Gaussian Bell Curve Research Articles

Gaussian Bell Curve with Right Triangle and Pythagorean Relation 2pi+e=9.001

Gaussian Bell Curve with Right Triangle and Pythagorean Relation 2pi+e=9.001

Biosynthesized composites of Au-Ag nanoparticles using Trapa peel extract induced ROS-mediated p53 independent apoptosis in cancer cells

The current study highlights rapid, sustainable, and cost-effective biosynthesis of silver (Ag), gold (Au) nanoparticles (NPs), and bimetallic Au-AgNPs composites using bio-waste extract of Trapa natans. Growth of the NPs was monitored spectrophotometrically and peak was observed at ∼525 nm, ∼450 nm, and ∼495 nm corresponding to Plasmon absorbance of AuNPs, AgNPs, and Au-AgNPs, respectively. Transmission electron microscopy (TEM) revealed the size of AgNPs (∼15 nm), AuNPs (∼25 nm), and Au-AgNPs (∼26–90 nm). Synthesized NPs follow the Gaussian bell curve and its crystalline nature was identified by X-ray diffraction (XRD). Furthermore, Au-AgNPs induced cytotoxicity in various cancer cells (HCT116, MDA-MB-231, and HeLa) effectively at 200 μg/mL. Au-AgNPs-exposed cancer cells exhibited apoptotic features such as nuclear condensation, mitochondrial membrane potential loss, and cleavage of casp-3 and poly (ADP-ribose) polymerase-1 (PARP). Au-AgNPs exposure enhanced reactive oxygen species (ROS) and upon inhibition of ROS, apoptosis was reduced effectively. NPs treatment killed HCT116 WT and p53 knockout cells without any significant difference. Mechanistically, Au-AgNPs derived with Trapa peel extract significantly enhance ROS which trigger p53-independent apoptosis in various cancer cells effectively. Our study explores the use of bio-waste for the green synthesis of NPs, which can be attractive candidates for cancer therapy.

THE SOLUTION OF THE APPROXIMATION PROBLEM OF NONLINEAR DEPENDANCES USING ARTIFICIAL NEURAL NETWORKS

The paper discusses issues connected with the use of an artificial neural network (ANN) to approximate the experimental data. One of the problems in the development of the ANN is the choice of an appropriate activation function for neurons of the hidden layer and adjusting the parameters of the function in the learning process of the network. The article discusses a three-layer perceptron with one hidden layer, each neuron of which has the activation function in the form of a Gaussian curve. The choice of radial basis activation function allows the use of the direct method of determining the weight coefficients – method of least squares in the process of network training. Thus the quality of the approximation depends on the correct choice of the value parameter of the activation function, which in this case is the width of the Gaussian bell curve. In practice, this parameter is determined by conducting numerical experiments. This is a rather time-taking process. In this paper we propose to define the value of this parameter by the training set, representing the coordinates of the test curve points set with the desired properties. These properties are based on the a priori data of the approximated functions (linear, quadratic, logarithmic, exponential relationship). Because the test curve is given in explicit form, the parameter of activation function is determined from the condition of reaching the minimum of the integral from the squared difference between the values of the test functions and the output of the network. This approach guarantees obtaining the approximating curve with good properties, in particular, it is characterized by the absence of so-called "oscillations" – many inflection points in its graph.

A high precision bandgap voltage reference

In order to meet the market demand for wide temperature range and high precision bandgap voltage reference, this paper designs a bandgap reference with wide temperature range and low temperature coefficient. In this paper, the basic implementation principle of the bandgap reference is analyzed.On the basis of the traditional bandgap reference circuit structure,this design adds a trimming network and a temperature compensation network. A new Gaussian bell curve compensation technique is adopted to compensate the low temperature section, and the normal temperature section and the high temperature section respectively. Compared with the existing compensation technology, the versatility and the compensation effect is better. The designed circuit is designed and manufactured based on the Huahong HHNECGE0.35um process. The results show that the output voltage is 2.5V at 2.7V supply voltage and temperature range of -40-125°C.at typical process angle ,the temperature coefficient is 0.54618 PPm/°C,and is within 1PPm/°C at other process angles.

