/usr/share/applications/ is in mate-control-center 1.8.3+dfsg1-2.
This file is owned by root:root, with mode 0o755.
..
/usr/share/applications/mate-settings-mouse.desktop
/usr/share/applications/matecc.desktop
/usr/share/applications/mate-network-properties.desktop
/usr/share/applications/mate-at-properties.desktop
/usr/share/applications/mate-font-viewer.desktop
/usr/share/applications/mate-keyboard.desktop
/usr/share/applications/mate-theme-installer.desktop
/usr/share/applications/mate-about-me.desktop
/usr/share/applications/mate-default-applications-properties.desktop
/usr/share/applications/mate-appearance-properties.desktop
/usr/share/applications/mate-keybinding.desktop
/usr/share/applications/mate-display-properties.desktop
/usr/share/applications/mate-window-properties.desktop