Orthogonal Segments Research Articles

Exploiting the Potential of Urban DAS Grids: Ambient-Noise Subsurface Imaging Using Joint Rayleigh and Love Waves

Abstract Distributed acoustic sensing (DAS) data become important for seismic monitoring of subsurface structures in urban areas. Different from the previous studies that only focused on Rayleigh waves, we report successful observation and analysis of both Rayleigh and Love waves extracted from ambient-noise interferometry, using orthogonal segments of fiber-optic cables in San Jose, California. Theoretical angular responses of DAS ambient-noise cross correlation, together with numerical experiments, help identify DAS channel pairs expected to record stronger Love waves than Rayleigh waves. Based on these waveforms, we further obtain clear Rayleigh- and Love-wave dispersion maps, including both phase and group velocities, with various channel pair orientations. Finally, we perform a joint inversion of Rayleigh- and Love-wave dispersion curves to obtain depth-dependent subsurface velocity structures of the top 100 m. Our inversion result is consistent with the model from the previous study based on Rayleigh-wave dispersion and horizontal-to-vertical spectral ratio. In addition, the joint inversion of Love and Rayleigh is more robust than that of the independent inversion of either type of wave. Our new study demonstrates the potential of surface-wave analysis on fiber-optic cables with complex geometry, which can further advance the seismic monitoring of urban areas.

Application of four-segments annular Silicon drift detector for 3-D surface topography reconstruction by micro-PIXE

Information about the surface topography is very important to achieve the correct elemental concentrations from the 2D X-ray intensity maps in micro-PIXE. Previously, an innovative approach of stereo-PIXE has been introduced to reconstruct the surface topography using two X-ray spectrometers in the lateral direction of the detector positions. Here, we developed the stereo-PIXE method to the four-segment Silicon drift detector (SDD), mounted at the Jožef Stefan Institute (JSI) microprobe, by considering a set of stereovision maps acquired by orthogonal segments to reconstruct the surface topography both in the lateral and longitudinal directions of the scanned area. To this aim, X-ray intensity disparity from the opposing segments was simulated for an ideal flat inclined model of the sample to infer the inclination angle across the opposing segments. Then, the obtained two gradient components of the surface topography from the inclination angles, along the axes that connect the two opposing segments, were reoriented along the scanned area with a proper rotation angle. Thus, to reconstruct the 3-D sample surface topography profile, the integration of the surface topography gradient was numerically performed in the two dimensions along the sample surface. The feasibility of the method is demonstrated on the pure Ti sample with scratched structures.

Modeling D2D Underlaying Cellular Network for Hotspot Communications with Poisson Cluster and Hole Processes

This paper develops a new approach to the modeling and analysis of device-to-device (D2D) underlaying multi-tier cellular network for dense hotspot communications, which consists of macro base stations (MBSs), pico BSs (PBSs), femto BSs (FBSs). A typicl user equipment (UE) can work either in D2D mode or cellular mode. Considering the dense hotspot communications, this work employs Poisson point process (PPP) to model the locations of MBSs and PBSs, and uses Poisson cluster process (PCP) to model the ones of UEs and FBSs. The locations of PBSs are also modeled as the centers of hotspots, referred to as the centers of PCPs. UEs and FBSs cluster around the common parent process PBSs. To guard the cluster-edge UEs, the clustered-UE classification and modified fractional frequency reuse (FFR) are jointly used, by which both the UEs and FBSs are classified two sets, cluster-center UEs and cluster-edge UEs, cluster-center FBSs and cluster-edge FBSs, respectively. The total frequency band is divided into two orthogonal segments, one of which is shared by D2D devices, cluster-edge FBSs, and PBSs, and the other segment of which is shared by cluster-center FBSs and MBSs. For such clustered multi-tier network, by using the methods from PPP, PCP, and PHP, this paper presents a tractable approach for modeling and analyzing the performance of cellular and D2D networks and gives the statistical descriptions of the experienced interferences at a typical D2D or cellular receiver by using the approximated Poisson hole processes (PHP) theory. This yields the derivations of the coverage probabilities of both the D2D receivers and cellular destinations. In additon, during the analysis of cellular UEs, to derive the coverage probabilities, this paper specially constructs one UE association criterion as well as the derivations of both the association probabilities and the statistical descriptions of association distances for cluster-center and cluster-edge UEs. The simulations results exploit the effect of various network parameters on the network performance and give the insights in terms of the proposed schemes as well as the comparison between cluster-center and cluster-edge UEs.

