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. A

    Is there an explicit solution to the equation \sqrt{Ax-x^3}+\sqrt{Bx-x^3}=C?

    Solving a cubic... sort of! Hi, Can the equation \sqrt{Ax-x^3}+\sqrt{Bx-x^3}=C be solved explicitly? All of MathLab, Maple and WolframAlpha seem to give an explicit solution but they don't show how they come to it. I'm afraid they may be missing other possible solutions. Thanks,
  2. N

    Discover the Magic of Cubic Splines

    Cubic Splines! It looks like the message i wrote was not allowed because i gave you my excersize as it was. Well now i ' ll post again the picture i have but i don't want to give me the answer , but only a help how to start . Please give some idea , i have only five hours left to give my...
  3. F

    (2,0,0) plane for simple cubic lattice

    Hi All, Does the plane of miller index (2,0,0) exist in simple cubic lattice? It is easy to understand that (1,0,0) plane exist. But for (2,0,0) plane, I feel confused. If (2,0,0) plane exists, the plane intersect with the x-axis at 1/2*a, if a is the lattice constant; and the plane is...
  4. B

    Another form of cubic folium equation

    Hello, I am looking for a way to express the equation of folium x3 + y3 = 3axy into x + y =\frac{3a}{\frac{x}{y}+\frac{y}{x}-1} thanks bluemoon2188
  5. M

    Solving Cubic Equation: x^3 + 27 = 0 | Quadratic Formula | Complex Solutions

    Homework Statement x^3 +27 =0 Homework Equations \begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array} The Attempt at a Solution (x +3)(x^2 -3x +9)= 0 (x +3) = 0, x = -3 (x^2 -3x +9)= 0 Here is where...
  6. M

    Real and complex Roots of A cubic equation

    Homework Statement Find the roots of y-y^3=1 Homework Equations The Attempt at a Solution Factor theorem doesn't help in this equation. Found from Wikipedia, a very complex formula is needed to solve cubic eq. Can someone show me the steps to find the root? Thank you ^^
  7. A

    Simplest Way of finding zeros of cubic eq when rational roots test fails

    Homework Statement Find the zeros of the cubic equation: y = x^3 -9x^2 + 15x + 30 How do we find the zeros of this? In this case, subbing in x-values that will make it equal 0 does not work.
  8. T

    Factorising a Cubic: An Easy Way?

    I am attempting to derive the formula for the variance of a continuous uniform distribution where f(x) = \left\{ \begin{array}{ll} \frac{1}{b-a} & \mbox{$a \leq $x$ \leq b$};\\ 0 & \mbox{otherwise}.\end{array} \right. I was successful, but only after using Wolfram Alpha to...
  9. A

    How are cubic equations converted into this form?

    y = a(x-b)^3 + c I'm not sure what it's called, my book doesn't mention on how it's derived.
  10. P

    Global error data set & mathematica cubic spline

    Hey, I have a data set (electronic device output) which we need to find the best fit via approximation and interpolation. I've done a cubic least squares, then found the local error for all the given points (actual - approximate). We need to also find the global errors for the methods we choose...
  11. E

    Probabilities Inside Cubic 3D Infinite Well

    Homework Statement An electron is trapped in a cubic 3D infinite well. In the states (nx,ny,nz) = (a)(2,1,1), (b)(1,2,1) (c)(1,1,2), what is the probability of finding the electron in the region (0 ≤ x ≤ L, 1/3L ≤ y ≤ 2/3L, 0 ≤ z ≤ L)? Homework Equations My normalized wave function in the...
  12. J

    Heat Exchange Between Air & Water: 1 Cubic Meter Each

    If i have let's say have 1 cubic meter of water at a temperature of 23 degree, in a closest system connected to a 1 cubic meter of air of 20 degree, how long time does it take for the heat to balance out, the surface between the two a 1 square meter.
  13. M