EVALUATION OF THE NON-ELEMENTARY INTEGRAL ∫eλx^α, α≥2, AND OTHER RELATED INTEGRALS

A formula for the non-elementary integral $\int e^{\lambda x^\alpha} dx$ where $\alpha$ is real and greater or equal two, is obtained in terms of the confluent hypergeometric function $_1F_1$. This result is verified by directly evaluating the area under the Gaussian Bell curve, corresponding to $\alpha = 2$, using the asymptotic expression for the confluent hypergeometric function and the Fundamental Theorem of Calculus (FTC). Two different but equivalent expressions, one in terms of the confluent hypergeometric function $_1F_1$ and another one in terms of the hypergeometric function $_1F_2$, are obtained for each of these integrals, $\int \cosh(\lambda x^\alpha)dx$, $\int \sinh(\lambda x^\alpha)dx$, $\int \cos(\lambda x^\alpha)dx$ and $\int \sin(\lambda x^\alpha)dx$, $\lambda\in \mathbb{C}, \alpha\ge2$. And the hypergeometric function $_1F_2$ is expressed in terms of the confluent hypergeometric function $_1F_1$. Some of the applications of the non-elementary integral $\int e^{\lambda x^\alpha}dx,\alpha\ge2$ such as the Gaussian distribution and the Maxwell-Bortsman distribution are given.

Double Whammy – How ICT Projects are Fooled by Randomness and Screwed by Political Intent

The Iron Triangle formulates the holy trinity of objectives of project management – cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindness cause forecasts to fall short of actual costs. Firstly, optimism bias has been linked to effects of deception and delusion, which is caused by taking the inside-view and ignoring distributional information when making decisions. Secondly, we argued before that Black Swan Blindness makes decision-makers ignore outlying events even if decisions and judgements are based on the outside view. Using a sample of 1,471 ICT projects with a total value of USD 241 billion – we answer the question: Can we show the different effects of Normal Performance, delusion, and Deception? We calculated the cumulative distribution function (CDF) of (actual-forecast)/forecast. Our results show that the CDF changes at two tipping points – the first one transforms an exponential function into a Gaussian bell curve. The second tipping point transforms the bell curve into a power law distribution with the power of 2. We argue that these results show that project performance up to the first tipping point is politically motivated and project performance above the second tipping point indicates that project managers and decision-makers are fooled by random outliers, because they are blind to thick tails. We then show that Black Swan ICT projects are a significant source of uncertainty to an organisation and that management needs to be aware of. Finally, we draw implications about the underlying generative processes that lead to power law behaviour, which might help to further understand the pitfalls and shortcomings of cost and cost risk management in ICT projects.

Global comparisons of metal finishing sectors: Part 1, variations in economic and structural factors

Economic data for different national sub-contract surface finishing sectors from official statistics (Eurostat, for EU countries, and the US Census Bureau) as well as major commercial databases (Kompass and Solusource/Global.com) have been analysed and compared. Parameters examined include economic indicators based on sector turnover, numbers of firms and personnel. Where possible, changes over the decade to 2010 have been identified. Growth in the former East European bloc, partly as a result of transfer of West European manufacturing and its associated surface finishing, has been significant over this period. Fundamental structural differences appear to exist in different countries regarding company size distribution, with some sectors revealing a preponderance of small companies and others fitting a Gaussian bell curve type of distribution. However, growth of average company size, previously thought to be a sustainability must, appears not to have happened, either in the US or throughout European sectors, implying an unexpected strength in the existing sector in general. Although the US and European sectors show some similarities in both structure and economic indicators, as well as changes occurring over time, some national differences are marked and there seems little evidence that globalisation of manufacturing is leading to growing similarity in surface finishing in national sectors.

