Abstract: An interactive recommendation system generates one or more recommendations (e.g., recommended products, travel destinations, etc.) for a user based on a recommendation model. The recommendation model includes one or more criteria that are used to analyze a datastore of user characteristics (e.g., a user's age, location, past online behavior, etc.) and generate one or more recommendations based thereon. The interactive recommendation system further presents a user interface that allows the user to interactively modify the criteria of the recommendation model and to apply the modified recommendation model to the datastore in order to generate one or more modified recommendations. In this manner, for example, the user can customize the recommendations he or she receives by interacting with the recommendation system to modify the recommendation model used to generate such recommendations.

Abstract: An application defined by expressions whose execution may be dynamically distributed over multiple devices. An application defined by expressions may include a number of expressions that provide a symbolic representation of computations to be performed. The application defined by expressions may have input variables and output variables and provide a solution for the output variables using the input variables and the expressions that define the application. In providing a solution for the output variables, an expression engine may determine dependencies for the expressions to be solved and distribute the solution of some of those expressions dynamically at runtime to other devices based on the capabilities of the devices, privacy and security concerns, communications bandwidth and latency, the resources available to devices, and commercial or cost implications of where the processing is done.

Abstract: A method, system, and data structure for storing information in a computer system memory using a directed acyclic graph structure having related data nodes. Any node can "own" other nodes in hierarchical relationships. Data is stored in a file structure with (1) a heap for storing chunks or nodes of data in memory locations, and (2) an index containing information about the relationships between nodes. Each node is referenced and accessed by information stored in the index. Each ownership relationship between nodes is referenced uniquely by the triple consisting of the identification of the parent node, the identification of the child node and a child identification value. The inclusion of a child identification value in the triple allows a node to be a child of another node a multiplicity of times. The index is a table of entries, one entry for each node. Each entry contains the identifier of the node and, if there are relationships with other nodes, a list of one or more references to child nodes.

Abstract: A computer-implemented system for scripting an animation sequence. The scripting system creates an instance of a script interpreter in response to an event. The script interpreter instance is assigned to a graphical object (GOB) having a graphical image associated with the animation sequence, and is invoked in response to an event received by the GOB. A script is attached to the script interpreter instance, the attached script comprising control logic for implementing the animated sequence. The control logic supports interactive animation by enabling the attached script to communicate with another GOB or another program module, such as an application program. The attached script is executed on the script interpreter instance to conduct the animated sequence. In response to executing the script, the animated sequence is displayed. The attached script and the script interpreter are destroyed in response to executing the attached script.

Abstract: In association with a computer system, a method and system for implementing a graphical dissolve effect of a first image into a second image displayed on a computer screen. The sequence in which each pixel comprising the first image is replaced with a corresponding pixel in the second image is determined mathematically such that the sequence appears random, thereby producing a dissolve effect that is visually pleasing. The sequence in which the pixels of a first image having a width and height of "w" and "h" pixels, respectively, are replaced is determined by first selecting a value for the variables p and m. The number p is a prime number and the number m is selected such that the numbers m, m.sup.2, m.sup.3, . . . , m.sup.p-1, when taken modulo p, yield a reordering of the numbers 1, 2, 3, . . . , p-1. A random number k.sub.0 is selected between 1 and p-1 and a number k is set equal to k.sub.0. A number j is then calculated according to the formula j=(w*h)+k-p.