Search

One of the important issues being explored in Industry 4.0 is collaborative mobile robots. This collaboration requires precise navigation systems, especially indoor navigation systems where GNSS (Global Navigation Satellite System) cannot be used. To enable the precise localization of robots, different variations of navigation systems are being developed, mainly based on trilateration and triangulation methods. Triangulation systems are distinguished by the fact that they allow for the precise determination of an object's orientation, which is important for mobile robots. An important feature of positioning systems is the frequency of position updates based on measurements. For most systems, it is 10–20 Hz. In our work, we propose a high-speed 50 Hz positioning system based on the triangulation method with infrared transmitters and receivers. In addition, our system is completely static, i.e., it has no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear of components, etc.). In this paper, we describe the principle of the system as well as its design. Finally, we present tests of the built system, which show a beacon bearing accuracy of Δ φ = 0.51 ° , which corresponds to a positioning accuracy of Δ R = 6.55 cm, with a position update frequency of f u p d a t e = 50 Hz. [ABSTRACT FROM AUTHOR]

The Earth's crust is exposed by tectonic processes and is not static over time. Modelling of the Earth's surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth's surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties. [ABSTRACT FROM AUTHOR]

Structured light (SL) sensing technology, based on the triangulation principle, is widely employed for depth perception in various applications such as face recognition, human‐computer interaction, machine vision, and more. In this approach, the baseline length, which refers to the distance between the projection device and the camera, is a critical parameter that affects depth measurement and system miniaturization. Recently, metasurfaces have emerged as promising devices for constructing compact optoelectronic systems due to their excellent performance in wavefront modulation of light and ultra‐thin characteristics. In this study, a metasurface‐based monocular SL depth detection scheme is proposed that incorporates a specially designed 3D holographic projection. Under this projected light field, the entire 3D space is labeled, and depth information can be obtained without considering the baseline length, which can further reduce the volume of SL systems. Additionally, a template‐matching algorithm based on correlation coefficient analysis is developed and experimentally demonstrates its feasibility by precisely positioning objects. It is believed that this work opens up a new perspective for compact, lightweight, and flexible design of SL sensing systems, and has a promising future in quantitative detection, automatic location, and industrial measurement. [ABSTRACT FROM AUTHOR]

Background and Aim: Drinking alcohol may cause harm to an individual's health and social relationships, while a drinking culture may harm societies as it may increase crime rates and make an area feel less safe. Local councils in Greater Manchester, UK, developed the Communities in Charge of Alcohol (CICA) intervention, in which volunteers were trained to give alcohol‐related advice to the public and taught how to influence policies to restrict when, where and how alcohol is sold. As part of a larger study, the aim of the current project is to measure the impact of CICA on health and crime outcomes at the lower super output (LSOA) geographical aggregation. Design: Quantitative evaluation using four time series analytic methods (stepped‐wedge design, and comparisons to local controls, national controls and synthetic controls) with findings triangulated across these methods. A cost–benefit analysis was carried out alongside the effectiveness analysis. Setting and Participants: The general public in Greater Manchester, UK, between 2010 and 2020. Measurements: The primary outcome of interest was alcohol‐related hospital admissions. Secondary outcomes were accident and emergency (A&E) attendances, ambulance callouts, recorded crimes and anti‐social behaviour incidents. Findings Triangulation of the results did not indicate any consistent effect on area‐level alcohol‐related hospital admissions, A&E attendances, ambulance callouts, reported crimes or anti‐social behaviour associated with the implementation of CICA. The primary stepped‐wedge analysis indicated an increase in alcohol‐related hospital admissions following the implementation of CICA of 13.4% (95% confidence interval −3.3%, +30.1%), which was consistent with analyses based on other methods with point estimates ranging from +3.4% to 16.4%. Conclusion: There is no evidence of a measurable impact of the Communities in Charge of Alcohol (CICA) programme on area‐level health and crime outcomes in Greater Manchester, UK, within 3 years of the programme start. The increase in alcohol‐related hospital admissions was likely the result of other temporal trends rather than the CICA programme. Possible explanations include insufficient follow‐up time, too few volunteers trained, volunteers being unwilling to get involved in licensing decisions or that the intervention has no direct impact on the selected outcomes. [ABSTRACT FROM AUTHOR]

Triangulation is a classical geodetic practice to establish survey control networks by using measurements of angles and some spare distances. In this way, a series of reference points or simply called 'trigs' is spreading over the country. This paper aims to review geodetic survey work that was carried out for the East Malaysia and Brunei from 1918 to 1968 which is covering about 204,119 square kilometres'. However, this classical geodetic datum is not directly compatible with the current surveying trends based on Global Navigation Satellite System technologies. Therefore, in this review covered concepts and history of triangulation systems, datums and the status of transformation plan to modernise geodetic datum for Sarawak. [ABSTRACT FROM AUTHOR]

Mixed methods research—methodologies that synthesize qualitative and quantitative approaches in the design, collection, analysis, and dissemination of research related to a specific topic or aim—is increasingly common, offering innovative empirical insight into families and relationships. We first elaborate on our definition of mixed methods research, emphasizing that there is significant heterogeneity within mixed methods approaches to studying families and relationships. Second, we discuss benefits of mixed methods projects within family and relationship research, including theory building and innovation. Third, we provide practical suggestions for designing and implementing a mixed methods project, highlighting useful resources for researchers as they develop research questions, plan designs, collect and analyze data, and disseminate findings. We emphasize the unique opportunities from abductive analytic approaches for mixed methods researchers and point to the need for reflexivity. Fourth, we consider common obstacles associated with disseminating mixed methods research and explain why family researchers need “mixed methods literacy” regardless of their research paradigm. Finally, we identify key areas of future growth for mixed methods researchers. We advocate that understanding mixed methods research has practical benefits, even for researchers not using these approaches. To cohesively build—and critique—our knowledge of families and relationships, family and relationship researchers across paradigms should be familiar with the basic tenets, strengths, and limitations of qualitative, quantitative, and mixed methods research. [ABSTRACT FROM AUTHOR]

