Straight-line Length Research Articles

From paths to blocks: New measures for street patterns

The street network is an important aspect of cities and contains crucial information about their organization and evolution. Characterizing and comparing various street networks could then be helpful for a better understanding of the mechanisms governing the formation and evolution of these systems. Their characterization is however not easy: there are no simple tools to classify planar networks and most of the measures developed for complex networks are not useful when space is relevant. Here, we describe recent efforts in this direction and new methods adapted to spatial networks. We will first discuss measures based on the structure of shortest paths, among which the betweenness centrality. In particular for time-evolving road networks, we will show that the spatial distribution of the betweenness centrality is able to reveal the impact of important structural transformations. Shortest paths are however not the only relevant ones. In particular, they can be very different from those with the smallest number of turns—the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a nontrivial and nonlocal information about the spatial organization of planar graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. Measuring these quantities on artificial (roads, highways, railways) and natural networks (leaves, insect wings) show that there are fundamental differences—probably related to their different function—in the organization of urban and biological systems: there is a clear hierarchy of the lengths of straight lines in biological cases, but they are randomly distributed in urban systems. The paths are however not enough to fully characterize the spatial pattern of planar networks such as streets and roads. Another promising direction is to analyze the statistics of blocks of the planar network. More precisely, we can use the conditional probability distribution of the shape factor of blocks with a given area, and define what could constitute the fingerprint of a city. These fingerprints can then serve as a basis for a classification of cities based on their street patterns. This method applied on more than 130 cities in the world leads to four broad families of cities characterized by different abundances of blocks of a certain area and shape. This classification will be helpful for identifying dominant mechanisms governing the formation and evolution of street patterns.

Governing Rule for Dynamic Formation of Grain Boundaries in Grown Graphene

Grains and grain boundaries (GBs) in graphene are vital for the control of its properties; however, engineering or controlling them by growth remains a great challenge. Here we discover that the dynamic formation of GBs within chemical vapor deposited polygonal graphene flakes is described by a geometric rule. A GB is formed to be symmetrically tilted and a continuous straight line, and the key parameters including end point, direction of GB line, and misorientation angles between adjacent graphene grains can be determined solely by the geometries of the polygonal graphene flakes. We also show the growth control over the length of straight graphene GB lines and demonstrate the capability of parallel fabrication of field-effect transistor devices across predicted GBs in a straightforward manner. This work constitutes a significant step forward in engineering grains and GBs in graphene.

Development of an Automated Measure of Iliac Artery Tortuosity that Successfully Predicts Early Graft-Related Complications Associated with Endovascular Aneurysm Repair

Iliac artery tortuosity has been linked to the likelihood of complications following endovascular aneurysm repair (EVAR). Measures of tortuosity can be established from CT images; however, the reproducibility of existing scoring techniques has not been clearly established. It remains unclear whether it is tortuosity at focal locations or for the vessel as a whole that is most relevant to adverse events. The two aims of this study were to develop an automated measure of iliac artery tortuosity to assist with surgical planning by providing an objective assessment of procedural difficulty, and to correlate this measure with early postoperative outcomes. Unlike existing approaches, the present measure of tortuosity considers spatial scale, which incorporates the effects of local anatomy. A computerized imaging algorithm was used to segment vasculature and establish a medial line and vascular boundary from contrast enhanced CT scans of 150 patients undergoing EVAR. Two tortuosity measures were examined: curvature and vessel to straight-line length (L1/L2-ratio). For a given spatial scale, the maximum tortuosity was computed on both iliac arteries and the artery with the lower maximum was selected for analysis. Correlation of tortuosity with early (<30 day) and longer-term graft-related complications was assessed. Maximal tortuosity at a 10 mm scale was a significant predictor of early (<30 day) complications (p = .016 for curvature and p = .006 for L1/L2-ratio), but not of long-term complications. Aneurysmal diameter was independent of tortuosity (Pearson's r value = -.006). The results demonstrate that, at a local scale, tortuosity measures are correlated with early outcomes. The spatial scale at which tortuosity is measured is important. The optimal scale of 10 mm implies that adverse events could be linked to a focal anatomical location.