    Miller Indices of Simple Cubic Lattice

    I'm trying to get my head around indexing x-ray diffraction patterns and this thought experiment stumps me. Let's say I have a crystal with a simple cubic lattice structure: http://ecee.colorado.edu/~bart/book/sc.gif I align a narrow x-ray beam incident on the crystal so that the x-ray...
  14. P

    Need a review on how to factor cubic polynomials

    So long story short, I have a friend who wants me to help her learn how to factor cubic polynomials. Normally I would just fess up and say I don't remember but it's something I'd like to review myself and lessons online aren't the clearest. Here's one of the questions: 2x3+3x2-8x+3 I...
  15. T

    Find the cubic polynomial

    Question: Find the cubic polynomial, which take the following values: y(0) = 1, y(1)=0, y(2)=1 and y(3)=10 Hence obtain y(4).
  16. P

    Calculating Integral of Cubic Lattice Sum

    If I have cubic lattice and need to calculate sum \frac{1}{N}\sum_{\vec{k}}\frac{1}{\sqrt{1-\gamma^2(\vec{k})}}coth\frac{6SI\sqrt{1-\gamma^2(\vec{k})}}{2T} where \gamma(\vec{k})=\frac{1}{3}(cosk_xa+cosk_ya+cosk_za) I must go from sum to integral...
  17. A

    Finding intercepts of a cubic function

    Hey guys, new member here. I've decided to join this forum since I am a current Calculus student, and will be taking Physics next semester. Anyways, I do have a question about one of my homework problems. Homework Statement Consider the function: f(x) = -2x^(3) + 6x^(2) - 3. Find its...
  18. M

    Space group for cubic structure

    Hello all, I am having trouble figuring out the space group for a cubic structure having A atoms at 000 and B atoms at 1/2 1/2 0, 1/2 0 1/2 & 0 1/2 1/2. Now, I know that it is Pm3m, but what is confusing me is why is there not a 4 fold axis at the first m, thus, giving you a P(4/m)3m...
  19. A

    Elephant toothpaste per cubic meter

    what is the best formula for elephants toothpaste not using yeast using potassium iodine and hydrogen-peroxide(30%) and of course soap. how much reactants would i need to fill let's say... 100m cubed (im not going to do that much but its easier to work with) * how long would the reaction take...
  20. J

    Cantilever beam: cubic stiffness question

    Hello. Supose that we have a cantilever beam. For a small force P applied at the free side of the beam, we can find an expression for the maximum deflection: \delta=\frac{P l^3}{3 E I} If we want to use this beam as a string, we can find its equivalent stiffnes noting that P=K_{eq} \delta, so...
  21. M

    Planes of simple cubic structure and X-ray diffraction experiment

    In the book of the Dr. Ronald Askeland the problem about x-ray diffraction use the next planes indices to calculate the interplanar distance, but I don't understand why to use such planes indices? Are these planes all of planes in a cubic structure? (111) (200) (211)...
  22. QuarkCharmer

    Finding the Inverse of a Cubic Polynomial

    Homework Statement Find the inverse of the function. f(x)=2x^{3}+5Homework Equations Possibly the quadratic equation.The Attempt at a Solutionf(x)=2x^{3}+5 y=2x^{3}+5 -2x^{3}=-y+5 x^{3}= \frac{-y+5}{-2} x= \pm\sqrt[3]{\frac{-y+5}{-2}} y= \pm\sqrt[3]{\frac{-x+5}{-2}}So the solution is two...
  23. B

    Why is the Second to Last Sample Off Scale in My Cubic Spline Boundary Problem?

