Zeroes of Riemann's zeta function on the critical line with 40000 decimal digits accuracy

The project aims at computing Riemann's zeroes with high accuracy through an analysis of large determinants using Matyasievich's Artless method. Location of Riemann's zeroes is the famous 8th Hilbert problem, and one of Clay's Institute millennium problems.

Evaluation and comparison of type reduction algorithms from a forecast accuracy perspective

A variety of type reduction (TR) algorithms have been proposed for interval type-2 fuzzy logic systems (IT2 FLSs). The focus of existing literature is mainly on computational requirements of TR algorithm. Often researchers give more rewards to computationally less expensive TR algorithms. This paper evaluates and compares five frequently used TR algorithms from a forecasting performance perspective. Algorithms are judged based on the generalization power of IT2 FLS models developed using them. Four synthetic and real world case studies with different levels of uncertainty are considered to examine effects of TR algorithms on forecasts accuracies. It is found that Coupland-Jonh TR algorithm leads to models with a better forecasting performance. However, there is no clear relationship between the width of the type reduced set and TR algorithm.

Predictive validity and classification accuracy of ActiGraph energy expenditure equations and cut-points in young children

Objectives
Evaluate the predictive validity of ActiGraph energy expenditure equations and the classification accuracy of physical activity intensity cut-points in preschoolers.

Methods
Forty children aged 4–6 years (5.3±1.0 years) completed a ~150-min room calorimeter protocol involving age-appropriate sedentary, light and moderate-to vigorous-intensity physical activities. Children wore an ActiGraph GT3X on the right mid-axillary line of the hip. Energy expenditure measured by room calorimetry and physical activity intensity classified using direct observation were the criterion methods. Energy expenditure was predicted using Pate and Puyau equations. Physical activity intensity was classified using Evenson, Sirard, Van Cauwenberghe, Pate, Puyau, and Reilly, ActiGraph cut-points.

Results
The Pate equation significantly overestimated VO2 during sedentary behaviors, light physical activities and total VO2 (P<0.001). No difference was found between measured and predicted VO2 during moderate-to vigorous-intensity physical activities (P = 0.072). The Puyau equation significantly underestimated activity energy expenditure during moderate-to vigorous-intensity physical activities, light-intensity physical activities and total activity energy expenditure (P<0.0125). However, no overestimation of activity energy expenditure during sedentary behavior was found. The Evenson cut-point demonstrated significantly higher accuracy for classifying sedentary behaviors and light-intensity physical activities than others. Classification accuracy for moderate-to vigorous-intensity physical activities was significantly higher for Pate than others.

Conclusion
Available ActiGraph equations do not provide accurate estimates of energy expenditure across physical activity intensities in preschoolers. Cut-points of ≤25counts⋅15 s−1 and ≥420 counts⋅15 s−1 for classifying sedentary behaviors and moderate-to vigorous-intensity physical activities, respectively, are recommended.

Measuring depth accuracy in RGBD cameras

This paper presents the comparison between the Microsoft Kinect depth sensor and the Asus Xtion for computer vision applications. Depth sensors, known as RGBD cameras,
project an infrared pattern and calculate the depth from the reflected light using an infrared sensitive camera. In this research, we compare the depth sensing capabilities of the two sensors under various conditions. The purpose is to give the reader a background to whether use the Microsoft Kinect or Asus Xtion sensor to solve a specific computer vision problem. The properties of the two depth sensors were investigated by conducting a series of experiments evaluating the accuracy of the sensors under various conditions, which shows the advantages and disadvantages of both Microsoft Kinect and Asus Xtion sensor.

Zeros of Dirichlet L-functions on the critical line with the accuracy of 40000 decimal places

The zeros of Dirichlet L-functions for various moduli and characters are being computed with very high accuracy on a cluster of workstations at Deakin University. This collection is growing to include more zeros (other moduli and characters).

Effects of type reduction algorithms on forecasting accuracy of IT2FLS models

Type reduction (TR) is one of the key components of interval type-2 fuzzy logic systems (IT2FLSs). Minimizing the computational requirements has been one of the key design criteria for developing TR algorithms. Often researchers give more rewards to computationally less expensive TR algorithms. This paper evaluates and compares five frequently used TR algorithms based on their contribution to the forecasting performance of IT2FLS models. Algorithms are judged based on the generalization power of IT2FLS models developed using them. Synthetic and real world case studies with different levels of uncertainty are considered to examine effects of TR algorithms on forecasts' accuracies. As per obtained results, Coupland-Jonh TR algorithm leads to models with a higher and more stable forecasting performance. However, there is no obvious and consistent relationship between the widths of the type reduced set and the TR algorithm. © 2013 Elsevier B.V.

The accuracy of Fastloc-GPS locations and implications for animal tracking

Over recent years, a major breakthrough in marine animal tracking has occurred with the advent of Fastloc-GPS that provides highly accurate location data even for animals that only surface briefly such as sea turtles, marine mammals and penguins. We assessed the accuracy of Fastloc-GPS locations using fixed trials of tags in which >45 000 locations were obtained. Procedures for determining the speed of travel and heading were developed by simulating tracks and then adding Fastloc-GPS location errors. The levels of detail achievable for speed and heading estimates were illustrated by using empirical Fastloc-GPS data for a green turtle (Chelonia mydas, Linnaeus, 1758) travelling over 3000 km across the Indian Ocean. The accuracy of Fastloc-GPS locations varied as a function of the number of GPS satellites used in the location calculation. For example, when Fastloc-GPS locations were calculated using 4 GPS satellites, 50% of locations were within 36 m and 95% within 724 m of the true position. These values improved to 18 and 70 m, respectively, when 6 satellites were used. Simulations indicated that for animals travelling around 2·5 km h-1 (e.g. turtles, penguins and seals) and depending on the number of satellites used in the location calculation, robust speed and heading estimates would usually be obtained for locations only 1-6 h apart. Fastloc-GPS accuracy is several orders of magnitude better that conventional Argos tracking or light-based geolocation and consequently will allow new insights into small-scale movement patterns of marine animals.

Aggregation of Pi-based forecast to enhance prediction accuracy

In contrast to point forecast, prediction interval-based neural network offers itself as an effective tool to quantify the uncertainty and disturbances that associated with process data. However, single best neural network (NN) does not always guarantee to predict better quality of forecast for different data sets or a whole range of data set. Literature reported that ensemble of NNs using forecast combination produces stable and consistence forecast than single best NN. In this work, a NNs ensemble procedure is introduced to construct better quality of Pis. Weighted averaging forecasts combination mechanism is employed to combine the Pi-based forecast. As the key contribution of this paper, a new Pi-based cost function is proposed to optimize the individual weights for NN in combination process. An optimization algorithm, named simulated annealing (SA) is used to minimize the PI-based cost function. Finally, the proposed method is examined in two different case studies and compared the results with the individual best NNs and available simple averaging Pis aggregating method. Simulation results demonstrated that the proposed method improved the quality of Pis than individual best NNs and simple averaging ensemble method.