## Determining the existence probability of a thinned Poisson Point Process

From the figure below, a total of $$\lambda$$ nodes (of type X in blue) are distributed based on the Poisson point process. Then, the probability of another set of nodes (of type Y in yellow) existing within the intersection region is given as $$P_c = 1-\exp(-\lambda_1 \chi)$$ where $$\chi$$ is the area of the intersection of the two circles and $$\lambda_1$$ is the density of nodes of type Y. For nodes of type X to communicate through nodes of type Y, a total of $$\lambda_c = \lambda \times P_c$$ can communicate through any yellow node/point C in type Y while $$\lambda (1-P_c)$$ nodes of type X can communicate with each other (e.g A straight to B) without passing through nodes of type Y (e.g any C in Y). Suppose randomly located points which is a thinned portion of Y (in black) is also Poisson distributed within this intersection region (since thinning is a property of the Poisson point process), I am a bit confused as to whether the new probability of having the black ‘colored’ nodes/points is $$P_{new} = 1-\exp(-\lambda_c \times A)$$ or $$P_{new} = 1-\exp(-\lambda_c)$$. I had been thinking that the second option also made sense since the area $$\chi$$ was initially factored into $$P_c$$? Could someone shed more light on this? I have tried asking elsewhere but I haven’t gotten a clue still.

## Complexity of Determining the Edges of Planar Convex Hulls

Question:

can the set of edges that resemble the convex hull ($$CH$$ for short) of $$n$$ points in the euclidean plane be determined in $$O(n)$$ time?

I know that the time complexity of determining the $$CH$$ of $$n$$ points is $$O(n\log h)$$ where $$h$$ is the number of points constituting to the $$CH$$ and is achieved by the Kirkpatrick-Seidel algorithm, but that includes reporting the points of $$CH$$ in sorted order.

So, can the $$\log h$$ factor be saved if the edges of the $$CH$$ can be reported in random order?

## Determining source of periodic Apache SIGTERM

Running Ubuntu 18.04.1 LTS on a custom built home server (i5-6500, 16GB RAM).

I have been struggling with determining the source of periodic Apache crashes at frequencies ranging from hourly to daily. Apache has run well since the server was built about 2 years ago, until this issue began to occur several months ago. When it crashes, it must be manually restarted using systemctl restart apache2.

The contents of /var/log/apache2/error.log several seconds prior to the SIGTERM:

