What is Cubic: Definition and 427 Discussions

CUBIC (abbreviation for “clear, unobstructed brain/body imaging cocktails and computational analysis) is a histology method that allows tissues to be transparent (process called “tissue clearing”). As a result it makes investigation of large biological samples with microscopy easier and faster.
The method was published in 2014 by Etsuo A. Susaki and Hiroki R. Ueda, primarily for use in neurobiology research of brains from model organisms like rodents or small primates. But in upcoming years there were other works published, using CUBIC method on other tissues like lymph nodes or mammary glands. CUBIC can be also combined with CLARITY-based tissue clearing methods.

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  1. Alex299792458

    How many cubic planck lengths are in the observable universe?

    If you take the size of the observable universe can you find out how many cubic plank lengths can fit in the observable universe and it doesn't have to be exact just approximation.Also the math and formulas would be helpful too.
  2. S

    Restricted (Natural) cubic spline - wrong equation?

    My Restricted (Natural) Cubic Spline Equation is Wrong ? I am trying to fit a restricted cubic spline (natural cubic spline) to toy data, attempting to follow Hastie, Tibshirani, Friedman 2nd ed. 5.2.1 p.144-146, Eqs 5.4 and 5.5. Data: Is basically a transposed ‘S’ shape. R-code is: n <© 100 x...
  3. mooncrater

    A cubic equation and its roots

    Homework Statement The question says that : Find the value of ##a## so that the equation $$x^3-6x^2+11x+a-6=0$$ has exactly three integer solitions. Homework Equations IF ##p##,##q##,##r## are the roots of this equation then: ##p+q+r=6## ##pq+pr+rq=11## ##pqr=6-a## The Attempt at a Solution I...
  4. B

    Computing the Inverse of a Cubic Matrix

    Be the matrix A defined by [aijk] (a matrix 2x2x2), do you know how to compute a inverse this cubic matrix?
  5. Matt atkinson

    Statistical Physics: Cubic lattice of two molecules

    Homework Statement A mixture of two substances exists on a cubic lattice of N sites, each of which is occupied by either an A molecule or a B molecule. The number of A molecules is NA and the number of B molecules is NB, such that NA + NB = N. The energy of interaction is k_BT\chi_{AA} between...
  6. P

    Proving a cubic is surjective.

    Homework Statement $$f:\mathbb{R}\rightarrow\mathbb{R}~~\text{where}~~f(x)=x^3+2x^2-x+1$$ Show if f is injective, surjective or bijective. Homework EquationsThe Attempt at a Solution f is obviously not injective (and thus not bijective), one counter example is x=-1 and x=1. I can see from the...
  7. B

    What is the significance of cubic in a cubic spline?

    What is the meaning of "cubic" term in a cubic spline? Is it mean a spline with a degree of 3?
  8. anemone

    MHB Finding $b(a+c)$ Given Roots of a Cubic Equation

    let $a>b>c$ be roots of $\sqrt{2015}x^3-4031x^2+2=0$, find $ b(a+c)$.
  9. G

    Electric potential of a cube of 8 point charges

    Homework Statement Find the Electrostatic potential energy of a cubical configuration of point charges. (One charge on each corner of a cube). Each of the charges is 3.00e and the edge of the cube is 3 cm. Homework Equations U = kqQ/r The Attempt at a Solution I'm pretty sure I understand...
  10. P

    2 Cubic Blocks on a Right Triangle

    Homework Statement A right-triangular wooden block of mass M is at rest on a table, as shown in figure. Two smaller wooden cubes, both with mass m, initially rest on the two sides of the larger block. As all contact surfaces are frictionless, the smaller cubes start sliding down the larger...
  11. anemone

    MHB Solving Cubic Polynomial: Prove Two Distinct Roots

    Let $p,\,q,\,r,\,s,\,t$ be any real numbers and $s\ne 0$. Prove that the equation $x^3+(p+q+r)x^2+(pq+qr+rp-s^2)x+t=0$ has at least two distinct roots.
  12. anemone

    MHB Can the Roots of a Cubic Equation be Bounded?

