The meansquare fluctuation MSF is a measure of the deviation between the position of particle i and some reference position. math MSF frac 1 T sum t j 1 T x i t j tilde x i 2 math , where T is the time over which one wants to average, and math tilde x i math is the reference position of particle i. Typically this reference position will be the time averaged position of the same particle i, i.e. math overline x i math Note that the difference between Rootmeansquare deviation bioinformatics RMSD and RMSF is that with the latter the average is taken over time, giving a value for each particle i. With RMSD the average is taken over the particles, giving time specific values. See also Rootmeansquare Quadratic meanRootmeansquare deviation bioinformatics RootMeanSquare Fluctuation calculated by GROMACS http www.gromacs.org documentation reference online g rmsf.html Category Statistical deviation and dispersion bioinformatics stub ... more details
for the application of rootmeansquare deviation to bioinformatics Rootmeansquare deviation bioinformatics The rootmeansquare deviation RMSD or rootmeansquare error RMSE is a frequently used measure of the differences between values predicted by a model or an estimator and the values actually observed. RMSD is a good measure of Accuracy and precision accuracy . Citation needed date January 2012 These individual differences are also called Errors and residuals in statistics residuals , and the RMSD serves to aggregate them into a single measure of predictive power. Formula The RMSD of an estimator math hat theta math with respect to the estimated parameter math theta math is defined as the squareroot of the meansquare error math operatorname RMSD hat theta sqrt operatorname MSE hat theta sqrt operatorname E hat theta theta 2 . math For an unbiased estimator , the RMSD is the squareroot of the variance, known as the standard error statistics standard error . In some disciplines, the RMSD is used to compare differences between two things that may vary, neither of which is accepted as the standard . For example, when measuring the average distance between two oblong objects, expressed as random vector s math mathbf theta 1 begin bmatrix x 1,1 x 1,2 vdots x 1,n end bmatrix qquad mathrm and qquad mathbf theta 2 begin bmatrix x 2,1 x 2,2 vdots x 2,n end bmatrix . math The formula becomes math operatorname RMSD mathbf theta 1, mathbf theta 2 sqrt operatorname MSE mathbf theta 1, mathbf theta 2 sqrt operatorname E mathbf theta 1 mathbf theta 2 2 sqrt frac sum i 1 n x 1,i x 2,i 2 n . math Normalized rootmeansquare deviation The normalized rootmeansquare deviation or error NRMSD or NRMSE is the RMSD divided by the range of observed values, Citation needed date February ... RMSE are used to calibrate models to measured building performance. See also Rootmeansquare Squared ..., CV RMSD , or more commonly CV RMSE , is defined as the RMSD normalized to the mean of the observed ... more details
Refimprove date March 2010 Other uses RMS disambiguation RMS In mathematics , the rootmeansquare abbreviated RMS or rms , also known as the quadratic mean , is a statistics statistical measure of the magnitude ... function . The name comes from the fact that it is the squareroot of the mean of the square algebra squares of the values. It is a special case of the generalized mean with the exponent p 2. Definition The RMS value of a set of values or a continuous time waveform is the squareroot of the arithmetic mean average of the square algebra squares of the original values or the square ... with RMS voltage and RMS current, RMS power is the squareroot of the mean of the square of the power ... P mathrm input t rangle I Q V CC langle I mathrm out t rangle V CC . , math Rootmeansquare speed main Rootmeansquare speed In the physics of gas molecules, the rootmeansquare speed is defined as the squareroot of the average speed squared. The RMS speed of an ideal gas is Maxwell Boltzmann ... speed, the average velocity for a stationary gas is zero. Rootmeansquare error Main Rootmeansquare ... rootmeansquare as a synonym for standard deviation when referring to the squareroot of the mean ... being the rootmeansquare of a signal s variation about the mean, rather than about 0, the DC component ... Mean squared error Rootmeansquare deviation Table of mathematical symbols True RMS converter ... Rms.htm A Java applet on learning RMS DEFAULTSORT RootMeanSquare Category Statistical deviation .... By taking the squareroot of both these equations and multiplying them together, we get the equation ... of the RMS statistic of a random process , the expected value is used instead of the mean. RMS of common waveforms Image Waveforms.svg thumb 400px sine wave Sine , square wave square , triangle ... y a , math math a , math Sine wave math y a sin 2 pi ft , math math frac a sqrt 2 math Square wave ... square wave math y begin cases 0 & ft 0.25 a & 0.25 ft 0.5 0 & 0.5 ft 0.75 a & ft 0.75 end cases math ... more details
