Gaussian Definition and 772 Threads

Hello all, I have used Expectation Maximization algorithm to approximate a probability density function (pdf) using a mixture of gaussians. I need to square the pdf corresponding to the mixture of gaussians( it is a weighted sum of normal distributions with non-identical parameters). Rather...

I was browsing old threads at Physics Forums, and I came across some information in this thread from 2008 that got my interest. The thread is titled "Child molester avoids prison because he is short." PF member stickythighs wrote the following: "Since the average American man is 5'10", there...

I am looking at a surface where the height is described by a zero-mean gaussian process with cov(h_1,h_2)=\sigma^2\exp[-0.5\frac{(x_1-x_2)}{a^2}]. Given that h(x=0) = 0, what is the probability that a surface realization will go above the black line going from x=0 to infinity in the figure...

Homework Statement [/B] Hello, I trying to solve for the minimum value that the x and y components reach in plot (A). I know that you can perform this using IgorPro but I would like to know how to solve for it using Excel. The plot was constructed using the following data points: 110...

How do you calculate the necessary points in a function to numerically integrate it using the Gaussian Quadrature? If I were to evaluate a function using two points, the Gaussian Quadrature needs the value of the function at ##\displaystyle{\pm \sqrt{\frac{1}{3}}}## with weights of unity. How...

Is there anything that would make a single mode fibre's speckle pattern not look Gaussian? I've attached two images (below) The Fibre C speckle pattern looks multimode The Fibre A speckle pattern doesn't really look convincingly like multimode or like single mode. A HeNe laser was used to...

I'm hoping someone can help check whether my final contour plots look plausible based on the surface. I haven't done too much differential geometry but I've needed to work with Gaussian/Mean curvature for a simple 3D gaussian surface. Here's an example: (A = 7, a=b=1/(3.5)^2) It's...

Heads up, I only recently got into quantum mechanics and don't feel like I got a solid grasp on the material yet. 1. Homework Statement Given is the wave function of a free particle in one dimension: \begin{equation} \psi(x,0) = \left( \frac{2}{\pi a^2} \right)^{1/4} e^{i k_0 x} e^{-x^2/a^2}...

Homework Statement http://cafeptthumb2.phinf.naver.net/MjAxNzAzMTVfMjcw/MDAxNDg5NTY5MTEwOTk5.FfccOAaDqBZbb9wXwuUWda8EN1aVvzMdcXO0GvaWwTsg.EjdATfmPtj-DteqAXFu9urHMslV8JTeridwC4ZNoJ68g.PNG.nikel92/asfasf.PNG?type=w740 Homework EquationsThe Attempt at a Solution...

Hello! Starting from a gaussian waveform propagating in a dispersive medium, is it possible to obtain an expression for the waveform at a generic time t, when the dispersion is not negligible? I know that a generic gaussian pulse (considered as an envelope of a carrier at frequency k_c) can be...

Hi I am measuring the impedance of an operating antenna over time. Assuming the environment is not changing and the antenna temperature remain constant (No thermal drift) I am receiving the impedance value and additional noise that I want to model as Gaussian noise. So my simple model is: Y = X...

I'm trying to put together a function that sums multiple 2D Gaussian functions in one graph (i.e.; multiple Gaussian pyramids). So far from my research, I formed the following function definition: I'm not sure if my research led me to the correct way of forming the function. Is this how...

Homework Statement In my book , the author stated that when we do the pivoting , we need to make the element below the leading element = 0 . For example for 3x3 matrix , for the first column , we have to make a11 = max , and make sure that a21 and a31 less than a11 , for the second column , we...

Homework Statement I am asked to solve this question using pivoting technique ... so , in I , I switched the R1 and R2 so that a11 is max , in III , i switched R9 nad R10 , so that a22 is max . But , in IV , i found that the a31 become -2/9 , which is not 0 anymore , what's wrong with my...

Homework Statement Homework EquationsThe Attempt at a Solution Okay, parts a-c are zero as they are within both shells. Lets begin with d because i fear I am just repeating the same error in all of the following parts. Part d qenclosed=ρ(4πr^3/3-4πa^3/3) =...