    Let $p,\,q,\,r$ be real numbers such that the roots of the cubic equation $x^3+px^2+qx+r=0$ are all real. Prove that these roots are bounded above by $\dfrac{2\sqrt{p^2-3q}-p}{3}$.
  13. C

    MHB Taking cubic with log in the grouping symbols

    Use Logarithms to compute the following, correct to four- accuracy. (In find N from Log N, don't interpolate).26. $$(\log\left({0.007211}\right))^3$$ Let N=$$(\log\left({0.007211}\right))^3$$ Then $\log\left({(\log\left({0.007211}\right))^3}\right)$=$$\log\left({N}\right) $\therefore$...
  14. PcumP_Ravenclaw

    Solution to a complex cubic equations

    Homework Statement Solve the equation ## z^3 + 6z = 20 ## (this was considered by Cardan in Ars magna). Homework Equations Please see the 2nd attachement. The Attempt at a Solution I want to know if my solution is correct because the book (2nd attachment) says that there should only be 3...
  15. PcumP_Ravenclaw

    Understanding Cardano's method of solving Cubic equation

    Dear All, I am trying to understanding Cardano's method to solve the cubic equation. Please first see the reference text that is attached (Alan F. Beardon, Algebra and Geometry). My rough understanding is that we make 2 substitutions (## P1(z - a/3)## and ##P(z - b/z) ## ) to...
  16. J

    A cubic foot is equal 7.48 gallons. How many cubic feet wil

    Homework Statement 2. A cubic foot is equal 7.48 gallons. How many cubic feet will the tank describe in question #6 hold? Homework EquationsThe Attempt at a Solution Tank has a volume of 8000 gallons. 1 feet3 = 7.44 gallons (given) Therefore, 8000 gallon = 8000gallon x...
  17. PcumP_Ravenclaw

    Understanding the method to solve the cubic equation

    Dear All, I am trying to understanding Cardano's method to solve the cubic equation. The reference text is attached (Alan F. Beardon, Algebra and Geometry). My rough understanding is that we make 2 substitutions (## P1(z - a/3) and P(z - b/z) ## ) to simplify the cubic equation...
  18. PcumP_Ravenclaw

    Solving a complex numbered cubic equation

    Homework Statement Solve the equation ## z^3 − z^2 + z − 1 = 0 ## first by inspection, and then by the method described above. where Z is a complex number. (Alan F. Beardon, Algebra and Geometry) The method described above is shown in the attachment. Homework Equations The method is shown in...
  19. U

    Cubic phase modulation of a gaussian beam

    Hi all, I'm reading a paper on light sheet microscopy, i won't go into detail here but they are generating the light sheet by use of an Airy beam. They are using a term i don't understand when describing how the airy beam is generated. Quote "An Airy beam can be generated through the Fourier...
  20. T

    Turn cubic zirconia into glass?

    Can you make glass out of cubic zirconia, like you can with sapphire?
  21. C

    Simplifying Cubic: Find Local Extrema

    I need to find the local extrema of \pi r^2(\frac{16}{(r+.5)^2}-1) which I derived and simplified to \frac{16 \pi r}{(r+.5)^3}=2 \pi r which simplifies to \frac {16 \pi r}{2 \pi r}=(r+.5)^3 The radius cannot be zero, so I simplified 8=(r+.5)^3 I used the binomial theorem and more algebra...
  22. ZetaOfThree

    Young's modulus for cubic Van der Waals crystal

    Homework Statement Calculate the Young’s moduli for Van der Waals solids with sc, bcc, and fcc structures.Homework Equations Definition of Young's Modulus $$Y=\frac{stress}{strain}$$ Total energy due to Van der Waals interaction: $$U_{tot}=\frac{1}{2}N(4 \epsilon) \left( \sum_j{ \left( \frac{...
  23. D

    Finding the zeroes for cubic equation

    Homework Statement Find all zeroes for the function f(x) f(x)=x^3+25xHomework Equations The Attempt at a Solution I tried factoring out x out of it. x(x^2+25) and again to give x[(x+5i)(x-5i)] this would give me the 0,-5i,+5i as the zeroes. Doesn't seem to be right though. Any...
  24. Spinnor

    Cubic lattice, masses and springs, fire little mass at it.

