A New Accurate Approximation of the Gaussian Q-Function with Relative Error Less Than 1 Thousandth in a Significant Domain

2021 ◽  
Author(s):  
Alessandro Soranzo ◽  
Francesca Vatta ◽  
Massimiliano Comisso ◽  
Giulia Buttazzoni ◽  
Fulvio Babich
Keyword(s):  
Relative Error ◽  
Accurate Approximation ◽  
Q Function

scholarly journals Shortcomings of NPV Calculation: Does One Error Annul the Other?

2021 ◽  
Author(s):  
Nikolett Sereg
Keyword(s):  
Probability Distribution ◽  
Flow Pattern ◽  
Relative Error ◽  
Cash Flow ◽  
The Other ◽  
Accurate Approximation ◽  
Present Value ◽  
Absolute Value ◽  
Aggregate Effect ◽  
The Subject

The research aims at analyzing the aggregate effect of possible errors related to the "textbook" method of present value calculation. Two main errors could stem from end-of-period convention and calculation according to expected lifespan. The magnitude of such errors depends on the cash flow pattern and the probability distribution of asset life, therefore the combination that may be regarded as the most typical in practice has been chosen as the subject of the examination, i.e., the continuous exponential cash flow pattern with exponentially distributed life. Based on the result of previous studies examining the errors separately, it seems possible that the two errors lead to a more accurate approximation – considering the absolute value of the relative error – compared to making only one of the errors. After the examination, I conclude that in the most typical cases of practice, it is not worth to take either the correct cash flow pattern or the life uncertainty into account beyond the "textbook" method.

Class of tight bounds on the Q ‐function with closed‐form upper bound on relative error

2019 ◽  
Vol 42 (6) ◽  
pp. 1786-1794 ◽  
Author(s):  
Zoran H. Perić ◽  
Jelena R. Nikolić ◽  
Marko D. Petković
Keyword(s):  
Closed Form ◽  
Relative Error ◽  
Upper Bound ◽  
Q Function

scholarly journals RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD

2021 ◽  
pp. 1-24
Author(s):  
Lorenzo Camponovo ◽  
Yukitoshi Matsushita ◽  
Taisuke Otsu
Keyword(s):  
Relative Error ◽  
Generating Functions ◽  
Large Deviation ◽  
Moment Condition ◽  
Accurate Approximation ◽  
Test Statistic ◽  
Exponential Tilting ◽  
Moment Conditions ◽  
Nonparametric Likelihood ◽  
Relative Errors

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order n−1 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.

Application of pyrometer and standard sample to determine surface temperature of studied materials

2019 ◽  
pp. 9-13
Author(s):  
V.Ya. Mendeleyev ◽  
V.A. Petrov ◽  
A.V. Yashin ◽  
A.I. Vangonen ◽  
O.K. Taganov
Keyword(s):  
Composite Material ◽  
Surface Temperature ◽  
Relative Error ◽  
Wavelength Range ◽  
Standard Sample ◽  
A Priori ◽  
Temperature Changes ◽  
Surface Temperatures ◽  
Relative Errors ◽  
Normal Emissivity

Determining the surface temperature of materials with unknown emissivity is studied. A method for determining the surface temperature using a standard sample of average spectral normal emissivity in the wavelength range of 1,65–1,80 μm and an industrially produced Metis M322 pyrometer operating in the same wavelength range. The surface temperature of studied samples of the composite material and platinum was determined experimentally from the temperature of a standard sample located on the studied surfaces. The relative error in determining the surface temperature of the studied materials, introduced by the proposed method, was calculated taking into account the temperatures of the platinum and the composite material, determined from the temperature of the standard sample located on the studied surfaces, and from the temperature of the studied surfaces in the absence of the standard sample. The relative errors thus obtained did not exceed 1,7 % for the composite material and 0,5% for the platinum at surface temperatures of about 973 K. It was also found that: the inaccuracy of a priori data on the emissivity of the standard sample in the range (–0,01; 0,01) relative to the average emissivity increases the relative error in determining the temperature of the composite material by 0,68 %, and the installation of a standard sample on the studied materials leads to temperature changes on the periphery of the surface not exceeding 0,47 % for composite material and 0,05 % for platinum.

