Reverse Turing test if the subject is or is not human. As of 2004, such procedures, called CAPTCHAs, are used in some anti-spam systems to prevent automated bulk use of communications systems. The use of captchas is controversial. Circumvention methods exist that reduce their effectiveness. Also, many implementations of captchas (particularly ones desired to counter circumvention) are inaccessible to humans with disabilities, and/or are difficult for humans to pass. Note that "CAPTCHA" is an acronym for "Completely Automated Public Turing test to tell Computers and Humans Apart" so that the original designers of the test regard the test as a Turing test to
Characteristic class Characteristic class In mathematics, a characteristic class is a way of associating to each principal bundle "X" a cohomology class of "X". The cohomology class measures the extent the bundle is "twisted" — and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure from a global product structure. They are one of the unifying geometric concepts in algebraic topology, differential geometry, and algebraic geometry. The notion of characteristic class arose in 1935 in the work of Eduard Stiefel and Hassler Whitney about vector fields on manifolds. Let "G" be a topological