Refimprove date December 2009 Rootmeansquare speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the kinetic theory of gases. It is defined as the squareroot of the average velocity squared of the molecules in a gas. It is given by the formula ref cite book title College Physics, Volume 1 edition 9th author Raymond A. Serway, Jerry S. Faughn, and Chris Vuille publisher 9780840068484 year 2011 isbn page 352 url http books.google.com books?id HLxV IKYO5IC&pg PA352 ref math v mathrm rms sqrt 3RT over M m math where v sub rms sub is the rootmeansquare of the speed, M sub m sub is the molar mass of the gas, R is the molar gas constant , and T is the temperature in kelvin . Although the molecules in a sample of gas have an average kinetic energy and therefore an average speed the individual molecules move at various speeds, i.e. they exhibit a distribution of speeds. Some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. This equation is derived from kinetic theory of gases using Maxwell Boltzmann distribution function. The higher the temperature, the greater the mean velocity will be. This works well for both nearly ideal, atomic gases like helium and for Molecule molecular gas es like diatomic oxygen . This is because despite the larger internal energy in many molecules compared to that for an atom , 3 RT 2 is still the mean Translation physics translational kinetic energy kinetic energy. This can also be written in terms of the Boltzmann constant k as math v mathrm rms sqrt 3kT over m math where m is the mass of one molecule of the gas. This can be derived with energy methods math E mathrm k 3 over 2 nRT frac 3 2 NkT math where E sub k sub is the kinetic energy and N is the number of gas molecules. math E mathrm k,molecule 1 over 2 ... math sqrt frac 3kT m math References reflist DEFAULTSORT RootMeanSquare Speed Category Gases cs St edn ... more details
The rootmeansquare deviation RMSD is the measure of the average distance between the atoms usually the backbone atoms of protein structural alignment superimposed proteins . In the study of globular protein conformations, one customarily measures the similarity in three dimensional structure by the RMSD of the C&alpha atomic coordinates after optimal rigid body superposition. When a dynamical system fluctuates about some well defined average position the RMSD from the average over time can be referred to as the RMSF or rootmeansquare fluctuation . The size of this fluctuation can be measured, for example using M ssbauer spectroscopy or nuclear magnetic resonance , and can provide important physical information. The Lindemann index is a method of placing the RMSF in the context of the parameters of the system. A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the RMSD. Coutsias, et al. presented a simple derivation, based on quaternion s, for the optimal solid body transformation rotation translation that minimizes the RMSD between two sets of vectors. ref name Coutsias2004 cite journal author Coutsias EA, Seok C, Dill KA title Using quaternions to calculate RMSD journal J Comput Chem volume 25 issue 15 pages 1849 1857 year 2004 pmid 15376254 doi 10.1002 jcc.20110 ref They proved that the quaternion method is equivalent to the well known Kabsch algorithm . ref name Kabsch1976 cite journal author Kabsch W title A solution for the best rotation to relate two sets of vectors journal Acta Crystallographica volume 32 pages 922 923 year 1976 doi 10.1107 S0567739476001873 issue ... also Rootmeansquare deviation Rootmeansquare fluctuation Quaternion used to optimise RMSD calculations ... author Maiorov VN, Crippen GM year 1994 title Significance of rootmeansquare deviation in comparing ... rootmeansquare deviation RMSD &mdash another tutorial on how to calculate RMSD with example code http ... more details
, where h is the height and g is the acceleration of gravity. In mathematics , a squareroot of a number ... books?id Z9z7iliyFD0C&pg PA120 Extract of page 120 ref For example, 4 is a squareroot of 16 because 4 sup 2 sup 16. Every non negative real number a has a unique non negative squareroot, called the principal squareroot , which is denoted by math scriptstyle sqrt a math , where is called radical sign . For example, the principal squareroot of 9 is 3, denoted math scriptstyle sqrt ... roots are denoted math scriptstyle pm sqrt a math see shorthand . Although the principal squareroot of a positive number is only one of its two square roots, the designation the squareroot is often used to refer to the principal squareroot. For positive a , the principal squareroot can also be written ... page n14 mode 1up year 1908 publisher Cambridge University Press page 3 ref Squareroot ... of a square geometry square with side length 1. Properties Image Squareroot 0 25.svg thumb ... directrix . The principal squareroot function math scriptstyle f x sqrt x math usually just referred to as the squareroot function is a function mathematics function that maps the Set mathematics set of non negative real numbers onto itself. In geometry geometrical terms, the squareroot function maps the area of a square to its side length. The squareroot of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. See squareroot ... non square natural numbers. The squareroot function maps rational numbers into algebraic number s a Subset ... The squareroot function is Continuous function continuous for all non negative x and derivative differentiable for all positive x . If f denotes the squareroot function, its derivative is given ... s have a squareroot key. Computer spreadsheet s and other software are also frequently used to calculate ... function and the natural logarithm or common logarithm , and use them to compute the squareroot ... more details