We study the cohomology of families of |$(\varphi ,\Gamma)$| -modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify rank- |$1$| |$(\varphi ,\Gamma)$| -modules and deduce that triangulations of pseudorigid families of |$(\varphi ,\Gamma)$| -modules can be interpolated, extending a result of [ 29 ]. We then apply this to study extended eigenvarieties at the boundary of weight space, proving in particular that the eigencurve is proper at the boundary and that Galois representations attached to certain characteristic |$p$| points are trianguline. [ABSTRACT FROM AUTHOR]

For the problem of underwater single- eye non- contact measurement of fish size, it is usually necessary to measure the distance of underwater fish to obtain the three-dimensional information of its surface, this paper proposes a fish distance measurement scheme based on the laser triangulation method and conducts research on underwater laser ranging technology. According to the principle of optical path, multiple parameters need to be measured for ranging, which makes the process complex, error-prone, and slow in calculation. This paper first corrects the distortion of the image and restores its authenticity through Zhang Zhengyou's calibration method. The OpenCv open-source library is used to recognize the laser contour on the surface of the fish body, and a self-defined algorithm improves the accuracy of contour recognition. Centroid analysis is applied to the laser contour to obtain the centroid coordinates of laser brightness. By analyzing the displacement relationship between the coordinates of the laser image points and the spatial coordinates, a polynomial regression model with a one- variable fifth- order is fitted to predict the distance, simplifying the parameters. The experimental results indicate that the laser center of gravity recognition is not continuous, but can accurately identify on the fish body. The average error of the ranging model is 5. 6 mm. In 80% of the tested samples, the error of the predicted results is within 7. 0 mm, and the maximum error is within 2 cm of calibration, which meets the required accuracy for fish body distance measurement. The research suggests that this method can provide reference for further acquisition of surface three-dimensional information of fish body size. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using the idea of the Method of Orienting Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization 18(1) (1987) 65–81 and Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner, Optimization 18(3) (1987) 349–359). The concepts of orienting and final circles are introduced. The Delaunay edges are determined by orienting circles and a final circle. Our algorithm has O (n log n) worst-case running time. The algorithm is implemented in Python and some numerical examples are presented. [ABSTRACT FROM AUTHOR]

Background: Studies on disease-related obstructions experienced in everyday life of younger people with dementia (YOD ≤ 65 years) and their families are encouraged. Aim: To explore how the family carers experience six predefined topics that influence the everyday life and needs of persons with YOD. Method: A quantitative and a qualitative study including family carers of persons with young-onset Alzheimer's dementia (AD) and frontotemporal dementia (FTD). Seventy-four informants responded to the Camberwell Assessment of Needs in the Elderly (CANE) and individual interviews were conducted with 13 informants. Results: Family carers of persons with YOD reported few unmet needs in the CANE assessment. Needs related to behavior and close relationships were reported significantly more frequent (p < 0.1) in persons with FTD than in persons with AD. From the qualitative data, six main themes were emphasized: daily activities turned upside down, involuntary loss of previous social network, losing close relationship, but maintaining a friendship with the spouse, unpredictable behavior adds burdens to a changing life, health and life risks, and economic insecurity for future life and caring costs. Conclusion: Whilst family carers quantitatively reported unmet needs, the individual interviews reported several major difficulties in everyday life. [ABSTRACT FROM AUTHOR]

Traditional isosurface extraction methods for a single geological interface is complex and inefficient when it comes to the surface reconstruction of multi-region geological bodies. In this paper, to deal with the problem of implicit surface reconstruction with multiple geological interfaces, we propose the multi-labeled regularized marching tetrahedra method by extending the original regularized marching tetrahedra (RMT) method. The method can directly extract isosurfaces of multi-region geological objects (such as multi-layer geobodies and multi-material geological objects). It inherits the advantages of the RMT method and can generate high-quality meshes preserving the original topology of geological interfaces through vertex clustering. The method includes three steps: (1) intersection calculation by linear interpolation; (2) mesh simplification based on the vertex clustering method; (3) triangular patch extraction using the tetrahedral label indices based on geological region labels. Different labels are utilized to represent different geological regions of sampling points. The triangulation rules and schemes for tetrahedra with different label configurations are defined to distinguish between different geological interfaces. In order to ensure that the boundary of all geological regions in geological bodies can be correctly extracted (continuous outer boundaries of geological regions and consistent model topology), we propose tetrahedral triangulation schemes suitable for multi-region modeling by introducing auxiliary points on tetrahedral faces and inside the tetrahedron. In addition, we construct a look-up table containing 75 tetrahedral configurations to simplify the process of triangular patch extraction and improve the efficiency of the algorithm. The experimental results show that the method can be effectively applied to the surface reconstruction of multi-region geological bodies. [ABSTRACT FROM AUTHOR]