Error-aware Design Procedure to Implement Energy-efficient Approximate Squaring Hardware

2020 ◽  
Vol 10 (4) ◽  
pp. 471-477
Author(s):  
Merin Loukrakpam ◽  
Ch. Lison Singh ◽  
Madhuchhanda Choudhury
Keyword(s):  
Energy Saving ◽  
Relative Error ◽  
Energy Efficient ◽  
Piecewise Linear ◽  
Arithmetic Operation ◽  
Design Procedure ◽  
Digital Signal ◽  
Maximum Relative Error ◽  
Square Function ◽  
Efficient Design

Background:: In recent years, there has been a high demand for executing digital signal processing and machine learning applications on energy-constrained devices. Squaring is a vital arithmetic operation used in such applications. Hence, improving the energy efficiency of squaring is crucial. Objective:: In this paper, a novel approximation method based on piecewise linear segmentation of the square function is proposed. Methods: Two-segment, four-segment and eight-segment accurate and energy-efficient 32-bit approximate designs for squaring were implemented using this method. The proposed 2-segment approximate squaring hardware showed 12.5% maximum relative error and delivered up to 55.6% energy saving when compared with state-of-the-art approximate multipliers used for squaring. Results: The proposed 4-segment hardware achieved a maximum relative error of 3.13% with up to 46.5% energy saving. Conclusion:: The proposed 8-segment design emerged as the most accurate squaring hardware with a maximum relative error of 0.78%. The comparison also revealed that the 8-segment design is the most efficient design in terms of error-area-delay-power product.

scholarly journals Modeling Spatiotemporal Population Changes by Integrating DMSP-OLS and NPP-VIIRS Nighttime Light Data in Chongqing, China

2021 ◽  
Vol 13 (2) ◽  
pp. 284
Author(s):  
Dan Lu ◽  
Yahui Wang ◽  
Qingyuan Yang ◽  
Kangchuan Su ◽  
Haozhe Zhang ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Relative Error ◽  
Urban Areas ◽  
Large Scale ◽  
Population Distribution ◽  
Spatial Optimization ◽  
Distribution Data ◽  
Mountainous Areas ◽  
Mean Relative Error ◽  
Nighttime Light

The sustained growth of non-farm wages has led to large-scale migration of rural population to cities in China, especially in mountainous areas. It is of great significance to study the spatial and temporal pattern of population migration mentioned above for guiding population spatial optimization and the effective supply of public services in the mountainous areas. Here, we determined the spatiotemporal evolution of population in the Chongqing municipality of China from 2000–2018 by employing multi-period spatial distribution data, including nighttime light (NTL) data from the Defense Meteorological Satellite Program’s Operational Linescan System (DMSP-OLS) and the Suomi National Polar-orbiting Partnership Visible Infrared Imaging Radiometer Suite (NPP-VIIRS). There was a power function relationship between the two datasets at the pixel scale, with a mean relative error of NTL integration of 8.19%, 4.78% less than achieved by a previous study at the provincial scale. The spatial simulations of population distribution achieved a mean relative error of 26.98%, improved the simulation accuracy for mountainous population by nearly 20% and confirmed the feasibility of this method in Chongqing. During the study period, the spatial distribution of Chongqing’s population has increased in the west and decreased in the east, while also increased in low-altitude areas and decreased in medium-high altitude areas. Population agglomeration was common in all of districts and counties and the population density of central urban areas and its surrounding areas significantly increased, while that of non-urban areas such as northeast Chongqing significantly decreased.

scholarly journals A Fuzzy Optimization Model for High-Speed Railway Timetable Rescheduling

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Wang ◽  
Yong Qin ◽  
Jie Xu ◽  
Limin Jia
Keyword(s):  
Optimization Model ◽  
High Speed ◽  
Fuzzy Optimization ◽  
Soft Constraints ◽  
Accurate Approximation ◽  
Total Delay ◽  
High Speed Rail ◽  
High Speed Railway ◽  
Tolerance Approach ◽  
Rail Line