Double Whammy – How ICT Projects are Fooled by Randomness and Screwed by Political Intent

The cost-benefit analysis formulates the holy trinity of objectives of project management - cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindness cause forecasts to fall short of actual costs. Firstly, optimism bias has been linked to effects of deception and delusion, which is caused by taking the inside-view and ignoring distributional information when making decisions. Secondly, we argued before that Black Swan Blindness makes decision-makers ignore outlying events even if decisions and judgements are based on the outside view. Using a sample of 1,471 ICT projects with a total value of USD 241 billion - we answer the question: Can we show the different effects of Normal Performance, Delusion, and Deception? We calculated the cumulative distribution function (CDF) of (actual-forecast)/forecast. Our results show that the CDF changes at two tipping points - the first one transforms an exponential function into a Gaussian bell curve. The second tipping point transforms the bell curve into a power law distribution with the power of 2. We argue that these results show that project performance up to the first tipping point is politically motivated and project performance above the second tipping point indicates that project managers and decision-makers are fooled by random outliers, because they are blind to thick tails. We then show that Black Swan ICT projects are a significant source of uncertainty to an organisation and that management needs to be aware of.

Differential diagnosis of muscle tension dysphonia and adductor spasmodic dysphonia using spectral moments of the long‐term average spectrum

Adductor spasmodic dysphonia (ADSD) can mimic the voice characteristics of muscle tension dysphonia (MTD) contributing to diagnostic confusion and inappropriate management. Elevated spectral noise has been reported in MTD, which may aid in differential diagnosis. The long-term average spectrum (LTAS) can be compared to a Gaussian bell curve using spectral moments analysis. Four moments describe features of the LTAS: spectral mean (moment 1), standard deviation (moment 2), skewness (moment 3), and kurtosis (moment 4). This investigation evaluated spectral moments analysis of the LTAS as an objective test to distinguish ADSD from MTD. Case-control comparison. Pretreatment voice samples from 59 subjects with MTD (10 males and 49 females) and 41 subjects with ADSD (19 males and 22 females) were analyzed. Groups were separated by gender, adjusted for age, and results from the analysis were compared across different analyzing bandwidths. Diagnostic precision estimates were calculated including sensitivity, specificity, positive and negative predictive values, and positive and negative likelihood ratios. No significant spectral differences were found between men in both groups. However, significant between-group differences were identified for all spectral moments for women. Logistic stepwise regression identified that spectral standard deviation (moment 2) uniquely distinguished women with MTD and ADSD. No other spectral moments contributed significant discriminatory information. The results suggest that moment 2 of the LTAS provides respectable diagnostic precision by highlighting spectral noise differences between females with MTD and ADSD. Automated spectral moments analysis deserves further attention as a possible test for differential diagnosis.

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Time-Domain Dyadic Green's Function for an Electric Source in a Conductive Plate

We have determined the quasi-static time-domain dyadic Green's function for an electric source in a conductive plate for use in electric field integral equations. Starting with a frequency-domain representation, we constructed the dyadic kernel from electric and magnetic scalar potentials defined with respect to a preferred direction normal to plate. The final time-domain expression has three parts: a free-space term, multiple image terms, and partial reflection terms. The free-space fundamental solution is expressed in terms of a three-dimensional Gaussian bell curve satisfying the diffusion equation. Similarly, the image terms are expressed in the same form with coordinates shifted so that each Gaussian curve centers on an image point. In order to carry out the inverse Laplace transform from the frequency domain to the time domain, we expand the partial reflection functions as asymptotic series before transforming them analytically. The resulting expression for dyadic Green's kernel can be evaluated efficiently and with well-controlled accuracy.

Spectral Moments of the Long-term Average Spectrum: Sensitive Indices of Voice Change After Therapy?