Research on retail food environment (RFE) relies on data availability and accuracy. However, the discrepancies in RFE datasets may lead to imprecision when measuring association with health outcomes. In this research, we present a two-tier hierarchical point of interest (POI) matching framework to compare and triangulate food outlets across multiple geospatial data sources. Two matching parameters were used including the geodesic distance between businesses and the similarity of business names according to Levenshtein distance (LD) and Double Metaphone (DM). Sensitivity analysis was conducted to determine thresholds of matching parameters. Our Tier 1 matching used more restricted parameters to generate high confidence-matched POIs, whereas in Tier 2 we opted for relaxed matching parameters and applied a weighted multi-attribute model on the previously unmatched records. Our case study in San Diego County, California used government, commercial, and crowdsourced data and returned 20.2% matched records from Tier 1 and 18.6% matched from Tier 2. Our manual validation shows a 100% matching rate for Tier 1 and up to 30.6% for Tier 2. Matched and unmatched records from Tier 1 were further analyzed for spatial patterns and categorical differences. Our hierarchical POI matching framework generated highly confident food POIs by conflating datasets and identified some food POIs that are unique to specific data sources. Triangulating RFE data can reduce uncertain and invalid POI listings when representing food environment using multiple data sources. Studies investigating associations between food environment and health outcomes may benefit from improved quality of RFE. [ABSTRACT FROM AUTHOR]

Background: Higher maternal pre-pregnancy body mass index (BMI) is associated with adverse pregnancy and perinatal outcomes. However, whether these associations are causal remains unclear. Methods: We explored the relation of maternal pre-/early-pregnancy BMI with 20 pregnancy and perinatal outcomes by integrating evidence from three different approaches (i.e. multivariable regression, Mendelian randomisation, and paternal negative control analyses), including data from over 400,000 women. Results: All three analytical approaches supported associations of higher maternal BMI with lower odds of maternal anaemia, delivering a small-for-gestational-age baby and initiating breastfeeding, but higher odds of hypertensive disorders of pregnancy, gestational hypertension, preeclampsia, gestational diabetes, pre-labour membrane rupture, induction of labour, caesarean section, large-for-gestational age, high birthweight, low Apgar score at 1 min, and neonatal intensive care unit admission. For example, higher maternal BMI was associated with higher risk of gestational hypertension in multivariable regression (OR = 1.67; 95% CI = 1.63, 1.70 per standard unit in BMI) and Mendelian randomisation (OR = 1.59; 95% CI = 1.38, 1.83), which was not seen for paternal BMI (OR = 1.01; 95% CI = 0.98, 1.04). Findings did not support a relation between maternal BMI and perinatal depression. For other outcomes, evidence was inconclusive due to inconsistencies across the applied approaches or substantial imprecision in effect estimates from Mendelian randomisation. Conclusions: Our findings support a causal role for maternal pre-/early-pregnancy BMI on 14 out of 20 adverse pregnancy and perinatal outcomes. Pre-conception interventions to support women maintaining a healthy BMI may reduce the burden of obstetric and neonatal complications. Funding: Medical Research Council, British Heart Foundation, European Research Council, National Institutes of Health, National Institute for Health Research, Research Council of Norway, Wellcome Trust. [ABSTRACT FROM AUTHOR]

In recent years, biographical interviews with former pupils have become important sources for boarding school history. This raises the question as to whether these retrospective sources can be combined with contemporary written material and how to go about that. This paper argues for a triangulation of written with oral sources and the related methods of historical biography research and reconstructive social research. The combination of data and methods turns boarding school history into an interdisciplinary project that poses new challenges for research. At the same time, it also offers a way to a deeper understanding of boarding school history and its long-term effects. [ABSTRACT FROM AUTHOR]

• Work addresses methodological considerations relevant for psychoneuroimmunology. • Different forms of reductionism and notions of mechanism and system are discussed. • Several positions in medicine and science regarding the mind–body problem are covered. • Recommendations for more robust and interdisciplinary science are provided. In medicine and science, one is typically taught the main theories in a discipline or field along with standard models before receiving more instructions on how to apply certain methods. The aim of this work is not to address one method, but rather methodology, the study and evaluation of methods, by taking a philosophy of science detour. In this, a critique of biomedicine will be used as a starting point to address some positions regarding reductionism, specifying notions such as systems and mechanisms, as well as regarding the mind–body problem discussing psychosomatic medicine and psychoneuroimmunology. Some recommendations to make science more pluralistic, robust and translationally-relevant will then be made as a way to foster constructive debates on reductionism and the mind–body problem and, in turn, favor more interdisciplinary research. [ABSTRACT FROM AUTHOR]

The idea of studying trisections of closed smooth 4-manifolds via (singular) triangulations, endowed with a suitable vertex-labelling by three colors, is due to Bell, Hass, Rubinstein and Tillmann, and has been applied by Spreer and Tillmann to standard simply-connected 4-manifolds, via the so-called simple crystallizations. In the present paper we propose generalizations of these ideas by taking into consideration a possible extension of trisections to compact PL 4-manifolds with connected boundary, which is related to Birman's special Heegaard sewing, and by analyzing gem-induced trisections, i.e. trisections that can be induced not only by simple crystallizations, but also by any 5-colored graph encoding a PL 4-manifold with empty or connected boundary. This last notion gives rise to that of G-trisection genus, as an analogue, in this context, of the well-known trisection genus. We give conditions on a 5-colored graph ensuring one of its gem-induced trisections – if any – to realize the G-trisection genus, and prove how to determine it directly from the graph. As a consequence, we detect a class of closed simply-connected 4-manifolds, comprehending all standard ones, for which both G-trisection genus and trisection genus coincide with the second Betti number and also with half the value of the graph-defined PL invariant regular genus. Moreover, the existence of gem-induced trisections and an estimation of the G-trisection genus via surgery description is obtained, for each compact PL 4-manifold admitting a handle decomposition lacking in 3-handles. [ABSTRACT FROM AUTHOR]

