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# Search results with tag "Gaussian"

### Introduction to Gaussian 09 - University of Minnesota ...

www.msi.umn.edu

Introduction to Gaussian 09 Benjamin Lynch November 24, 2009 ... • GaussView: – Graphical interface for Gaussian 09 – sketch molecules – setup Gaussian 09 input files ... module load gaussian • Launch GaussView gv Building with GaussView. www.msi.umn.edu Supercomputing Institute

### The EM Algorithm for Gaussian Mixtures

www.ics.uci.edu

Gaussian Mixture Models For x ∈ Rd we can deﬁne a Gaussian mixture model by making each of the K components a Gaussian density with parameters µ k and Σ k. Each component is a multivariate Gaussian density p k(x|θ k) = 1 (2π)d/2|Σ k|1/2 e− 1 2 (x−µ k)tΣ− k (x−µ ) with its own parameters θ k = {µ k,Σ k}. The EM Algorithm ...

### ENGINEERING OPTICS WITH MAT LAB*

dru5cjyjifvrg.cloudfront.net

2.3.6 Resonators and Gaussian beams 86 2.4 Gaussian Beam Optics and MATLAB Examples 97 2.4.1 q-transformation of Gaussian beams 99 2.4.2 MATLAB example: propagation of a Gaussian beam. 102 3. Beam Propagation in Inhomogeneous Media 3.1 Wave Propagation in a Linear Inhomogeneous Medium Ill 3.2 Optical Propagation in Square-Law Media 112

### Conditional Joint Distributions - Stanford University

web.stanford.edu

Gaussian Blur In image processing, a Gaussian blur is the result of blurring an image by a Gaussian function. It is a widely used effect in graphics software, typically to reduce image noise. Gaussian blurring with StDev= 3, is based on a joint probability distribution: f X,Y (x,y)= 1 2⇡ · 32 e x2+y2 2·32 F X,Y (x,y)= ⇣ x 3 ⌘ · ⇣ y 3 ...

### Lecture 2 Image Processing and Filtering

courses.cs.washington.edu

Kernel approximates Gaussian function: What happens if you increase σ? Mean versus Gaussian filtering Input Image Mean filtered Gaussian filtered. Filtering an impulse 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Impulse signal ab c de f gh i Kernel Output = ?

### Machine Learning: Generative and Discriminative Models

cedar.buffalo.edu

• Gaussians, Naïve Bayes, Mixtures of multinomials • Mixtures of Gaussians, Mixtures of experts, Hidden Markov Models (HMM) ... – by fitting Gaussian class-conditional densities will result in . 2M . parameters for means, M(M+1)/2 ... Markov Random Field (MRF)

### Introduction to Gaussian program1

www.tau.ac.il

Introduction to Gaussian program1 In this lab, we will use the Gaussian program in Windows environments. ... This method keyword requests a Hartree-Fock calculation. Unless explicitly specified, RHF is used for singlets and UHF for higher multiplicities. In the latter case, separate ... • Molecular orbitals and orbital energies

### The Gaussian or Normal PDF, Page 1 The Gaussian or Normal ...

www.me.psu.edu

(deviations) are purely random. o A plot of the standard normal (Gaussian) density function was generated in Excel, using the above equation for f(z). It is shown to the right. o It turns out that the probability that variable x lies between some range x 1 and x 2 is the same as the probability that the transformed variable z lies

### Multivariate Gaussian Distribution - Mathematics Home

www.math.ucdavis.edu

Multivariate Gaussian Distribution The random vector X = (X 1,X 2,...,X p) is said to have a multivariate Gaussian distribution if the joint distribution of X 1,X 2,...,X p has density f X(x 1,x 2,...,x p) = 1 (2π)p/2 det(Σ)1/2 exp − 1 2 (x−µ)tΣ−1(x−µ) (1) follows: x is the column vector x = x 1 x 2... x p , µ is the column vector ...

### Visualizing Data using t-SNE - Journal of Machine Learning ...

jmlr.csail.mit.edu

almost inﬁnitesimal (for reasonable values of the variance of the Gaussian, σi). Mathematically, the conditional probability pjji is given by pjji = exp k xi xjk2=2σ2 i ∑k6= i exp k xi xkk2=2σ2 i; (1) where σi is the variance of the Gaussian that is centered on datapoint xi. The method for determining the value of σi is presented later ...