    Suppose I have a cubic lattice of N^3 masses, M, each connected to six nearest neighbors with springs of constant k free to move but at rest. Now fire a single mass, m, with velocity v at surface of the lattice such that no rotation can be imparted to the cubic lattice. Let the fired mass bounce...
  25. P

    Parametric equation of a basic cubic function

    Homework Statement Find a parametric form for the part-cubic curve with equation y = x3, 0 ≤ y ≤ 8; starting point (2, 8), The Attempt at a Solution The question beforehand was the exact same but the starting and ending points reversed. My answer for that was; r(t) = (t, t^3) for t an...
  26. Dethrone

    MHB Calculus involving cubic discriminants

    My question is on this site: https://ca.answers.yahoo.com/question/index?qid=20070217181026AAe29O6 There are two methods to do it, and I do not understand the first one in which the person uses cubic discriminants. A cubic function is $ax^3+bx^2+cx+d=0$, and the function we are trying to find...
  27. Y

    MHB Understanding Cubic Roots of 1: Exploring cis 120k

    Hello I didn't know in which forum to put this... I solved a linear algebra question, and my answer was: {1}^{1/3} which to my understanding is 1. In the book however, they said it is equal to cis 120k k=0,1,2,... where 120 is degrees. I tried taking the complex number 1+0i and turn it into...
  28. gfd43tg

    Cubic interpolation with matrix

    Hello, I am trying to understand the slides in the PDF I posted. I am looking particularly at slides 20-24. I am so confused how the matrices are set up with two separate coefficient conditions. The context of these slides is that we are learning how to interpolate with cubic splines. What...
  29. A

    Cubic approximation multivariable taylor series

    hi everyone , i don't understand these steps for Taylor Expansion , it has used for state space equations the equations are the approximations for sin and cos the equation for Taylor series is ( i don't understand at all ) please help me if you can
  30. Z

    How to Convert .4350 into Cubic Centimeters?

    Hello all: Can someone please convert .4350 (math is not one of my stronger areas) into cubic centimeters for me? If this is not the right forum, please direct me to where i need to be. Thanks, "Z."
  31. anemone

    MHB Cubic Equation Challenge: What is the value of $mn^2+nk^2+km^2$?

    For all real $m,\,n,\,k$ where $m>n>k$, these three real numbers are the roots for the equation $x^3-2x^2-x+1=0$. Evaluate $mn^2+nk^2+km^2$.
  32. D

    Find Cubic Equation from Four Points?

    I am working on finding the area of a solid object. I have 4 points that I need to calculate a cubic equation from. I have tried relentlessly but to no avail I always get the wrong answer. The four points are;(0,2.7) (0.5, 2.9) (1,3.2) (1.9, 3.4) Using excel, the formula should be...
  33. B

    Thermal Energy in 1 cubic meter of air at room temperature

    Homework Statement How much thermal energy was in 1 cubic meter of air at room temperature. Give your answer in Joules. How much kinetic energy does one cubic meter of air have if it were to hit the ground after falling 100 m? Give your answer in Joules. Which has more energy...
  34. G

    MHB Solving Cubic Equations using Origami

    I have to write a research paper on a mathematical topic for my class; I chose the above topic. I understand that a parabola can be formed using a focus and directrix, both created by origami folds, and that Axiom 6 of Origami-Folding (Given two points p1 and p2 and two lines l1 and l2, there...
  35. B

    Finding Solutions to a Cubic Equation with Multiple Roots

    I'm finding it hard to find the solutions to this cubic equation: 1/2 x^3 - 2.025647693*10^14 x^2 + 8.102590772*10^11 x - 8.102590772*10^8 = 0 I'm looking for the smallest real positive solution but no matter what solver I use I keep getting only one root (the one of order of magnitude...
  36. M

    Problem of solving the cubic function

    Guys, I may need your help. There is a question saying that how to solve the cubic function in general form, which means that y=ax^3+bx^2+cx+d. How do you guys solve for x? To be honest, I have no idea of this question. Probably, it uses the same way as the quartic function. Thanks!
  37. maistral

    Cubic EoS - only VAPOR root is converging o_o

    Hello. I would like to inquire as to how to deal with the said topic title. I'm trying to generate a VLE graph for ethylene oxide-water. While I know that EO will quickly vaporize since the boiling point of EO is quite low, I'm still trying to generate a VLE using SRK. So while the vapor...
  38. anemone

    MHB What is the value of the sum of reciprocals of the roots in a cubic equation?