Homework Statement A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R is...

Homework Statement An electric field given by https://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest2560893entrance1_N10030.mml?size=14&ver=1486488694211 =...

Homework Statement Homework Equations σ=q/(4πr^2)→q=σ(4πr^2) E=q/(4πEod^2) E=(4πr^2σ)/(4πEod^2)The Attempt at a Solution So the first thing that i could include was that the point p was inside Shell 1 and therefor would not be affected by Shell 1. So it should be a fairly simple plug in the...

I have been exploring the paper: Statistical Tests for the Gaussian Nature of Primordial Fluctuations Through CBR Experiments http://lss.fnal.gov/archive/1993/pub/Pub-93-294-A.pdf . Here is a quote. Cosmic inflation [1], on one hand, provides a natural way to generate Gaussian initial...

Homework Statement Hi, I am trying to follow my book's hint that to find the normalization factor one should "Diagnoalize ##\Sigma^{-1}## to get ##n## Gaussian which will have variance given by the eigenvalues of ##\Sigma## . Then integrate gives ##\sqrt{2\pi}\Lambda_i##, then use that the...

Hello, guys. I am trying to solve for characteristic function of normal distribution and I've got to the point where some manipulation has been made with the term in integrands exponent. And a new term of t2σ2/2 has appeared. Could you be so kind and explain that to me, please...

Can anyone explain intuitively or give a better explanation of multi gaussian beams and the ABCD matrix approach for sound (ultrasonics) and not light? Thanks!

Homework Statement system of equations is as follows 4x +2y -2z = 0 2x + y -z= 1 3x +y -2z = 1 Homework EquationsThe Attempt at a Solution [/B] Using gaussian elimination we can multiply mid-eq, by (-2) [[[actually... it is simply a basic equation procedure]]] 2x+y-z=1 |*(-2) = -4x -2y...

I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?

I would like to prove that ##\displaystyle{\int dx'\ \frac{1}{\sqrt{AB}}\exp\bigg[i\frac{(x''-x')^{2}}{A}\bigg]\exp\bigg[i\frac{(x'-x)^{2}}{B}\bigg]=\frac{1}{\sqrt{A+B}}\exp\bigg[i\frac{(x''-x)^{2}}{A+B}\bigg]}## Is there an easy way to do this integration that does not involve squaring the...

Consider the partition function ##Z[J]## of the Klein-Gordon theory ##Z[J] =\int \mathcal{D}\phi\ e^{i\int d^{4}x\ [\frac{1}{2}(\partial\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}+J\phi]} =\int \mathcal{D}\phi\ e^{-i\int d^{4}x\ [\frac{1}{2}\phi(\partial^{2}+m^{2})\phi]}\ e^{i\int d^{4}x\...

Usually when gravitational lensing is discussed, the examples are those of matter bending spacetime into a positive curvature. https://commons.wikimedia.org/wiki/File:Gravitational_lens-full.jpg In these cases, distortion of light is clearly evident as images of galaxies from behind these...

Homework Statement What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way) This is what I have done so far: Homework Equations $$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...

Homework Statement A thin spherical shell with radius R1 = 2.00 cm is concentric with a larger thin spherical shell with radius 6.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge...

Homework Statement Given the wave function of a particle \Psi(x,0) = \left(\frac{2b}{\pi}\right)^{1/4}e^{-bx^2} , what is the probability of finding the particle between 0 and \Delta x , where \Delta x can be assumed to be infinitesimal. Homework EquationsThe Attempt at a Solution I proceed...

Homework Statement Please help! I'm new to Gaussian and I've been on this problem for hours, I can't crack it at all (no pun intended) can anyone provide a detailed walk through the answers? On average 5% of eggs contain a hereditary condition. Use Gaussian distribution to find the...

Homework Statement I want to evaluate the following definite integral of the form, I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy where a, b, c, and d are constants, as part of a larger problem I am doing, Homework...

Hi all, I think there is a really obvious answer to this, but I just don't see it yet. Suppose you had N data sets that all measured the same quantity as a function of time. Each data set shows the same signal plus a random noise component which is normally distributed about the signal with a...