### Linear Discriminant Analysis

personal.psu.edu

Linear Discriminant Analysis Estimate Gaussian Distributions I In practice, we need to estimate the Gaussian distribution. I ˆπ k = N k/N, where N k is the number of class-k samples. I µˆ k = P g i=k x (i)/N k. I Σ =ˆ P K k=1 P g i=k (x (i) −µˆ k)(x(i) −µˆ k)T/(N −K). I Note that x(i) denotes the ith sample vector. Jia Li http ...

### Gaussview/Gaussian Guide and Exercise Manual

users.df.uba.ar

Gaussian calculations are best prepared using the Gaussview interface. Gaussview allow you to build the required molecule on your screen and using menu pull-dowms ... For graphical representations of orbital and electron densities the checkpoint, .chk, file is required.

### Introduction to GaussView and Gaussian

comp.chem.umn.edu

wavefunctions. www.msi.umn.edu Creating Input Files for Gaussian Description • Input • Submit • Visualize. www.msi.umn.edu Description • Input • Submit • Visualize %mem=32mb #p hf/6-31g opt hf/6-31g optimization of water 0 1 o h 1 oh h 1 oh 2 …

### Lecture 2 Quantum mechanics in one dimension

www.tcm.phy.cam.ac.uk

The Fourier transform of a normalized Gaussian wave packet, ψ(x)= " 1 2πα # 1/4 eik0x e− x2 4α. (moving at velocity v = !k 0/m) is also a Gaussian, ψ(k)= " 2α π # 1/4 e−α(k−k0) 2, Although we can localize a wave packet to a region of space, this …

### Lecture21. TheMultivariateNormalDistribution

faculty.math.illinois.edu

n aresaidtohavethemultivariate normal distribution ortobejointly Gaussian (wealsosaythattherandomvector(X 1,...,X n) isGaussian)if M(t 1,...,t n)=exp(t 1µ 1 +···+t nµ n)exp 1 2 n i,j=1 t ia ijt j wherethet i andµ j arearbitraryrealnumbers,andthematrixA issymmetricand positivedeﬁnite. Beforewedoanythingelse ...

### Conjugate Bayesian analysis of the Gaussian distribution

www.cs.ubc.ca

The Gaussian or normal distribution is one of the most widely used in statistics. Estimating its parameters using Bayesian inference and conjugate priors is also widely used. The use of conjugate priors allows all the results to be derived in closed form. Unfortunately, different books use different conventions on how to parameterize the various

### 1 Multivariate Normal Distribution - Princeton University

www.cs.princeton.edu

Gaussian Models (9/9/13) Lecturer: Barbara Engelhardt Scribes: Xi He, Jiangwei Pan, Ali Razeen, Animesh Srivastava 1 Multivariate Normal Distribution The multivariate normal distribution (MVN), also known as multivariate gaussian, is a generalization of the one-dimensional normal distribution to higher dimensions.

### Self-study notes - GAUSSIAN PLUMES

www.eng.uwo.ca

Self-study notes - GAUSSIAN PLUMES You should read appropriate text books in order to understand the m eaning of those w ords w hich are given here in italics. Consider a point source som ewhere in the air where a pollutant is released at a constant rate Q (kg/s). The wind is

### The Gaussian distribution

www.cse.wustl.edu

The d-dimensional multivariate Gaussian distribution is speci˙ed by the parameters and . Without any further restrictions, specifying requires dparameters and specifying requires a further d 2 = ( 1) 2. The number of parameters therefore grows quadratically in the dimension,

### Beyond a Gaussian Denoiser: Residual Learning of Deep …

www4.comp.polyu.edu.hk

and boosting the denoising performance. While this paper aims to design a more effective Gaussian denoiser, we observe that when v is the difference between the ... gradient-based optimization algorithms , , , batch normalization  and …

### IV. Gauss’s Law - Worked Examples - MIT

web.mit.edu

Figure 5.2 Gaussian surfaces for uniformly charged spherical shell with ra≤ Step 5a: The flux through the Gaussian surface is (2) E S Φ=∫∫EA⋅dE=A=E4πr GG w (5.2) Step 6a: Since all the charge is located on the shell, the charge enclosed in …

### Lecture 8 The Kalman ﬁlter - Stanford University

web.stanford.edu

13.35 −0.03 −0.03 11.75 covariance of xt converges to ... are all jointly Gaussian (i.e., the process x, w, v, y is Gaussian) The Kalman ﬁlter 8–9. Statistical properties • sensor …

