Abstract: Generally described, embodiments of the present invention provide the ability to graphically modulating structured data, in a spreadsheet application and other applications, by applying any kind of cell formatting properties or design features to a given cell. Graphical modulation is determined based on formulae characteristics. In embodiments of the present invention, formula characteristics include various types of formula contained in a given cell. Formula types include, but are not limited to the following formula types, “workbook linked formula”, “sheet linked formula”, “cell linked formula”, “sensitivity formula”, “array formula”, “retrieving formula”, “calculative formula”, “computed input formula”, and “input formula”. In other embodiments of the present invention, formula characteristics include calculation complexity levels in formula contained in a given cell.

Abstract: Certain drinking straw device embodiments comprise an inner tube having a hole along its length and an actuator for actively introducing a gas or fluid through the hole into a liquid flowing through the inner tube. In an embodiment, the actuator stores and releases a pressurized gas. In some embodiments, the actuator stores and releases a second liquid or gel. In some embodiments, a device comprises a non-pressurized gas or fluid substance introduction mechanism, which, when activated, allows the gas or fluid substance to enter and be mixed with a liquid flowing through the inner tube.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for identifying entities that are related to an entity to which a search query is directed. One of the methods includes receiving a search query, wherein the search query has been determined to relate to a first entity of a first entity type, and wherein one or more entities of a second entity type have a relationship with the first entity; receiving search results for the search query; determining that a count of search results identifying a resource containing a reference to the first entity satisfies a first threshold value; determining that a count of search results identifying a resource having the second entity type as a relevant entity type satisfies a second threshold value; and transmitting information identifying the one or more entities of the second entity type as part of the response to the search query.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for receiving a first search query from a user device; receiving search results for the first search query provided by a search engine, wherein each of the search results identifies a respective resource; determining from the search results that the first search query relates to a first entity of a first entity type; determining that one or more entities of a second entity type have a predetermined relationship with the first entity; and transmitting information identifying the one or more entities of the second type to the user device as part of a response to the first search query.

Abstract: A method for simplifying resolution proofs in DAG format where each leaf node represents a clause and each internal node represents a resolution between its children includes representing a SAT proof as a stripped proof, analyzing pivots to identify redundant resolutions, and constructing a simplified proof without the redundant resolutions.

Abstract: The present embodiment keeps track of a set of resolution required for generating each one of the clauses added by the simplification Method. This information is used by the method that generates the unsat core in order to extract the original clauses that generated the simplified clauses. This work integrates resolution based CNF simplification technique inside the SAT-based abstraction refinement scheme in a unique way that overcomes the difficulties.

Abstract: The present embodiment keeps track of a set of resolution required for generating each one of the clauses added by the simplification method. This information is used by the method that generates the unsat core in order to extract the original clauses that generated the simplified clauses. This work integrates resolution based CNF simplification technique inside the SAT-based abstraction refinement scheme in a unique way that overcomes the difficulties.

Abstract: A portable hand holdable electric cigarette lighter conveniently locatable on top of furniture or a shelf, plugged into an electrical outlet, stored and/or moved, ready for immediate and routine use. The lighter includes an electrical resistance heating element contactable by a cigarette and connected to an electromechanical circuit supplied electrical power from an externally located alternating current, or from a built-in internally located direct current, power supply, and includes a portable hand holdable housing. The electromechanical circuit is connected to the heating element and connectable to ac power of 110 or 220 volts, and includes a step-down voltage transformer for providing voltage of 0.5-25 volts to the heating element, or, the electromechanical circuit is connected to the heating element and to dc power being batteries or an electromagnetic generator.

Abstract: An optical combiner for use with an optical eyepiece which is adjusted for viewing a first image, and which injects a non-collimated light beam from a second image substantially along an optical axis of the eyepiece so as to present a combined image to an observer. The combiner comprises a beam splitter for inserting into the eyepiece and having an entry aperture for intercepting the non-collimated light beam and directing a portion thereof outside the eyepiece so as to superimpose the second image on the first image.