Calculation Method for Grading Size and Grading Bounding Box of Virtual Aggregate Based on DEM

The grading size, which can be defined as the side length of the smallest square hole through which an aggregate with irregular shape can directly pass, is an important morphology parameter and can be used to calculate the gradation of mixture material. The grading bounding box, which can be defined as the circumscribed cuboid with central axis length being the grading size, is an important visual tool for observing the size and direction of the aggregate. Virtual test to calculate the grading size of a virtual aggregate is environmentally friendly and efficient, but the result provided by current research is imprecise and the grading bounding box is also rarely mentioned. In this paper, the multilevel complete projection algorithm is proposed to precisely calculate the grading size of a virtual aggregate. The whole process of the algorithm can be expressed by formula after the operation of sphere discretization by converting the virtual aggregate shell into the discrete aggregate. Then, the discrete aggregate is projected onto a complete series of the plane to form several 2D figures, and then, each 2D figure is projected onto a complete series of the orthogonal axis to form orthogonal segments. The grading size can finally be obtained by comparing the length of the above orthogonal segments based on the key central axis length principle. The influencing factors of computational accuracy and efficiency are considered in the algorithm. Finally, the grading bounding box can be built by using the Rodrigues transformation according to the information obtained from the above algorithm.

A simple proportional fair scheduling for downlink power domain non-orthogonal multiple access systems

Currently, non-orthogonal multiple access technologies have gained high relevance in wireless multi-user broadband communications. Many papers have shown that non-orthogonal multiplexing can significantly increase the capacity of the system. Despite this, it technology is still far from practical implementation due to unresolved issues. One such issue is radio resource scheduling in communication systems using non-orthogonal multiple access which poses a high computational complexity and turns out to be a problem for a base station with a large number of users it serves. In our paper, we propose our own resource scheduling method for systems with non-orthogonal multiplexing using proportional fair strategy. This method allows for simultaneous resource scheduling in two segments – an orthogonal segment (time-frequency domain) and a non-orthogonal segment (power domain). To assess the effectiveness of the proposed method, we use the developed simulation model of resource scheduling for a communication system with a single cell. The effectiveness of the proposed scheduling method is confirmed by the simulation result, and its use allows achieving the proportional fair strategy implementation. In the final part, we use iterative simulation to compare the throughput of systems with orthogonal and non-orthogonal multiplexing using proposed proportional fair scheduler. The result of comparison showed that using the proposed proportional fair scheduling can increase the system capacity by an average of 28%. The results can be applied to create communication systems with different non-orthogonal multiple access implementations.

Extraction of the Level Lines of a Bilinear Image

We detail precisely an algorithm for the extraction of the level lines of a bilinear image, which is a continuous function interpolating bilinearly a discrete image. If we discard the levels of the discrete image, where topological difficulties arise, a level line is a concatenation of branches of hyperbolas. The algorithm tracks these branches and provides a sampling of the level lines in the form of closed polygons. If the level line contains a saddle point, the hyperbola degenerates to orthogonal segments, where an arbitrary but consistent choice is adopted for the tracking at the bifurcation. In any case, the extracted polygons are disjoint and enclose a bounded region. This allows to order the level lines in an enclosure tree hierarchy, which may be used for a variety of filters. Recovering this tree is a simple post-processing of the extraction algorithm.

Two Approaches to Building Time-Windowed Geometric Data Structures

Given a set of geometric objects each associated with a time value, we wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time window. We call such problems time-windowed decision problems, and they have been the subject of much recent attention, for instance studied by Bokal et al. (in: Proceedings of the 31st International Symposium on Computational Geometry (SoCG), pp 240–254, 2015). In this paper, we present new approaches to this class of problems that are conceptually simpler than Bokal et al. ’s, and also lead to faster algorithms. For instance, we present algorithms for preprocessing for both the time-windowed 2D diameter decision problem and the time-windowed 2D convex hull area decision problem in $$O(n \log n)$$ time, improving Bokal et al. ’s $$O(n \log ^2 n)$$ and $$O(n \log n \log \log n)$$ solutions respectively. Our first approach is to reduce time-windowed decision problems to a generalized range successor problem, which we solve using a novel way to search range trees. Our other approach is to use dynamic data structures directly, taking advantage of a new observation that the total number of combinatorial changes to a planar convex hull is linear for any FIFO update sequence, in which deletions occur in the same order as insertions. We also apply these approaches to obtain the first $$O(n\, \mathrm{polylog}\, n)$$ algorithms for the time-windowed 3D diameter decision and 2D orthogonal segment intersection detection problems.