Indoor localization involves pinpointing the location of an object in an interior space and has several applications, including navigation, asset tracking, and shift management. However, this technology has not yet been perfected, and many methods, such as triangulation, Kalman filters, and machine learning models have been proposed to address indoor localization problems. Unfortunately, these methods still have a large degree of error that makes them ill-suited for difficult cases in real-time. In this study, we propose a hybrid model for Bluetooth low energy-based indoor localization. In this model, the triangulation method is combined with several machine learning methods (naïve Bayes, k-nearest neighbor, logistic regression, support vector machines, and artificial neural networks) that are optimized and tested in three different environments. In the experiment, the proposed model performed similarly to the solo triangulation model in easy and medium cases; however, the proposed model obtained a much smaller degree of error for hard cases than either solo triangulation or machine learning models alone. [ABSTRACT FROM AUTHOR]

We show that every simple planar near‐triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning. [ABSTRACT FROM AUTHOR]

A monotone polyomino is a set of grid cells pierced by a continuous monotone function f : [ a , b ] → R . We prove that the minimum number of monotone polyominos in a tiling of the n × n lattice square is n. Surprisingly, this turns out to be equivalent with the statement that every triangulation of the n × n lattice square into minimum lattice triangles contains at least 2n right angled triangles. [ABSTRACT FROM AUTHOR]

A construction due to Burago and Zalgaller (Vestnik Leningrad Univ 15:66–80, 1960; St Petersburg Math J 7(3):369–385, 1995) shows that every orientable polyhedral surface, one that is obtained by gluing Euclidean polygons, has an isometric piecewise linear embedding into Euclidean space E 3 . A flat torus, resulting from the identification of the opposite sides of a Euclidean parallelogram, is a simple example of polyhedral surface. The embeddings constructed according to Burago and Zalgaller may have a huge number of vertices, moreover distinct for every flat torus. Based on another construction of Zalgaller (J Math Sci 100(3):2228–2238, 2000. https://doi.org/10.1007/s10958-000-0007-3) and on recent works by Arnoux et al. (2021, in preparation), we exhibit a universal triangulation with 2434 triangles which can be embedded linearly on each triangle in order to realize the metric of any flat torus. [ABSTRACT FROM AUTHOR]

A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by planar diagrams, whereas their exteriors, which are compact 3-manifolds with torus boundary, are encoded by triangulations. Here, we give the first practical algorithm for finding a diagram of a knot given a triangulation of its exterior. Our method applies to links as well as knots, and allows us to recover links with hundreds of crossings. We use it to find the first diagrams known for 23 principal congruence arithmetic link exteriors; the largest has over 2500 crossings. Other applications include finding pairs of knots with the same 0-surgery, which relates to questions about slice knots and the smooth 4D Poincaré conjecture. [ABSTRACT FROM AUTHOR]

Polyline and building simplification remain challenging in cartography. Most proposed algorithms are geometric-based and rely on specific rules. In this study, we propose a deep learning approach to simplify polylines and buildings based on a graph autoencoder (GAE). The model receives the coordinates of line vertices as inputs and obtains a simplified representation by reconstructing the original inputs with fewer vertices through pooling, in which the graph convolution based on graph Fourier transform is used for the layer-by-layer feature computation. By adjusting the loss functions, constraints such as area and shape preservation and angle-characteristic enhancement are flexibly configured under a unified learning framework. Our results confirmed the applicability of the GAE approach to the multi-scale simplification of land-cover boundaries and contours by adjusting the number of output nodes. Compared with existing Douglas‒Peukcer, Fourier transform, and Delaunay triangulation approaches, the GAE approach was superior in achieving morphological abstraction while producing reasonably low position, area, and shape changes. Furthermore, we applied it to simplify buildings and demonstrated the potential for preserving the diversified characteristics of different types of lines. [ABSTRACT FROM AUTHOR]

We present a O (n 3 2 ) -time algorithm for the shortest (diagonal) flip path problem for lattice triangulations with n points, improving over previous O (n 2) -time algorithms. For a large, natural class of inputs, our bound is tight in the sense that our algorithm runs in time linear in the number of flips in the output flip path. Our results rely on an independently interesting structural elucidation of shortest flip paths as the linear orderings of a unique partially ordered set, called a minimum flip plan , constructed by a novel use of Farey sequences from elementary number theory. Flip paths between general (not necessarily lattice) triangulations have been studied in the combinatorial setting for nearly a century. In the Euclidean geometric setting, finding a shortest flip path between two triangulations is NP-complete. However, for lattice triangulations, which are studied as spin systems, there are known O n 2 -time algorithms to find shortest flip paths. These algorithms, as well as ours, apply to constrained flip paths that ensure a set of constraint edges are present in every triangulation along the path. Implications for determining simultaneously flippable edges, i.e. finding optimal simultaneous flip paths between lattice triangulations, and for counting lattice triangulations are discussed. [ABSTRACT FROM AUTHOR]

Traffic deaths and injuries are one of the major global public health concerns. The present study considers accident records in an urban environment to explore and analyze spatial and temporal in the incidence of road traffic accidents. We propose a spatio-temporal model to provide predictions of the number of traffic collisions on any given road segment, to further generate a risk map of the entire road network. A Bayesian methodology using Integrated nested Laplace approximations with stochastic partial differential equations (SPDE) has been applied in the modeling process. As a novelty, we have introduced SPDE network triangulation to estimate the spatial autocorrelation restricted to the linear network. The resulting risk maps provide information to identify safe routes between source and destination points, and can be useful for accident prevention and multi-disciplinary road safety measures. [ABSTRACT FROM AUTHOR]

