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Is there a good option for creation of custom branching rules in branch-and-bound for MILPs in Python?

Basically, I want to recreate the conceptual results from the paper "Learning to Branch in Mixed Integer Programming" by Khalil, et al, at the same time avoiding, if possible:
1)The necessity of obtaining an academic license for CPLEX (which was used in the paper) or similar serious commercial solver
2)The necessity of using C based API. This is not a strict requirement, but Python has the benefit of having good and very accessible ML libraries, which seems like a great advantage for this specific goal
I am aware, that there is a great number of open source Python based MILP solvers, but a lot of them focus on the end-to-end solution of relatively simple problems in their presentation and, if we also consider, that a lot of them (if not all) hook up to other C based solvers, it is highly non-obvious to judge, which ones actually have needed customization potential.
So, if anyone has more in-depth experience with trying to customize Python solvers for their highly specific needs, I would appreciate the advice.

I'm afraid you will hit a roadblock at some point there. It's really hard to do that without doing C/C++ work (imho).
Python-way
I only know three projects with some low-level functionality (and it's still hard to say if those fit your needs).
https://github.com/coin-or/python-mip
relatively new
promises interactive cut-gen
has a chapter Developing Customized Branch-&-Cut algorithms
but i'm not sure if there is enough freedom for your task (seems to focus on cuts for now)
build around open-source solver Cbc/Clp (besides Gurobi)
https://github.com/coin-or/CyLP
not much develeopment for years now
the whole python-3 dev was sad (see issues; pull-request not processed for years; it's a resource problem: the maintainers are nice people!)
was designed to research pivoting
but it also says: For example, you may
.. define cut generators, branch-and-bound strategies
hard to see how to achieve what you look for except for abstract LP-relax - fix - resolve
might be hard to control specifics (warm-start vs. hot-start)
build around open-source Cbc/Clp
https://github.com/SCIP-Interfaces/PySCIPOpt
basic docs show more high-level usage
but it's internal code at least has entries for branchexeclp and co.
maybe it's ready to use (maybe not)
raw list of interface classes
as those things (maybe) wrap the original C-API, there is a lot of good documentation in the parent-project!
build around open-source solver SCIP
easier to grab the solver in academic setting, but by no means free (i'm not a lawyer and won't try to find the right words)
at least one developer of it is active on StackOverflow
Alternative: C++
If trying to get full-control; which might be needed, with minimal need for understanding the underlying solver in all it's details, you probably want to use C/C++ within Coin OSI. Sadly the Cbc part is unmaintained, but depending on your exact task, you might only need Clp for example.
Alternative: Julia
I did not follow the recent developments there, but the language did have a strong early focus on Mathematical Optimization (driven by a big group of people) surpassing python even in it's early days (imho!).
But i'm not sure if MathOptInterface is fine-grained enough for your task.

ABM under python with advanced visualization

sorry if this all seem nooby and unclear, but I'm currently learning Netlogo to model agent-based collective behavior and would love to hear some advice on alternative software choices. My main thing is that I'd very much like to take advantage of PyCuda since, from what I understand, it enables parallel computation. However, does that mean I still have to write the numerical script in some other environment and implement the visuals in yet another one???
If so, my questions are:
What numerical package should I use? PyEvolve, DEAP, or something else? It appears that PyEvolve is no longer being developed and DEAP is just a wrapper on the outdated(?) EAP.
Graphic-wise, I find mayavi2 and vtk promising. The problem is, none of the numerical package seems to bind to these readily. Is there no better alternative than to save the numerical output to datafile and feed them into, say, mayavi2?
Another option is to generate the data via Netlogo and feed them into a graphing package from (2). Is there any disadvantage to doing this?
Thank you so much for shedding light on this confusion.

You almost certainly do not want to use CUDA unless you are running into a significant performance problem. In general CUDA is best used for solving floating point linear algebra problems. If you are looking for a framework built around parallel computations, I'd look towards OpenCL which can take advantage of GPUs if needed..
In terms of visualization, I'd strongly suggest targeting a a specific data interchange format and then letting some other program do that rendering for you. The only reason I'd use something like VTK is if for some reason you need more control over the visualization process or you are looking for a real time solution.

Probably the best choice for visualization would be to use an intermediate format and do it in another program. But for performance, i'd rather configure a JVM for a cluster and run NetLogo on it. I've not tried it yet but i'm thinking seriously to try NetLogo on a Beowulf style cluster.
BTW, there is an ABM platform called Repast that is said to have Python interface if you're planning to implement your code in Python.

