Abstract: To authorize an access to an application, a user interface renders a geometrical pattern on receiving a trigger to access the application. The rendered geometrical pattern includes an instance of an arrangement of one or more first nodes and one or more second nodes. The rendered geometrical pattern is associated with an input type to receive a selection of the first nodes and the second nodes. The selection of the first nodes and the second nodes is received as an authorizing key. The authorizing key is matched with an authorizing passcode stored in memory to provide access to the application.

Abstract: To authorize an access to an application, a user interface renders a geometrical pattern on receiving a trigger to access the application. The rendered geometrical pattern includes an instance of an arrangement of one or more first nodes and one or more second nodes. The rendered geometrical pattern is associated with an input type to receive a selection of the first nodes and the second nodes. The selection of the first nodes and the second nodes is received as an authorizing key. The authorizing key is matched with an authorizing passcode stored in memory to provide access to the application.

Abstract: To perform a relative trend analysis of a business scenario, a graphical illustration of a trend for a business scenario under analysis is displayed on a user interface. The user interface renders and receives a user selection of one or more parameters associated with the business scenario under analysis. Based on the user selection, a database is queried to determine trend-splits of the business scenario under analysis. The trend-splits of the business scenario under analysis are matched with one or more gradient-splits of other business scenarios residing in a database. Based on the matching, the related business scenarios are determined and the gradient-splits of the related business scenarios are retrieved from the database. A graphical illustration of the trend of business scenario under analysis and gradient of the related business scenarios is rendered on the user interface.