    If $p,\,q,\,r$ are roots of the equation $x^3+ax^2-4x+3=0$, find the value of $\dfrac{1}{p^2}+\dfrac{1}{q^2}+\dfrac{1}{r^2}$ in terms of $a$.
  39. G

    Convergence of 10^-2^n. Linear, quadratic, cubic, quartic, hectic

    Homework Statement Show that the sequence {(p_{n})}^{∞}_{n=0}=10^{-2^{n}} converges quadratically to 0. Homework Equations \stackrel{limit}{_{n→∞}}\frac{|p_{n+1}-p|}{|p_{n}-p|^{α}}=λ where α is order of convergence; α=1 implies linear convergence, α=2 implies quadratic convergence, and so...
  40. O

    How can I find the zeros to this cubic equation?

    4x^3 + 8x^2 + 41x + 37
  41. P

    MHB Solving a Cubic: Help Appreciated!

    I'm trying to solve the cubic: 2t^3=5t-11t^2 Been stuck on this for awhile. Any help is appreciated. First I took everything over to one side, so.. 2t^3-5t+11t^2 then set it to zero 2t^3-5t+11t^2=0 then didivded by t..so t(2t^2-5+11t) Then I tried multiplying 11 by 2 which =22 but 22 and 5...
  42. C

    MHB Cubic Transformations - Graph shown is best represented by the equation:

    I am confused about using horizontal transformations such as f(x+a) and f(x-a) to interpret these graphs.
  43. T

    Interpreting Complex Solutions in Cubic Bezier Curve Problems

    Hello. I have a program that, given a value for (x), needs to find the corresponding y-value along a cubic Bezier curve. So long as the Bezier does not switch direction in (x), there is always one, and only one, value of (y) for every value of (x). In solving for (y), I discovered that...
  44. A

    Surface energy simple cubic crystal

    I want to calculate the surface energy for the (001) plane in a simple cubic lattice. My idea is this: When I cleave a simple cubic crystal I create 2 surfaces each sharing an amount of broken bonds. I want to find the amount of broken bonds per area, because I can associate an energy with...
  45. evinda

    MHB Interpolation with cubic splines

    Hello! :) I am looking at the proof of this theorem: Let $f \in C^{1}([a,b]),P:a=x_{0}<x_{1}<...<x_{n}=b $ uniform partition of $[a,b]$.Then there is exactly one function $s \in S_{3}(P)$ so that $s(x_{i})=f(x_{i}),i=0,...,n$ and $s,s',s''$ continuous at...
  46. S

    Which way does the magnetism of the cubic iron struture point?

    If you apply a field to iron the various domains move around, are the individual atoms of the FCC or BCC iron aligning with the field or does the unit cube tend to have an overall orientation which moves? If so then how would you know how the unit cubes are aligned relative to their poles...
  47. S

    Coefficient Matrix Of Cubic Spline Interpolation.

    Homework Statement I'm trying to derive the coefficient matrix (a) of a parabolically terminated cubic spline. This is the matrix of coefficients ##a_i \rightarrow a_n## where n is the number of data points provided. With this matrix you can find all the other coefficients (b and c) that...
  48. Seydlitz

    Finding trigonometric solution to a cubic equation using computer

    Hello, Homework Statement I get this question from Mathematical Methods by Boas page 74 problem 25. The question states: "Use a computer to find the three solutions of the equation ##x^3-3x-1=0##. Find a way to show that the solutions can be written as ##2cos(\frac{\pi}{9})##...
  49. D

    Discriminant of cubic equation in terms of coefficients

    1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...
  50. F

    Efficiently Solving a Cubic Equation Using Synthetic Division

    Homework Statement Find the real solutions of x^3+6x^2-8x+1 Homework Equations quadraticThe Attempt at a Solution First I tried simple numbers starting with 1 and found that +1 was a solution and therefore I could write x^3+6x^2-8x+1=(x-1)(Ax^2+Bx+C) \\ x^3+6x^2-8x+1=Ax^3+Bx^2+Cx-Ax^2-Bx-C...
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