A Unified Subdivision Scheme for Arcs and Circles

2006 ◽  
Author(s):  
Shanglong Wang ◽  
Kwun-Lon Ting
Keyword(s):  
Subdivision Scheme ◽  
End Points ◽  
B Splines ◽  
End Point ◽  
Trigonometric Splines ◽  
Subdivision Rules

This paper proposes a subdivision scheme that is capable of expressing arcs and circles in a consistent form. This curve scheme is based on the unified subdivision rules for cubic B-splines, splines-in-tension, and some trigonometric splines that are capable of generating circles. The most important feature of the scheme is to change the end point rule such that the end points are forced to locate on lines connecting the center to the start point as well as the end point. With the proposed scheme, generating arcs and circles also becomes much more intuitive.

scholarly journals Time Interval to Biochemical Failure as a Surrogate End Point in Locally Advanced Prostate Cancer: Analysis of Randomized Trial NRG/RTOG 9202

2019 ◽  
Vol 37 (3) ◽  
pp. 213-221 ◽  
Author(s):  
James J. Dignam ◽  
Daniel A. Hamstra ◽  
Herbert Lepor ◽  
David Grignon ◽  
Harmar Brereton ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Randomized Trial ◽  
Locally Advanced ◽  
Biochemical Failure ◽  
Mediating Effect ◽  
Time Interval ◽  
Short Term ◽  
End Points ◽  
End Point

Background In prostate cancer, end points that reliably portend prognosis and treatment benefit (surrogate end points) can accelerate therapy development. Although surrogate end point candidates have been evaluated in the context of radiotherapy and short-term androgen deprivation (AD), potential surrogates under long-term (24 month) AD, a proven therapy in high-risk localized disease, have not been investigated. Materials and Methods In the NRG/RTOG 9202 randomized trial (N = 1,520) of short-term AD (4 months) versus long-term AD (LTAD; 28 months), the time interval free of biochemical failure (IBF) was evaluated in relation to clinical end points of prostate cancer–specific survival (PCSS) and overall survival (OS). Survival modeling and landmark analysis methods were applied to evaluate LTAD benefit on IBF and clinical end points, association between IBF and clinical end points, and the mediating effect of IBF on LTAD clinical end point benefits. Results LTAD was superior to short-term AD for both biochemical failure (BF) and the clinical end points. Men remaining free of BF for 3 years had relative risk reductions of 39% for OS and 73% for PCSS. Accounting for 3-year IBF status reduced the LTAD OS benefit from 12% (hazard ratio [HR], 0.88; 95% CI, 0.79 to 0.98) to 6% (HR, 0.94; 95% CI, 0.83 to 1.07). For PCSS, the LTAD benefit was reduced from 30% (HR, 0.70; 95% CI, 0.52 to 0.82) to 6% (HR, 0.94; 95% CI, 0.72 to 1.22). Among men with BF, by 3 years, 50% of subsequent deaths were attributed to prostate cancer, compared with 19% among men free of BF through 3 years. Conclusion The IBF satisfied surrogacy criteria and identified the benefit of LTAD on disease-specific survival and OS. The IBF may serve as a valid end point in clinical trials and may also aid in risk monitoring after initial treatment.

New Supervised Learning Theory Applied to Cerebellar Modeling for Suppression of Variability of Saccade End Points

2013 ◽  
Vol 25 (6) ◽  
pp. 1440-1471 ◽  
Author(s):  
Masahiko Fujita
Keyword(s):  
Supervised Learning ◽  
Cerebellar Cortex ◽  
Learning Theory ◽  
Learning System ◽  
Learning Ability ◽  
Motor Center ◽  
End Points ◽  
Noise Effects ◽  
End Point ◽  
Control Scheme

A new supervised learning theory is proposed for a hierarchical neural network with a single hidden layer of threshold units, which can approximate any continuous transformation, and applied to a cerebellar function to suppress the end-point variability of saccades. In motor systems, feedback control can reduce noise effects if the noise is added in a pathway from a motor center to a peripheral effector; however, it cannot reduce noise effects if the noise is generated in the motor center itself: a new control scheme is necessary for such noise. The cerebellar cortex is well known as a supervised learning system, and a novel theory of cerebellar cortical function developed in this study can explain the capability of the cerebellum to feedforwardly reduce noise effects, such as end-point variability of saccades. This theory assumes that a Golgi-granule cell system can encode the strength of a mossy fiber input as the state of neuronal activity of parallel fibers. By combining these parallel fiber signals with appropriate connection weights to produce a Purkinje cell output, an arbitrary continuous input-output relationship can be obtained. By incorporating such flexible computation and learning ability in a process of saccadic gain adaptation, a new control scheme in which the cerebellar cortex feedforwardly suppresses the end-point variability when it detects a variation in saccadic commands can be devised. Computer simulation confirmed the efficiency of such learning and showed a reduction in the variability of saccadic end points, similar to results obtained from experimental data.

