Abstract: Aspects of the present disclosure integrate pixelated multi-state panels (e.g., liquid crystal dimming panels) into artificial reality (XR) displays (e.g., augmented reality (AR) glasses) or conventional glasses. Conventional visual displays for XR displays can be expensive, have a low field-of-view, and consume high power. On the other hand, pixelated multi-state panels consume lower power, have a wide field-of-view, and are light, inexpensive, and computationally simple. The multi-state panels can have 4 configurations: 1) included on the periphery of an XR display, 2) as a standalone display, 3) as a display that's overlaid onto an XR display, and/or 4) as a secondary externally facing display. The multi-state panels can be selectively activated based on a trigger, such as identification of an object in the real-world environment, based on an event occurring in an XR application executing on the XR display, based on detected audio, etc.

Abstract: Methods, systems, and computer programs encoded on a computer storage medium, that relate to conditionally interpreting a single style definition within a same page. Methods include receiving a request to present third party content in a third party content block on a publisher-provided content page. A single style identifier and one or more attributes are obtained from the content page. Subsequently, a third party content item is selected from a content source. Using the single style identifier and the one or more attributes, a first rule is identified that specifies a set of style parameters for content selected for presentation in the third party content block from among a plurality of rules specifying different styles for a respective plurality of third party content blocks. The third party content item is formatted according to the style parameters of the first rule and provided for presentation with the third party content block.

Abstract: Methods, systems, and computer programs encoded on a computer storage medium, that relate to conditionally interpreting a single style definition within a same page. Methods include receiving a request to present third party content in a third party content block on a publisher-provided content page. A single style identifier and one or more attributes are obtained from the content page. Subsequently, a third party content item is selected from a content source. Using the single style identifier and the one or more attributes, a first rule is identified that specifies a set of style parameters for content selected for presentation in the third party content block from among a plurality of rules specifying different styles for a respective plurality of third party content blocks. The third party content item is formatted according to the style parameters of the first rule and provided for presentation with the third party content block.

Abstract: Systems and methods for progressively parsing user input of a mathematical expression are provided. One disclosed method includes looping through characters in an input string, and on each loop, extracting a next token from the input string and determining a current grammar context based on the token or tokens extracted thus far. If it is determined that the current grammar context matches a predetermined condition, then the method may include modifying the tokens extracted from the input string in a predetermined manner associated with the predetermined condition. A parsing result may be obtained based on the modified tokens. The parsing result may be converted to a modified input string.

Abstract: Mathematical expressions and functions are graphed using a computer implemented method that automatically determines an appropriate graph range. One implementation of the method begins with determining an initial variable seed range. A number of points within this seed range are randomly selected. The method determines whether the selected points correspond to the mathematical expression (i.e., whether they produce valid results when the expression is evaluated at each point). When the selected points produce valid results, the points can be used to generate and display a graph of the mathematical expression on a user display device, with a graph range based on the seed range. If not, the variable seed range can be expanded until a predetermined number of the selected points correspond to the mathematical expression, so that a graph of the mathematical expression can be generated and displayed.

Abstract: A centralized view and management of stored variables for calculators and pieces of software emulating calculators is provided. Users can glance at the status bar and know what variables are stored. A single click then brings up a window within which a list of the stored variables and their values is shown. In this window users can clear individual variables or the entire variable list. Users can be reminded that their calculations contain stored variables by displaying the stored variable names in one or more different colors so that errors can be easily detected and corrected.

Abstract: A piece of software running on either a computer or a calculator for receiving a mathematical expression is described. The mathematical expression is evaluated to obtain its symbolic result. If the symbolic result can be resolved to its numeric result, the software executes to obtain the numeric result. The software displays contemporaneously the symbolic result and the numeric result.

Abstract: RF receiver topologies and systems incorporating such topologies are described. Various implementations allow the intelligent monitoring of transmission formats, multi-format reception, and real-time receiver parameter optimization.