Abstract 490: Vertebral Artery Tortuosity Index is a Novel Biomarker of Surgery and Aortic Dissection or Rupture in Children and Young Adults: Findings From the National Registry of Genetically Triggered Thoracic Aortic Aneurysms and Cardiovascular Conditions

Background: Little is known about reliable predictors of thoracic aortic dissection or rupture (TAD) in children and young adults. We sought to determine whether elevated vertebral artery tortuosity is a biomarker of TAD or aortic surgery at an early age. Methods: We identified 208 patients ≤50 years old in the GenTAC Registry who had ≥2.5 cm of either vertebral artery visualized on a computed tomography angiogram (CTA). In a blinded fashion, using a volume-rendered projection, each patient’s vertebral artery tortuosity index (VTI) was calculated using the larger distance factor (% by which actual length exceeds straight-line length) of the two vertebral arteries. We then investigated associations between VTI and freedom from prophylactic or post-TAD surgery. Results: Subjects included 73 with Marfan syndrome (MS), 34 with bicuspid aortic valve, 18 with Loeys-Dietz syndrome (LDS), 16 with familial thoracic aneurysms and dissections, 12 with Ehlers-Danlos syndrome type IV (EDS), 6 with congenital heart disease, and 49 with other aneurysms and dissections. Median age was 38.5 years [interquartile range (IQR) 29.6-44.6]; 23 were ≤18 years. Indication for first surgery was prophylactic in 80 patients and TAD in 49. VTI was highest in LDS (median 50, IQR 21-72), followed by MS (median VTI 27, IQR 16-52), and lowest in EDS (median 7, IQR 4-13). VTI was not associated with age at CTA. When controlling for diagnosis and race/ethnicity, higher VTI was associated with younger age at prophylactic surgery [HR 1.28, 95%CI 1.09-1.50 for every increase in VTI of 20 (VTI20)] and at surgery for TAD (HR 1.38, 95%CI 1.13-1.69 for VTI20). There was no difference in freedom from prophylactic or post-TAD surgery among LDS and MS subgroups (adjusted p=0.95 and p=0.17 respectively). In patients ≤18 years, the association between increased VTI and age at prophylactic surgery was strongest: HR 1.73 (95%CI 1.11-2.69 for VTI20). One patient ≤18 had TAD with VTI 105. Conclusions: Increased vertebral artery tortuosity is associated with earlier thoracic aortic surgery and dissection in patients under 50 years, and may be most predictive in children. VTI can identify patients at high risk for TAD who may benefit from targeted therapies.

Exact Location of the Weighted Fermat–Torricelli Point on Flat Surfaces of Revolution

We find the exact location of the weighted Fermat–Torricelli point of a geodesic triangle on flat surfaces of revolution (circular cylinder and circular cone) in the three dimensional Euclidean space by applying a cosine law of three circular helixes which form a geodesic triangle on a circular cylinder, an explicit solution of the corresponding weighted Fermat–Torricelli point in the dimensional Euclidean space by calculating some lengths of geodesic arcs and angles and by using some lengths of straight lines on a circular cone which connect the vertices of the geodesic triangle with the vertex of the circular cone.

Glenoid Bone Loss: Assessment with MR Imaging

To investigate the agreement among magnetic resonance (MR) imaging, computed tomography (CT), and arthroscopy in the measurement of glenoid bone loss. This study was approved by the institutional ethics committee. One hundred seventy-six patients (158 male and 18 female patients; mean age, 26.8 years ± 12.3) with anterior shoulder dislocation underwent both shoulder MR imaging and CT examination. Anterior straight line length, glenoid width, and best-fit bone loss were measured with MR imaging and CT. Sixty-five patients also underwent arthroscopy, which was used as the standard of reference. Assessment of glenoid bone loss at MR imaging was compared with that at CT and arthroscopy. Inter- and intrareader reproducibility of MR imaging-derived measurements of glenoid bone loss was evaluated. There was excellent correlation between CT and MR imaging with regard to anterior straight line length (r = 0.97, P < .0001), glenoid width (r = 0.95, P < .0001), and severity of glenoid bone loss-particularly with use of best-fit circle width (r = 0.83, P < .0001) rather than best-fit circle area (r = 0.82, P < .0001). In the assessment of glenoid bone loss, the correlation between CT and arthroscopy (r = 0.91, P < .0001) was marginally better than that between MR imaging and arthroscopy (r = 0.84, P < .0001). The inter- and intrareader correlations of MR imaging-derived measurements of glenoid bone loss were excellent (R = 0.90-0.95). MR imaging assessment of glenoid bone loss, particularly with use of glenoid width, is almost as accurate as CT assessment.

