Infinite Integral of Gaussian Function

2012 ◽  
pp. 303-304
Keyword(s):  
Gaussian Function ◽  
Infinite Integral

APPLICATION OF THE GAUSSIAN FUNCTION TO APPROXIMATION OF THE EARTH’S SURFACE SUBSIDENCE CURVES

2017 ◽  
Vol 8 ◽  
pp. 187-194
Author(s):  
Yu.V. Posyl'nyy ◽  
◽  
A.V. Vyal'tsev ◽  
V.V. Popov ◽  
F.I. Yagodkin ◽  
...  
Keyword(s):  
Gaussian Function ◽  
Surface Subsidence

scholarly journals Hardware implementation of radial-basis neural networks with Gaussian activation functions on FPGA

2021 ◽  
Author(s):  
Volodymyr Shymkovych ◽  
Sergii Telenyk ◽  
Petro Kravets
Keyword(s):  
Neural Networks ◽  
Hardware Implementation ◽  
Gaussian Function ◽  
Activation Function ◽  
Rbf Neural Networks ◽  
Activation Functions ◽  
Rbf Network ◽  
Combination Scheme ◽  
Radial Basis ◽  
Hidden Layer

AbstractThis article introduces a method for realizing the Gaussian activation function of radial-basis (RBF) neural networks with their hardware implementation on field-programmable gaits area (FPGAs). The results of modeling of the Gaussian function on FPGA chips of different families have been presented. RBF neural networks of various topologies have been synthesized and investigated. The hardware component implemented by this algorithm is an RBF neural network with four neurons of the latent layer and one neuron with a sigmoid activation function on an FPGA using 16-bit numbers with a fixed point, which took 1193 logic matrix gate (LUTs—LookUpTable). Each hidden layer neuron of the RBF network is designed on an FPGA as a separate computing unit. The speed as a total delay of the combination scheme of the block RBF network was 101.579 ns. The implementation of the Gaussian activation functions of the hidden layer of the RBF network occupies 106 LUTs, and the speed of the Gaussian activation functions is 29.33 ns. The absolute error is ± 0.005. The Spartan 3 family of chips for modeling has been used to get these results. Modeling on chips of other series has been also introduced in the article. RBF neural networks of various topologies have been synthesized and investigated. Hardware implementation of RBF neural networks with such speed allows them to be used in real-time control systems for high-speed objects.

scholarly journals Predicting specific impulse distributions for spherical explosives in the extreme near-field using a Gaussian function

2021 ◽  
pp. 204141962199349
Author(s):  
Jordan J Pannell ◽  
George Panoutsos ◽  
Sam B Cooke ◽  
Dan J Pope ◽  
Sam E Rigby
Keyword(s):  
Scaling Laws ◽  
Near Field ◽  
Specific Impulse ◽  
Gaussian Function ◽  
Data Driven ◽  
Blast Load ◽  
Structural Deformation ◽  
Load Prediction ◽  
Validation Data ◽  
Wide Range

Accurate quantification of the blast load arising from detonation of a high explosive has applications in transport security, infrastructure assessment and defence. In order to design efficient and safe protective systems in such aggressive environments, it is of critical importance to understand the magnitude and distribution of loading on a structural component located close to an explosive charge. In particular, peak specific impulse is the primary parameter that governs structural deformation under short-duration loading. Within this so-called extreme near-field region, existing semi-empirical methods are known to be inaccurate, and high-fidelity numerical schemes are generally hampered by a lack of available experimental validation data. As such, the blast protection community is not currently equipped with a satisfactory fast-running tool for load prediction in the near-field. In this article, a validated computational model is used to develop a suite of numerical near-field blast load distributions, which are shown to follow a similar normalised shape. This forms the basis of the data-driven predictive model developed herein: a Gaussian function is fit to the normalised loading distributions, and a power law is used to calculate the magnitude of the curve according to established scaling laws. The predictive method is rigorously assessed against the existing numerical dataset, and is validated against new test models and available experimental data. High levels of agreement are demonstrated throughout, with typical variations of <5% between experiment/model and prediction. The new approach presented in this article allows the analyst to rapidly compute the distribution of specific impulse across the loaded face of a wide range of target sizes and near-field scaled distances and provides a benchmark for data-driven modelling approaches to capture blast loading phenomena in more complex scenarios.

