Novel Polynomial Basis and Its Application to Reed-Solomon Erasure Codes

In this paper, we present a new basis of polynomial over finite fields of characteristic two and then apply it to the encoding/decoding of Reed-Solomon erasure codes. The proposed polynomial basis allows that $h$-point polynomial evaluation can be computed in $O(h\log_2(h))$ finite field operations with small leading constant. As compared with the canonical polynomial basis, the proposed basis improves the arithmetic complexity of addition, multiplication, and the determination of polynomial degree from $O(h\log_2(h)\log_2\log_2(h))$ to $O(h\log_2(h))$. Based on this basis, we then develop the encoding and erasure decoding algorithms for the $(n=2^r,k)$ Reed-Solomon codes. Thanks to the efficiency of transform based on the polynomial basis, the encoding can be completed in $O(n\log_2(k))$ finite field operations, and the erasure decoding in $O(n\log_2(n))$ finite field operations. To the best of our knowledge, this is the first approach supporting Reed-Solomon erasure codes over characteristic-2 finite fields while achieving a complexity of $O(n\log_2(n))$, in both additive and multiplicative complexities. As the complexity leading factor is small, the algorithms are advantageous in practical applications

Compliance with Intensity-Focused Prescription of Physical Activity Using Real-Time Cadence

The utility of wearable activity monitors can provide a better guide to increase adherence to the recommended physical activity levels for health improvement. However, the extent of participants’ ability to comply with the physical activity prescription using a newly developed, intensity-focused value, real-time cadence, remains unclear. PURPOSE: To examine the participants’ ability to comply with a given physical activity prescription focusing on intensity (i.e., real-time cadence). METHODS: Thirty-six healthy adult individuals (age 18-65 yrs; 18 female) participated in the study. During a 2-min over-ground walking trial, participants were prescribed to walk at any cadences (steps/min; an indicative of intensity of ambulatory activities) faster than 120 (i.e., equivalent to a brisk walking) using either one of the following devices in a counter-balanced order: (1) Garmin Forerunner 235 (GM) and (2) Polar M430 (PL), (3) Garmin Foot Pot (FP) and (4) Polar Stride Sensor (SS). Descriptive statistics were used to calculate the % of participants who complied accordingly with the given physical activity prescription as well as the means of cadence performed in each trial. Pearson correlation was conducted to determine the relationship between a criterion (i.e., hand count) and the measures from each device. RESULTS: In general, greater than 90% of the participants (91.7%, 97.2%, 100%, and 97.2% for the device (1) through (4), respectively) were able to maintain walking intensity at the prescribed level using real-time cadence. Mean cadences performed in the protocol were barely above the prescribed intensity, 120 steps/min (i.e., approximately 123 steps/min). The correlations showed strong relationships between the criterion and the measures of the monitors (p \u3c.001). GM and PL sometimes showed a value of zero (0), indicating no detection of steps, during the protocol (from 4 and 11 participants, respectively). CONCLUSION: The results suggest the potential to use the activity monitors providing real-time cadence for physical activity prescription and clarify the participants’ capability to manipulate the values of real-time cadence to maintain the targeted intensity of physical activity. A highly aimed intensity prescription rather than minimum requirement might help individuals ensure the compliance with targeted intensity

Pain and Suffering Damages in Wrongful Death Cases: An Empirical Study

Most jurisdictions in the United States award pain and suffering damages to spouses of victims in wrongful death cases. In several East Asian countries, spouses, parents, and children of the victim can all demand pain and suffering damages. Despite the prevalence of this type of damages, and the oft‐enormous amount of compensation, there has been no large‐scale empirical study on how judges achieve the difficult task of assessing pain and suffering damages. Using a unique data set containing hundreds of car accident cases rendered by the court of first instance in Taiwan, with single‐equation and structural‐equation models, we find the plaintiffs\u27 ad damnum has a statistically significant influence on the court‐adjudicated pain and suffering damages. That could be evidence for the anchoring effect. Nevertheless, courts are very sensitive to the possibility of pushing defendants into financial hardship. When defendants\u27 out‐of‐pocket payments of pecuniary damages, divided by defendants\u27 income, are positive, this amount has a negative effect on the amount of pain and suffering damages, whereas when they are negative (this could happen because the amount of compulsory insurance payment had to be deducted), the amount in absolute value has a positive effect. Not all next‐of‐kin received the same amount. Spouses of the victim received more than other next‐of‐kin, and adult children received the least among eligible relatives. Parents, however, tended to be awarded a high amount of pain and suffering damages when they were the only familial group suing the defendant