Chemical Dispersivity Affected by Homogeneous and Fractal Porous Media

In transport relationships for porous media, chemical dispersivity is an important parameter for estimation of pollutant migration. This study was conducted to evaluate the effects of scale on dispersivity for homogeneous media and fractal media. The approach used to estimate scale was transport distance along the column downstream from the applied chemical. Columns containing homogeneous media and fractal media were evaluated for chemical breakthrough using computed tomography (CT) imaging. The advection-dispersion transport equation appeared to be appropriate for estimating the parameters. Some columns showed that dispersivity was potentially a function of distance from the upstream end of the column. These tests indicated that dispersivity through the fractal media was not consistently dependent upon distance. Estimates were obtained for individual CT image scan pixels or selected groups of pixels. Some values determined from a curve fit method or a mean breakthrough slope method were found to be scale dependent. Results from this experiment suggest dispersivity may be dependent upon the sampling fraction rather than the straight-line length solute travels through media.

Influence of Scale on Chemical Dispersivity in Geomedia

Chemical dispersivity is a common parameter needed for pollutant fate and transport models in geomedia environments. This study estimated the effect of distance on dispersivity measured in columns using X-ray computed tomography. Columns containing natural and homogeneous media were evaluated. The convection- dispersion equation appeared to be appropriate for the column distances used in this study. Dispersivity was found to be a function of distance from the upstream end in the column studies for the natural porous media but not the homogeneous porous media. Dispersivities were estimated using the average breakthrough slope for selected scan planes (mean slope method), using the solution of the convection-dispersion equation fit to the average breakthrough for selected scan planes (curve fit method), and using groups of pixels in the selected scan planes (group pixel method). Values estimated using the mean slope method or the curve fit method were found to be scale dependent; however values with the group pixel method were not. Fractal dimension values appeared within appropriate ranges when estimated for the core samples using the mass versus radius relationship. Results suggest dispersivity may be dependent upon the sampling volume rather than the straight-line length solute travels through media.

Evidence of Different Developmental Trajectories for Length Estimation According to Egocentric and Allocentric Viewpoints in Children and Adults

This study investigated the influence of egocentric and allocentric viewpoints on a comparison task of length estimation in children and adults. A total of 100 participants ranging in age from 5 years to adulthood were presented with virtual scenes representing a park landscape with two paths, one straight and one serpentine. Scenes were presented either from an egocentric or allocentric viewpoint. Results showed that when the two paths had the same length, participants always overestimated the length of the straight line for allocentric trials, whereas a development from a systematic overestimation in children to an underestimation of the straight line length in adults was found for egocentric trials. We discuss these findings in terms of the influences of both bias-inhibition processes and school acquisitions.

Accuracy assessment of the superposition principle for evaluating dose distributions of elongated and curved103Pd and192Ir brachytherapy sources

