I'm unclear about legal status of utilizing an algorithm from a published academic paper. Is there an implicit patent over that material? How about open source applications? Would it be ok to implement that algorithm in an open source app, with one of free software licenses?
Let's say I have access to paper A which describes algorithm B. How can I determine if I can use algorithm B in my commercial closed-source app C or open source app D? Is the answer always "no"? Is there an expiration date?
There's no such thing as an "implicit patent".
Unfortunately, I'd think you need to evaluate the IP restrictions for each paper.
One of the more famous situations where the algorithm described in an academic paper was ultimately encumbered by a patent as the RSA asymetric encryption algorithm. A paper, "On digital signatures and public-key cryptosystems", was published in an ACM journal in 1977 describing the algorithm, a patent was awarded in 1983 (US Patent 4,405,829).
I have not read the paper, so I don't know if the application for a patent was mentioned - I do know that the algorithm was rather widely implemented, then when the patent was awarded MIT/RSADSI started enforcing it. The patent became a rather big issue with PGP, for example. MIT/RSADSI ultimately permitted free use of the patent for non-commercial use, I believe.
A similar situation occured with the LZW compression: http://en.wikipedia.org/wiki/GIF#Unisys_and_LZW_patent_enforcement
As Michael said, there's no such thing as an implicit patent.
Generally, when an algorithm or any other research is published, the authors want to put it out into the world for other people to use. If you have access to a published paper which describes some algorithm, it's probably going to be okay for you to use it in any program you might create. However, some algorithms may be patented by their inventors before being published, and in that case if you want to use the algorithm you would have to come to some arrangement with the patent holder, regardless of whether your application is open-source or not. Basically to be safe, you need to check the specific restrictions on that algorithm. (The type of people who publish papers about algorithms are often more likely to let you use their algorithms if your application is open source than if it's proprietary.)
This is what happened with GIF, the compression algorithm was published openly but without mentioning that it had been patented.
Even if the authors of the paper claim not to have patented it - there is no guarantee that another algorithm hasn't already been patented and a court might decide that it covers that work.
Remember as well that inventing it yourself doesn't protect you from patents - you can invent an algorithm that you have never seen in print and later discover it's covered by some patent.
AFAIK, Having something published in a publicly-accessible way (e.g., academic paper) actually eliminates the possibility of a patent in Europe. In the US, there is a one year grace period from first publication to obtain a patent. Students and professors usually figure out the potential, and they apply to the university's technology transfer office that figures out what to do with it. This, for example, was the case with Captchas. If the paper is by commercial company (e.g., IBM), it is much more likely to get patented or to have additional protections because employees at Research are evaluated also based on number of patent applications.
The problem is that there is often no way to know because the patent lawyers will usually write a general name that has no contact to the original idea. So contacting the author just in case may be prudent. The author may also have an existing implementation available, often open-source.