We study groups of germs of complex diffeomorphisms having a
property called irreducibility. The notion is motivated by the
similar property of the fundamental group of the complement of an
irreducible hypersurface in the complex projective space. Natural
examples of such groups of germ maps are given by holonomy groups
and monodromy groups of integrable systems (foliations) under
certain conditions. We prove some finiteness results for these
groups extending previous results in [D. Cerveau and F. Loray,
Un théorème de Frobenius singulier via l’arithmétique élémentaire,
J. Number Theory 68 1998, 2, 217–228].
Applications are given to the framework of germs of holomorphic
foliations. We prove the existence of first integrals under certain
irreducibility or more general conditions on the tangent cone of
the foliation after a punctual blow-up.
This article describes research to build an embodied conversational agent (ECA) as an interface to a question-and-answer (Q/A) system about a National Science Foundation (NSF) program. We call this ECA the LifeLike Avatar, and it can interact with its users in spoken natural language to answer general as well as specific questions about specific topics. In an idealized case, the LifeLike Avatar could conceivably provide a user with a level of interaction such that he or she would not be certain as to whether he or she is talking to the actual person via video teleconference. This could be considered a (vastly) extended version of the seminal Turing test. Although passing such a test is still far off, our work moves the science in that direction. The Uncanny Valley notwithstanding, applications of such lifelike interfaces could include those where specific instructors/caregivers could be represented as stand-ins for the actual person in situations where personal representation is important. Possible areas that come to mind that might benefit from these lifelike ECAs include health-care support for elderly/disabled patients in extended home care, education/training, and knowledge preservation. Another more personal application would be to posthumously preserve elements of the persona of a loved one by family members. We apply this approach to a Q/A system for knowledge preservation and dissemination, where the specific individual who had this knowledge was to retire from the US National Science Foundation. The system is described in detail, and evaluations were performed to determine how well the system was perceived by users.