Abstract: A computerized method and system for creating, analyzing, and editing complex formulas so as to facilitate their use in software applications such as spreadsheets and database applications. The method and system employ multiple synchronized views for formulas, one view presenting the linear text required by the software application and the other views presenting clear indications of the meaning of that text. Examples of such views include mathematically typeset formulas and hierarchical diagrams that reveal the formula's structure. The method and system parse formulas to determine their structure, display that structure in multiple views, and provide a variety of controls and aids to assist in analyzing, debugging, and editing the formula so that it has the intended meaning and result. Additionally, it synchronizes the multiple views so that changes to the formula or to the presentation of the formula in one view are automatically reflected in the other views.

Abstract: Systems and methods for encoding and decoding data is disclosed. The system may receive data, and may create a field of marks corresponding to the data, along with one or more identifiers corresponding to positions within the field of marks. A decoding system may receive the field of marks, and may decode the marks into data based at least in part on the one or more identifiers.

Abstract: A computerized method and system for creating, analyzing, and editing complex formulas so as to facilitate their use in software applications such as spreadsheets and database applications. The method and system employ multiple synchronized views for formulas, one view presenting the linear text required by the software application and the other views presenting clear indications of the meaning of that text. Examples of such views include mathematically typeset formulas and hierarchical diagrams that reveal the formula's structure. The method and system parse formulas to determine their structure, display that structure in multiple views, and provide a variety of controls and aids to assist in analyzing, debugging, and editing the formula so that it has the intended meaning and result. Additionally, it synchronizes the multiple views so that changes to the formula or to the presentation of the formula in one view are automatically reflected in the other views.

Abstract: A network with parallel bridges transmits information packets over parallel paths between first and second terminals in a network having other terminals while maintaining conformity with a protocol that precludes establishing loops formed by links between terminals that allow information packets to recirculate indefinitely. There is a first pair of bridges with each bridge connected to a respective one of the first and second terminals and interconnected by a first link. There is a second pair of bridges each connected to a respective one of the first and second terminals and interconnected by a second link.