    Hi All, I am trying to convert a file that has three arrays of 528 samples into three arrays of 301. The first is log spaced frequency points the second is the impedance values at each frequency and the last is phase values. I have the routines spline and splint. My problem is the the second...
  24. r-soy

    One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg at 25°C. Determine

    One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg at 25°C. Determine the mass of 3.5 m3 of wa One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg at 25°C. Determine the mass of 3.5 m3 of water at 25°C. How i can solve this question ?
  25. T

    Determing t in a Cubic Bezier equation

    Hi Everyone, so I am having a small situation with cubic bezier curves and I must be missing something. I have generated a program in c# that allows a user to create curves over time and to edit them with control points as they see fit. I have gotten to the point where I am trying to export the...
  26. M

    Finding Roots of cubic equation

    Homework Statement Consider the motion of particle moving on the inside surface of a smooth cone of half-angle α, subject to the gravitational force. Although this problem does not involve a central force, certain aspects of the motion are the same as for a central-force motion. Show that the...
  27. J

    Factoring cubic polynomial help

    Homework Statement This is probably an easy question, but using the rational zero theorem I have not found any roots for this cubic polynomial. Factor the Following 6x^3-37x^2-8x+12 Homework Equations The Attempt at a Solution I have used all my knowledge of factoring and...
  28. G

    Solve cubic equations using neusis

    In an essence, using normal straightedge and compass construction, we can add, subtract, multiply, divide and find a square root. This means that we can find the real roots of a quadratic equation with rational coefficients because the quadratic formula consists of only these operations. The...
  29. C

    Linear Algebra - Cubic Equation from Given Points

    Linear Algebra -- Cubic Equation from Given Points Homework Statement Find the equation to the third polynomial that flows through the given points: (0,1); (1,0); (-1,0); (2, -15). Homework Equations f(t) = a + bt + ct^2 + dt^4 Need to find a, b, c, and d. The Attempt at a...
  30. R

    Finding Solutions to a Quartic Equation

    Homework Statement I've been given the following quartic equation in a question: x = (1 + 2a + a^2)x - (2a + 3a^2 + a^3)x^2 + (2a^2 + 2a^3)x^3 - a^3x^4 and need to show that two of the solutions (that aren't 0 and 1) can be given by: x= \frac{(2+a) \pm \sqrt{a^2 - 4}}{2a} 2. The attempt...
  31. R

    Standard cubic meter per minute

    gas flow rate has units of "sccm" that standard cubic centimeter per minute. what does "standard" means here? how is derived? if there is gas flow of 1 sccm then how much gas flows in cubic meters?
  32. N

    Finding the Cubic Spline for f(x) = sin(x^2) with M and S_i Formulas

    find the cubic spine of f(x)=sin(x^2) i have two formulas one for the M's the other for the sums S_i but i need a table of points to know what indexes to put and when here i don have it?
  33. J

    Finding a tangent in a Cubic Function

    Homework Statement My cubic function is y=(x-6)(x-1)(x-9) or y=x^3-16x^2+69x-54 I need to find the tangent at the point x=2.5Homework Equations The Attempt at a Solution All that I have managed to do is work out the y value for x=2.5, that is y=34.125 Please help someone!
  34. O

    Cubic equations with independent variables

    Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...
  35. O

    Solving a Cubic Equation with 2 Variables

    Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the equation are dependent on x only, except M is dependent on x and t. En, Ep, N and h are constants. i know...
  36. W

    How do I solve a cubic ODE using a series solution?

    Homework Statement Find the solution to the ODE via the power series: y = \Sigma_{i=0} a_j x^{2j + m} Homework Equations y' - y^3 = 0 The Attempt at a Solution I get \Sigma_{i=0} a_j (2j+m) x^{2j+m-1} - \Sigma_{i=0} (a_j)^3 x^{3(2j + m)} = 0 I don't know how to deal with the cubic...
  37. C

    Could a Cubic Block Stop the BP Spill?

    CUBIC BLOCK Make 10 ft sided cubic block (1000 cu ft) of concrete, rebar, and sand, on a barge. Then use 2 barges and pulleys perhaps to drop such block 2000 ft (10 secs?), which might penetrate 100 ft(?) into muck. Drop it slightly off target, so that sub-mud surface conduit collapses shut...
  38. C

    Why is E3 zero for cubic symmetry?

