An Elementary Study of Chaotic Behaviors in 1-D Maps

In this article, we have discussed basic concepts of one-dimensional maps like Cubic map, Sine map and analyzed their chaotic behaviors in several senses in the unit interval. We have mainly focused on Orbit Analysis, Time Series Analysis, Lyapunov Exponent Analysis, Sensitivity to Initial Conditions, Bifurcation Diagram, Cobweb Diagram, Histogram, Mathematical Analysis by Newton’s Iteration, Trajectories and Sensitivity to Numerical Inaccuracies of the said maps. We have tried to make decision about these mentioned maps whether chaotic or not on a unique interval of parameter value. We have performed numerical calculations and graphical representations for all parameter values on that interval and have tried to find if there is any single value of parameter for which those maps are chaotic. In our calculations we have found there are many values for which those maps are chaotic. We have showed numerical calculations and graphical representations for single value of the parameter only in this paper which gives a clear visualization of chaotic dynamics. We performed all graphical activities by using Mathematica and MATLAB.

Assessment of quality control system by sigma metrics and quality goal index ratio: A roadmap towards preparation for NABL

AIM To study sigma metrics and quality goal index ratio(QGI). METHODS The retrospective study was conducted at the Clinical Biochemistry Laboratory, PGIMS, Rohtak, which recently became a National Accreditation Board for Testing and Calibration of Laboratories accredited lab as per the International Organization for Standardization 15189:2012 and provides service to a > 1700-bed tertiary care hospital. Data of 16 analytes was extracted over a period of one year from January 2017 to December 2017 for calculation of precision, accuracy, sigma metrics, total error, and QGI. RESULTS The average coefficient of variation ranged from 2.12%(albumin) to 5.42%(creatinine) for level 2 internal quality control and 2%(albumin) to 3.62%(high density lipoprotein-cholesterol) for level 3 internal quality control. Average coefficient of variation of all the parameters was below 5%, reflecting very good precision. The sigma metrics for level 2 indicated that 11(68.5%) of the 16 parameters fall short of meeting Six Sigma quality performance. Of these, five failed to meet minimum sigma quality performance with metrics less than 3, and another six just met minimal acceptable performance with sigma metrics between 3 and 6. For level 3, the data collected indicated eight(50%) of the parameters did not achieve Six Sigma quality performance, out of which three had metrics less than 3, and five had metrics between 3 and 6. QGI ratio indicated that the main problem was inaccuracy in the case of total cholesterol, aspartate transaminase, and alanine transaminase(QGI > 1.2), imprecision in the case of urea(QGI < 0.8), and both imprecision and inaccuracy for glucose.CONCLUSION On the basis of sigma metrics and QGI, it may be concluded that the Clinical Biochemistry Laboratory, PGIMS, Rohtak was able to achieve satisfactory results with world class performance for many analytes one year preceding the accreditation by the National Accreditation Board for Testing and Calibration of Laboratories. Aspartate transaminase and alanine transaminase required strict external quality assurance scheme monitoring and modification in quality control procedure as their QGI ratio showed inaccuracy.

MOBILITY AIDED LOCALIZATION OF WIRELESS SENSOR NETWORKS WITH INACCURATE RANGE MEASUREMENTS

This paper studies the relationship between mobility, navigation and localization in the context of wireless sensor networks with mobile beacons. It is observed that mobility can aid in network node localization and that once localized, the network nodes can localize and track a mobile object and guide its navigation. A distributed kernel-based algorithm is proposed that enables the nodes to establish confident position estimates in the presence of ranging inaccuracies. The proposed approach features robustness with respect to range measurement inaccuracies, low complexity and distributed implementation, using only local information. Simulation validates our approach viable.

Clinical Impact of Targeting Inaccuracy Due to Distortion of the Leksell Stereotactic Frame

Background: Distortion of the Leksell stereotactic frame can occur during surgical and radiosurgical frame-based procedures. The targeting accuracies of surgical procedures such as DBS surgery or frame-based biopsy, or Gamma Knife radiosurgical procedures, are related to the stereotactic frame that is commonly referred to a non-deformable referential system. Objective: To evaluate the clinical impact of frame distortion on accuracy of targeting in various stereotactic procedures. Methods: We studied the influence of increasing levels of distortion of the Leksell frame both on surgical procedures using the stereotactic arch, and on radiosurgical procedures with the Gamma Knife. For surgical procedures we applied the Target Simulator of Elekta to a frame submitted to different levels of frame distortion, and we measured the modifications of accuracy of targeting. For radiosurgical procedures the Leksell frame was applied on an anthropomorphic phantom and modifications of target coordinates were measured by an imaging method using the stereotactic CBCT of the Gamma Knife ICON. Results: For surgical procedures, we found a linear relation between the amount of the frame distortion and the extent of the deviation from the stereotactic target using the stereotactic arch (R2 = 0.99709). The level of bending of the frame is also linearly related to the level of inaccuracy of stereotactic targeting based on acquisition of MRI and CTscan with the Elekta imaging boxes (R2 = 0.96825). The inaccuracy of targeting related to frame bending can be avoided by a systematic control at the end of frame placement and by the use of the CBCT of the Gamma Knife Icon. Conclusion: Distortion of the frame is a significant source of clinical inaccuracy of targeting for stereotactic procedures. Frame bending must be checked after each frame placement and corrected if needed to avoid targeting inaccuracy during stereotactic surgery and radio-surgery procedures.

Error rate of multi-level rapid prototyping trajectories for pedicle screw placement in lumbar and sacral spine

Objective：Free-hand pedicle screw placement has a high incidence of pedicle perforation which can be reduced with fluoroscopy,navigation or an alternative rapid prototyping drill guide template.In our study the error rate of multi-level templates for pedicle screw placement in lumbar and sacral regions was evaluated.Methods：A case series study was performed on 11 patients.Seventy-two screws were implanted using multilevel drill guide templates manufactured with selective laser sintering.According to the optimal screw direction preoperatively defined,an analysis of screw misplacement was performed.Displacement,deviation and screw length difference were measured.The learning curve was also estimated.Results：Twelve screws （17％） were placed more than 3.125 mm out of its optimal position in the centre of pedicle.The tip of the 16 screws （22％） was misplaced more than 6.25 mm out of the predicted optimal position.According to our predefined goal,19 screws （26％） were implanted inaccurately.In 10 cases the screw length was selected incorrectly：1 （1％） screw was too long and 9 （13％） were too short.No clinical signs of neurovascular lesion were observed.Learning curve was insignificantly noticeable （P=0.129）.Conclusion：In our study,the procedure of manufacturing and applying multi-level drill guide templates has a 26％ chance of screw misplacement.However,that rate does not coincide with pedicle perforation incidence and neurovascular injury.These facts along with a comparison to compatible studies make it possible to summarize that multi-level templates are satisfactorily accurate and allow precise screw placement with a clinically irrelevant mistake factor.Therefore templates could potentially represent a useful tool for routine pedicle screw placement.

Some Source Coding Theorems and 1:1 Coding Based on Generalized Inaccuracy Measure of Order α and Typeβ

In this paper,we have established some noiseless coding theorems for a generalized parametric‘useful’inaccuracy measure of orderαand typeβand generalized mean codeword length.Further,lower bounds on exponentiated useful code length for the best 1:1 code have been obtained in terms of the useful inaccuracy of orderαand typeβand the generalized average useful codeword length.