Nash equilibrium in Python

Is there a Python library out there that solves for the Nash equilibrium of two-person zero-games? I know the solution can be written down in terms of linear constraints and, in theory, scipy should be able to optimize it. However, for two-person zero-games the solution is exact and unique, but some of the solvers fail to converge for certain problems.
Rather than listing any of the libraries on Linear programing on the Python website, I would like to know what library would be most effective in terms of ease of use and speed.

Raymond Hettinger wrote a recipe for solving zero-sum payoff matrices. It should serve your purposes alright.
As for a more general library for solving game theory, there's nothing specifically designed for that. But, like you said, scipy can tackle optimization problems like this. You might be able to do something with GarlicSim, which claims to be for "any kind of simulation: Physics, game theory..." but I've never used it before so I can't recommend it.

There is Gambit, which is a little difficult to set up, but has a python API.

I've just started putting together some game theory python code: http://drvinceknight.github.com/Gamepy/
There's code which:
solves matching games,
calculates shapley values in cooperative games,
runs agent based simulations to identify emergent behaviour in normal form games,
(clumsily - my python foo is still growing) uses the lrs library (written in C: http://cgm.cs.mcgill.ca/~avis/C/lrs.html) to calculate the solutions to normal form games (this is I believe what you want).
The code is all available on github and that site (the first link at the beginning of this answer) explains how the code works and gives user examples.
You might also want to check out 'Gambit' which I've never used.

Simulation of molecular dynamics in Python

I am searching for a python package that I can use to simulate molecular dynamics in non-equilibrium situations. I need a setup that can handle a fairly large number of molecules in a primarily kinetic theory manner, and that can handle having solid surfaces present. With regards to the surfaces, I would need to be able to create arbitrary shapes and monitor pressure and other variables resulting from the molecular action. Alternatively, I could add the surface parts myself if I had molecules that could handle it.
Does anyone know of any packages that might be suitable?

Have you considered SimPy? SimPy is a rather generic Discrete Event Simulation package, but could feasibly meet your needs.
Better yet the Molecular Modelling ToolKit (MMTK) seems more specialized...
I have used neither, but this sounds like fun. Python, as a language, seems to be in privileged position for use in simulation software, whereby people can script the specific details of their model while relying on the framework for all the common logic, such as scheduling, visualization, monitoring etc. The unknown is how well such toolkits scale when fed with agent counts commensurate with biology models (BTW, how "big" is that?)

Lampps and gromacs are two well known molecular dynamics codes. These codes both have some python based wrapper stuff, but I am not sure how much functionality the wrappers expose. They may not give you enough control over the simulation.
Google for "GromacsWrapper" or google for "lammps" and "pizza.py"
Digital material and ASE are two molecular dynamics codes that expose a lot of functionality, but last time I looked, they were both fairly specialized. They may not allow you to use the force potentials that you want
Google for "digital material" and "cornell" or google for "ase" and dtu
Note to MJV: Normal MD-codes take one time step at a time, and they move all particles in each time step. Most of the time is spend calculating the total force on each atom. This involves iterating over a list of pairs of neighboring atoms. I think the best idea is to do the force calculation and a few more basics in c++ or fortran and then wrap that functionality in python. (But it could be fun to see how far one can get by using numpy matrices)

The following programs can be used to run MD symulations:
Gromacs
AMBER
charmm
OpenMM
many others...
The following Python packages are useful for preparing and analysing MD trajectories:
MDtraj and the OMNIA ecosystem
MDAnalysis
ProDy
MMTK

Another generic simulations framework is my own GarlicSim. You can try that. I could help you get a simpack up if you're serious about it.

I don't know if that programs does all the features you need but there is avogadro in the kde programs, i think it is extendable and since it is open source you could do anything with it. http://www.kde-apps.org/content/show.php/Avogadro?content=59521
It is really advanced and programmed by a friend of mine

I second MMTK, but take a look at VMD, which is the best MD software I'm aware of, and is Python-scriptable (in addition to Tk). See this for examples and tutorials.

