What is Parameter: Definition and 392 Discussions

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, electronic musical composition.
In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'.

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  1. BWV

    A You can overfit anything with just one parameter

    Interesting paper here: https://colala.bcs.rochester.edu/papers/piantadosi2018one.pdf which using a closed-form solution to the logistic map m(z) = 4z(1−z) of mk (θ) = sin2 [ 2k arcsin √ θ] with a finely tuned parameter θ (extending to hundreds of decimal places) can fit just about any 2...
  2. aphirst

    A Derivative of argmin/argmax w.r.t. auxiliary parameter?

    As part of my work, I'm making use of the familiar properties of function minima/maxima in a way which I can't seem to find in the literature. I was hoping that by describing it here, someone else might recognise it and be able to point me to a citation. I think it's highly unlikely that I'm the...
  3. F

    Converting a value material parameter

    Homework Statement I have E as a material parameter. It is a modulus of Elasticity It is given as: 109/E = 80/psi I want to write E as a value with units psi. Homework EquationsThe Attempt at a Solution Is this correct? 1/E = 80*109/psi So psi/E = 80*109 So E = 1.25*10^7 psi
  4. B

    Two pencils of planes have a common plane

    Homework Statement Find the value of the parameter α for which the pencil of planes through the straight line AB has a common plane with the pencil of planes through the straight line CD, where A(1, 2α, α), B(3, 2, 1), C(−α, 0, α) and D(−1, 3, −3). Homework Equations Let Δ be a line given by...
  5. binbagsss

    General Relativity - geodesic - affine parameter

    Homework Statement Question attached: Homework Equations see below The Attempt at a Solution [/B] my main question really is 1) what is meant by 'abstract tensors' as I have this for my definition: to part a) ##V^u\nabla_uV^a=0## but you do say that ##V^u=/dot{x^u}## ; x^u is a...
  6. K

    Unbiased estimate of a parameter in the Rice distribution

    I am trying to estimate the amplitude of a real signal with a particular frequency and unknown phase. The signal is sampled at a frequency much higher than the Nyquist frequency for the signal. For simplicity, I take an FFT period which is a multiple of the signal period (which conveniently is a...
  7. H

    MATLAB Parameter fitting with a numerical solution

    Suppose I have some experimental data on the diffusion of some concentrate into a cylindrical medium. I don't a priori know the initial concentration or diffusion constant. I have some code to solve the PDE given in the cylindrical domain which solves the equation for given initial...
  8. H

    About Huang-Rhys parameter and electron-phonon coupling

    Hello all, I am confused about Huang-Rhys parameter and electron-phonon coupling. I read a chapter of a book The biophysics of photosynthesis, called "Electron–Phonon and Exciton–Phonon Coupling in Light Harvesting, Insights from Line-Narrowing Spectroscopies". I am confused about the...
  9. I

    Classical ellipsoidal scattering Impact parameter

    Homework Statement (x^2 + y^2)/a^2 + z^2/c^2 = 1 Homework Equations [/B] The Attempt at a Solution the answer is : b(θ) = R / (f^2 * tan^2(θ/2) + 1)^0.5 I can't understand how to calculate this. My attempt : (x^2 + y^2)/a^2 + z^2/c^2 = 1 from this. b^2 + z^2/f^2 = a^2 , f = c/a, z =...
  10. Peter Alexander

    Critical Points of a Parameter Dependent Integral

    1. The problem statement, all variables, and given/known data Find and categorize extremes of the following function: $$F(y)=\int_{y}^{y^{2}}\frac{1}{\ln^{2}x}dx$$ for ##y>1##. Homework Equations $$\frac{d}{dx}\int_{a}^{b}f(x,y)dy=\int_{a}^{b}\frac{\partial}{\partial x}\left(f(x,y)\right)dy$$...
  11. H

    Bio Lab homework: Water Parameter Identification Chart

    Homework Statement Fill-in with the correct tank letter or the condition (eg. PPM of O2) Refer to above Chart A: __1. Which tank contained the lowest PPM of Oxygen? __2. Which of the 4 abiotic conditions(02, C02, PH, or Temperature) is most out of line in tank...A-G? __3. Which tank has a...
  12. H

    B Explanation of what a parameter is

    Please could someone explain, pretty simply, what a parameter and also its relation to graphs? And if possible give a couple of examples. I have trawled through the internet and can't find anything which I understand. Thank you very much.
  13. D