scholarly journals Composite Primary End Points in Cardiovascular Outcomes Trials Involving Type 2 Diabetes Patients: Should Unstable Angina Be Included in the Primary End Point?

Diabetes Care ◽  
2017 ◽  
Vol 40 (9) ◽  
pp. 1144-1151 ◽  
Author(s):  
Nikolaus Marx ◽  
Darren K. McGuire ◽  
Vlado Perkovic ◽  
Hans-Juergen Woerle ◽  
Uli C. Broedl ◽  
...  
Keyword(s):  
Type 2 Diabetes ◽  
Unstable Angina ◽  
Cardiovascular Outcomes ◽  
End Points ◽  
End Point ◽  
Diabetes Patients

scholarly journals Effective intracortical microstimulation parameters applied to primary motor cortex for evoking forelimb movements to stable spatial end points

2013 ◽  
Vol 110 (5) ◽  
pp. 1180-1189 ◽  
Author(s):  
Gustaf M. Van Acker ◽  
Sommer L. Amundsen ◽  
William G. Messamore ◽  
Hongyu Y. Zhang ◽  
Carl W. Luchies ◽  
...  
Keyword(s):  
Motor Cortex ◽  
Large Scale ◽  
Primary Motor Cortex ◽  
Emg Activity ◽  
Intracortical Microstimulation ◽  
End Points ◽  
End Point ◽  
Motor Effects ◽  
Forelimb Movements ◽  
Stimulation Of

High-frequency, long-duration intracortical microstimulation (HFLD-ICMS) applied to motor cortex is recognized as a useful and informative method for corticomotor mapping by evoking natural-appearing movements of the limb to consistent stable end-point positions. An important feature of these movements is that stimulation of a specific site in motor cortex evokes movement to the same spatial end point regardless of the starting position of the limb. The goal of this study was to delineate effective stimulus parameters for evoking forelimb movements to stable spatial end points from HFLD-ICMS applied to primary motor cortex (M1) in awake monkeys. We investigated stimulation of M1 as combinations of frequency (30–400 Hz), amplitude (30–200 μA), and duration (0.5–2 s) while concurrently recording electromyographic (EMG) activity from 24 forelimb muscles and movement kinematics with a motion capture system. Our results suggest a range of parameters (80–140 Hz, 80–140 μA, and 1,000-ms train duration) that are effective and safe for evoking forelimb translocation with subsequent stabilization at a spatial end point. The mean time for stimulation to elicit successful movement of the forelimb to a stable spatial end point was 475.8 ± 170.9 ms. Median successful frequency and amplitude were 110 Hz and 110 μA, respectively. Attenuated parameters resulted in inconsistent, truncated, or undetectable movements, while intensified parameters yielded no change to movement end points and increased potential for large-scale physiological spread and adverse focal motor effects. Establishing cortical stimulation parameters yielding consistent forelimb movements to stable spatial end points forms the basis for a systematic and comprehensive mapping of M1 in terms of evoked movements and associated muscle synergies. Additionally, the results increase our understanding of how the central nervous system may encode movement.

scholarly journals A 4D continuous representation of myocardial velocity fields from tissue phase mapping magnetic resonance imaging

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247826
Author(s):  
Bård A. Bendiksen ◽  
Gary McGinley ◽  
Ivar Sjaastad ◽  
Lili Zhang ◽  
Emil K. S. Espe
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
Tissue Phase Mapping ◽  
Continuous Representation ◽  
Resonance Imaging ◽  
Limits Of Agreement ◽  
B Splines ◽  
End Point ◽  
Tissue Phase ◽  
Linear B