Given a simple connected compact Lie group K and a maximal torus T of K , the Weyl group W = N K (T) / T naturally acts on T. First, we use the combinatorics of the (extended) affine Weyl group to provide an explicit W -equivariant triangulation of T. We describe the associated W -dg-ring. For a non-crystallographic Coxeter group W , using compact hyperbolic extensions rather than affine ones, we construct a compact W -manifold T (W) , which is an analogue of a torus for W. We exhibit a W -equivariant triangulation of T (W) and compute the associated W -dg-ring. Also, we derive its homology representation. [ABSTRACT FROM AUTHOR]

Why did the flurry of summitry in the Trump years to denuclearize North Korea fall short? What is the crux of the Korean security problem? To understand peninsular security, I argue that a more holistic approach is warranted to unpack and piece together the many crosscutting and overlapping security dynamics in a cogent and coherent manner. In this article, I first argue that the Korean Peninsula should be understood as a security system writ large, comprising the United States, China, and the two Koreas as indispensable players -in all major issues pertaining to peninsular security. The second section introduces complex systems theory as an analytical approach that injects more sophistication and dynamic into the otherwise overly structural analysis typical of the field. The third and fourth sections reconstruct the unfolding of major events in terms of a positive feedback loop – namely, how great power realpolitik and North Korea's provocations converged and ricocheted to cause the crisis in 2017, as well as a negative feedback loop in which triangular interactions both facilitated and obstructed US – North Korea wrangling. The conclusion offers some preliminary assessments of how things might play out in the future. [ABSTRACT FROM AUTHOR]

This article discusses approaches for expanding the dynamic range of measuring systems by implementing phase triangulation methods and structured illumination. These systems are designed for the high-precision measurement of the geometric parameters of complex profile products with arbitrary light-scattering surface properties. A method for expanding the dynamic range of thea measuring system is proposed, which is based on the automatic adjustment of the photodetector exposure duration, redundant collection of experimental data, and complex regression analysis. The results of experimental studies on the efficiency of the proposed method are presented. It has been demonstrated that the classical approach to interpreting images obtained using a photodetector with a fixed exposure duration almost always causes a large measurement error in the geometric parameters of a surface with a wide range of light-scattering properties. At low exposure values, the error in measuring the geometric parameters of the surface increases in the dark area, where the signal level is substantially weaker compared to the light areas of the measured surface. At high exposure values, the error in measuring the geometric parameters of the light area of the surface increases because the signal is outside the dynamic range of the photodetector. For the measured geometric parameters of surfaces with different light-scattering properties, the use of a photodetector with an extended range enables achieving a measurement error less than or approximately equal to the error of a measuring system containing a photodetector with a fixed exposure. Expanding the dynamic range simplifies automated measurements because there is no need to further optimize the photodetector parameters for the light-scattering properties of the surface of the measured object. [ABSTRACT FROM AUTHOR]

Based on the geometric characteristics of a tetrahedron, quantitative estimates of its degeneracy are proposed and their relationship with the condition number of local bases generated by the edges emerging from a single vertex is established. The concept of the tetrahedron degeneracy index is introduced in several versions, and their practical equivalence to each other is established. To assess the quality of a particular tetrahedral partition, we propose calculating the empirical distribution function of the degeneracy index on its tetrahedral elements. An irregular model triangulation (tetrahedralization or tetrahedral partition) of three-dimensional space is proposed, depending on a control parameter that determines the quality of its elements. The coordinates of the tetrahedra vertices of the model triangulation tetrahedra are the sums of the corresponding coordinates of the nodes of some given regular mesh and random increments to them. For various values of the control parameter, the empirical distribution function of the tetrahedron degeneracy index is calculated, which is considered as a quantitative characteristic of the quality of tetrahedra in the triangulation of a three-dimensional region. [ABSTRACT FROM AUTHOR]

We investigate the validity of the "Einstein relations" in the general setting of unimodular random networks. These are equalities relating scaling exponents: where dw is the walk dimension, df is the fractal dimension, ds is the spectral dimension, and is the resistance exponent. Roughly speaking, this relates the mean displacement and return probability of a random walker to the density and conductivity of the underlying medium. We show that if df and exist, then dw and ds exist, and the aforementioned equalities hold. Moreover, our primary new estimate is established for all . For the uniform infinite planar triangulation (UIPT), this yields the consequence dw=4 using df=4 (Angel in Geom. Funct. Anal. 13(5):935–974, 2003) and (established here as a consequence of the Liouville Quantum Gravity theory, following Gwynne-Miller 2020 and (Ding and Gwynne in Commun. Math. Phys. 374(3):1877–1934, 2020)). The conclusion dw=4 had been previously established by Gwynne and Hutchcroft (2018) using more elaborate methods. A new consequence is that dw=df for the uniform infinite Schnyder-wood decorated triangulation, implying that the simple random walk is subdiffusive, since df>2. [ABSTRACT FROM AUTHOR]

This paper explores the "triangulation approach" in social science research methods. Triangulation is an emerging method specifically in qualitative and multi-method studies. Researchers in the social sciences have increased their use of the triangulation approach recently due to the merits of this approach, especially to conduct in-depth studies through multiple inquiries. Simultaneously, this method has criticism and misconceptions among social researchers in terms of what it is, how it can be used, and the credibility of the findings when used. Therefore, this paper analyses in depth what triangulation is, the types of triangulations and how they can be applied in the social sciences. The study basically adopted systematic literature review and used 30 articles published in scientific journals. The paper critically reviewed journal articles related to triangulation, revealed how different types of triangulation methods have been applied in the social sciences and highlighted the merits and cautions of applying this method. The paper theoretically contributes to understanding the phenomenon of the triangulation approach and how it connects with qualitative and multi-method studies. In addition, it revealed that the following data collection techniques from multiple sources can be exploited: in-depth interviews, focus group discussions, literature, documents, and surveys on the triangulation method to improve the credibility and reliability of the research. Furthermore, the study empirically contributes to social science researchers applying this approach with proper understanding. [ABSTRACT FROM AUTHOR]