### TrueSkill 2: An improved Bayesian skill rating system

www.microsoft.com

drawn from a Gaussian distribution with mean m 0 and variance v 0. This sampling process is denoted skillt 0 i ˘N(m 0;v 0) (1) where t 0 is the time of the player’s rst match and (m 0;v 0) are tunable parameters. After each match, the player’s skill changes by a random amount, also drawn from a Gaussian:

### 分子軌道法計算プログラムGaussian 03 ―その2― 和佐田 祐 …

www2.itc.nagoya-u.ac.jp

### 分子軌道法計算プログラムGaussian 03 ―その9― 和佐田（ …

www2.itc.nagoya-u.ac.jp

### GAMESS/Gaussian/NWChem 2量体計算 分散力補正

winmostar.com

Title: Winmostar V10 チュートリアル GAMESS/Gaussian/NWChem 2量体計算（分散力補正） Created Date: 3/31/2021 1:40:06 AM

### Physics 198-730B: Quantum Field Theory

www.physics.mcgill.ca

Figure 2.5. Complex contour for evaluating complex Gaussian integral. Now let’s return to the 4-point function. When we do the contractions, we have the possibility of contracting the external ﬁelds with the ﬁelds from the interaction vertex. This new connected contribution (ﬁgure 3) comes in addition to the disconnected one shown in ...

### Strict-Sense and Wide-Sense Stationarity Autocorrelation ...

isl.stanford.edu

stationary Gaussian random process • The nonnegative deﬁnite condition may be diﬃcult to verify directly. It turns out, however, to be equivalent to the condition that the Fourier transform of RX(τ), which is called the power spectral density SX(f), is nonnegative for all frequencies f EE 278: Stationary Random Processes Page 7–9

### Atmospheric Dispersion Modeling

faculty.washington.edu

Gaussian Plume (Concentrations vary with x, y and z) For a given x, the max conc. is at the plume centerline and decreases exponentially away from the centerline at a rate dependent upon the sigma values, y and z. y and z are functions of x Plume Centerline

### HW-Sol-5-V1 - MIT

web.mit.edu

tial family of distribution. Recall that Gaussian distribution is a member of the exponential family of distribution and that random variables, X i’s and Y j’s, are mutually independent. Thus, their joint pdf belongs to the exponential family as well.

### Canonical Correlation a Tutorial

www.cs.cmu.edu

For Gaussian variables this means I (x; y)= 1 2 log Q i (1 2) = X i: (9) Kay  has shown that this relation plus a constant holds for all elliptically sym- ... and multivariate linear regression (MLR). The matrices are listed in table 1. 4. A B PCA C xx I PLS 0 C xy C yx 0 I I CCA 0 C xy C yx 0 xx yy MLR 0 C xy C yx 0 xx I Table 1: The ...

### IEOR E4602: Quantitative Risk Management Spring 2016 2016 ...

www.columbia.edu

nancial crisis { hence the infamy of the Gaussian copula model. 1 Introduction and Main Results Copulas are functions that enable us to separate the marginal distributions from the dependency structure of a given multivariate distribution. They are useful for several reasons. First, they help to expose and understand

### Pattern Recognition and Machine Learning - microsoft.com

www.microsoft.com

Sep 08, 2009 · outside the integral, leaving a normalized Gaussian distribution which integrates to 1, and so we obtain (1.49). To derive (1.50) we ﬁrst substitute the expression (1.46) for the no rmal distribution into the normalization result (1.48) and re-arrange to obtain Z∞ −∞ exp ˆ − 1 2σ2 (x−µ)2 ˙ dx= 2πσ2 1/2. (15)

### Basic Properties of Brownian Motion

www.stat.berkeley.edu

is a Gaussian processes, i.e. all its FDDs (ﬁnite dimensional distributions) are multivariate normal. Note that X is a Markov process, with stationary independent increments, with x the initial state, δ the drift parameter, σ2 the variance parameter. These three parameters determine all the FDDs of (X t,t ≥ 0), which

### Multivariate normal distribution

www.ccs.neu.edu

or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One possible definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate

### PARTICLE SIZE CHARACTERIZATION OF NANOPARTICLES …

ijmse.iust.ac.ir

characterization of nanoparticles is particle sizing. ... Nano ZS laser particle size analyzer. The instrument was equipped with a He-Ne laser source ( =633 nm) and at scattering angle of ... or Gaussian distribution formula, they should have a straight-line fit [8, 12]. However, the figure reveals that the distribution lies on ...

