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defining linear equations in Java

I am trying to implement a paper and I am facing problem while representing linear equations mentioned in the paper. I am using LPsolve (linear problem solver) to solve the equations. But not able to represent some equations in Java so that LPSOLVE can resolve. Anyone with expertise in this please do help me.
paper i am trying to implement is http://www.cs.cmu.edu/~dshahaf/kdd2010-shahaf-guestrin.pdf and equations are mentioned in section 2.2.1

Based on what I can tell, you seem to have trouble figuring out o implementing some functions that would represent how certain mathematical functions work. It doesn't sound like you've run into an error, so I'll write down a few tips I can think of.
First off, check if the functions you are looking for already exist in the basic library by taking a look in the documentation. Maybe it doesn't state it exactly like you want, but perhaps some of the functionality is there.
http://lpsolve.sourceforge.net/5.5/Java/docs/api/
If you can't find everything you want, then you've got two options. One is to program the functions you desire yourself, and the other is to use another fleshed out Java library such as Colt which has many features.
http://dst.lbl.gov/ACSSoftware/colt/

Is there any software for testing sequences for non-randomness in Java?

I looking for a program or library in Java capable of finding non-random properties of a byte sequence. Something when given a huge file, runs some statistical tests and reports if the data show any regularities.
I know three such programs, but not in Java. I tried all of them, but they don't really seem to work for me (which is quite surprising as one of them is by NIST). The oldest of them, diehard, works fine, but it's a bit hard to use.

As some of the commenters have stated, this is really an expert mathematics problem. The simplest explanation I could find for you is:
Run Tests for Non-randomness
Autocorrelation
It's interesting, but as it uses 'heads or tails' to simplify its example, you'll find you need to go much deeper to apply the same theory to encryption / cryptography etc - but it's a good start.

Another approach would be using Fuzzy logic. You can extract fuzzy associative rules from sets of data. Those rules are basically implications in the form:
if A then B, interpreted for example "if 01101 (is present) then 1111 (will follow)"
Googling "fuzzy data mining"/"extracting fuzzy associative rules" should yield you more than enough results.
Your problem domain is quite huge, actually, since this is what data/text mining is all about. That, and statistical & combinatorial analysis, just to name a few.
About a program that does that - take a look at this.

Not so much an answer to your question but to your comment that "any observable pattern is bad". Which got me thinking that randomness wasn't the problem but rather observable patterns, and to tackle this problem surely you need observers. So, in short, just set up a website and crowdsource it.
Some examples of this technique applied to colour naming: http://blog.xkcd.com/2010/05/03/color-survey-results/ and http://www.hpl.hp.com/personal/Nathan_Moroney/color-name-hpl.html

Easiest to code algorithm for Rubik's cube?

What would be a relatively easy algorithm to code in Java for solving a Rubik's cube. Efficiency is also important but a secondary consideration.

Perform random operations until you get the right solution. The easiest algorithm and the least efficient.

The simplest non-trivial algorithm I've found is this one:
http://www.chessandpoker.com/rubiks-cube-solution.html
It doesn't look too hard to code up. The link mentioned in Yannick M.'s answer looks good too, but the solution of 'the cross' step looks like it might be a little more complex to me.
There are a number of open source solver implementations which you might like to take a look at. Here's a Python implementation. This Java applet also includes a solver, and the source code is available. There's also a Javascript solver, also with downloadable source code.
Anthony Gatlin's answer makes an excellent point about the well-suitedness of Prolog for this task. Here's a detailed article about how to write your own Prolog solver. The heuristics it uses are particularly interesting.

Might want to check out: http://peter.stillhq.com/jasmine/rubikscubesolution.html
Has a graphical representation of an algorithm to solve a 3x3x3 Rubik's cube

I understand your question is related to Java, but on a practical note, languages like Prolog are much better suited problems like solving a Rubik's cube. I assume this is probably for a class though and you may have no leeway as to the choice of tool.

You can do it by doing BFS(Breadth-First-Search). I think the implementation is not that hard( It is one of the simplest algorithm under the category of the graph). By doing it with the data structure called queue, what you will really work on is to build a BFS tree and to find a so called shortest path from the given condition to the desire condition. The drawback of this algorithm is that it is not efficient enough( Without any modification, even to solver a 2x2x2 cubic the amount time needed is ~5 minutes). But you can always find some tricks to boost the speed.
To be honest, it is one of the homework of the course called "Introduction of Algorithm" from MIT. Here is the homework's link: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/assignments/MIT6_006F11_ps6.pdf. They have a few libraries to help you to visualize it and to help you avoid unnecessary effort.

For your reference, you can certainly look at this java implementation. -->
Uses two phase algorithm to solve rubik's cube. And have tried this code and it works as well.