We show that any polygon Γ has an acute triangulation T where every angle lies in the interval [ 30 ∘ , 75 ∘ ] , except for triangles that contain a vertex v of Γ where Γ has an interior angle θ v < 30 ∘ ; such triangles are isosceles with angles θ v , and 90 ∘ - θ v / 2 . [ABSTRACT FROM AUTHOR]

Mammography is the primary breast cancer screening strategy. Recent methods have been developed using the mammogram image to improve breast cancer risk prediction. However, it is unclear on the extent to which the effect of risk factors on breast cancer risk is mediated through tissue features summarized in mammogram images and the extent to which it is through other pathways. While mediation analysis has been conducted using mammographic density (a summary measure within the image), the mammogram image is not necessarily well described by a single summary measure and, in addition, such a measure provides no spatial information about the relationship between the exposure risk factor and the risk of breast cancer. Thus, to better understand the role of the mammogram images that provide spatial information about the state of the breast tissue that is causally predictive of the future occurrence of breast cancer, we propose a novel method of causal mediation analysis using mammogram image mediator while accommodating the irregular shape of the breast. We apply the proposed method to data from the Joanne Knight Breast Health Cohort and leverage new insights on the decomposition of the total association between risk factor and breast cancer risk that was mediated by the texture of the underlying breast tissue summarized in the mammogram image. [ABSTRACT FROM AUTHOR]

Challenges in assessing build quality is one the significant hurdles that limits widespread adoption of additive manufacturing (AM) for critical applications. Collecting acoustic process emissions is a compelling yet cost effective strategy for monitoring AM processes. However, several technical challenges need to be overcome initially in order to fully leverage the information content of the captured acoustic emissions and to potentially correlate specific acoustic sensor footprints to the process anomalies that can often associated with build defects and a reduction in part quality or performance. This paper aims to address some of these challenges, provide potential technical solutions, and offer guidelines in order to enable process monitoring of powder bed fusion (PBF) AM processes using acoustic sensors in the near future. Experimental data collected during a PBF-AM process is utilized to characterize the acoustic footprint of the interaction between the laser and the powder bed. Differences between active and inactive periods of the laser are highlighted in the frequency domain. A significant initial acoustic transient was observed, associated with laser turn-on. Automated data alignment strategies are explored that aim to compensate for the time of flight delay as a function of location on the build plate. Proper data alignment may be utilized to triangulate laser location using an array of microphones, which could open up potential for use on multi-laser PBF-AM systems or systems in which the laser position data is not available to the end-user. Triangulation is demonstrated using experimental data. [ABSTRACT FROM AUTHOR]

[Display omitted] • A new method was proposed to simulate surface morphology and quantify interfacial interactions. • The method integrates triangulation technique, SEI method and computer programming. • The new method was applied to assess antifouling of PVDF-NZPs membrane in MBR. • Significantly improved resistance to adhesive fouling caused by foulants was confirmed. • Original programming code was developed to facilitate widespread use of this method. To gain a thorough understanding of interfacial behaviors such as adhesion and flocculation controlling membrane fouling, it is necessary to simulate the actual membrane surface morphology and quantify interfacial interactions. In this work, a new method integrating the rough membrane morphology reconstruction technology (atomic force microscopy (AFM) combining with triangulation technique), the surface element integration (SEI) method, the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory, the compound Simpson's approach, and the computer programming was proposed. This new method can exactly mimic the real membrane surface in terms of roughness and shape, breaking the limitation of previous fractal theory and Gaussian method where the simulated membrane surface is only statistically similar to the real rough surface, thus achieving a precise description of the interfacial interactions between sludge foulants and the real membrane surface. This method was then applied to assess the antifouling propensity of a polyvinylidene fluoride (PVDF) membrane modified with Ni-ZnO particles (NZPs). The simulated results showed that the interfacial interactions between sludge foulants in a membrane bioreactor (MBR) and the modified PVDF-NZPs membrane transformed from an attractive force to a repulsive force. The phenomenon confirmed the significant antifouling propensity of the PVDF-NZPs membrane, which is highly consistent with the experimental findings and the interfacial interactions described in previous literature, suggesting the high feasibility and reliability of the proposed method. Meanwhile, the original programming code of the quantification was also developed, which further facilitates the widespread use of this method and enhances the value of this work. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new series of prehomogeneous vector spaces from figures made up of triangles, which we call triangle arrangements. Our main theorem states that, under suitable assumptions, we are able to construct a prehomogeneous vector space obtained from a triangle arrangement by attaching two triangle arrangements corresponding to prehomogeneous vector spaces at a vertex. We also give examples of prehomogeneous vector spaces obtained from triangle arrangements. Many of them seem to be new. [ABSTRACT FROM AUTHOR]

This paper approaches the process of 'reflection' as an interpersonal and intra-personal creative act. As commonly used, the word 'reflection' appears to reference two seemingly different processes; the returning of a mirror image and the process of reflective thought. Examining the intersection of these two definitions – from infant development, through attachment theory to post-Kleinian thinking and Lacan – this paper finds that the act of 'reflection' can be conceived of as an act of triangulation, in a mathematical sense, whereby a pre-existing but unknown point is found/made using two known points as the vertices. [ABSTRACT FROM AUTHOR]