### Syllabus for B.Tech(Computer Science & Engineering) Second ...

makautwb.ac.in

plumes and Gaussian plume model. 2L Definition of pollutants and contaminants, Primary and secondary pollutants: emission standard, criteria pollutant. Syllabus for B.Tech(Computer Science & Engineering) Second Year Revised Syllabus of B.Tech CSE (To be followed from the academic session, July 2011, i.e. for the students who were ...

### Chapter utorial: The Kalman Filter

web.mit.edu

as a Gaussian distribution. In suc h a case the MSE serv es to pro vide the v alue of ^ x k whic h maximises the lik eliho o d of the signal y k. In the follo wing deriv ation the ... and is assumed stationary o v er time, (nxm); w k is the asso ciated white noise pro cess with kno wn co v ariance, (nx1). Observ ations on this v ariable can b e ...

### 1 IEOR 4700: Notes on Brownian Motion - Columbia University

www.columbia.edu

variance t. Similarly, using the stationary and independent increments property, we conclude that B(t)−B(s) has a normal distribution with mean 0 and variance t−s, and more generally: the limiting BM process is a process with continuous sample paths that has both stationary and independent normally distributed (Gaussian) increments: If t 0 ...

### The Unscented Kalman Filter for Nonlinear Estimation

groups.seas.harvard.edu

agation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is ap-proximated by a GRV, which is then propagated analyti-cally through the ﬁrst-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may

### TIME VARYING MAGNETIC FIELDS AND MAXWELL’S …

ocw.nthu.edu.tw

A. STATIONARY LOOP IN TIME-VARYING B FIELD (TRANSFORMER EMF) This is the case portrayed in Figure 2 where a stationary conducting loop is in ... (Gaussian surface) is equal to the total charge inside the surface. 4. The fourth law …

### Probability Theory: STAT310/MATH230;August 27, 2013

web.stanford.edu

7.3. Gaussian and stationary processes 286 Chapter 8. Continuous time martingales and Markov processes 291 8.1. Continuous time ﬁltrations and stopping times 291 8.2. Continuous time martingales 296 8.3. Markov and Strong Markov processes 319 Chapter 9. The Brownian motion 343 9.1. Brownian transformations, hitting times and maxima 343 9.2.

### HPLC Basics – principles and parameters - KNAUER

www.knauer.net

This factor describes the peak asymmetry, i.e. to which extent the shape is approximated to the perfectly symmetric Gaussian curve. The tailing factor is mea - sured as: T=b/a a represents the width of the front half of the peak, is the width of the back half of the peak. The values are measured at 10 % of the peak height from the b

### Bluetooth® Core Specification Version 5.0 Feature …

www.bluetooth.com

Bluetooth LE uses a modulation scheme called Gaussian frequency shift keying which in simple terms involves shifting a central carrier signal up by a small frequency deviation to represent a digital value of one or down by the same frequency deviation value to …

### THE GAUSSIAN INTEGRAL

where the interchange of integrals is justi ed by Fubini’s theorem for improper Riemann integrals. (The appendix gives an approach using Fubini’s theorem for Riemann integrals on rectangles.) Since Z 1 0 ye ay2 dy= 1 2a for a>0, we have J2 …

### Gaussian Distribution - Welcome to CEDAR

cedar.buffalo.edu

• For a multivariate Gaussian distribution N(x| µ,Λ-1) for a D-dimensional variable x – Conjugate prior for mean µ assuming known precision is Gaussian – For known mean and unknown precision matrix Λ, conjugate prior is Wishart distribution – If both mean and precision are unknown conjugate prior is Gaussian-Wishart

### GAUSSIAN 09W TUTORIAL - McGill University

barrett-group.mcgill.ca

Gaussian 09W (G09) is a computational chemistry program that runs on any mod-ern Windows 32-bit PC. If you want to install G09 on a 64bit PC, there is a special procedure you must follow: 1.Insert the CD with G09 and copy its content onto you computer. Any folder will do; I copied directly into the :Cndirectory. 2.Open directory containing G09

### Gaussian Probability Density Functions: Properties and ...

users.isr.ist.utl.pt

second order moments of the pdf, renders its use very common in characterizing the uncertainty in various domains of application. For example, in robotics, it is ... • a two-dimensional vector with the position in a 2D environment, • a three-dimensional vector (2d-position and orientation) representing a mo-