Voice clinicians require an objective, reliable, and relatively automatic method to assess voice change after medical, surgical, or behavioral intervention. This measure must be sensitive to a variety of voice qualities and severities, and preferably should reflect voice in continuous speech. The long-term average spectrum (LTAS) is a fast Fourier transform-generated power spectrum whose properties can be compared with a Gaussian bell curve using spectral moments analysis. Four spectral moments describe features of the LTAS: Spectral mean (Moment 1) and standard deviation (Moment 2) represent the spectrum's central tendency and dispersion, respectively. Skewness (based on Moment 3) and kurtosis (based on Moment 4) represent the spectrum's tilt and peakedness, respectively. To examine whether the first four spectral moments of the LTAS were sensitive to perceived voice improvement after voice therapy, this investigation compared pretreatment and posttreatment voice samples of 93 patients with functional dysphonia using spectral moments analysis. Inspection of the results revealed that spectral mean and standard deviation lowered significantly with perceived voice improvement after successful behavioral management (p < 0.001). However, changes in skewness and kurtosis were not significant. Furthermore, lowering of the spectral mean uniquely accounted for approximately 14% of the variance in the pretreatment to posttreatment changes observed in perceptual ratings of voice severity (p < 0.001), indicating that spectral mean (ie, Moment 1) of the LTAS may be one acoustic marker sensitive to improvement in dysphonia severity.

Robust stochastic resonance: signal detection and adaptation in impulsive noise.

Stochastic resonance (SR) occurs when noise improves a system performance measure such as a spectral signal-to-noise ratio or a cross-correlation measure. All SR studies have assumed that the forcing noise has finite variance. Most have further assumed that the noise is Gaussian. We show that SR still occurs for the more general case of impulsive or infinite-variance noise. The SR effect fades as the noise grows more impulsive. We study this fading effect on the family of symmetric alpha-stable bell curves that includes the Gaussian bell curve as a special case. These bell curves have thicker tails as the parameter alpha falls from 2 (the Gaussian case) to 1 (the Cauchy case) to even lower values. Thicker tails create more frequent and more violent noise impulses. The main feedback and feedforward models in the SR literature show this fading SR effect for periodic forcing signals when we plot either the signal-to-noise ratio or a signal correlation measure against the dispersion of the alpha-stable noise. Linear regression shows that an exponential law gamma(opt)(alpha)=cA(alpha) describes this relation between the impulsive index alpha and the SR-optimal noise dispersion gamma(opt). The results show that SR is robust against noise "outliers." So SR may be more widespread in nature than previously believed. Such robustness also favors the use of SR in engineering systems. We further show that an adaptive system can learn the optimal noise dispersion for two standard SR models (the quartic bistable model and the FitzHugh-Nagumo neuron model) for the signal-to-noise ratio performance measure. This also favors practical applications of SR and suggests that evolution may have tuned the noise-sensitive parameters of biological systems.

Fuzzy prediction and filtering in impulsive noise

Additive fuzzy systems can filter impulsive noise from signals. Alpha-stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter α ranges through the interval (0, 2] and gives the Gaussian bell curve when α = 2 and gives the Cauchy bell curve when α = 1. The impulsiveness grows as α falls and the bell curves have thicker tails. Only the Gaussian statistics have finite variances or finite higher moments. An additive fuzzy system can learn ellipsoidal fuzzy rule patches from a new pseudo-covariation matrix or measure of alpha-stable covariation. Mahalanobis distance gives a joint set function for the learned if-part fuzzy sets of the if-then rules. The joint set function preserves input correlations that factored set functions ignore. Competitive learning tunes the local means and pseudo-covariations of the alpha-stable statistics and thus tunes the fuzzy rules. Then the covariation rules can both predict nonlinear signals in impulsive noise and filter the impulsive noise in time-series data. The fuzzy system filtered such noise better than did a benchmark radial basis neural network.