    A Asymmetry parameter while relating proper time with distance

    In special relativity, we know, (proper time)^{2} = - (proper distance)^{2}. But, in Causal Dynamical Triangulations (CDT), they introduce an asymmetry parameter \alpha as, (proper time)^{2} = - \alpha (proper distance)^{2} [Q. 1] Can you please explain me about, why we need to introduce \alpha...
  14. S

    I Radial BAO size method and Hubble parameter

    Hi! Can anyone tell me what the radial BAO size method is? how do people use it to get to the H(z)? I am reading the paper "Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data " by Zhang et al. and I think I am lost! Can anyone tell me very simple, how they do...
  15. M

    B Relationship Between Density and the Hubble parameter

    I'm just looking for conceptual clarification re: the relationship between matter density and the Hubble parameter in the Friedmann equation. Just for quick reference, the equation I'm looking at is H2 = 8πGρ/3 - ka-2 (I'm working through Liddle's Intro text, and for now we're ignoring the...
  16. L

    MHB Finding a parameter for which a line is orthogonal to a curve

    Hiya again, I am trying to solve this problem, I thought I got somewhere, but kinda stuck. The graph of y^2=x^3 is called a semicubical parabola. Determine the constant b so that the line y = -(1/3)x+b meets this graph orthogonally. I found the derivative of the curve by using implicit...
  17. J

    I Checking for Biased/Consistency

    Hello I am trying to check if the Method of Moments and Maximum Likelihood Estimators for parameter $\theta$ from a sample with population density $$f(x;\theta) = \frac 2 \theta x e^{\frac {-x^2}{\theta}} $$ for $$x \geq 0$, $\theta > 0$$ with $\theta$ being unknown. Taking the first moment of...
  18. binbagsss

    Landau Theory - Order parameter- Extensive or intensive?

    Homework Statement [/B] 1) Is the order paramter ##\phi(x)## intensive or extensive? 2) Is ##M## intensive or extensive? With the following definitions : Homework Equations The Attempt at a Solution 1) Free energy is extensive, however I don' think I can use this to deduce whether...
  19. K

    I How Does the Hubble Parameter Relate to Galaxy Movement?

    This is the time derivative to calculate the speed which a galaxy moves away from another galaxy. I don't understand how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1). Could anyone explain this? vi(t) = d/dt (ri(t) − r1(t)) = d/dt a(t)(xi − x1) = da/dt (xi − x1)...
  20. S

    A Constraining the parameter space of a function

    Consider the function $$f(x) = - \frac{1}{2}a^{2}x^{2} + \frac{1}{4}bx^{4} + d^{4}\cos(x/c),$$ where ##a##, ##b##, ##c## and ##d## are arbitrary parameters. For some region(s) of the parameter space, there are oscillations in the function. My goal is to identify these regions of the parameter...
  21. S

    MHB The parameter λ in linear integral equations

    Hi the parameter $\lambda$ in linear integral equations say Fredholm that appears in front of the integral containing the kernel i.e. $y(x)=f(x)+ \lambda \int_{a}^{b} \,k(x,t) y(t) dt $ can $\lambda$ be adjusted for the convergence of the method like in using Picard's successive...
  22. V

    I Derivation of phase change parameter in dispersive medium

    Hi, I'm trying to evaluate the derivates of first, second and third order of the phase change parameter in a dispersive medium. In such medium the refractive index is a function of the wavelength. In my case it depends on the wavelength in vacuum. \begin{equation*} n(\lambda_0 )\end{equation*}...
  23. M

    Show Regular Homotopy thru curve and its arclength parameters

    Homework Statement Let γ be a regular closed curve in Rn. Show that there is a regular homotopy Γ through closed curves with Γ(−, 0) = γ and Γ(−, 1) an arclength parametrization of γ Homework EquationsThe Attempt at a Solution Hey guys, I just posted another question about homotopy but often...
  24. E

    Java Recursively sorting an array of strings w/o aux. parameter

    One of my professor's assignments is proving particularly tricky for me. It reads: "Write the method public static void sort(String[] a) that sorts the array a in increasing order. The method must be a short recursive program. Do not use quicksort or merge sort. It should be a lot...
  25. Ravik Rocha

    MHB General definition of parameter

    I'm reading a very general definition of parameter on this site Parameter definition - Math Insight. I didn't understand why we call the variable $t$ of the curve $\alpha(t)=(\cos t,\sin t)$ a parameter. For me $t$ in this case is a variable too according to the definition of the site I...
  26. binbagsss