Pain and Suffering Damages in Wrongful Death Cases: An Empirical Study

Most jurisdictions in the United States award pain and suffering damages to spouses of victims in wrongful death cases. In several East Asian countries, spouses, parents, and children of the victim can all demand pain and suffering damages. Despite the prevalence of this type of damages, and the oft‐enormous amount of compensation, there has been no large‐scale empirical study on how judges achieve the difficult task of assessing pain and suffering damages. Using a unique data set containing hundreds of car accident cases rendered by the court of first instance in Taiwan, with single‐equation and structural‐equation models, we find the plaintiffs\u27 ad damnum has a statistically significant influence on the court‐adjudicated pain and suffering damages. That could be evidence for the anchoring effect. Nevertheless, courts are very sensitive to the possibility of pushing defendants into financial hardship. When defendants\u27 out‐of‐pocket payments of pecuniary damages, divided by defendants\u27 income, are positive, this amount has a negative effect on the amount of pain and suffering damages, whereas when they are negative (this could happen because the amount of compulsory insurance payment had to be deducted), the amount in absolute value has a positive effect. Not all next‐of‐kin received the same amount. Spouses of the victim received more than other next‐of‐kin, and adult children received the least among eligible relatives. Parents, however, tended to be awarded a high amount of pain and suffering damages when they were the only familial group suing the defendant

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

The official published version of this article can be found at the link below.This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60774073 and 60974030, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

Use of real-time cadence to prescribe aerobic physical activity intensity and its comparison with existing methods

The purpose of this study was to determine the effectiveness of physical activity intensity prescription using real-time cadence on achieving the required intensities for health benefits. Forty adults (18-65�years) participated in the study. The intensity prescriptions included Rating of Perceived Exertion, Talk Test, Heart Rate, and Real-Time Cadence. The participants performed a 2-min trial for both moderate- and vigorous-intensity according to each prescription. Atri-axial accelerometer was used as criterion measure. After completion of the trials, participant's preference for the prescriptions was assessed by three domains (e.g., understanding, performing, maintaining). The compliance and achievement rates of RC were calculated and compared to other prescription methods. Coefficient of Variance was used to evaluate the extent of variation of intensity during the trials. Higher compliance rates were found in both moderate- (92.1%) and vigorous-intensity (94.9%) when using RC. When using RC, most participants (92.5%) were able to achieve the targeted moderate-intensity, but not for vigorous-intensity although a significant difference was found between the two intensities (p�<�.001). Overall, RC was the most favoured method in all three domains. RC is a promising tool to prescribe moderate-intensity of physical activity for health benefits but still needs to be refined on prescribing vigorous-intensity.Peer reviewedCommunity Health Sciences, Counseling and Counseling Psycholog

Validation of wearable activity monitors for real-time cadence

The purpose of this study is to establish evidence of validity for wearable activity monitors providing real-time cadence against a criterion measure. Thirty-six healthy adults, aged 18-65 years, participated in the study. Four activity monitors including 2 watch-based monitors and 2 cadence sensors attaching to shoelaces were tested. Each participant completed the study protocol consisting of 2 distinct components: (1) treadmill protocol and (2) overground protocol. Lin's concordance correlation and mean absolute percentage error (MAPE) were calculated for the comparisons between the criterion and measures of the monitors. Bland-Altman analysis was performed to determine the mean bias and 95% limits of agreement. All activity monitors showed high correlations with the criterion measures (p < .01). Lower correlations were observed at slow walking speeds in the watch-based monitors. In contrast, consistent and strong correlations were found with both cadence sensors regardless of walking speeds (p < .01). Similar patterns were observed in the MAPE scores. Greater than 90% of the participants were able to maintain prescribed walking intensity using real-time cadence. The results suggest that the wearable activity monitors are an acceptable measure of real-time cadence and provide the potential to improve intensity-based prescription of physical activity using the monitors.Peer reviewedCommunity Health Sciences, Counseling and Counseling Psycholog

AMiBA: Broadband Heterodyne CMB Interferometry

The Y. T. Lee Array for Microwave Background (AMiBA) has reported the first science results on the detection of galaxy clusters via the Sunyaev Zel'dovich effect. The science objectives required small reflectors in order to sample large scale structures (20') while interferometry provided modest resolutions (2'). With these constraints, we designed for the best sensitivity by utilizing the maximum possible continuum bandwidth matched to the atmospheric window at 86-102GHz, with dual polarizations. A novel wide-band analog correlator was designed that is easily expandable for more interferometer elements. MMIC technology was used throughout as much as possible in order to miniaturize the components and to enhance mass production. These designs will find application in other upcoming astronomy projects. AMiBA is now in operations since 2006, and we are in the process to expand the array from 7 to 13 elements.Comment: 10 pages, 6 figures, ApJ in press; a version with high resolution figures available at http://www.asiaa.sinica.edu.tw/~keiichi/upfiles/AMiBA7/mtc_highreso.pd