    The total electric field is given as Etotal = E0 +E1 +E2 +E3 Where E0 is the applied field, E1 is the depolarization, E2 is caused by polarization of a hypothetical sphere while E3 is the one dependent on lattice geometry... How come E3 is zero for cubic symmetry? Can I picture this as...
  39. S

    Seperation of variables, infinite cubic well

    Suppose one is to find the stationary states of a particle in an infinite cubic well. Inside the box the time independent SE is: - \frac{\hbar}{2m} \big( \frac{\partial ^2 \psi}{\partial x ^2 } + \frac{\partial ^2 \psi}{\partial z ^2 } + \frac{\partial ^2 \psi}{\partial z ^2 } \big)= E\psi...
  40. C

    How Do You Solve Complex Roots in a Cubic Equation?

    I am feeling stupid over this one but I cannot remember how to solve it. I have the following cubic equation: 4x^3 - 32x = -12 I get the solution of x = -3 but not the other two. I initially had it factored as: 4x(x^2 - 8) = -12 Did 4x = -12, got x = -3 But then I could not get the other two...
  41. D

    Calculating Atom/Cell Volume in Simple Cubic Crystal

    What is the volume of atom/volume of cell?
  42. A

    MATLAB MATLAB Cubic Spline Interpolation

    Hey guys, I got this assignment last week and have been doing every bit of research I can to try to figure out what I am supposed to be doing. I have found a lot of cubic spline interpolation (csi) write-ups including one on here but we don't have a book in this class to help understand how to...
  43. T

    Tight binding in cubic crystals

    \phiHi all, I would like to make band structure calculations with tight binding method and I start reading about this method from Ashcroft - Mermin, Chapter 10: The Tight Binding Method and try to solve the problems at the and of the chapter. In problem 2 a. As a consequence of cubic...
  44. D

    Is there a general formula for solving cubic equations?

    Hi, I've been trying to solve this equation for hours no, hoping somebody here can help. I have the equation: -2m2w3 + 15Bmw2 - 27B2 = 0 where m, B are unknown constants and I'm trying to solve for w. Is there a general formula for solving cubic equations? Thanks in advance.
  45. P

    Matrices of simple face and cubic centered cubic lattice

    S= \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} for simple cubic I= \begin{bmatrix} -\frac{a}{2} & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & -\frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & -\frac{a}{2} \end{bmatrix}...
  46. S

    Cubic Formula: Step-by-Step Solution for Finding x

    How would you go about solving ax^3+bx^2+cd+d=0 for x. Please step by step! Thanks!
  47. L

    Finding x-intercept of cubic functions? / Factoring cubic functions

    Homework Statement My problem is that whenever I have to use cubic functions - whether it's finding the roots (when dy/dx kis a cubic function) or finding the x-intercepts... With quadratic functions I usually use the quadratic formula. I try to figure out how to factor these equations in my...
  48. D

    How can I factor a cubic equation by hand to find the x-intercepts?

    This is not a homework question, per se, because I'm not a student. But it is a problem I found in a book. Actually, the problem doesn't involve what I'm going to ask, but it did present an opportunity for me to explore the subject. I have the graph of f(x)=x^{3}+3x^{2}-9x+3. I know the x...
  49. I

    Cubic Equation Roots: Solving for α and β | p Value Calculation

    Homework Statement The equation x3 − 3x2 + px + 4 = 0, where p is a constant, has roots α −β , α and α + β , where β > 0. (a) Find the values of α and β . (b) Find the value of p. how do i start off? all i know is that sigma a= -b/a and ab= c/a and ab(gamma) = -d/a . Would this be one of...
  50. C

    Factoring Cubic Polynomials/Function

    Homework Statement Doing my vector mechanics dynamics homework and I cannot believe I am stuck on this part. trying to factor t^3 - 6t^2-36t - 40 = 0 Homework Equations The Attempt at a Solution I honestly do not remember where to begin. I remember there is a formula for perfect...
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