Facial Expression Recognition is a visual cue used for conveying emotions and intentions between human beings. The micro-expressions (MEs) are not visible to the human eye, making it challenging to capture the minute changes in the facial areas as the expressions change. As a result, automating the detection of ME is a challenging task. This work utilizes Delaunay Triangulation and Voronoi Diagram properties to segment Region of Interest (ROI) based on Action Unit indexes. The ROI-based feature extraction aided in improving the performance of the Micro-Expression Recognition (MER) system. The Cross-Database Evaluation (CDE) and Holdout Database Evaluation (HDE) are performed on three publicly available datasets CASMEII, SAMM, and SMIC (HS). The proposed approach resulted in an improved Unweighted Average Recall (UAR) and Unweighted F1 (UF1) scores by 6.09% and 4.36%, respectively. The results obtained with CDE and HDE demonstrate that the proposed model is robust compared to earlier studies. [ABSTRACT FROM AUTHOR]

Purpose: 1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method. Design/methodology/approach: Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane). Findings: By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics. Originality/value: The present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35]. [ABSTRACT FROM AUTHOR]

We investigate the optimal piecewise linear interpolation of the bivariate product xy over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the interpolation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using these as building blocks, we construct a triangulation scheme called crossing swords that requires at most - times the number of simplices in any optimal triangulation. In other words, we derive an approximation algorithm for the optimal triangulation problem. We also show that crossing swords yields optimal triangulations in the case that each simplex has at least one axis-parallel edge. Furthermore, we present approximation guarantees for other well-known triangulation schemes, namely for the red refinement and longest-edge bisection strategies as well as for a generalized version of K1-triangulations. Thereby, we are able to show that our novel approach dominates previous triangulation schemes from the literature, which is underlined by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

For a wide range of applications, we need DEM simulations of granular matter in contact with elastic flexible boundaries. We present a novel method to describe the interaction between granular particles and a flexible elastic membrane. Here, the standard mass-spring model approach is supplemented by surface patches given by triangulation of the membrane. In contrast to standard mass-spring models, our simulation method allows for an efficient simulation even for large particle size dispersion. The novel method allows coarsening of the mass-spring system leading to a substantial increase in computation efficiency. The simulation method is demonstrated and benchmarked for a triaxial test. [ABSTRACT FROM AUTHOR]

Monitoring plants growth dynamics requires continuously tracing their evolution over time. When using point cloud data, such a process requires associating the individual organs among scans, spatially aligning them, and accounting for their evolution, decay, or split. It is common to address this challenge by abstracting the point cloud into its skeletal form and defining point correspondence by Euclidean measures. As the paper demonstrates, standard skeletonization approaches do not capture the actual plant topology, and Euclidean measures do not document its evolving form. To address this alignment challenge, we propose in this paper a registration model that traces high-degree deformations and accommodates the complex plant topology. We develop an embedded deformation graph-based solution and introduce manifold measures to trace the plant non-isometric development. We demonstrate how a path-seeking strategy and invariant features capture the plant topological form, and then use a probabilistic linear assignment solution to associate organs across scans. By minimizing deviations from rigidity, our registration form maintains elasticity, and by solving locally rigid transformations, regularized by structure-related constraints, we secure smoothness and optimality. We also demonstrate how data arrangement and linear path-finding models make our solution computationally efficient. Our model is applied on high quality laser triangulation data, commonly tested in 4-D plant registration studies, but is also verified on low resolution and noisy pointsets reconstructed from a limited number of images by multiview stereo (MVS). Our results demonstrate 0. 1 mm levels of accuracy when applied to plant species exhibiting complex geometric structures. They improve by tenfold or more state-of-the-art results and transform correctly the plants form. Paper related resources are available at PLANT4D. [ABSTRACT FROM AUTHOR]

The study uses phase triangulation methods to examine the development of image processing algorithms for measuring a three-dimensional (3D) surface profile. An algorithm is proposed for decoding images of an object in structured light based on an iterative search for the minimum deviation of the model function using measurement results and compensating for the nonlinearity of the transceiver path of the measuring complex. A distinctive feature of the proposed method is that the search for the model function is desired in the form of a second-degree polynomial, ensuring the stability of the method against nonlinear distortions caused by power-law transformations of the transceiver path. The interval search method is used to reduce algorithmic complexity qualitatively. The proposed algorithm provides a stable search for the value of the initial phase shift in object images, is resistant to noise and nonlinear distortions, and allows image processing in 3D scanning systems based on triangulation methods using structured illumination and phase triangulation. Thus, the algorithm will be useful for data processing during the operation of measuring systems with a nonlinear transceiver path and measurement time constraints. [ABSTRACT FROM AUTHOR]

We show that if all internal vertices of a disc triangulation have degree at least 6, then the full structure can be determined from the pairwise graph distances between boundary vertices. A similar result holds for disc quadrangulations with all internal vertices having degree at least 4. This confirms a conjecture of Itai Benjamini. Both degree bounds are best possible, and correspond to local non-positive curvature. However, we show that a natural conjecture for a "mixed" version of the two results is not true. [ABSTRACT FROM AUTHOR]