Hierarchical Regularization of Building Boundaries in Noisy Aerial Laser Scanning and Photogrammetric Point Clouds

Aerial laser scanning or photogrammetric point clouds are often noisy at building boundaries. In order to produce regularized polygons from such noisy point clouds, this study proposes a hierarchical regularization method for the boundary points. Beginning with detected planar structures from raw point clouds, two stages of regularization are employed. In the first stage, the boundary points of an individual plane are consolidated locally by shifting them along their refined normal vector to resist noise, and then grouped into piecewise smooth segments. In the second stage, global regularities among different segments from different planes are softly enforced through a labeling process, in which the same label represents parallel or orthogonal segments. This is formulated as a Markov random field and solved efficiently via graph cut. The performance of the proposed method is evaluated for extracting 2D footprints and 3D polygons of buildings in metropolitan area. The results reveal that the proposed method is superior to the state-of-art methods both qualitatively and quantitatively in compactness. The simplified polygons could fit the original boundary points with an average residuals of 0.2 m, and in the meantime reduce up to 90% complexities of the edges. The satisfactory performances of the proposed method show a promising potential for 3D reconstruction of polygonal models from noisy point clouds.

Optimization of three-dimensional modeling for geometric precision and efficiency for healthy and diseased aortas

The study purpose is to optimize modeling parameters, specifically segmentation spacing and centerline extraction, to efficiently construct accurate 3D aortic models. Models are constructed by centerline extraction and orthogonal 2D segmentations. We examine the effect of segmentation interval spacing (2, 1, 0.5, 0.25 cm) and orthogonal segmentation and centerline extraction iteration (one, two, three iterations) for constructing models of Healthy, Tortuous, Aneurysmal, and Dissected human thoracic aortas. Aortic arclength, curvature, and cross-sectional axis ratio were computed to compare variations in modeling parameters. Centerline arclength is precisely characterized for all aortas with a single iteration of centerline extraction (≤1% deviation), however, complex anatomies required 1 cm segmentation intervals whereas the Healthy aorta only required 2 cm intervals. Centerline curvature is more sensitive to modeling methods, requiring 1 cm intervals for ≤5% deviation in peak curvature for the three diseased anatomies, and two iterations of segmentation and centerline extraction for the Aneurysmal and Dissected aortas. Accurate lumen cross-sectional characterization required 1 or 0.5 cm segmentation intervals, and two or three segmentation and centerline iterations, with greater refinement needed for more complex geometries. Depending on the geometric characteristic and complexity of anatomy and pathology, different levels of segmentation interval refinement and iterations of segmentation and centerline extraction are required.

Surface microdeformations and regulation of cell movements in Xenopus development

The velocities and directions of movements of individual outer ectodermal cells of Xenopus embryos in the course of normal development from the blastula to the early tail-bud stage, as well as after mechanical relaxation in the early gastrula, were measured. An alternation of the periods of directed movements of large cell masses and local cell wanderings was detected. In both cases, the trajectories of individual cells consisted primarily of orthogonal segments. Cell movements were measured on two scales. At a small-scale consideration (time intervals of the order of several hours and distances of the order of tens of microns), fairly slight linear stretching and compressive deformations were detected, which looked like gentle smooth gradients along which the upward morphogenetic movements of cells were directed. At a large-scale consideration (time intervals of the order of tens of minutes and distances of the order of microns), quasi-periodic fluctuations of velocities of individual cells partly correlated in time were found. The differences between these velocities generated microdeformations, which reached several tens of percent and developed within time intervals not more than 10 min. Measurements of relative magnitudes of mechanical forces influencing the cell walls suggests that microdeformations generate local stretching and compressive deformations modulating smoother tension gradients.