SquareRoot Day is an Holiday Unofficial holidays unofficial holiday celebrated on days when both the day of the month and the month are the squareroot of the last two numerical digit digit s of the year. ref cite news title A day getting to the root last Wong first Nicole C. work The Mercury News url http www.mercurynews.com mld mercurynews news 7854616.htm date 2004 02 02 accessdate 2007 02 20 archiveurl http web.archive.org web 20040818204722 http www.mercurynews.com mld mercurynews news 7854616.htm archivedate 2004 08 18 ref For example, the last SquareRoot Day was March 3, 2009 3 3 09 , and the next SquareRoot Day will be April 4, 2016 4 4 16 . The final SquareRoot Day of the century will occur on September 9, 2081. SquareRoot Days fall upon the same nine dates each century. Ron Gordon, a Redwood City, California high school teacher, created the first SquareRoot Day for September 9, 1981 9 9 81 . Gordon remains the holiday s publicist , sending news release s to world News media media outlets. ref cite news title Have a rootin tootin SquareRoot Day last Hill first Angela work ... share how they were celebrating the day. ref cite news title Math Fans to Celebrate SquareRoot Day work Yahoo News url http news.yahoo.com s ap 20090303 ap on fe st odd squareroot day date 2009 03 02 ... the holiday is by eating Square geometry square radish es, or other root vegetable s cut into shapes with square Cross section geometry cross section s thus creating a squareroot . ref cite news title SquareRoot Day revelers to party like it s 3 3 09 last Musil first Steven work cnet news url http ... 2009 03 02 ref Full list of SquareRoot Days SquareRoot Day occurs on the following dates ... 00 or 2100 . 10 is not the squareroot of 00 please re read the definition of SquareRoot Day in the text ..., etc. is a SquareRoot Day even by extension. Thank you. User Finell Distribution of SquareRoot Days The number of years between consecutive SquareRoot Days in a century are consecutive odd numbers ... more details
Expert subject statistics date February 2009 Meansquare weighted deviation is used extensively in geochronology , the science of obtaining information about the time of formation of, for example, rocks, minerals, bones, corals, or charcoal, or the time at which particular processes took place in a rock mass, for example recrystallization and grain growth, or alteration associated with the emplacement of metalliferous ore deposits.. Often the geochronologist will determine a series of age measurements on a single sample, with the measured value math x i math having a weighting math w i math and an associated error math sigma x i math for each age determination. As regards weighting, one can either weight all of the measured ages equally, or weight them by the proportion of the sample that they represent. For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement then one might weight the first measurement twice that of the second. The arithmetic mean of the age determinations is math overline x frac sum i 1 N x i N math but this value can be misleading unless each determination of the age is of equal significance. When each measured value can be assumed to have the same weighting, or significance, the biased and unbiased or population and Standard deviation With sample standard deviation sample , respectively estimators of the variance are computed as follows math sigma 2 frac sum i 1 N x i overline x 2 N rm and s 2 ... is the squareroot of the variance. When individual determinations of an age are not of equal significance it is better to use a weighted mean to obtain an average age, as follows math overline x ... standard deviation is the squareroot of the variance. The unbiased weighted estimator ... 2 cdot sum i 1 N w i sum i 1 N w i x i 2 sum i 1 N w i 2 sum i 1 N w i 2 math The unweighted meansquare ... N 1 . sum i 1 N frac x i overline x 2 sigma x i 2 math By analogy the weighted meansquare of the weighted ... more details
mean s. The squareroot of 2 can also be expressed in terms of the copies of the imaginary unit i using only the squareroot and arithmetic Arithmetic operations arithmetic operations math frac sqrt i i sqrt i i text and frac sqrt i i sqrt i i . math The squareroot of 2 is also the only real ...Image Squareroot of 2 triangle.svg thumb 200px The squareroot of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1. The squareroot of 2 , often known as root 2 and written ... 2 number 2 . It is more precisely called the principal squareroot of 2 , to distinguish it from the negative number with the same property. Geometrically the squareroot of 2 is the length of a diagonal ... root of 2. The quick approximation 99 70 1.41429 for the squareroot of two is frequently used. Despite ..., ancient Greeks treated as an official secret the discovery that the squareroot of two is irrational ..., 1945. ref The squareroot of two is occasionally called Pythagoras s number or Pythagoras ... computations performed and the greater n , the better approximation of the squareroot ... for a proof that the squareroot of any non square natural number is irrational. Proof by infinite .... Therefore the squareroot of 2 cannot be a rational number. This proof can be generalized to show that any root of any natural number which is not the square of a natural number is irrational. The article ... of the squareroot of two One half of sqrt 2 , also 1 divided by the squareroot of 2, approximately ... circ sin 45 circ . math One interesting property of the squareroot of 2 is as follows math 1 over ... 2 cdot cdot cdot 2 math The squareroot of 2 appears in Vieta formula Vi te s formula for math 2 ... year 1941 page 124 ref Similarly in appearance but with a finite number of terms, the squareroot ... fraction representation The squareroot of two has the following continued fraction representation ... the squareroot of two to increasing accuracy, and that are described by the Pell number s known ... more details