Myocardial velocities carry important diagnostic information in a range of cardiac diseases, and play an important role in diagnosing and grading left ventricular diastolic dysfunction. Tissue Phase Mapping (TPM) Magnetic Resonance Imaging (MRI) enables discrete sampling of the myocardium’s underlying smooth and continuous velocity field. This paper presents a post-processing framework for constructing a spatially and temporally smooth and continuous representation of the myocardium’s velocity field from TPM data. In the proposed scheme, the velocity field is represented through either linear or cubic B-spline basis functions. The framework facilitates both interpolation and noise reducing approximation. As a proof-of-concept, the framework was evaluated using artificially noisy (i.e., synthetic) velocity fields created by adding different levels of noise to an original TPM data. The framework’s ability to restore the original velocity field was investigated using Bland-Altman statistics. Moreover, we calculated myocardial material point trajectories through temporal integration of the original and synthetic fields. The effect of noise reduction on the calculated trajectories was investigated by assessing the distance between the start and end position of material points after one complete cardiac cycle (end point error). We found that the Bland-Altman limits of agreement between the original and the synthetic velocity fields were reduced after application of the framework. Furthermore, the integrated trajectories exhibited consistently lower end point error. These results suggest that the proposed method generates a realistic continuous representation of myocardial velocity fields from noisy and discrete TPM data. Linear B-splines resulted in narrower limits of agreement between the original and synthetic fields, compared to Cubic B-splines. The end point errors were also consistently lower for Linear B-splines than for cubic. Linear B-splines therefore appear to be more suitable for TPM data.

scholarly journals Method for determining the kinematic parameters of the vertical rotor blades for the destruction of the tuberous layer

2020 ◽  
pp. 82-90
Author(s):  
V. A. Volsky V. A. ◽  
V. S. Bonchik
Keyword(s):  
Hydraulic Drive ◽  
Extreme Points ◽  
Geometric Shape ◽  
Kinematic Parameters ◽  
End Points ◽  
End Point ◽  
Vertical Rotor ◽  
Starting Point ◽  
The Absolute ◽  
Angle Of Rotation

Annotation Purpose. Development of a technique for determining the velocities of collision of the blades with the tuberous layer, the trajectory of movement, the magnitude and direction of the velocities of the most characteristic points. Methods. The research was carried out using the basic provisions of theoretical mechanics, statistics, probability theory, methods of differential calculations, mathematical modeling and applied programming. The studies were carried out on a specially designed laboratory installation using a vertical rotor hydraulic drive and strain gauge equipment mounted on a tractor, as well as a set of variable connecting plates for setting the machine operating modes. Results. The calculations of the absolute collision velocities of the blades of the lower and upper beaters of the vertical rotor at the start and end points, respectively, are performed. The geometric shape of the working surfaces and the direction of rotation for the extreme points of the outer contours of the blades of the lower and upper beaters of the vertical rotor of the potato harvester are substantiated. Conclusions. Using the above technique, as well as graphical dependences, we calculated the rational kinematic parameters of the blades of the lower and upper beaters of the vertical rotor, respectively, at the start and end points, where the greatest destruction of the tuber layer. For the lower beater blade, the absolute collision speed at the angle of rotation ωнt = 120° at the starting point = 1.6 m/s, at the end point – = 1.94 m/s. For the upper beater blade, the absolute collision speed at the angle of rotation ωвt = 120° at the starting point = 1.4 m/s, at the end point – = 1.92 m/s. Therefore, according to the specified rational kinematic parameters of the blades of the lower and upper beaters of the vertical rotor, it is possible to design the geometric shape of the surfaces of the crushing working bodies of potato harvesters. Keywords: blade, breaking surface, breasts, potatoes.

European Network on the Determination of Site End Points for Radiologically Contaminated Land

2007 ◽  
Author(s):  
Peter Booth ◽  
Chris Lennon
Keyword(s):  
Best Practice ◽  
Good Practice ◽  
State Agency ◽  
European Network ◽  
End Points ◽  
Contaminated Land ◽  
End Point ◽  
Land Site ◽  
High Level

Nexia Solutions are currently running a small European network entitled “European Network on the Determination of Site End Points for Radiologically Contaminated Land (ENDSEP)”. Other network members include NRG (Netherlands), UKAEA (UK), CEA (France), SOGIN (Italy), Wismut (Germany), Saxon State Agency of Environment and Geology (Germany). The network is focused on the technical and socio-economical issues associated with the determination of end points for sites potentially, or actually, impacted by radiological contamination. Such issues will cover: • Those associated with the run up to establishing a site end point; • Those associated with verifying that the end points have been met; and • Those associated with post closure. The network’s current high level objectives can be summarized as follows: • Share experience and best practice in the key issues running up to determining site end points; • Gain a better understanding of the potential effects of recent and forthcoming EU legislation; • Assess consistency between approaches; • Highlight potential gaps within the remit of site end point determination and management; and • Consider the formulation of research projects with a view to sharing time and expense. The programme of work revolves around the following key tasks: • Share information, experience and existing good practice. • Look to determine sustainable approaches to contaminated land site end point management. • Through site visits, gain first hand experience of determining an appropriate end point strategy, and identifying and resolving end point issues. • Highlight the key data gaps and consider the development of programmes to either close out these gaps or to build confidence in the approaches taken. • Production of position papers on each technical area highlighting how different countries approach/resolve a specific problem.

