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All applications that are in Software Center are available without the need of Administrative rights. For applications that do require administrative rights, please see Make Me Admin. Clicking the desired software from the Applications tab will bring you to the Application Description page which will give you a brief informational of the software and any requirements that are necessary to install said application.
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These updates will be silently downloaded and installed to the machine as long as it is powered on and connected to the internet. If a high priority update installs and requires a restart, you will be prompted that a restart is required.
Once the high priority update has been installed, there is a five business day window that the machine would have to be restarted manually. At the end of that time period, a dialog box on the machine will prompt for a forced restart. Once this happens, you will have one hour to save and close anything your are currently working on.