The squareroot of 5 is the positive real number that, when multiplied by itself, gives the prime number 5 number 5 . It is more precisely called the principal squareroot of 5 , to distinguish it from ... of the squareroot of 5 ref Proof of irrationality This irrationality proof for the squareroot ... between the squareroot of 5, the golden ratio and the golden ratio Golden ratio conjugate conjugate ... 1 2 . math See section below for their geometrical interpretation as decompositions of a root 5 rectangle. The squareroot of 5 then naturally figures in the closed form expression for the Fibonacci ... smaller triangles. geometry Geometrically , the squareroot of 5 corresponds to the diagonal ... corresponds to the length of the cube diagonal, which is the squareroot of three times the edge . Citation ... root of 2 and the squareroot of 3 , as it is the length of the hypotenuse of a right triangle ... constructed using the diagonal of the previous root rectangle, starting from a square. ref ... be constructed from a 1 2 rectangle the root 4 rectangle , or directly from a square in a manner similar ... fraction 5 2 to both sides. Trigonometry Like 2 and 3, the squareroot of 5 appears extensively in the formulae ... numbers. The Kronecker Weber theorem therefore guarantees that the squareroot of five ... e 6 pi i 5 e 8 pi i 5 . , math Identities of Ramanujan The squareroot of 5 appears in various identities ... ratio SquarerootSquareroot of 2 Squareroot of 3 References reflist Category Mathematical constants ... ratio . It can be denoted in nth root surd form as math sqrt 5 . , math It is an irrational ... is computed with the Methods of computing square roots Babylonian method Babylonian method , starting ... thumb The fraction 5 2 diagonal of a half square forms the basis for the geometrical construction of a golden rectangle . This golden ratio is the arithmetic mean of 1 number 1 and the squareroot of 5. ref Browne, Malcolm W. July 30, 1985 New York Times Puzzling Crystals Plunge Scientists ... more details
In mathematics , the squareroot of a matrix extends the notion of squareroot from numbers to Matrix mathematics matrices . A matrix B is said to be a squareroot of A if the matrix product B B is equal ... April year 1986 title Newton s Method for the Matrix SquareRoot journal Mathematics of Computation ... definite squareroot, which can be called its principal squareroot. While the squareroot of an integer ... a squareroot whose entries are rational, yet not integral. For example, the matrix math bigl begin smallmatrix 0&4 1&5 end smallmatrix bigr math has a squareroot math bigl begin smallmatrix 2 3&4 3 1 3&7 3 end smallmatrix bigr math , as well as a squareroot that is an integer matrix math bigl ... is any squareroot matrix of D , which must be diagonal with diagonal elements equal to square roots of the diagonal elements of D since there are two possible choices for a squareroot of each diagonal ... squareroot a positive definite matrix has only positive eigenvalues, and each of these eigenvalues has only one positive squareroot and since the eigenvalues of the squareroot matrix are the diagonal elements of math D 1 math , for the squareroot matrix to be itself positive definite necessitates ... numbers , a real matrix may fail to have a real squareroot, but have a squareroot with Complex ... root of a 2 by 2 matrix explicit formulas that give up to four square roots, if the matrix has any roots. If D is a diagonal matrix diagonal n × n matrix, one can obtain a squareroot by taking a diagonal matrix R , where each element along the diagonal is a squareroot of the corresponding ... as columns, and a squareroot of math A math is math R V S V 1 , , math where S is any squareroot ... begin smallmatrix 81&0 0&9 end smallmatrix bigr math . math D math has principal squareroot math D 1 2 bigl begin smallmatrix 9&0 0&3 end smallmatrix bigr math , giving the squareroot math A 1 2 V ... in logarithm of a matrix . By Denman Beavers iteration Another way to find the squareroot of an n ... more details
orange span , i.e., the sine s functional squareroot the functional squareroot of that, the quarter ... SquareRoot Category Functional analysis mathanalysis stub es Media iteraci n eo Funkcia kvadrata ... more details
Multiple issues unreferenced October 2007 Meansquare quantization error MSQE is a figure of merit for the process of Analog to digital converter analog to digital conversion . As the input is varied, the input s value is recorded when the digital output changes. For each digital output, the input s difference from ideal is normalized to the value of the least significant bit , then squared, summed, and normalized to the number of samples. Category Statistical deviation and dispersion technology stub ... more details