An Upper Bound on the k-Modem Illumination Problem

A variation on the classical polygon illumination problem was introduced in [Aichholzer et al. EuroCG’09]. In this variant light sources are replaced by wireless devices called [Formula: see text]-modems, which can penetrate a fixed number [Formula: see text], of “walls”. A point in the interior of a polygon is “illuminated” by a [Formula: see text]-modem if the line segment joining them intersects at most [Formula: see text] edges of the polygon. It is easy to construct polygons of [Formula: see text] vertices where the number of [Formula: see text]-modems required to illuminate all interior points is [Formula: see text]. However, no non-trivial upper bound is known. In this paper we prove that the number of kmodems required to illuminate any polygon of [Formula: see text] vertices is [Formula: see text]. For the cases of illuminating an orthogonal polygon or a set of disjoint orthogonal segments, we give a tighter bound of [Formula: see text]. Moreover, we present an [Formula: see text] time algorithm to achieve this bound.

Analysis of Soccer Players' Positional Variability During the 2012 UEFA European Championship: A Case Study.

The purpose of this study was to analyse players’ positional variability during the 2012 UEFA European Championship by applying principal component analysis (PCA) to data gathered from heat maps posted on the UEFA website. We analysed the teams that reached the finals and semi-finals of the competition. The players’ 2D coordinates from each match were obtained by applying an image-processing algorithm to the heat maps. With all the players’ 2D coordinates for each match, we applied PCA to identify the directions of greatest variability. Then, two orthogonal segments were centred on each player’s mean position for all matches. The segments’ directions were driven by the eigenvectors of the PCA, and the length of each segment was defined as one standard deviation around the mean. Finally, an ellipse was circumscribed around both segments. To represent player variability, segment lengths and elliptical areas were analysed. The results demonstrate that Portugal exhibited the lowest variability, followed by Germany, Spain and Italy. Additionally, a graphical representation of every player’s ellipse provided insight into the teams’ organisational features throughout the competition. The presented study provides important information regarding soccer teams’ tactical strategy in high-level championships that allows coaches to better control team organisation on the pitch.

Analogue modeling of positive inversion tectonics along differently oriented pre-thrusting normal faults: An application to the Central-Northern Apennines of Italy

Inversion tectonics represent a key process in many orogens worldwide. The related mechanisms of fault reactivation and the effects of an articulated preshortening setting on thrust and fold development are still challenging questions. Modes and geometries of inversion have been the object of several analogue models. In this work, we analyzed the influence of an articulated high-angle preexisting discontinuity in the development of thrusts using sandbox modeling. The model geometry is based on the architecture of the major faults in the Central-Northern Apennines of Italy, where differently oriented Mesozoic–Cenozoic inherited extensional structures are clearly detectable and display contrasting styles of positive inversion tectonics. Quartz-sand is the analogue material adopted to model Mesozoic–Cenozoic sedimentary successions, and glass microbeads represent preexisting fault rocks. The geometry of the segmented preexisting structure is composed of two segments with the same dip (∼60°): one oblique and another orthogonal to the shortening direction. Our results show that different styles of positive inversion tectonics can coexist and that the obliquity angle between inherited structures and the shortening direction is a leading factor controlling the degree of inversion: The oblique segment of the discontinuity exhibits a complete reactivation, whereas along the orthogonal segment, shortcut is the prevalent mechanism. The oblique element, moreover, represents a cross-strike discontinuity that guides the localization and curved geometry of the thrusts, compartmentalizing the deformation. Our findings can be applied to fold-and-thrust belts characterized by the presence of cross-strike discontinuities.

An Algorithm for Generating a Family of Alternating Knots

An algorithm for generating a family of alternating knots (which are described by means of a chain code) is presented. The family of alternating knots is represented on the cubic lattice, that is, each alternating knot is composed of constant orthogonal straight-line segments and is described by means of a chain code. This chain code is represented by a numerical string of finite length over a finite alphabet, allowing the usage of formal-language techniques for alternating-knot representation. When an alternating knot is described by a chain, it is possible to obtain its mirroring image in an easy way. Also, we have a compression efficiency for representing alternating knots, because chain codes preserve information and allow a considerable data reduction.

Retinal Vascular Fractal Dimension Measurement and Its Influence from Imaging Variation: Results of Two Segmentation Methods

Aim: To assess the influences of imaging variation (different photographic angle) on the measurement of retinal vascular fractal dimension (Df), using two segmentation methods.Materials and methods: Nonlinear orthogonal projection segmentation (International Retinal Imaging Software-Fractal, termed IRIS-Fractal) and curvature-based segmentation (Singapore Institute Vessel Assessment-Fractal, termed SIVA-Fractal) methods were used to measure Df and were assessed for their reproducibility in detecting retinal vessels of 30 stereoscopic pairs of optic disc color images. Each pair was taken from the same eye with slightly different angles of incidence. Each photograph of the pairs had subtle variations in brightness between areas temporal and nasal to the optic disc.Results: Intragrader reproducibility of Df measurement was similar (intraclass correlation 0.81 and 0.96, respectively) for IRIS-Fractal and SIVA-Fractal. Within-image pair Pearson’s correlation coefficients (r) of Df measurements were moderate for both methods (0.57 and 0.48, respectively).Conclusions: Both nonlinear orthogonal projection and curvature-based retinal vessel segmentation methods were found to be sensitive to variations in image brightness, resulting from iris shadowing associated with different angle of photographic incidence.