A fuzzy optimization model based on improved symmetric tolerance approach is introduced, which allows for rescheduling high-speed railway timetable under unexpected interferences. The model nests different parameters of the soft constraints with uncertainty margin to describe their importance to the optimization purpose and treats the objective in the same manner. Thus a new optimal instrument is expected to achieve a new timetable subject to little slack of constraints. The section between Nanjing and Shanghai, which is the busiest, of Beijing-Shanghai high-speed rail line in China is used as the simulated measurement. The fuzzy optimization model provides an accurate approximation on train running time and headway time, and hence the results suggest that the number of seriously impacted trains and total delay time can be reduced significantly subject to little cost and risk.

scholarly journals Lightweight Blockchain Processing. Case Study: Scanned Document Tracking on Tezos Blockchain

2021 ◽  
Vol 11 (15) ◽  
pp. 7169
Author(s):  
Mohamed Allouche ◽  
Tarek Frikha ◽  
Mihai Mitrea ◽  
Gérard Memmi ◽  
Faten Chaabane
Keyword(s):  
Load Balancing ◽  
Relative Error ◽  
Execution Time ◽  
General Purpose ◽  
Experimental Results ◽  
Raspberry Pi ◽  
Embedded Platform ◽  
Memory Resources ◽  
Processing Solution

To bridge the current gap between the Blockchain expectancies and their intensive computation constraints, the present paper advances a lightweight processing solution, based on a load-balancing architecture, compatible with the lightweight/embedding processing paradigms. In this way, the execution of complex operations is securely delegated to an off-chain general-purpose computing machine while the intimate Blockchain operations are kept on-chain. The illustrations correspond to an on-chain Tezos configuration and to a multiprocessor ARM embedded platform (integrated into a Raspberry Pi). The performances are assessed in terms of security, execution time, and CPU consumption when achieving a visual document fingerprint task. It is thus demonstrated that the advanced solution makes it possible for a computing intensive application to be deployed under severely constrained computation and memory resources, as set by a Raspberry Pi 3. The experimental results show that up to nine Tezos nodes can be deployed on a single Raspberry Pi 3 and that the limitation is not derived from the memory but from the computation resources. The execution time with a limited number of fingerprints is 40% higher than using a classical PC solution (value computed with 95% relative error lower than 5%).

A modified physical model of high-strength water hydraulic artificial muscles considering the effects of geometry and material properties

2021 ◽  
pp. 095440622199907
Author(s):  
Zengmeng Zhang ◽  
Jinkai Che ◽  
Peipei Liu ◽  
Yunrui Jia ◽  
Yongjun Gong
Keyword(s):  
Physical Model ◽  
Relative Error ◽  
Wall Thickness ◽  
Material Properties ◽  
High Strength ◽  
Artificial Muscles ◽  
Operating Pressure ◽  
Rubber Tube ◽  
Contraction Ratio ◽  
Water Hydraulic

Compared with pneumatic artificial muscles (PAMs), water hydraulic artificial muscles (WHAMs) have the advantages of high force/weight ratio, high stiffness, rapid response speed, large operating pressure range, low working noise, etc. Although the physical models of PAMs have been widely studied, the model of WHAMs still need to be researched for the different structure parameters and work conditions between PAMs and WHAMs. Therefore, the geometry and the material properties need to be considered in models, including the wall thickness of rubber tube, the geometry of ends, the elastic force of rubber tube, the elongation of fibers, and the friction among fiber strands. WHAMs with different wall thickness and fiber materials were manufactured, and static characteristic experiments were performed when the actuator is static and fixed on both ends, which reflects the relationship between contraction force and pressure under the different contraction ratio. The deviations between theoretical values and experimental results were analyzed to investigate the effect of each physical factor on the modified physical model accuracy at different operating pressures. The results show the relative error of the modified physical model was 7.1% and the relative error of the ideal model was 17.4%. When contraction ratio is below 10% and operating pressure is 4 MPa, the wall thickness of rubber tube was the strongest factor on the accuracy of modified model. When the WHAM contraction ratio from 3% to 20%, the relative error between the modified physical model and the experimental data was within ±10%. Considering the various physical factors, the accuracy of the modified physical model of WHAM is improved, which lays a foundation of non-linear control of the high-strength, tightly fiber-braided and thick-walled WHAMs.

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