scholarly journals A Privacy-Preserving Trajectory Publication Method Based on Secure Start-Points and End-Points

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yannian Zhao ◽  
Yonglong Luo ◽  
Qingying Yu ◽  
Zhaoyan Hu
Keyword(s):  
Theoretical Analysis ◽  
Privacy Preservation ◽  
Privacy Preserving ◽  
Third Parties ◽  
Algorithm Complexity ◽  
Experimental Results ◽  
End Points ◽  
End Point ◽  
Trajectory Similarity ◽  
Candidate Set

By judging whether the start-point and end-point of a trajectory conform to the user’s behavioral habits, an attacker who possesses background knowledge can breach the anonymous trajectory. Traditional trajectory privacy preservation schemes often generate an anonymous set of trajectories without considering the security of the trajectory start- and end-points. To address this problem, this paper proposes a privacy-preserving trajectory publication method based on generating secure start- and end-points. First, a candidate set containing a secure start-point and end-point is generated according to the user’s habits. Second, k−1 anonymous trajectories are generated bidirectionally according to that secure candidate set. Finally, accessibility corrections are made for each anonymous trajectory. This method integrates features such as local geographic reachability and trajectory similarity when generating an anonymized set of trajectories. This provides users with privacy preservation at the k-anonymity level, without relying on the trusted third parties and with low algorithm complexity. Compared with existing methods such as trajectory rotation and unidirectional generation, theoretical analysis and experimental results on the datasets of real trajectories show that the anonymous trajectories generated by the proposed method can ensure the security of trajectory privacy while maintaining a higher trajectory similarity.

scholarly journals Resampling the N9741 Trial to Compare Tumor Dynamic Versus Conventional End Points in Randomized Phase II Trials

2015 ◽  
Vol 33 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Manish R. Sharma ◽  
Elizabeth Gray ◽  
Richard M. Goldberg ◽  
Daniel J. Sargent ◽  
Theodore G. Karrison
Keyword(s):  
Colorectal Cancer ◽  
Metastatic Colorectal Cancer ◽  
Phase Ii ◽  
Phase Iii ◽  
Rank Test ◽  
Phase Ii Trials ◽  
End Points ◽  
End Point ◽  
Randomized Phase Ii ◽  
Log Ratio

Purpose The optimal end point for randomized phase II trials of anticancer therapies remains controversial. We simulated phase II trials by resampling patients from N9741, a randomized phase III trial of chemotherapy regimens for metastatic colorectal cancer, and compared the power of various end points to detect the superior therapy (FOLFOX [infusional fluorouracil, leucovorin, and oxaliplatin] had longer overall survival than both IROX [irinotecan plus oxaliplatin] and IFL [irinotecan and bolus fluorouracil plus leucovorin]). Methods Tumor measurements and progression-free survival (PFS) data were obtained for 1,471 patients; 1,002 had consistently measured tumors and were resampled (5,000 replicates) to simulate two-arm, randomized phase II trials with α = 0.10 (one sided) and 20 to 80 patients per arm. End points included log ratio of tumor size at 6, 12, and 18 weeks relative to baseline; time to tumor growth (TTG), estimated using a nonlinear mixed-effects model; and PFS. Arms were compared using rank sum tests for log ratio and TTG and a log-rank test for PFS. Results For FOLFOX versus IFL, TTG and PFS had similar power, with both exceeding the power of log ratio at 18 weeks; for FOLFOX versus IROX, TTG and log ratio at 18 weeks had similar power, with both exceeding the power of PFS. The best end points exhibited > 80% power with 60 to 80 patients per arm. Conclusion TTG is a powerful end point for randomized phase II trials of cytotoxic therapies in metastatic colorectal cancer; it was either comparable or superior to PFS and log ratio at 18 weeks. Additional studies will be needed to clarify the potential of TTG as a phase II end point.

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