Many stable and convergent numerical methods are not pressure robust for an incompressible flow problem, due to the relaxation of a discrete divergence constraint called poor mass conservation. As a result, the velocity error is polluted by the pressure error, particularly when the fluid viscosity is relatively small and pressure is comparably large. A grad-div stabilization is an efficient remedy in conforming finite element methods. In this paper, an analogue of the grad-div stabilization that the penalization of the jumps of the normal velocities over facets of the triangulation in discontinuous Galerkin (DG) methods is investigated for a coupled Stokes and Darcy problem, it can efficiently improve the accuracy of velocity and mass conservation. Firstly, we present the existence and uniqueness of a solution, unconditional stability and a priori estimates for the DG method. Then, by using the principle of superposition and orthogonal decomposition cleverly, we prove the limiting behavior that the DG method with an analogue of grad-div stabilization for a coupled Stokes and Darcy problem converge to the strongly conservative BDM DG method with a convergence rate of O (λ f − 1 + λ s − 1) , it allows for arbitrarily large stabilization parameters. Finally, some numerical tests are given to validate the optimal convergence rates and their effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of polynomial order k ≥ 1 on conforming triangulations and discontinuous pressure approximations of order k − 1. We will bound the inf-sup constant from below independent of the mesh size and show that it depends only logarithmically on k. Our assumptions on the mesh are very mild: for odd k we require that the triangulations contain at least one inner vertex while for even k we assume that the triangulations consist of more than a single triangle. [ABSTRACT FROM AUTHOR]

As incrementally formed sheets show large geometric deviations resulting from the deflection of the forming tool, an in-process measurement of the tool tip position is required. In order to cover a measuring volume of 2.0 m × 1.0 m × 0.2 m and to achieve measuring uncertainties of less than 50 µm, a multi-sensor system based on triangulation is realized. Each shadow imaging sensor in the multi-sensor system evaluates the direction vector to an LED attached to the tool, and the three-dimensional position of the LED is then determined from the combination of two sensors. Experimental results show that the angle of view from the sensor to the LED limits both the measurement range and the measurement uncertainty. The measurement uncertainty is dominated by systematic deviations, but these can be compensated, so that the measurement uncertainty required for measuring the tool tip position in the ISF is achieved. [ABSTRACT FROM AUTHOR]

The calculation of volumes for irregular bodies holds significant relevance across various production processes. This spans tasks such as evaluating the growth status of crops and fruits, conducting morphological analyses of spatial objects based on volume parameters, and estimating quantities for earthwork and excavation. While methods like drainage, surface reconstruction, and triangulation suffice for smaller irregular bodies, larger ones introduce heightened complexity. Technological advancements, such as UAV photogrammetry and LiDAR, have introduced efficient point cloud data acquisition methods, bolstering precision and efficiency in calculating volumes for substantial irregular bodies. Notably, open-pit mines, characterized by their dynamic surface alterations, exemplify the challenges posed by large irregular bodies. Ensuring accurate excavation quantity calculations in such mines is pivotal, impacting operational considerations, acceptance, as well as production cost management and project oversight. Thus, this study employs UAV-acquired point cloud data from open-pit mines as a case study. In practice, calculating volumes for substantial irregular bodies often relies on the point cloud slicing method. However, this approach grapples with distinguishing multi-contour boundaries, leading to inaccuracies. To surmount this hurdle, this paper introduces an enhanced point cloud slicing method. The methodology involves segmenting point cloud data at fixed intervals, followed by the segmentation of slice contours using the Euclidean clustering method. Subsequently, the concave hull algorithm extracts the contour polygons of each slice. The final volume calculation involves multiplying the area of each polygon by the spacing and aggregating these products. To validate the efficacy of our approach, we employ model-derived volumes as benchmarks, comparing errors arising from both the traditional slicing method and our proposed technique. Experimental outcomes underscore the superiority of our point cloud volume calculation method, manifesting in an average relative error of 1.17%, outperforming the conventional point cloud slicing method in terms of accuracy. [ABSTRACT FROM AUTHOR]

This study aimed to evaluate the role of the Arab media, digital security media in raising public awareness in the Arab world about cryptocurrency crimes and to show the extent to which these crucial groups contribute to immunizing the Arab Public against these crimes according to the theories of social responsibility and inoculation. The study relied on an exploratory sequential mixed-methods design, which begins first with the exploration and analysis of quantitative data, and then uses the results in a qualitative next stage; Thus, the study relied on the methodological triangulation, relying on the questionnaire tool to investigate the opinions of a sample of the Arab Public (1305 respondents) about their knowledge of digital currency crimes, their exposure to awareness messages about these crimes, and the organized interviews with a sample of the Arab Public who filled out the questionnaire (10% from the size of the original sample) to ascertain the nature of the message they were exposed to. In addition, other interviews with Arab experts, academics, and specialists (20 experts) after presenting the questionnaire results to them to come up with a set of necessary interventions to educate the Arab Public about cryptocurrency crimes. Finally, the study employed content analysis to analyze a sample of digital security media pages on Facebook (10 pages) to show the extent of their contribution to the Public Awareness of cryptocurrency crimes and to identify the most critical persuasive methods used in the awareness message according to Aristotle's rhetorical triangle . The study showed that although more than 35% of the study sample held graduate degrees between master’s and doctorate and 42% of the bachelor’s degrees, the vast majority (64%) did not have any information about cryptocurrency crimes. The results also showed that the vast majority of respondents did not receive any education or raising awareness messages about these crimes from traditional or electronic media, digital security media, or Arab influencers alike, which indicates the failure of these parties in social responsibility in the cryptocurrency crimes. The content analysis results also showed that the digital security media did not address the issue of digital currencies in its general landscape or the crimes resulting from them . In light of these results, the study came out with a set of recommendations, including, for example, but not limited to, the need for a decision at the level of the Arab Interior Ministers Council to direct the security media in Arab countries to carry out awareness campaigns regarding cryptocurrency crimes. The study also recommended that the Association of Arab Universities' secretariat urge Arab academic institutions to hold scientific conferences related to digital currencies and related offenses. A review of the literature and previous studies showed the Arab Library's lack of such vital studies. [ABSTRACT FROM AUTHOR]