There are already a number of apps that plug into Android's notification service to mirror the notification shade on your desktop, Pushbullet being perhaps the most prominent example. Notifications+ is a new entrant in this category, but it focuses only on feature-rich notification mirroring.

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Notifications+ requires a Chrome extension like both Pushbullet and Krome, but it has a few settings the others don't yet support. You can control the popup timeout on the desktop side on a per-app basis. For example, Gmail could stay up for 30 seconds and Hangouts could disappear after only 5 seconds. Alerts can even be ignored by the Chrome extension if you're not on WiFi, or if the device's screen is on (Krome also does the WiFi thing).

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This app also supports dismissing notifications on the device from your computer (as does Pushbullet). Setting up Notifications+ includes a private password that automatically encrypts all your notifications – that's an optional feature in Krome. The basic notification mirroring is free so you can test Notifications+, but the fine-grained settings require a $2.42 pro key. It's not the first app to do this, but it has a nice combination of features worth checking out.