Abstract: Debaters encode the logical structure of their arguments in a framework designed so that these arguments can be processed by a computer. A system uses this structure to algorithmically identify logical contradictions and disputed points—places where one debater's views would make another debater's views obviously impossible. The disputed points are represented as short questions whose answers distinguish which debater is right. An end user is presented with these questions, and the user's answers are used to filter out debaters whose views are impossible. The user doesn't need to actually read the debaters' arguments, but can find out which views are right just by answering the questions that have been presented.

Abstract: Prior to fabrication of an optical fiber with desired optical properties, a preform geometry is determined dependent upon a fiber geometry that possesses the desired optical properties. The desired geometry may contain a large number of channels. The processor determines the preform geometry by tracking backwards in time the parameters of a set of conformal mappings that describe the cross section of the fiber. Some of the drawing process parameters may be specified, while other parameters may be determined along with the preform geometry. The determined preform geometry may be used to fabricate the required preform. Using this preform, the determined drawing process parameters may be used to draw the desired fiber.

Abstract: Prior to fabrication of an optical fiber with desired optical properties, a preform geometry is determined dependent upon a fiber geometry that possesses the desired optical properties. The desired geometry may contain a large number of channels. The processor determines the preform geometry by tracking backwards in time the parameters of a set of conformal mappings that describe the cross section of the fiber. Some of the drawing process parameters may be specified, while other parameters may be determined along with the preform geometry. The determined preform geometry may be used to fabricate the required preform. Using this preform, the determined drawing process parameters may be used to draw the desired fiber.