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Matplotlib 3d Plot Colorbar Scale

I have a 3d plot with a colorbar and I would like the colorbar's size to scale with the size of the projection, no matter the orientation I select with ax.view_init.
It would also be great if I could get the aspect ratio of the 3d plot to be equal at the same time as well.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.colors
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=90, azim=0)
x = np.arange(3)
X,Y = np.meshgrid(x,x)
Z = np.ones_like(X)
V = np.array([[3,2,2],[1,0,3],[2,1,0]])
norm = matplotlib.colors.Normalize(vmin=0, vmax=3)
ax.plot_surface(X, Y, Z, facecolors=plt.cm.jet(norm(V)), shade=False)
m = cm.ScalarMappable(cmap=plt.cm.jet, norm=norm)
m.set_array([])
plt.colorbar(m)
ax.set_xlabel('x')
ax.set_ylabel('y')
plt.show()
Example code stolen shamelessly from this question

How to set title position inside graph in scatter plot?

MWE:
I would like the title position same as in the graph :
Here is my code :
import matplotlib.pyplot as plt
import numpy as np
import random
fig, ax = plt.subplots()
x = random.sample(range(256),200)
y = random.sample(range(256),200)
cor=np.corrcoef(x,y)
plt.scatter(x,y, color='b', s=5, marker=".")
#plt.scatter(x,y, label='skitscat', color='b', s=5, marker=".")
ax.set_xlim(0,300)
ax.set_ylim(0,300)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Correlation Coefficient: %f'%cor[0][1])
#plt.legend()
fig.savefig('plot.png', dpi=fig.dpi)
#plt.show()
But this gives :
How do I fix this title position?

assign two corresponded value to X and Y axis. notice! to have title inside graph, values should be in (0,1) interval. you can see a sample code here:
import matplotlib. pyplot as plt
A= [2,1,4,5]; B = [3,2,-2,1]
plt.scatter(A,B)
plt.title("title", x=0.9, y=0.9)
plt.xlabel("x-axis")
plt.ylabel("y-axis")
plt.show()

It will be unnecessarily complicated to move the title at some arbitrary position inside the axes.
Instead one would rather create a text at the desired position.
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.random.randint(256,size=200)
y = np.random.randint(256,size=200)
cor=np.corrcoef(x,y)
ax.scatter(x,y, color='b', s=5, marker=".")
ax.set_xlim(0,300)
ax.set_ylim(0,300)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.text(0.9, 0.9, 'Correlation Coefficient: %f'%cor[0][1],
transform=ax.transAxes, ha="right")
plt.show()

No color when I make python scatter color plot using third variable to define color

I try to make colorful scatter plot using third variable to define color. It is simple to use the following code:
plt.scatter(mH, mA, s=1, c=mHc)
plt.colorbar()
plt.show()
But I do not have many choices to modify the frame of the plot. I am trying the following code to make colorful scatter plot, at the same time I try to optimize the frame of the plot:
import numpy as np
import math
from matplotlib import rcParams
import matplotlib.pyplot as plt
from matplotlib.ticker import AutoMinorLocator
fig, ax = plt.subplots()
cax = ax.scatter(mH,mA,s=0.5,c=mHc) ### mH, mA, mHC are the dataset
fig.colorbar(cax)
minor_locator1 = AutoMinorLocator(6)
minor_locator2 = AutoMinorLocator(6)
ax.xaxis.set_minor_locator(minor_locator1)
ax.yaxis.set_minor_locator(minor_locator2)
ax.tick_params('both', length=10, width=2, which='major')
ax.tick_params('both', length=5, width=2, which='minor')
ax.set_xlabel(r'$m_H$')
ax.set_ylabel(r'$m_A$')
ax.set_xticks([300,600,900,1200,1500])
ax.set_yticks([300,600,900,1200,1500])
plt.savefig('mH_mA.png',bbox_inches='tight')
plt.show()
But the plot I got is black-white. It looks like the problem lies in the marker size argument, but I do not have much idea how to correct it. I want to have smaller marker size. Anyone can offer me some idea to approach this issue. Thanks.

size=0.5 is extremely small - probably all you are seeing is the marker outlines. I would suggest you increase the size a bit, and perhaps pass edgecolors="none" to turn off the marker edge stroke:
import numpy as np
from matplotlib import pyplot as plt
n = 10000
x, y = np.random.randn(2, n)
z = -(x**2 + y**2)**0.5
fig, ax = plt.subplots(1, 1)
ax.scatter(x, y, s=5, c=z, cmap="jet", edgecolors="none")
You might also want to experiment with making the points semi-transparent using the alpha= parameter:
ax.scatter(x, y, s=20, c=z, alpha=0.1, cmap="jet", edgecolors="none")
It can be difficult to get scatter plots to look nice when you have such a massive number of overlapping points. I would be tempted to plot your data as a 2D histogram or contour plot instead, or perhaps even a combination of a scatter plot and a contour plot:
density, xe, ye = np.histogram2d(x, y, bins=20, normed=True)
ax.hold(True)
ax.scatter(x, y, s=5, c=z, cmap="jet", edgecolors="none")
ax.contour(0.5*(xe[:-1] + xe[1:]), 0.5*(ye[:-1] + ye[1:]), density,
colors='k')

How to set fontsize of axis label with LaTex symbol on matplotlib/seaborn?

In matplotlib, how can I change the font size of a latex symbol?
I have the following code:
import matplotlib.pyplot as plt
import seaborn as sns
# get x and y from file
plt.plot(x, y, linestyle='--', marker='o', color='b')
plt.xlabel(r'$\alpha$ (distance weighted)', fontsize='large')
plt.ylabel('AUC')
plt.show()
But I get the following graph:
Notice that the $\alpha$ is still small.

To increase the size of the fonts set the desired value to fontsize. One way to mitigate the difference between the "normal" font and the "latex" one is by using \mathrm. The example below shows the behaviour of doing this:
import matplotlib.pyplot as plt
import seaborn as sns
x = np.arange(10)
y = np.random.rand(10)
fig = plt.figure(1, figsize=(10,10))
for i, j in zip(np.arange(4), [10,15,20,30]):
ax = fig.add_subplot(2,2,i+1)
ax.plot(x, y, linestyle='--', marker='o', color='b')
ax.set_xlabel(r'$\mathrm{\alpha \ (distance \ weighted)}$', fontsize=j)
ax.set_ylabel('AUC')
plt.show()

Python plotting 2d data on to 3d axes

I've had a look at matplotlib's examples of 3d plots, but none of these give me what I want to plot, something like:
The plot shows a series of measurements on the y-axis (N) and each measurement has an intensity spectrum (p/2hk_L), i.e. N is fixed for each line you see in the graph. What is the easiest function to use to plot data like this?

Here is a try:
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = np.linspace(-50,50,100)
y = np.arange(25)
X,Y = np.meshgrid(x,y)
Z = np.zeros((len(y),len(x)))
for i in range(len(y)):
damp = (i/float(len(y)))**2
Z[i] = 5*damp*(1 - np.sqrt(np.abs(x/50)))
Z[i] += np.random.uniform(0,.1,len(Z[i]))
ax.plot_surface(X, Y, Z, rstride=1, cstride=1000, color='w', shade=False, lw=.5)
ax.set_zlim(0, 5)
ax.set_xlim(-51, 51)
ax.set_zlabel("Intensity")
ax.view_init(20,-120)
plt.show()