Squareroot biased sampling is a sampling method proposed by William H. Press , a computer sciences computer scientist and computational biology computational biologist , for use in Airport security airport screenings . It is the mathematically optimal compromise between Simple random sample simple random sampling and Offender profiling strong profiling that most quickly finds a rare malfeasor, given fixed screening resources. ref name the paper Cite journal last Press first William H. authorlink coauthors title Strong profiling is not mathematically optimal for discovering rare malfeasors journal Proceedings of the National Academy of Sciences volume 106 issue 6 pages 1716 1719 publisher location date February 10, 2009 url http www.pnas.org content 106 6 1716.full doi 10.1073 pnas.0813202106 id accessdate 2009 11 28 ref ref name homeland ref Using this method, if a group is math alt n n math times as likely than the average to be a security risk, then persons from that group will be math alt squareroot of n sqrt n math times as likely to undergo Airport security Process and equipment additional screening . ref name the paper ref For example, if someone from a profiled group is nine times more likely than the average person to be a security risk, then when using squareroot biased sampling, people from the profiled group would be screened three times more often than the average person. History Press developed squareroot biased sampling as a way to sample long sequences of DNA . ref name texas It had also been developed independently by Ruben Abagyan, a professor at Scripps ... L. Shooman, who used squareroot biased sampling in a test apportionment model for software reliability ... Press later proposal to use squareroot biased sampling for airport security was published in 2009 ... first2 author2 link title Squareroot bias and airport security screening newspaper Homeland Security Newswire pages year 2009 date 2009 02 03 url http homelandsecuritynewswire.com squareroot bias and airport ... more details
tfrac m n sqrt 3 math . Geometry and trigonometry Image Root 3 Hexagon.svg thumb 200px The squareroot ... and the cosine of 30 both equal half of math sqrt 3 math . The squareroot of 3 also appears in algebraic ... axis ratio equal to the squareroot of three, this can be shown by constructing two equilateral triangles .... See also Squareroot of 2 Squareroot of 5 References reflist cite journal title 22900D approximations to the square roots of the primes less than 100 journal Mathematics of Computation volume ... Theodorus Constant at MathWorld DEFAULTSORT Squareroot of three Category Algebraic ... more details
In statistics and signal processing , a minimum meansquare error MMSE estimator describes the approach which minimizes the meansquare error MSE , which is a common measure of estimator quality. The term MMSE specifically refers to estimation in a Bayesian inference Bayesian setting, since in the alternative frequentist setting there does not exist a single estimator having minimal MSE. A somewhat similar concept can be obtained within the frequentist point of view if one requires unbiased estimator unbiasedness , since an estimator may exist that minimizes the variance and hence the MSE among unbiased estimators. Such an estimator is then called the minimum variance unbiased estimator MVUE . Definition Let math X math be an unknown random variable, and let math Y math be a known random variable the measurement . An estimator math hat X y math is any function of the measurement math Y math , and its mean squared error MSE is given by math mathrm MSE E left hat X X 2 right math where the expectation is taken over both math X math and math Y math . The MMSE estimator is then defined as the estimator achieving minimal MSE. In many cases, it is not possible to determine a closed form for the MMSE estimator. In these cases, one possibility is to seek the technique minimizing the MSE within a particular class, such as the class of linear estimators. The linear MMSE estimator is the estimator ... for math hat X 4 . math Computing the minimum meansquare error then gives math left Vert e right ... Mean Squared Error Estimators . Connexions Prediction and Improved Estimation in Linear Models , by J. Bibby, H. Toutenburg Wiley, 1977 . This book looks almost exclusively at minimum meansquare error ... Hall. 2000. Use dmy dates date September 2010 DEFAULTSORT Minimum MeanSquare Error Category ... are real Gaussian random variables with zero mean and covariance matrix given by math operatorname ... example can be found in orthogonality principle . See also Bayesian estimator Mean squared error ... more details
In number theory , the integer squareroot isqrt of a positive integer n is the positive integer m which is the floor and ceiling functions greatest integer less than or equal to the squareroot of n , math mbox isqrt n lfloor sqrt n rfloor. math For example, math mbox isqrt 27 5 math because math 5 cdot 5 25 le 27 math and math 6 cdot 6 36 27 math . Algorithm One way of calculating math sqrt n math and math mbox isqrt n math is to use Newton s method to find a solution for the equation math x 2 n 0 math , giving the Recursion recursive formula math x k 1 frac 1 2 left x k frac n x k right , quad k ge 0, quad x 0 0. math The sequence math x k math Limit mathematics converges Rate of convergence quadratically to math sqrt n math as math k to infty math . It can be proven that if math x 0 n math is chosen as the initial guess, one can stop as soon as math x k 1 x k 1 math to ensure that math lfloor x k 1 rfloor lfloor sqrt n rfloor. math Domain of computation Although math sqrt n math is irrational number irrational for almost all math n math , the sequence math x k math contains only rational number rational terms when math x 0 math is rational. Thus, with this method it is unnecessary to exit the field mathematics field of rational numbers in order to calculate math mbox isqrt n math , a fact which has some theoretical advantages. Stopping criterion One can prove that math c 1 math is the largest possible number for which the stopping criterion math x k 1 x k c math ensures math lfloor x k 1 rfloor lfloor sqrt n rfloor math in the algorithm above. Since actual computer calculations involve roundoff errors, a stopping constant less than 1 should be used, e.g. math x k 1 x k 0.5. math See also Methods of computing square roots External links http mathcentral.uregina.ca RR database RR.09.95 grzesina1.html A geometric view of the squareroot algorithm number theoretic algorithms Category Number theoretic algorithms Category Number theory Category Root finding algorithms ... more details