scholarly journals Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

scholarly journals Solar Radiation, Air Temperature, Relative Humidity, and Dew Point Study: Damak, Jhapa, Nepal

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Arun Kumar Shrestha ◽  
Arati Thapa ◽  
Hima Gautam
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Air Temperature ◽  
Gaussian Function ◽  
Great Influence ◽  
Dew Point ◽  
Upward Trend ◽  
Summer Maximum ◽  
Online Calculator ◽  
Climatic Phenomenon

Monitoring and prediction of the climatic phenomenon are of keen interest in recent years because it has great influence in the lives of people and their environments. This paper is aimed at reporting the variation of daily and monthly solar radiation, air temperature, relative humidity (RH), and dew point over the year of 2013 based on the data obtained from the weather station situated in Damak, Nepal. The result shows that on a clear day, the variation of solar radiation and RH follows the Gaussian function in which the first one has an upward trend and the second one has a downward trend. However, the change in air temperature satisfies the sine function. The dew point temperature shows somewhat complex behavior. Monthly variation of solar radiation, air temperature, and dew point shows a similar pattern, lower at winter and higher in summer. Maximum solar radiation (331 Wm-2) was observed in May and minimum (170 Wm-2) in December. Air temperature and dew point had the highest value from June to September nearly at 29°C and 25°C, respectively. The lowest value of the relative humidity (55.4%) in April indicates the driest month of the year. Dew point was also calculated from the actual readings of air temperature and relative humidity using the online calculator, and the calculated value showed the exact linear relationship with the observed value. The diurnal and nocturnal temperature of each month showed that temperature difference was relatively lower (less than 10°C) at summer rather than in winter.

scholarly journals Mapping the Spatial-Temporal Dynamics of Vegetation Response Lag to Drought in a Semi-Arid Region

2019 ◽  
Vol 11 (16) ◽  
pp. 1873 ◽  
Author(s):  
Li Hua ◽  
Huidong Wang ◽  
Haigang Sui ◽  
Brian Wardlow ◽  
Michael J. Hayes ◽  
...  
Keyword(s):  
Vegetation Index ◽  
Temporal Dynamics ◽  
Risk Mitigation ◽  
Scientific Information ◽  
Gaussian Function ◽  
Drought Risk ◽  
Severe Drought ◽  
Similar Response ◽  
Vegetation Types ◽  
Data Set

Drought, as an extreme climate event, affects the ecological environment for vegetation and agricultural production. Studies of the vegetative response to drought are paramount to providing scientific information for drought risk mitigation. In this paper, the spatial-temporal pattern of drought and the response lag of vegetation in Nebraska were analyzed from 2000 to 2015. Based on the long-term Daymet data set, the standard precipitation index (SPI) was computed to identify precipitation anomalies, and the Gaussian function was applied to obtain temperature anomalies. Vegetation anomaly was identified by dynamic time warping technique using a remote sensing Normalized Difference Vegetation Index (NDVI) time series. Finally, multilayer correlation analysis was applied to obtain the response lag of different vegetation types. The results show that Nebraska suffered severe drought events in 2002 and 2012. The response lag of vegetation to drought typically ranged from 30 to 45 days varying for different vegetation types and human activities (water use and management). Grasslands had the shortest response lag (~35 days), while forests had the longest lag period (~48 days). For specific crop types, the response lag of winter wheat varied among different regions of Nebraska (35–45 days), while soybeans, corn and alfalfa had similar response lag times of approximately 40 days.

A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

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