AN EASY AND FAST ALGORITHM FOR OBTAINING MINIMAL DISCRETE KNOTS

An easy and fast algorithm for obtaining minimal discrete knots is presented. A minimal discrete knot is the digitalized representation of a knot, which is composed of the minimum number of constant orthogonal straight-line segments and is represented by the knot-number notation. The proposed algorithm for obtaining minimal discrete knots tries to reduce the number of straight-line segments of a given discrete knot preserving its shape. This algorithm is based on two fundamental transformations: U and L. In order to prove the efficiency and rapidity of the algorithm, a great variety of examples of discrete knots are presented: complete families of discrete knots at different orders; random discrete knots; examples of non-trivial and unsolved discrete knots.

사이클링 초최대운동(Supra maximal training)시 RPM과 족관절의 운동학적 분석

The purpose of this study was to determine the kinematic characteristics of the ankle joint and RPM(repetition per minutes) during the supra maximal training in cycling. For this study, 8 national representative cyclists, distance cyclists in track and road, were selected. During the super-maximum pedalling, kinematic data were collected using a six-camera(240Hz) Qualisys system. the room coordinate system was right-handed and fixed in the back of a roller for cycle, with right-handed orthogonal segment coordinate systems defined for the leg and foot. Lateral kinematic data were recorded at least for 3 minutes while the participants pedal on a roller. Two-dimensional Cartesian coordinates for each marker were determined at the time of recording using a nonlinear transformation technique. Coordinate data were low-pass filtered using a fourth-order Butterworth recursive filter with cutoff frequency of 15Hz. Variables analyzed in this study were compared using a one factor(time) ANOVA with repeated measures. The results of investigation suggest that the number of rotating pedal was decreased with time phase during the super-maximum pedaling. Maximum angle of the ankle joint showed little in change with time phase compared with minimum angle of that.

A METHOD FOR COMPUTING FAMILIES OF DISCRETE KNOTS USING KNOT NUMBERS

A method for generating families of particular 3D curves which differs from random self-avoiding walks is presented. This method is based on a chain code called knot numbers. The knot-number notation describes discrete knots. A discrete knot is the digitalized representation of a knot and is composed of constant orthogonal straight-line segments. The orthogonal direction changes of the contiguous straight-line segments of the knot define the chain elements. There are only five possible orthogonal direction changes for representing any discrete knot. Thus, the chain elements are considered as one base-five integer number (knot number). In this manner, we obtain a unique knot descriptor. This description is invariant under translation, rotation, starting point, and coding direction of the discrete knot.By evaluating all possible combinations of chain elements of curves and considering some restrictions, we obtain interesting families of curves which allow us to find the smallest nontrivial knot. Finally, we present a modest attempt at building the table of minimal discrete knots.

Optimal and near-optimal algorithms for generalized intersection reporting on pointer machines

We develop efficient algorithms for a number of generalized intersection reporting problems, including orthogonal and general segment intersection, 2D range searching, rectangular point enclosure, and rectangle intersection search. Our results for orthogonal and general segment intersection, 3-sided 2D range searching, and rectangular pointer enclosure problems match the lower bounds for their corresponding standard versions under the pointer machine model. Our results for the remaining problems improve upon the best known previous algorithms.

Novel Transformation Techniques Using Q-Heaps with Applications to Computational Geometry

Using the notions of Q-heaps and fusion trees developed by Fredman and Willard, we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces. In particular, we develop a fast fractional cascading technique, which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by $O(\log^{\epsilon}n)$ for some constant $\epsilon >0$, where $n$ is the total size of all the lists stored in the tree. We apply the fast fractional cascading technique in combination with the other techniques to derive the first linear-space sublogarithmic time algorithms for two fundamental geometric retrieval problems: orthogonal segment intersection and rectangular point enclosure.