[Fri Jan 18 04:19:20.651049 2019] [fcgid:info] [pid 29012] mod_fcgid: Process manager 29012 stopped [Fri Jan 18 04:19:20.675851 2019] [fcgid:info] [pid 29109] mod_fcgid: Process manager 29109 started [Fri Jan 18 04:19:20.678539 2019] [:notice] [pid 29108] FastCGI: process manager initialized (pid 29108) [Fri Jan 18 04:19:20.767449 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(401): AH00821: shmcb_init allocated 512000 bytes of shared memory [Fri Jan 18 04:19:20.767461 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(417): AH00822: for 511912 bytes (512000 including header), recommending 32 subcaches, 88 indexes each [Fri Jan 18 04:19:20.767463 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(450): AH00824: shmcb_init_memory choices follow [Fri Jan 18 04:19:20.767466 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(452): AH00825: subcache_num = 32 [Fri Jan 18 04:19:20.767468 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(454): AH00826: subcache_size = 15992 [Fri Jan 18 04:19:20.767469 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(456): AH00827: subcache_data_offset = 2128 [Fri Jan 18 04:19:20.767471 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(458): AH00828: subcache_data_size = 13864 [Fri Jan 18 04:19:20.767473 2019] [socache_shmcb:debug] [pid 28514] mod_socache_shmcb.c(460): AH00829: index_num = 88 [Fri Jan 18 04:19:20.767519 2019] [socache_shmcb:info] [pid 28514] AH00830: Shared memory socache initialised [Fri Jan 18 04:19:20.767522 2019] [ssl:info] [pid 28514] AH01887: Init: Initializing (virtual) servers for SSL [Fri Jan 18 04:19:20.771807 2019] [ssl:info] [pid 28514] AH01914: Configuring server cloud.MY_DOMAIN.net:443 for SSL protocol [Fri Jan 18 04:19:20.771812 2019] [ssl:debug] [pid 28514] ssl_engine_init.c(1658): AH: Init: (cloud.MY_DOMAIN.net:443) mod_md support is unavailable. [Fri Jan 18 04:19:20.771931 2019] [ssl:debug] [pid 28514] ssl_engine_init.c(492): AH01893: Configuring TLS extension handling [Fri Jan 18 04:19:20.772076 2019] [ssl:debug] [pid 28514] ssl_util_ssl.c(470): AH02412: [cloud.MY_DOMAIN.net:443] Cert matches for name 'cloud.MY_DOMAIN.net' [subject: CN=MY_DOMAIN.net / issuer: CN=Let's Encrypt Authority X3,O=Let's Encrypt,C=US / serial: ################################ / notbefore: Dec  1 07:03:19 2018 GMT / notafter: Mar  1 07:03:19 2019 GMT] [Fri Jan 18 04:19:20.772080 2019] [ssl:info] [pid 28514] AH02568: Certificate and private key cloud.MY_DOMAIN.net:443:0 configured from /etc/letsencrypt/live/MY_DOMAIN.net-0009/fullchain.pem and /etc/letsencrypt/live/MY_DOMAIN.net-0009/privkey.pem [Fri Jan 18 04:19:20.772436 2019] [ssl:info] [pid 28514] AH01914: Configuring server www.MY_DOMAIN.net:443 for SSL protocol [Fri Jan 18 04:19:20.772439 2019] [ssl:debug] [pid 28514] ssl_engine_init.c(1658): AH: Init: (www.MY_DOMAIN.net:443) mod_md support is unavailable. [Fri Jan 18 04:19:20.772541 2019] [ssl:debug] [pid 28514] ssl_engine_init.c(492): AH01893: Configuring TLS extension handling [Fri Jan 18 04:19:20.772687 2019] [ssl:debug] [pid 28514] ssl_util_ssl.c(470): AH02412: [www.MY_DOMAIN.net:443] Cert matches for name 'www.MY_DOMAIN.net' [subject: CN=MY_DOMAIN.net / issuer: CN=Let's Encrypt Authority X3,O=Let's Encrypt,C=US / serial: ################################ / notbefore: Dec  1 07:03:19 2018 GMT / notafter: Mar  1 07:03:19 2019 GMT] [Fri Jan 18 04:19:20.772691 2019] [ssl:info] [pid 28514] AH02568: Certificate and private key www.MY_DOMAIN.net:443:0 configured from /etc/letsencrypt/live/MY_DOMAIN.net-0009/fullchain.pem and /etc/letsencrypt/live/MY_DOMAIN.net-0009/privkey.pem [Fri Jan 18 04:19:20.772785 2019] [ssl:info] [pid 28514] AH01876: mod_ssl/2.4.29 compiled against Server: Apache/2.4.29, Library: OpenSSL/1.1.0g [Fri Jan 18 04:19:20.772807 2019] [watchdog:debug] [pid 28514] mod_watchdog.c(454): AH010033: Watchdog: Running with WatchdogInterval 1000ms [Fri Jan 18 04:19:20.772811 2019] [watchdog:debug] [pid 28514] mod_watchdog.c(462): AH02974: Watchdog: found parent providers. [Fri Jan 18 04:19:20.772813 2019] [watchdog:debug] [pid 28514] mod_watchdog.c(508): AH02977: Watchdog: found child providers. [Fri Jan 18 04:19:20.772816 2019] [watchdog:debug] [pid 28514] mod_watchdog.c(516): AH02978: Watchdog: Looking for child (_singleton_). [Fri Jan 18 04:19:20.772818 2019] [watchdog:debug] [pid 28514] mod_watchdog.c(516): AH02978: Watchdog: Looking for child (_default_). [Fri Jan 18 04:19:20.773834 2019] [mpm_prefork:notice] [pid 28514] AH00163: Apache/2.4.29 (Ubuntu) mod_fastcgi/mod_fastcgi-SNAP-0910052141 mod_fcgid/2.3.9 OpenSSL/1.1.0g configured -- resuming normal operations [Fri Jan 18 04:19:20.773842 2019] [mpm_prefork:info] [pid 28514] AH00164: Server built: 2018-10-10T18:59:25 [Fri Jan 18 04:19:20.773849 2019] [core:notice] [pid 28514] AH00094: Command line: '/usr/sbin/apache2' [Fri Jan 18 04:19:20.773851 2019] [core:debug] [pid 28514] log.c(1570): AH02639: Using SO_REUSEPORT: yes (1) [Fri Jan 18 04:19:20.773867 2019] [mpm_prefork:debug] [pid 28514] prefork.c(923): AH00165: Accept mutex: fcntl (default: sysvsem) [Fri Jan 18 04:19:20.777421 2019] [watchdog:debug] [pid 29114] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:20.777503 2019] [proxy:debug] [pid 29114] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:20.777510 