influence of the inertial effect of fluid flow on the non-Darcy coefficient (β). The results showed that the non-Darcy coefficient (β), apparent permeability (k a), and hydraulic aperture (e h) decreased with the increase of Reynolds number (Re), which indicated that the non-Darcy coefficient depended on the geometric properties of a single fracture and the fluid inertial effect. The quantification model of the non-Darcy coefficient was improved. Under the guidance of fluid inertial effect, the β performed a positive power-law relationship with e h ; under the coupling effect of fluid inertial effect and fracture geometric properties, the β behaved negative power-law relationship with e h , which was similar to the non-Darcy coefficient quantitative model that ignored the fluid inertial effect in the previous study. Therefore, the geometric properties were the dominant ones for fracture flow when it was affected by the coupling effect of geometric properties and inertial effects. Then, the quantitative model of the non-Darcy coefficient was improved. Based on the improved non-Darcy coefficient quantitative model, a new critical Reynolds number prediction model (CRN model) was constructed. Compared with other CRN models, the new CRN model considering the coupling effect of fluid and media properties could more accurately predict the critical Reynolds number (Re c) in rough single fractures, which further proved the existence and importance of the inertial dependence of the non-Darcy coefficient. [ABSTRACT FROM AUTHOR]

In the present paper, stability and convergence properties of linear multistep methods are investigated. The attention is focused on parabolic problems and variable stepsizes. Under weak assumptions on the method and the stepsize sequence an asymptotic stability result is shown. Further, stability bounds for linear nonautonomous parabolic problems with Ho¨lder continuous operator are given. With the help of these results, convergence estimates for semilinear and fully nonlinear parabolic problems are derived. [Copyright &y& Elsevier]

• Design and manufacture of a manual compressed earth block (CEB) machine. • Physical and numerical testing of un-stabilised CEBs with different geometries. • Macro finite element analysis for un-stabilised CEBs using a Solid65 material model. • Sensitivity analysis of numerical model to account for block imperfections. This paper presents a parametric investigation into the influence of geometry on the compressive and flexural strength of un-stabilised compressed earth blocks (CEBs). Three CEBs with dissimilar geometric properties were manufactured and subjected to physical testing and Finite Element Analysis (FEA) using ANSYS Workbench 19.1. The compressive and flexural strength of the CEBs were shown to be dependent on their geometric properties and ranged from 3.74 to 6.73 MPa and 0.63–1.31 MPa respectively. A modified Solid65 element command was utilised within the FEA and was shown to successfully replicate the non-linear elasto-plastic behaviour observed in physical testing. [ABSTRACT FROM AUTHOR]

Traditional member-based two-step design approaches included in current structural codes for steel structures, as well as more recent system-based direct-design alternatives, require building rigorous structural reliability frameworks for the calibration of partial coefficients (resistance factors) to achieve specified target reliability requirements. Key design parameters affecting the strength of structures and their random variations are generally modelled by nominal or characteristic values in design standards, which are combined with partial coefficients that need to be calibrated from measurements on real samples. While the statistical characterization of material and geometric properties of structural steels has been consolidated over the last decades, information about the characterization of structural stainless steels is virtually non-existent due to the limited pool of available data. Thus, this paper presents the basic ingredient for developing reliability frameworks for stainless steel structures and components by statistically characterizing the main random parameters affecting their strength through a comprehensive database collected from the literature. Based on the collected data, appropriate probabilistic models are proposed for geometric properties, material properties, imperfections and residual stresses of different stainless steel alloys and cross-section or product types. The data is equally applicable to member-based reliability analyses as described in existing codes and system-based analyses targeted at the direct-design of stainless steel structures by advanced analysis. Unlabelled Image • Data on most relevant random variables is collected through a comprehensive literature review. • Data for different stainless steel alloys and cross-section types are analysed. • The variability of parameters affecting the strength of stainless steel structures is statistically characterized. • Appropriate statistical functions and probabilistic models are provided for geometry, material, imperfections and residual stresses. • Foundational data is provided for complete member- and system-based reliability frameworks, from which safety factors and resistance factors can be derived. [ABSTRACT FROM AUTHOR]

The present study numerically investigates the breaking and spectral characteristics and geometric properties of breaking irregular waves over slopes for different incident waves. The growth of wave non-linearity and wave energy redistribution during shoaling and breaking process are observed to be major factors in determining the free surface elevation skewness and spectral bandwidth. In general, the variation of the breaker indices with the surf similarity parameter is found to be mainly governed by the type of wave breakers. The wave breaker type further depends on the seabed slope, incident wave parameters and water depth at the location of wave breaking. The study further explores the geometric properties for both spilling and plunging irregular wave breakers. The wave deformation due to wave-seabed interaction plays a major role in affecting the breaker shapes. Every individual breaking wave in the irregular wave train possesses different wave profiles and breaker characteristics. In order to study these parameters in a probabilistic way, the statistics of the breaker characteristics and the breaker shape parameters are investigated. The lognormal distribution is noticed to be the most suitable fit for the wave crest steepness and asymmetry factors. This study is performed using the open-source computational fluid dynamics (CFD) based numerical model. The numerical model is validated for a submerged bar under breaking irregular waves and the numerical results are compared with experimental data. The transformations of the free surface elevation due to wave shoaling, wave breaking and wave decomposition are explored. • Numerical modelling of breaking irregular waves. • Validation of numerical model with experimental data. • Hydrodynamic and spectral characteristics of breaking irregular waves. • Wave profile geometric properties of breaking irregular waves. • Statistics of hydrodynamic and wave profile geometric properties. [ABSTRACT FROM AUTHOR]

• 3D scanning and reverse engineering approach to acquire the geometry of bamboo poles. • Creation of 3D models and numerical database with relevant geometric information. • Geometric variability of bamboo poles from three species was digitally analysed. • Results showed a wide range of variability throughout the studied species. • Proposed methodology showed potential to support new design and construction processes. The implementation of sustainable building materials is currently one of the principal global challenges faced by the construction industry. Natural bamboo culms are a potential alternative to tackle this challenge due to its favourable environmental credentials as well as affordability. However, the organic geometry of bamboo culms is one of the barriers that prevents them from being implemented in formal design procedures. This work presents the details of a new digitisation workflow to systematically capture the geometry of bamboo culms through the application of 3D scanning technologies and reverse engineering principles. This workflow is applied to carry out a comprehensive analysis of the geometric variability of Guadua angustifolia kunth (Guadua), Phillostachys pubescens (Moso) and Bambusa oldhamii (Oldhamii) to identify potential correlation patterns. This geometric analysis showed a wide variation in the geometric properties of all species and no particular pattern was found which could be adopted for a potential visual grading system. These results highlight the challenges that the use of bamboo culms pose for the traditional design and fabrication processes developed for manufactured structural elements. The proposed reverse engineering methodology adopted for this study can be used to quantify and manage the geometric variability of bamboo culms to support the development of new formal design and fabrication processes for this natural structural element. [ABSTRACT FROM AUTHOR]