The current brachytherapy dose calculation formalism determines clinical dose distributions using the superposition principle. However, this approach cannot account for intersource attenuation for extended brachytherapy sources such as elongated and curved sources. The purpose of this study is to determine the line segment length required for optimal accuracy of dose calculations in the vicinity of elongated and curved 103Pd and 192Ir sources using the superposition technique intrinsic to the AAPM TG-43 formalism. Monte Carlo (MC) simulations were performed in water for 103Pd and 192Ir sources with linear, toroidal, and hairpin geometries. Dose distributions for 0.1-8.0 cm line segments from MC simulations were entered into treatment planning system (TPS) using the TG-43 approach with 0.05 cm spatial resolution. Line source dose distributions were benchmarked using MC-to-MC comparisons with the superposition principle, TPS-to-TPS fluence map comparisons, and MC-to-TPS gamma-index comparisons. Toroidal and hairpin geometries were constructed using line segments in the TPS, then TPS-calculated dose distributions were compared to the MC-simulation results. Gamma-index comparisons were performed in the iba(Dosimetry) Omni-Pro I'mRT software using 2 mm distance-to-agreement Ad and 2% dose error deltaD criteria, with a passing rate of > or = 98% of pixels meeting the gamma < or = 1.00 tolerance deemed acceptable. For the MC-to-MC superposition check for line source, the average ratio of the superposition to the solid source length was 1.051 for 103Pd and 1.009 for 192Ir through the whole volume with maximum ratios of 1.34 and 1.32, respectively. TPS-to-TPS comparisons between a solid line source and multiple line segments also provided good agreement. The MC-to-TPS benchmarking indicated where the gamma-index comparison failed were inside the source and within 0.25 cm of the source long-axis. Excluding these regions, 99.6% and 99.9% of the 57 600 in-plane pixels satisfied the gamma-index criteria for 103Pd and 192Ir, respectively. The optimal line segment length for both 103Pd and 192Ir toroidal sources was about 0.5 cm or one-fifth of the torus diameter, whichever was smaller. For all toroidal geometries and all line segment lengths examined, at least 98.9% and 100.0% pixels met the gamma-index criteria for 103Pd and 192Ir, respectively. For both 103Pd and 192Ir hairpin source, all geometric variations had passing rates exceeding 99.2%. However, the best results were obtained from 0.4 cm line segments on the curved part for 103Pd while it was independent of line segment length for 192Ir. A method for using a conventional TPS for brachytherapy treatment planning of elongated and curvilinear brachytherapy sources was developed and benchmarked. This method was evaluated using a gamma-index comparison technique, where appropriate pass-rate criteria were identified. Using a variety of subsegment lengths, the total length for a straight-line source was generally reproduced with accuracy improving as subsegment length increased, approaching the total straight-line length. Toroidal sources were similarly modeled with line segments, and an accuracy tradeoff was found between geometric errors and simulating dose anisotropy along the long-axes. The gamma-index comparison method to analyze the results was shown to be more powerful than point-wise comparison methods, and more versatile than dose ratios on the same plane.

Analysis of the Maximum Straight Line Length for Prairie Highway using Driver's Heart Rate Variability

The attention of driver traveling along a long straight line of prairie highway is easy to be distracted. In this paper, the correlation of straight line length and driver's attention is studied through laboratory simulation experiment and regression analysis. It can be theoretically concluded that the maximum straight line length for prairie highway within which the driver could travel with proper attention is 5km. This study is significant both for prairie highway construction and Intelligent Transportation System.

Temporal change in the morphometry–body mass relationship of polar bears

AbstractAccurate information on animal body mass is often an essential component of wildlife research and management. However, for many large‐bodied species, obtaining direct scale weights from individuals may be difficult. In these cases, morphometric equations (e.g., based on girth or length) may provide accurate and precise estimates of body mass. We developed predictive equations to estimate the body mass of free‐ranging polar bears (Ursus maritimus) in western Hudson Bay, Canada. Using multiple linear and non‐linear regression, we identified a strong relationship between polar bear body weight and linear measures of straight line length and axillary girth. The mass–morphometry relationship appeared to change over time and we developed separate equations for polar bears measured during 2 time periods, 1980–1996 and 2007–2009. Non‐linear models were more accurate and provided body mass estimates within 5.8% (R2 = 0.98) and 6.1% (R2 = 0.98) of scale weight in the earlier and later time periods, respectively. Earlier equations developed for polar bears in this subpopulation performed poorly when applied to recently sampled individuals. In contrast, some contemporary equations from other regions performed reasonably well, suggesting that temporal changes within a subpopulation may be more pronounced than regional differences and can render earlier predictive equations obsolete. Our results have important implications for current and future studies of polar bear body condition and the effects of ongoing climate warming. © 2011 The Wildlife Society.

A Synthesis and Optimal Method for Straight Line Mechanism with Burmester Points

When a Burmester point coincides with the Ball point at the inflection circle pole, given a fixed joint and the point, which is on the expecting straight-line and direction can synthesize an infinite number of mechanisms with coupler curve having a five-point contacts with its tangent, namely, Burmester point. Any displacement is corresponding to three four-bar straight-line linkages with the synthesis formulations given. The property charts, which include the bar ratio, the sum of bars, the relative straight-line length, mechanism types, and so on, are drawn by developing a mechanism software based on vc++6.0 with the solution region method. So the users can find out the involved linkages information intuitively, and also the aimlessness in choosing optimal mechanisms is avoided effectively.