I recommend to use molecular dynamics software to run MD simulations like Gromacs. This software is highly optimized for that particular purpose. You can also run on GPU's and you will be able to run larger systems in less time.
Afterwards, you run only the analysis with python packages using the generated trajectories.
mdtraj
pmx

Machine vision in Python

I would like to perform a few basic machine vision tasks using Python and I'd like to know where I could find tutorials to help me get started.
As far as I know, the only free library for Python that does machine vision is PyCV (which is a wrapper for OpenCV apparently), but I can't find any appropriate tutorials.
My main tasks are to acquire an image from FireWire. Segment the image in different regions. And then perform statistics on each regions to determine pixel area and center of mass.
Previously, I've used Matlab's Image Processing Tootlbox without any problems. The functions I would like to find an equivalent in Python are graythresh, regionprops and gray2ind.
Thanks!

OpenCV is probably your best bet for a library; you have your choice of wrappers for them. I looked at the SWIG wrapper that comes with the standard OpenCV install, but ended up using ctypes-opencv because the memory management seemed cleaner.
They are both very thin wrappers around the C code, so any C references you can find will be applicable to the Python.
OpenCV is huge and not especially well documented, but there are some decent samples included in the samples directory that you can use to get started. A searchable OpenCV API reference is here.
You didn't mention if you were looking for online or print sources, but I have the O'Reilly book and it's quite good (examples in C, but easily translatable).
The FindContours function is a bit similar to regionprops; it will get you a list of the connected components, which you can then inspect to get their info.
For thresholding you can try Threshold. I was sure you could pass a flag to it to use Otsu's method, but it doesn't seem to be listed in the docs there.
I haven't come across specific functions corresponding to gray2ind, but they may be in there.

documentation: A few years ago I used OpenCV wrapped for Python quite a lot. OpenCV is extensively documented, ships with many examples, and there's even a book. The Python wrappers I was using were thin enough so that very little wrapper specific documentation was required (and this is typical for many other wrapped libraries). I imagine that a few minutes looking at an example, like the PyCV unit tests would be all you need, and then you could focus on the OpenCV documentation that suited your needs.
analysis: As for whether there's a better library than OpenCV, my somewhat outdated opinion is that OpenCV is great if you want to do fairly advanced stuff (e.g. object tracking), but it is possibly overkill for your needs. It sounds like scipy ndimage combined with some basic numpy array manipulation might be enough.
acquisition: The options I know of for acquisition are OpenCV, Motmot, or using ctypes to directly interface to the drivers. Of these, I've never used Motmot because I had trouble installing it. The other methods I found fairly straightforward, though I don't remember the details (which is a good thing, since it means it was easy).

I've started a website on this subject: pythonvision.org. It has some tutorials, &c and some links to software. There are more links and tutorials there.

You probably would be well served by SciPy. Here is the introductory tutorial for SciPy. It has a lot of similarities to Matlab. Especially the included matplotlib package, which is explicitly made to emulate the Matlab plotting functions. I don't believe SciPy has equivalents for the functions you mentioned. There are some things which are similar. For example, threshold is a very simple version of graythresh. It doesn't implement "Otsu's" method, it just does a simple threshold, but that might be close enough.
I'm sorry that I don't know of any tutorials which are closer to the task you described. But if you are accustomed to Matlab, and you want to do this in Python, SciPy is a good starting point.

I don't know much about this package Motmot or how it compares to OpenCV, but I have imported and used a class or two from it. Much of the image processing is done via numpy arrays and might be similar enough to how you've used Matlab to meet your needs.

I've acquired image from FW camera using .NET and IronPython. On CPython I would checkout ctypes library, unless you find any library support for grabbing.

Foreword: This book is more for people who want a good hands on introduction into computer or machine vision, even though it covers what the original question asked.
[BOOK]: Programming Computer Vision with Python
At the moment you can download the final draft from the book's website for free as pdf:
http://programmingcomputervision.com/
From the introduction:
The idea behind this book is to give an easily accessible entry point to hands-on
computer vision with enough understanding of the underlying theory and algorithms
to be a foundation for students, researchers and enthusiasts.
What you need to know
Basic programming experience. You need to know how to use an editor and run
scripts, how to structure code as well as basic data types. Familiarity with Python or other scripting style languages like Ruby or Matlab will help.
Basic mathematics. To make full use of the examples it helps if you know about
matrices, vectors, matrix multiplication, the standard mathematical functions
and concepts like derivatives and gradients. Some of the more advanced mathe-
matical examples can be easily skipped.
What you will learn
Hands-on programming with images using Python.
Computer vision techniques behind a wide variety of real-world applications.
Many of the fundamental algorithms and how to implement and apply them your-
self.