    I Solve Null Geodesic: Affine Parameter & Coordinate Time - Q1,Q2,Q3

    I am asked a question about how far a light ray travels, the question is to be solved by solving for the null goedesic. I am given the initial data: the light ray is fired in the ##x## direction at ##t=0##. The relvant coordinates in the question are ##t,x,y,z##, let ##s## be the affine...
  27. ZenSerpent

    Relating Transformer Parameter I2 to V1 (Non-ideal) Updated

    ≪ mod note: thread moved from technical forum so template is missing ≫ Homework Statement Relate secondary current to primary voltage in a single-phase transformer having resistive load for non-ideal situation. Homework Equations KVL, Voltage across resistor and inductor, ac voltage as a sine...
  28. Rahul Shenoy

    Parameter sensitivity analysis for nonlinear system

    I am working on a problem, where I have arrived at the following nonlinear state space equation: dx1/dt = x2; dx2/dt = c11 x1 + c21x2 + c31x3 + c41x4 + c51x1x22; dx3/dt = x4; dx4/dt = c12 x1 + c22x2 + c32x3 + c42x4 + c52x1x22; c11, c21, c31, c41, c51, c12, c22, c32, c42, c52 are all a function...
  29. S

    How to parameterize these surfaces?

    Homework Statement Calculate ##\iint { y+{ z }^{ 2 }ds } ## where the surface is the upper part of a hemisphere with radius a centered at the origin with ##x\ge 0## Homework Equations Parameterizations: ##\sigma =\left< asin\phi cos\theta ,asin\phi sin\theta ,acos\phi \right> ,0\le \phi \le...
  30. Bloopy

    B Doubt regarding Rutherford's Alpha Scattering Experiment and Impact Parameter

    It is mentioned in my Textbook that if alpha-particle has large impact parameter, it gets scattered through small angles and vice versa. I understand that impact parameter is defined as the perpendicular distance between the path of a projectile and the center of the nucleus. I am unsure how...
  31. TheSodesa

    A real parameter guaranteeing subspace invariance

    Homework Statement Let ##A## and ##B## be square matrices, such that ##AB = \alpha BA##. Investigate, with which value of ##\alpha \in \mathbb{R}## the subspace ##N(B)## is ##A##-invariant. Homework Equations If ##S## is a subspace and ##A \in \mathbb{C}^{n \times n}##, we define multiplying...
  32. S

    Scattering angle as a function of impact parameter

    Homework Statement This is the problem 3.34 from Goldstein, 3rd Edition: Consider a truncated repulsive Coulomb potential defined as V=k/r, for r>a and V=k/a, for r<=a. For a total energy E>k/a, obtain expressions for the scattering angle ##\Theta## as a function of ##s/s_0##, where ##s_0##...
  33. B

    A Primitive cell parameter given chemical unit cell info

    Experimentalists usually provide chemical unit cell information including full symmetry (space group) information of the crystal together with coordinates of independent atoms. But this cannot be directly used by ab initio packages, which requires either primitive cell or unit cell information...
  34. throneoo

    I Understanding the curvature parameter k

    1.) According to my understanding, k is a constant in the Robertson-Walker metric and the Friedmann equations. Its value (-1,0 or 1) is determined by observation (e.g. the bending of light) and doesn't change over time, unlike the curvature density parameter ##\Omega_k##. Therefore a strictly...
  35. Kernul

    Line orthogonal to a plane with variable parameter

    Homework Statement I have to find for which values of the real parameter ##b## the following plane is orthogonal to the following line: ##\pi : 5x + (2b - 1)y - (1 + 8b)z + 3 = 0## ##s : \begin{cases} x + z - 4 = 0 \\ x - 3y + z + 2 \end{cases}## Homework EquationsThe Attempt at a Solution For...
  36. Elnur Hajiyev

    A Hubble parameter vs Scale factor's derivative

    How does Hubble parameter and scale factor's derivative differ geometrically? I am reading S. Caroll's GR book. But I cannot get the full representation of these two parameters. On the book, it says How can \dot{H} and \ddot{a} be opposite of each other on the same instance if both are...
  37. V

    A Geodesic defined for a non affine parameter

    The geodesic general condition, i.e. for a non affine parameter, is that the directional covariant derivative is an operator which scales the tangent vector: $$\zeta^{\mu}\nabla_{\mu}\zeta_{\nu}=\eta(\alpha)\zeta_{\nu}$$ I have three related questions. When $$\alpha$$ is an affine parameter...
  38. S

    I What is the purpose of Arc-Length Parameterization?