Analysis of the Maximum Straight Line Length for Prairie Highway using Driver's Heart Rate Variability

Analysis of the Maximum Straight Line Length for Prairie Highway using Driver's Heart Rate Variability

RESPONSE OF ALANINE AND BARIUM DITHIONATE EPR DOSIMETERS

The response of alanine and barium dithionate EPR dosimeters to proton irradiation with energies ranging from 6.6-25 MeV has been investigated. EPR dosimeters were calibrated using calibrated gamma sources. Alanine dosimeters show a value 29% higher than those obtained by a Markus chamber at the same energy, and barium dithionate shows a value 22% smaller. The response of the EPR dosimeters to irradiation at a mean dose of about 40 Gy depends on the proton energy. Using experimental data, the yield of the radicals in the tracks for the alanine pellets was calculated. The yield of the radicals was determined to be proportional to the linear energy transfer (LET) on the straight-line length of the proton track, and the proportional coefficient for alanine is equal to 0.109 eV-1. In the area of the Bragg peak, the probability of recombination of the ionized electrons with cations is increased. As a result, approximately 4.6 MeV of proton energy is used for ionization that results in electron-cation recombination instead of formation of radicals, and maximum LET does not coincide with the maximum concentration of the radicals.

Optimal spatial transportation networks where link costs are sublinear in linkcapacity

Consider designing a transportation network onn vertices in the plane, with traffic demand uniform over all source–destination pairs.Suppose the cost of a link of length and capacity c scales as for fixed 0<β<1. Under appropriate standardization, the cost of the minimum cost Gilbert network grows essentiallyas nα(β),where α(β) = 1−(β/2) on and on . This quantity is an upper bound in the worst case (of vertex positions) and a lowerbound under mild regularity assumptions. Essentially the same bounds hold if weconstrain the network to be efficient in the sense that average route length is only1+o(1) times the average straight line length. The transition at corresponds to the dominant cost contribution changing from short links tolong links. The upper bounds arise in the following type of hierarchical networks,which are therefore optimal in an order-of-magnitude sense. On the largescale, we use a sparse Poisson line process to provide long-range links. On themedium scale, we use hierarchical routing on the square lattice. On the smallscale, we link vertices directly to medium-grid points. We discuss one of the manypossible variant models, in which links also have a designed maximum speeds and the cost becomes .

The Effects of Curvature on Haptic Judgments of Extent in Sighted and Blind People

A series of experiments was carried out to examine the effect of curvature on haptic judgments of extent in sighted and blind individuals. Experiment 1 showed that diameters connecting the endpoints of semicircular lines were underestimated with respect to straight lines, but failed to show an effect of visual experience on length judgments. In experiment 2 we tested are lengths. The effects of curvature on perceived path length were weaker, but were still present in this experiment. Visual experience had no effect on path length judgments. Another experiment was performed to examine the effect of repeated tracing (1, 5, 9, or unlimited number of traces) on judgments of the lengths of straight lines and diameters of semicircles. Judgments of extent were more accurate when subjects engaged in larger numbers of traces. There was no effect of number of traces on curve-height judgments, suggesting that subjects were not using height estimates to judge diameters of semicircles. In a further experiment we tested the effect of number of traces on curves that varied in height. Restricting subjects to a single trace magnified the effect of path length on judgments of the distance between the endpoints of curves. Additional experiments showed that curvature effects on diameter judgments were not eliminated when stimuli were in the frontal plane or when the curves were explored with the use of two hands. Arm support had no effect on judged length in experiment 7. A final experiment showed a robust horizontal vertical illusion in haptic perception of convex curves, with overestimation of the heights of the curves compared with their widths. The practical and theoretical implications of the results are discussed.