person shooter OpenArena use the fast inverse squareroot code to compute Angle of incidence angles of incidence and reflection. Fast inverse squareroot sometimes referred to as Fast InvSqrt or by the hexadecimal ... reciprocal or multiplicative inverse of a squareroot for a 32 bit floating point number in Single ... hexadecimal 0x 5f3759df. This is the first approximation of the inverse squareroot of the input ... a more precise approximation. This computes an approximation of the inverse squareroot of a floating ... here. The inverse squareroot of a floating point number is used in calculating a Unit vector ... is determined by calculating its Euclidean norm the squareroot of the sum of squares of the vector ... hat v boldsymbol v sqrt x math , which relates the unit vector to the inverse squareroot of the distance components. Quake III Arena used the fast inverse squareroot algorithm to speed graphics processing ... Overview of the code The following code is the fast inverse squareroot implementation from Quake III ... return y source In order to determine the inverse squareroot, an approximation for math x 1 2 ... 2003 InvSqrt.pdf title Fast Inverse SquareRoot last Lomont first Chris date February, 2003 page ... The Mathematics Behind the Fast Inverse SquareRoot Function Code last McEniry first Charles date ... offered by the fast inverse squareroot Kludge In computer science kludge came from treating the longword ... name Eberly 2 Cite document last Eberly first David title Fast Inverse SquareRoot publisher Geometric ... when treated as a floating point number is a rough approximation for the inverse squareroot of the input ... url http assemblyrequired.crashworks.org 2009 10 16 timing squareroot title Timing squareroot work ... and M the significand. Since the inverse squareroot function deals only with positive numbers, the floating ... as a mechanism to approximate the inverse squareroot, Charles McEniry first determined how the choice of any constant R could give a first approximation for the inverse squareroot. Recalling ... more details
A squareroot of a matrix squareroot of a 2 by 2 matrix mathematics matrix M is another 2 by 2 matrix R such that M R sup 2 sup , where R sup 2 sup stands for the matrix product of R with itself. In many cases, such a matrix R can be obtained by an explicit formula. ref name somayya1 P. C. Somayya 1997 , http mathforum.org kb servlet JiveServlet download 13 1879293 6653929 548390 A 20Method 20for 20finding 20a 20Square 20Root 20of 20a 202x2 20Matrix.doc Root of a 2x2 Matrix , The Mathematics Education Vol.. XXXI. No. 1. Siwan, Bihar State. INDIA ref The general formula Let math M left begin array cc A & B C & D end array right math where A , B , C , and D may be real or complex numbers. Furthermore, let A D be the trace mathematics trace of M , and AD BC be its determinant . Let s be such that s sup 2 sup , and t be such that t sup 2 sup 2 s . That is, math s pm sqrt delta quad quad t pm sqrt tau 2 s math Then, if t 0, a squareroot of M is math R frac 1 t left begin array cc A s & B C & D s end array right math Indeed, the square of R is math begin array rcl R 2 & & displaystyle frac 1 t 2 left begin array cc A s 2 B C & A s B B D s C A s D s C & D s 2 B C end array right 3ex & & displaystyle frac 1 A D 2 s left begin array cc A A D 2s & A D 2s B C A D 2 s & D A D 2 s end array right M end array math Note that R may have complex entries even if M is a real matrix this will be the case, in particular, if the determinant is negative. Special cases of the formula In general, the formula above will provide four distinct square roots R , one for each choice of signs for s and t . If the determinant is zero but the trace is nonzero, the formula will give only two distinct solutions. Ditto if is nonzero and sup 2 sup 4 , in which case one of the choices for s will make the denominator t be zero. The general formula above fails completely if and are both ... matrix is also a squareroot of M othwerwise M has no squareroot. Simplified formulas ... more details
average of functions and a quadratic average or rootmeansquare of functions. Mean of a probability ... below Moving average Rootmeansquare R nyi s entropy a generalized f mean Stolarsky mean Weighted ...About the statistical concept In statistics , mean has two related meanings the arithmetic mean and is distinguished from the geometric mean or harmonic mean . the expected value of a random variable , which is also called the population mean . There are other statistical measures that should not be confused ... . For a real valued random variable X , the mean is the expectation operator expectation of X . Note that not every probability distribution has a defined mean or variance see the Cauchy distribution for an example. For a data set , the mean is the sum of the values divided by the number of values. The mean of a set of numbers x sub 1 sub , x sub 2 sub , ..., x sub n sub is typically denoted by math bar x math , pronounced x bar . This mean is a type of arithmetic mean. If the data set were based on a series of observations obtained by sampling statistics sampling a statistical population , this mean is termed the sample mean math bar x math to distinguish it from the population mean math mu math or math mu math sub x sub . The mean is often quoted along with the standard deviation the mean ... measure of dispersion is the mean deviation, equivalent to the average absolute deviation from the mean. It is less sensitive to outliers, but less mathematically tractable. If a series of observations ... to construct a population mean , which is also the expected value for a sample drawn from this population ... mean of the given property for every member of the population. For a probability distribution, this would ... convention to represent the population mean by the symbol math mu math . ref Underhill ... distribution , the mean of a discrete random variable x is given by taking the product of each ... books?id DWCAh7jWO98C&lpg PP1&pg PA279 v onepage&q&f false p. 279 ref The sample mean ... more details
refimprove date March 2012 root is the name of a database record of the DNS root zone root zone in the Domain Name System of the Internet that was occasionally used as a diagnostic marker. Its presence demonstrated the root zone was not truncated upon loading by a root nameserver . According to technical observers the single .root entry was replaced in 2006 with just vrsn end of zone marker dummy record , to be reintroduced later in 2006 in its original form. Citation needed date July 2010 The entry was deleted again during the preparations for the DNSSEC Deployment at the DNS root deployment of DNSSEC at the root zone in 2010. ref name dns operations cite mailing list url https lists.dns oarc.net pipermail dns operations 2010 May 005501.html title plenus no more date 2010 05 05 accessdate 2010 05 05 mailinglist dns operations last Arends first Roy ref ref name h online cite news title DNSSEC on all root servers newspaper The H date 2010 05 06 url http www.h online.com security news item DNSSEC on all root servers 994744.html accessdate 2010 05 07 ref The existence of the record was observed with the domain information groper dig utility by querying for a TXT record for the domain name dig vrsn end of zone marker dummy record.root This entry returned the word wikt plenus plenus , which is Latin for full or complete . References references External links http www.internic.net zones root.zone The root zone file GTLD DEFAULTSORT ROOT Category Pseudo top level domains ca .root cs .root da .root es .root gl .root it .root ja Vrsn end of zone marker dummy record.root no .root pl .root sv Toppdom n Generiska toppdom ner ur Root. ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name Root image root band.jpg caption L R Henri Root, Joe Root, Barnaby Root, DC Root, Doug Lee Root, Steve Root image size Only for images narrower ... Root br Henri Root br Doug Lee Root br Steve Root br Owen Root br Barnaby Root br Smiley Root br Joe Root infrequent live member Root stylised ROOT is an Australia n rock group from Melbourne formed ... History Some time in 2004 05, Root began as a series of demos written solely by lead singer DC Root. In late 2006, guitarist Henri Root was hired as a tradesperson to build a set of shelves for DC. Henri ... . ref Root, DC. 3RRR Best of the Brat Interview October 16, 2007. ref During 2006, the group was fleshed out with Steve Root on keyboards and Barnaby Root on drums. Their first concert as a group ... page, the creation of a fan website entitled The Root Compendium , and growing demand for an album. ref http rootcompendium.net archive 2007june17.php The Root Compendium Archive June 17, 2007. After the gig I managed to catch up with DC Root who claimed that a CD s worth of material had been completed and was ready to go, Review by Adam. ref Root appeared at a handful of other performances over the next few months, whilst re recording tracks for their debut album, Root Supposed He Was Out Of The Question . In 2008, the band played live with additional musicians Joe Talia aka Joe Root, pedal steel and banjo and Douglas Lee Robertson aka Doug Lee Root, bass . ref name CompendiumOldNewsFeb08 http www.rootcompendium.net oldnews 08february.php The Root Compendium Old News February 2008 I was accompanied to my left by the ... figure of Doug Lee Root on bass and vocals. ... the bassist and singer for Melbourne s much loved, critically acclaimed Ice Cream Hands DC Root ref The album, Root Supposed ... formerly Root Is The Money Of All Evil ref name CompendiumOldNewsOctober08 http rootcompendium.net oldnews 08october.php The Root Compendium Old News October, 2008 See Root play their forthcoming ... more details