Hi, I am trying to understand the functional form of B3LYP from the Gaussian output file. I have tried to relate the details in the output file with the functional form of B3LYP. But I am not sure what certain terms correspond to. I have mentioned below the details. Can you pleaese help me. In...

Homework Statement Use Mathematica to calculate the Gaussian curvature of the plane Ax+By+Cz=D, in which A, B, C, and D are constants and C≠0. Use the following data: Homework Equations The Attempt at a Solution First I found the line curvature. As here: That code gets the result = 0...

Homework Statement Basically I have to convert from Gaussian Units in a Transmission Line Experiment. I don't get what the point of expressing Capacitance in cm is and I find this very confusing. Homework Equations The equation I've been given is C'=Q'/V=w/4πh, (1) where the prime denotes "per...

Hi, I have a simple/fast question... Can you reliably use a Poisson function to fit on data that seem to be Gaussian distributed (although that is due to the large number of the mean)?

In an image processing paper, it was explained that a 2D Gabor filter is constructed in the Fourier domain using the following formula: $$ H(u,v)=H_R(u,v) + i \cdot H_I(u,v)$$ where HR(u,v) and HI(u,v) are the real and imaginary components, respectively. It also mentions that the real and...

The superposition of a gaussian beam and a plane wave generates a pattern of rings whose phase shift before and after the focal plane (of the gaussian beam) is ##\pi##. This means that if you measure interference before and after you'll see the minimums and maximums of intensity invert. We can...

Hello, I have been I am trying to optimize a molecule (crowded) with the chemical formula C60H52O18P4S4W2. The problem arises after 2 days, which means that the initial geometry was not a problem. " GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad Berny optimization...

Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same) Flux is the dot product of electric field and surface area, so wouldn't it change if surface area is changed?

Hi, I was looking at derivation of a multi gaussian beam to represent the ultrasonic beam from a transducer through a fluid. In the derivation a complex valued symmetrical 2x2 matrix is used whose imaginary part of eigen values is more than zero. Can someone please tell me what are the...

We start by writing the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} 2 & -2 & 1 & 1 & \phantom{-}4 \\ 4 & -1 & 2 & 3 & -\frac{5}{2} \\ 4 & -4 & 5 & 1 & \phantom{-}8 \\ 0 & \phantom{-}2 & 3 & 4 & -5 \end{matrix} \right] \end{align*}$ Once we have used...

We write the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}1 & 4 & \phantom{-}1 & 0 & \phantom{-}5 \\ \phantom{-}1 & 6 & -1 & 4 & \phantom{-}7 \\ -1 & 2 & -9 & 2 & -9 \\ \phantom{-}0 & 1 & \phantom{-}2 & 0 & \phantom{-}4 \end{matrix} \right]...

This system can be written as a matrix equation $\displaystyle \begin{align*} A\,\mathbf{x} = \mathbf{b} \end{align*}$ as $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}2 & 4 & \phantom{-}0 & 1 \\ \phantom{-}2 & 8 & -2 & 7 \\ -2 & 2 & -2 & 7 \\ \phantom{-}0 & 8 & -5 & 11...

Probably a stupid question, but I do not get it... Here you can see an experiment demonstrating the Gaussian gun: Here I understand how momentum is conserved, i.e. the smaller mass of the ejected ball times its high speed is equal the bigger total mass of the recoiling masses times its...

I'm not sure where you're getting the idea that z = 2, as this is not correct. I'm assuming this is to be done without pivoting... Set up your augmented matrix: $\displaystyle \begin{align*} \left[ \begin{matrix} 2 & \phantom{-}1 & -3 & -5 \\ 1 & -1 & \phantom{-}2 & 12 \\ 7 & -2 & \phantom{-}...

Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me. I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread...

Hey, folks. I'm doing a problem wherein I have to evaluate a slight variation of the Gaussian integral for the first time, but I'm not totally sure how to go about it; this is part of an integration by parts problem where the dv is similar to a gaussian integral...

Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...