Cranial suture complexity in white-tailed deer (Odocoileus virginianus)

Neurocranial expansion and mastication are commonly implicated as the two major biomechanical factors affecting suture morphology. In deer the antlers provide an additional source of biomechanical stress acting on the skull. Equivalent stresses are not found in females, who lack antlers. We analyzed the complexity and interdigitation of the interfrontal and coronal sutures that surround the antler-bearing frontal bones of (n = 67) white-tailed deer (Odocoileus virginianus) to 1) evaluate changes in suture morphology throughout ontogeny, and 2) test the hypothesis that male deer have more complex sutures than females. Two methods were used to quantify suture morphology: fractal analysis and length-ratios (actual suture length divided by direct straightline length). Both techniques produced similar results, although the two methods cannot be considered equivalent. Suture complexity increases markedly throughout ontogeny, but appears to level off after animals have reached adulthood. Cranial size in males, but not females, continues to increase in adults. No significant increase in suture complexity with age in the adult cohort was detected. While deer are highly dimorphic in size and the presence of antlers, no significant differences existed between males and females for any measure of suture complexity. No consistent patterns emerged between suture complexity and skull size or antler characteristics. The presence of antlers appears to have a minimal effect on suture complexity in white-tailed deer. Factors that may contribute to the lack of dimorphism in suture complexity are discussed.

COMPARISON OF ULTRASONOGRAPHY, COMPUTED TOMOGRAPHY AND MAGNETIC RESONANCE IMAGING WITH INTRAOPERATIVE MEASUREMENTS IN THE EVALUATION OF ABDOMINAL AORTIC ANEURYSMS

To study the imaging exams more commonly used for abdominal aortic aneurysms evaluation - ultrasonography, conventional computerized tomography, helical computerized tomography and nuclear magnetic angioresonance - comparing the preoperative measurements reached by those radiological methods with the measurements made during the surgical procedures. Patients who had indication of elective transperitoneal surgical treatment for their abdominal aortic aneurysms were included in the study. The initial diagnosis of the aortic dilatation was made by ultrasonography and, after the surgical treatment was indicated, the patient was submitted to another imaging method. Sixty patients were divided into 3 groups according to the complementary imaging method (conventional computerised tomography, helical computerized tomography, nuclear magnetic angioresonance). The ultrasonography of the first 20 patients were joined in a fourth group. There were considered in the study the measurements of the transversal diameter of the proximal neck, maximum transversal diameter of the aneurysm, straight-line length and transversal diameter of the common iliac arteries given by the imaging methods. The same measurements were made by using a caliper during the surgical procedure, and then compared to the values obtained from the radiological exams. The maximum transverse diameter had a range measurement variation of 4.5 to 13.6 cm in the intraoperative, with no statistically significant differences when compared with all the imaging tests. The ultrasonography, however, overestimated the measurements of the proximal neck and the common iliac arteries, in comparison with intraoperative measures. The length of the aorta aneurysm obtained by the conventional computerized tomography was significantly lower if compared to the measures done with the calliper during the operation. The helical computerized tomography and the nuclear magnetic angioresonance provided measurements with no significant differences in the statistic view when compared to the intraoperative measures. Ultrasonography is a reliable method for the diagnosis and follow-up of the aorta abdominal aneurysms, but insufficient for endovascular surgery planning. The conventional computed tomography can provoke distortion in the length measurements of the aorta dilatation. Helical computed tomography and nuclear magnetic angioresonance provided precise measurements of all the studied parameters, being of great utility for surgical planning.

Classification of binaural-activity patterns

The three-dimensional, time-variant output of a computational model of the human auditory system was investigated with the aim of extracting perceptually patterns as relevant to spatial impression. To this end, the same stimuli with which the model was excited were also presented to human listeners which evaluated (i) the auditory source width (ASW), i.e., the horizontal extent of the auditory event, and (ii) the listener envelopment (LEV), i.e., the amount of envelopment by the auditory event. The listeners had to be trained beforehand as the discrimination of source- and room-related parameters of auditory events is not a common task to them. To allow for natural localization and to enable interactive listening, the stimuli were presented through head-tracked headphones. Trained listeners appeared to produce consistent results when depicting auditory objects on a compass-rose-shaped plane, where they had to mark the position and broadening of the auditory event(s) by the position(s) and length(s) of straight lines, and the envelopment by the position and size of an ellipse.