    My teacher just briefly introduced arc length parameterization and went on to frenet serret frames, without any explanation or motivation. What is the purpose of arc length parameterization? What role does it play in TNB? What is the purpose of TNB frames anyways?
  39. S

    What is the arc-length parameterization for a given vector function?

    Homework Statement Find the arc-length parameterization for r(t)=\left< { e }^{ 2t },{ e }^{ -2t },2\sqrt { 2 } t \right> ,t\ge 0 Homework Equations s(t)=\int { \left| \dot { r } (t) \right| dt } The Attempt at a Solution \dot { r } (t)=\left< { 2e }^{ 2t },-2{ e }^{ -2t },2\sqrt { 2 }...
  40. Kevin McHugh

    I Impact Parameter: Dependence on Scatter & Wave

    Is the impact parameter more dependent on the scattering center, the incoming wave, or both?
  41. S

    Density parameter against scale factor for perfect fluids

    Homework Statement This is a basic cosmology problem. The Friedmann equations are ##\Big( \frac{\dot{a}}{a}\Big)^{2}+\frac{k}{a^{2}}=\frac{8\pi}{3m_{Pl}^{2}}\rho## and ##\Big( \frac{\ddot{a}}{a} \Big) = - \frac{4\pi}{3m_{Pl}^{2}}(\rho + 3p)##. Using the density parameter ##\Omega \equiv...
  42. munirah

    Understanding the Parameters of SU(4) and SU(2)

    Homework Statement Good day, From my reading, SU(4) have 15 parameter and SU(2) has 3 paramater that range differently with certain parameter(rotation angle). And all the parameter is linearly independent to each other. My question are: 1. What the characteristic of each of the parameter? 2...
  43. F

    I Hubble parameter in terms of the scale factor

    From Introduction to Cosmology by Matt Roos, he wanted to derive the Hubble parameter in terms of the scale factor. From the Friedmann's equation, ##\frac{R'^2 + kc^2}{R^2} = \frac{8πG}{3}ρ## The density parameter is ##~Ω(a) = \frac{8πG}{3H_o^2}ρ(a)~## and let ##~Ω_k = \frac{-kc^2}{H_o^2}##...
  44. G

    I Parametrizing a path through spacetime

    It is customary, when discussing a particle's motion through spacetime, to talk about its path x^{\mu}(\lambda) , where x^{\mu} are the the spacetime coordinates of the particle in some frame, and \lambda is some parameter. I have a doubt regarding this parameter. Everywhere I've looked...
  45. myra2016

    Find Null Geodesics with affine parameter

    Homework Statement The metric is given by https://dl.dropboxusercontent.com/u/86990331/metric12334.jpg H is constant; s is an affine parameter, and so r(0)=t(0)=0. Apologise in advance because I'm not very good with LaTex. So I used Word for equations, and upload handwritten attempt at...
  46. J

    I Mandel-Q Parameter and Phonon Statistics

    Hi, I'm struggling to understand how the Mandel-Q parameter (MQ) can be used to evaluate the quantum dynamics of a single trapped ion. A trapped ion has a quantised degree of motional freedom so can be discussed in terms of the phonon. Im studying the dynamics of a trapped ion which is subject...
  47. ChrisVer

    A Signal strength parameter (interpretation)

    How can in general the signal strength parameter ##\mu## be interpreted? I am talking for the parameter defined in Eq.1 here and plots like the Fig.1 here: http://arxiv.org/abs/1507.04548 It says that it's the ratio of the i->H->f of the observed over what's expected by the SM... is the last...
  48. T

    A Regarding the Continous Wavelet Transform 'a' parameter

    Hi there, I've recently been doing some studying into time-frequency analysis. I've covered some of the basic materials regarding the Short-Time Fourier Transform (STFT) along with the concepts of temporal and frequency resolution (along with the uncertainty principle of course). I've now...
  49. T

    MHB How to swap the first and last elements of a vector using a function in C++?

    What i am doing work because i can only get 40 30 30 40 as output? Write a function SwapVectorEnds() that swaps the first and last elements of its vector parameter. Ex: sortVector = {10, 20, 30, 40} becomes {40, 20, 30, 10}. The vector's size may differ from 4. #include <iostream> #include...
  50. H

    I Density Curvature Parameter: Can We Predict?

    If I know the density curvature parameter for today $$ \Omega_{k,0} = \frac{-c^{2}k}{R_{0}H_{0}} $$ then is it possible to surmise what it would be, say, during the matter dominated era $$ \Omega_{k,t} = \frac{-c^{2}k}{R(t)H(t)}$$ ?
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