One solution is to I guess simultaneously run all possible routes. That does sound stupid but here's the logic - over 99% of possible scrambles will be solvable in under 20 moves. This means that although you cycle through huge numbers of possibilities you are still going to do it eventually. Essentially this would work by having your first step as the scrambled cube. Then you would have new cubes stored in variables for each possible move on that first cube. For each of these new cubes you do the same thing. After each possible move check if it is complete and if so then that is the solution. Here to make sure you have the solution you would need an extra bit of data on each Rubiks cube saying the moves done to get to that stage.

Solving nonlinear equations numerically

I need to solve nonlinear minimization (least residual squares of N unknowns) problems in my Java program. The usual way to solve these is the Levenberg-Marquardt algorithm. I have a couple of questions
Does anybody have experience on the different LM implementations available? There exist slightly different flavors of LM, and I've heard that the exact implementation of the algorithm has a major effect on the its numerical stability. My functions are pretty well-behaved so this will probably not be a problem, but of course I'd like to choose one of the better alternatives. Here are some alternatives I've found:
FPL Statistics Group's Nonlinear Optimization Java Package. This includes a Java translation of the classic Fortran MINPACK routines.
JLAPACK, another Fortran translation.
Optimization Algorithm Toolkit.
Javanumerics.
Some Python implementation. Pure Python would be fine, since it can be compiled to Java with jythonc.
Are there any commonly used heuristics to do the initial guess that LM requires?
In my application I need to set some constraints on the solution, but luckily they are simple: I just require that the solutions (in order to be physical solutions) are nonnegative. Slightly negative solutions are result of measurement inaccuracies in the data, and should obviously be zero. I was thinking to use "regular" LM but iterate so that if some of the unknowns becomes negative, I set it to zero and resolve the rest from that. Real mathematicians will probably laugh at me, but do you think that this could work?
Thanks for any opinions!
Update: This is not rocket science, the number of parameters to solve (N) is at most 5 and the data sets are barely big enough to make solving possible, so I believe Java is quite efficient enough to solve this. And I believe that this problem has been solved numerous times by clever applied mathematicians, so I'm just looking for some ready solution rather than cooking my own. E.g. Scipy.optimize.minpack.leastsq would probably be fine if it was pure Python..

The closer your initial guess is to the solution, the faster you'll converge.
You said it was a non-linear problem. You can do a least squares solution that's linearized. Maybe you can use that solution as a first guess. A few non-linear iterations will tell you something about how good or bad an assumption that is.
Another idea would be trying another optimization algorithm. Genetic and ant colony algorithms can be a good choice if you can run them on many CPUs. They also don't require continuous derivatives, so they're nice if you have discrete, discontinuous data.

You should not use an unconstrained solver if your problem has constraints. For
instance if know that some of your variables must be nonnegative you should tell
this to your solver.
If you are happy to use Scipy, I would recommend scipy.optimize.fmin_l_bfgs_b
You can place simple bounds on your variables with L-BFGS-B.
Note that L-BFGS-B takes a general nonlinear objective function, not just
a nonlinear least-squares problem.

I agree with codehippo; I think that the best way to solve problems with constraints is to use algorithms which are specifically designed to deal with them. The L-BFGS-B algorithm should probably be a good solution in this case.
However, if using python's scipy.optimize.fmin_l_bfgs_b module is not a viable option in your case (because you are using Java), you can try using a library I have written: a Java wrapper for the original Fortran code of the L-BFGS-B algorithm. You can download it from http://www.mini.pw.edu.pl/~mkobos/programs/lbfgsb_wrapper and see if it matches your needs.

The FPL package is quite reliable but has a few quirks (array access starts at 1) due to its very literal interpretation of the old fortran code. The LM method itself is quite reliable if your function is well behaved. A simple way to force non-negative constraints is to use the square of parameters instead of the parameters directly. This can introduce spurious solutions but for simple models, these solutions are easy to screen out.
There is code available for a "constrained" LM method. Look here http://www.physics.wisc.edu/~craigm/idl/fitting.html for mpfit. There is a python (relies on Numeric unfortunately) and a C version. The LM method is around 1500 lines of code, so you might be inclined to port the C to Java. In fact, the "constrained" LM method is not much different than the method you envisioned. In mpfit, the code adjusts the step size relative to bounds on the variables. I've had good results with mpfit as well.
I don't have that much experience with BFGS, but the code is much more complex and I've never been clear on the licensing of the code.
Good luck.

