Abstract: Live editing a workbook with multiple clients including receiving, by a workbook manager from a first workbook client, a first workbook patch comprising a base version ID and a first workbook edit; determining, by the workbook manager, that the base version ID from the first workbook patch matches the version ID for a confirmed workbook on the workbook manager; applying, by the workbook manager, the first workbook edit to the confirmed workbook on the workbook manager; advancing, by the workbook manager, the version ID for the confirmed workbook; and sending, by the workbook manager, an acknowledgement of the first workbook patch to the first workbook client.

Abstract: Live editing a workbook with multiple clients including receiving, by a table manager, a request by a first client on a first client computing system to edit a workbook in an exploration mode that displays edits to the workbook without altering the workbook; receiving, by the table manager from the first client, an exploration edit targeting the exploration of the workbook; applying, by the table manager, the exploration edit to the exploration of the workbook; and presenting, by the table manager to a second client on a second client computing system, the application of the exploration edit to the exploration of the workbook.

Abstract: An input mesh can be decomposed into component meshes that can be independently simplified. A computing device can calculate costs of performing candidate edge collapses for a component mesh. The candidate edge collapses can include boundary edge collapses and interior edge collapses. To simplify a component mesh, the execution of boundary edge collapses and the execution of interior edge collapses are interleaved in an order based on the costs of performing the candidate edge collapses. The position of a vertex resulting from a boundary edge collapse can be calculated independently of the interior of the component mesh. When component meshes are simplified in parallel, a boundary that is common to the component meshes can be simplified identically.

Abstract: An input mesh can be decomposed into component meshes that can be independently simplified. A computing device can calculate costs of performing candidate edge collapses for a component mesh. The candidate edge collapses can include boundary edge collapses and interior edge collapses. To simplify a component mesh, the execution of boundary edge collapses and the execution of interior edge collapses are interleaved in an order based on the costs of performing the candidate edge collapses. The position of a vertex resulting from a boundary edge collapse can be calculated independently of the interior of the component mesh. When component meshes are simplified in parallel, a boundary that is common to the component meshes can be simplified identically.

Abstract: A compressed digital audio signal is transmitted from an audio source along a connection wire to an audio receiver. The digital audio signal can encode digital audio data having different sampling frequencies, frames sizes, and other information. The audio receiver that receives the digital audio signal can decode and convert the compressed digital audio signal into multiple synchronized analog signals, which are used to drive multiple speakers. The audio receiver may also synchronize the audio data with associated video data so that the audio playback and video playback are “in sync”, despite delay introduced by the audio signal decoding at the audio receiver.

Abstract: A compressed digital audio signal is transmitted from an audio source along a connection wire to an audio receiver. The digital audio signal can encode digital audio data having different sampling frequencies, frames sizes, and other information. The audio receiver that receives the digital audio signal can decode and convert the compressed digital audio signal into multiple synchronized analog signals, which are used to drive multiple speakers. The audio receiver may also synchronize the audio data with associated video data so that the audio playback and video playback are “in sync”, despite delay introduced by the audio signal decoding at the audio receiver.