know what I mean? That s what The Root is. She got it on me. And I m just fucked up. It was good ...about the D Angelo song the online magazine The Root magazine other uses Root disambiguation Infobox Song See Wikipedia WikiProject Songs Name The Root Cover Border Caption Type Artist D Angelo alt Artist Album Voodoo D Angelo album Voodoo Published Released January 25, 2000 track no 8 Recorded 1998 1999 br Electric Lady Studios br small New York, New York small Genre Neo soul , funk , Soul music soul Language English language English Length 6 33 Writer Composer D Angelo, Charlie Hunter C. Hunter ... no 7 next Spanish Joint next no 9 Misc Extra musicsample filename The Root sample.ogg format Ogg title The Root Type Song The Root is a song by American recording artist D Angelo , released January ... on his second studio album, Voodoo D Angelo album Voodoo 2000 . The Root was recorded and produced ... by D Angelo, guitarist Charlie Hunter , and Luther Archer, D Angelo s brother. The Root features ... s narrator whose lament is depicted in the lyrics. Recording and production The Root was recorded and produced ... Academy . Retrieved on 2008 10 13. ref He played the guitar and bass sections on The Root with a custom ... The Root is performed in mid tempo and its Groove music groove based sound is accompanied by Charlie ... Wayne News Sentinel 11SU. February 26, 2000. ref A mid tempo heartbreak song, the lyrics of The Root ... . The Village Voice . Retrieved on 2008 12 25. ref The final two minutes of The Root feature an emphatic ... , D Angelo discussed the therapeutic nature of recording The Root , stating It was kinda therapeutic ... of the Washington City Paper called The Root catchy and sexy. ref name Drumming Drumming, Neil ... as some vengeful woman done worked a root on him . ref name Lewis NME compared the lyrics, in particular ... on 2009 09 06. ref and Exclaim cited The Root as one of Voodoo s finest moments , and noted the song ... Root Category 2000 songs Category D Angelo songs ... more details
For other uses of rootroot disambiguation Infobox software name ROOT logo File Rootdrawing.gif 70px ROOT logo screenshot File 2D ROI.jpg 300px Example ROOT plot showing regions of interest in a 2D distribution caption Example ROOT plot showing regions of interest in a 2D distribution developer CERN ... Public License GPL website http root.cern.ch ROOT is an Object oriented programming object oriented ... discontinued in 2003 in favour of ROOT, written in C . ROOT development was initiated by Ren Brun ... . The packages provided by ROOT include those for histogram ming and Graph of a function graphing ... s. A key feature of ROOT is a data container called tree , with its substructures branches and leaves ... while handling buffering invisibly. ROOT is designed for high computer performance computing efficiency ... petabyte s per year. As of 2009 ROOT is mainly used in data analysis and data acquisition in high ... Physics Subfields subfields are obtained using ROOT. The inclusion of the CINT C interpreter makes ... similar to commercial products like MATLAB . Criticisms of ROOT include its difficulty for beginners ... extreme code bloat, heavy use of global variables, ref http insectnation.org howto problems with root The problem with ROOT ref and a perverse class hierarchy. ref http www.cernlove.org blog 2009 10 root rants histogram hierarchy and pyroot histogram hierarchy and a little PyROOT ref From time to time these issues are discussed on the ROOT users mailing list. ref http root.cern.ch root roottalk roottalk06 0763.html ROOTTALK 27 July 2006 ref ref http root.cern.ch root roottalk roottalk06 0782.html ROOTTALK 28 July 2008 ref While scientists dissatisfied with ROOT have in the past manage to work around its flaws, ref http zzz.physics.umn.edu computing contrib root localdoc recommendations to root users Recommendations to ROOT users ref some of the shortcomings are slowly being addressed by the ROOT team. The CINT interpreter, for example, is in the process of being phased out, ref http ... more details
roots in a cotton plant In vascular plant s, the root is the plant organ organ of a plant that typically lies below the surface of the soil. This is not always the case, however, since a root can also be aerial root aerial growing above the ground or aerating growing up above the ground or especially ... see rhizome . So, it is better to define root as a part of a plant body that bears no leaves, and therefore ... stems and roots. The first root that comes from a plant is called the radicle . The four major ... to the ground, and aerial root supporting it, 3 storage of food and nutrient s, 4 vegetative reproduction ... When dissected, the arrangement of the cells in a root is root hair , Epidermis botany epidermis ... of a root to transport the water absorbed by the root to other places of the plant. Root growth Early root growth is one of the functions of the apical meristem located near the tip of the root. The meristem cells more or less continuously divide, producing more meristem, root cap cells these are sacrificed to protect the meristem , and undifferentiated root cells. The latter become the primary tissues of the root, first undergoing elongation, a process that pushes the root tip forward in the growing medium. Gradually these cells differentiate and mature into specialized cells of the root ... that also causes the shoot to grow upward. In some plants such as ivy , the root actually clings ..., forms a cylinder geometry cylinder of tissue along the Plant stem stem and root. The vascular .... As secondary xylem accumulates, the girth lateral dimensions of the stem and root increases. As a result ... Unreferenced section date March 2010 A true root system consists of a primary root and secondary roots or lateral roots . the diffuse root system the primary root is not dominant the whole root system ... root is to anchor the plant. Specialized roots File Mangroves.jpg thumb Aerating roots of a mangrove File Root tip.JPG thumb The growing tip of a fine root File Socratea exorriza2002 03 12.JPG thumb ... more details
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