I haven't actually used any of those Java libraries so take this with a grain of salt: based on the backends I would probably look at JLAPACK first. I believe LAPACK is the backend of Numpy, which is essentially the standard for doing linear algebra/mathematical manipulations in Python. At least, you definitely should use a well-optimized C or Fortran library rather than pure Java, because for large data sets these kinds of tasks can become extremely time-consuming.
For creating the initial guess, it really depends on what kind of function you're trying to fit (and what kind of data you have). Basically, just look for some relatively quick (probably O(N) or better) computation that will give an approximate value for the parameter you want. (I recently did this with a Gaussian distribution in Numpy and I estimated the mean as just average(values, weights = counts) - that is, a weighted average of the counts in the histogram, which was the true mean of the data set. It wasn't the exact center of the peak I was looking for, but it got close enough, and the algorithm went the rest of the way.)
As for keeping the constraints positive, your method seems reasonable. Since you're writing a program to do the work, maybe just make a boolean flag that lets you easily enable or disable the "force-non-negative" behavior, and run it both ways for comparison. Only if you get a large discrepancy (or if one version of the algorithm takes unreasonably long), it might be something to worry about. (And REAL mathematicians would do least-squares minimization analytically, from scratch ;-P so I think you're the one who can laugh at them.... kidding. Maybe.)

Good 15 minute Java question to ask recent college graduate [closed]

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When interviewing college coops/interns or recent graduates it helps to have a Java programming question that they can do on a white board in 15 minutes. Does anyone have examples of good questions like this? A C++ question I was once asked in an interview was to write a string to integer function which is along the lines of the level of question I am looking for examples of.

Is there any reason why it has to be on a whiteboard? Personally, I'd rather sit them in front of a keyboard and have them write some code. Our test used to be a simple 100 (IIRC) line Swing text editor. We then broke it a few simple ways, some making the code not compile and some a little more subtle, and gave the candidates half and hour and a list of problems to fix.
Even if you can't have them do anything hands on make sure that you do give them some explicitly technical questions. In another round of interviews there were a surprising number of recent graduates who were just buzzword-spouting IDE-jockeys, so they could look OKish waving their hands around in front of a whiteboard talking about Enterprise-this and SOA-that, but when given a simple Java fundamentals multiple choice exam asking things about what final and protected meant did horrifyingly badly.

I've always thought that algorithmic questions should be language agnostic. If you want to test the java level of a student, focus on the language: its keywords (from common one like static to more exotic one, like volatile), generics, overloading, boxing/unboxing of variable, standard libraries.

Some stuff that has showed up on SO:
IsPalindrome(string s)
ReverseWordsInString(string s): "I know java" --> "java know I"
Other stuff that springs to mind:
multiply a Vector with a Matrix (can this be done OO-Style?)
echo (yes, a simple clone of the unix tool)
cat (15 min should be enough, should weed out the clueless)
a simple container for ints. Like ArrayList. Bonus question: Generic?

Write a function to swap variable values using pointers (Really poor ones will fall for this)
Write a program to find the distance between two points in the XY plane. Make use of a class to store the points.
Demonstrate the use of polymorphism in java using as simple program.
Write a program to print the first n prime numbers.
Write a program to replace a string in a file with another.

If you don't know what questions to ask them, then may be you are not the right one to interview them in Java. With all due respect, I hate when people ask me questions in interviews which they themselves don't know answers for. Answers for most of the questions can be found online by googling in a few secs. If someone has experience in Java, they will definitely know Abstract class, interface etc as they are the core building blocks. If he/she does not know 'volatile' keyword - big deal.

I agree with Nicolas in regards to separating the algorithmic questions from the actual language questions.
One thing that you might want to consider is giving them a couple simple algorithm questions that they can write up the pseudo code for on the white board (ex. "Explain to me the Bubble sort and show me the pseudo code for it."
Then once they have demonstrated their algorithmic knowledge you can move on to the Java questions. Since some people work better in front of a computer than in front of the whiteboard, I would give them something simple, but leveraging their knowledge of Java, that they can implement in 30 minutes or so in using the same IDE that you are using at the company. This way if they claim to know the IDE you can also get an idea of how well they know it.

Write a function that merges two sorted lists -- stopping at limit. Look for the easy optimizations and correct boundary checks / sublist calls. Tell them T implements compareTo.
public List<T> merge(List<T> one, List<T> two, int limit)
Write a function that returns true if any two integers in the array sum to the given sum. Have them try to do better than n squared using some sort of set or data structure.
public boolean containsSum(int[] nums, int sum)

I would avoid asking them questions that would have been covered in their undergrad classes. I would be more curious about their ability to apply everything they've learned to solve complex technical problems. If your business has a specific need for an IT solution you could use that as a starting point. You could ask the candidate what technologies they would use and the pros and cons of using those technologies versus alternate technologies. As the discussion progresses you could get a feel for their technical skills, problem solving skills, interpersonal skills, etc. I think it is important to avoid coaching them, even in awkward moments. This is important to weed out the BSers.