Twitter was next on my 'to do' list

Meanwhile, does anyone know what the following entries are in my HH3 Event Log, all from during the night when we were asleep and no computers switched on:
06:29:27, 14 Nov. Host 58:55:ca:65:d5:56 connected to SSID 'BTHub3-NXR6' at 65 Mbps
06:22:38, 14 Nov. (432022.050000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username
06:22:38, 14 Nov. (432021.740000) Initializing transaction for event code 2 PERIODIC
03:09:33, 14 Nov. Host 58:55:ca:65:d5:56 connected to SSID 'BTHub3-NXR6' at 65 Mbps
03:05:09, 14 Nov. (420168.640000) Time synchronized with server 213.123.20.170
03:05:09, 14 Nov. (420168.600000) Requesting time from server 213.123.20.170
01:59:24, 14 Nov. Host 58:55:ca:65:d5:56 connected to SSID 'BTHub3-NXR6' at 65 Mbps
01:56:04, 14 Nov. (416023.710000) Lease for IP 192.168.1.73 renewed by host Unknown-00-24-be-1a-bb-e7 (MAC 00:24:be:1a:bb:e7). Lease duration: 720 min
01:56:04, 14 Nov. (416023.680000) Lease requested
23:59:31, 13 Nov. Host 58:55:ca:65:d5:56 connected to SSID 'BTHub3-NXR6' at 65 Mbps
23:53:18, 13 Nov. (408658.020000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username
23:53:16, 13 Nov. (408655.870000) WAN operating mode is Ethernet
23:53:16, 13 Nov. (408655.870000) Last WAN operating mode was Ethernet
23:53:16, 13 Nov. (408655.770000) PPPoE is up
23:53:15, 13 Nov. (408655.170000) CHAP authentication successful
23:53:15, 13 Nov. (408655.110000) Starting CHAP authentication with peer
23:53:15, 13 Nov. (408654.690000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username
23:52:44, 13 Nov. (408624.360000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username
23:52:42, 13 Nov. (408621.600000) PPPoE is down after 16 minutes uptime
23:39:47, 13 Nov. Host 58:55:ca:65:d5:56 connected to SSID 'BTHub3-NXR6' at 65 Mbps
23:36:41, 13 Nov. (407660.440000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username
23:36:38, 13 Nov. (407658.080000) WAN operating mode is Ethernet
23:36:38, 13 Nov. (407658.080000) Last WAN operating mode was Ethernet
23:36:38, 13 Nov. (407658.030000) PPPoE is up
23:36:38, 13 Nov. (407657.470000) CHAP authentication successful
23:36:37, 13 Nov. (407657.400000) Starting CHAP authentication with peer
23:36:37, 13 Nov. (407656.530000) Server URL:
https://pbthdm.bt.motive.com; Connecting as user: ACS username