2019] [proxy:debug] [pid 29114] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:20.777525 2019] [proxy:debug] [pid 29114] proxy_util.c(1878): AH00931: initialized single connection worker in child 29114 for (*) [Fri Jan 18 04:19:20.778007 2019] [ssl:info] [pid 29114] [client 192.168.1.1:47184] AH01964: Connection to child 1 established (server www.MY_DOMAIN.net:443) [Fri Jan 18 04:19:20.778241 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(2139): [client 192.168.1.1:47184] AH02043: SSL virtual host for servername cloud.MY_DOMAIN.net found [Fri Jan 18 04:19:20.778267 2019] [core:debug] [pid 29114] protocol.c(2257): [client 192.168.1.1:47184] AH03155: select protocol from , choices=h2,http/1.1 for server cloud.MY_DOMAIN.net [Fri Jan 18 04:19:20.781857 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(2067): [client 192.168.1.1:47184] AH02041: Protocol: TLSv1.2, Cipher: ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits) [Fri Jan 18 04:19:20.782763 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Initial (No.1) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:20.783793 2019] [watchdog:debug] [pid 29115] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:20.783874 2019] [proxy:debug] [pid 29115] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:20.783881 2019] [proxy:debug] [pid 29115] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:20.783898 2019] [proxy:debug] [pid 29115] proxy_util.c(1878): AH00931: initialized single connection worker in child 29115 for (*) [Fri Jan 18 04:19:21.779826 2019] [watchdog:debug] [pid 29120] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:21.779935 2019] [proxy:debug] [pid 29120] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:21.779942 2019] [proxy:debug] [pid 29120] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:21.779971 2019] [proxy:debug] [pid 29120] proxy_util.c(1878): AH00931: initialized single connection worker in child 29120 for (*) [Fri Jan 18 04:19:23.304175 2019] [ssl:info] [pid 29115] [client 192.168.1.1:47190] AH01964: Connection to child 2 established (server www.MY_DOMAIN.net:443) [Fri Jan 18 04:19:23.304484 2019] [ssl:debug] [pid 29115] ssl_engine_kernel.c(2139): [client 192.168.1.1:47190] AH02043: SSL virtual host for servername cloud.MY_DOMAIN.net found [Fri Jan 18 04:19:23.304499 2019] [core:debug] [pid 29115] protocol.c(2257): [client 192.168.1.1:47190] AH03155: select protocol from , choices=h2,http/1.1 for server cloud.MY_DOMAIN.net [Fri Jan 18 04:19:23.305841 2019] [ssl:debug] [pid 29115] ssl_engine_kernel.c(2067): [client 192.168.1.1:47190] AH02041: Protocol: TLSv1.2, Cipher: ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits) [Fri Jan 18 04:19:23.305954 2019] [ssl:debug] [pid 29115] ssl_engine_kernel.c(377): [client 192.168.1.1:47190] AH02034: Initial (No.1) HTTPS request received for child 2 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:23.782768 2019] [watchdog:debug] [pid 29134] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:23.782860 2019] [proxy:debug] [pid 29134] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:23.782866 2019] [proxy:debug] [pid 29134] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:23.782881 2019] [proxy:debug] [pid 29134] proxy_util.c(1878): AH00931: initialized single connection worker in child 29134 for (*) [Fri Jan 18 04:19:23.795902 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.2) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:23.860810 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.3) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:23.955395 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.4) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:24.092544 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.5) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:24.237533 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.6) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.200469 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.7) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.237710 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.8) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.338693 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.9) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.642150 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.10) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.869587 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.11) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:25.974026 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.12) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.118787 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.13) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.229663 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.14) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.340689 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.15) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.681396 2019] [ssl:debug] [pid 28656] ssl_engine_kernel.c(377): [client 192.168.1.1:63023] AH02034: Subsequent (No.4) HTTPS request received for child 3 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.823089 2019] [ssl:debug] [pid 28656] ssl_engine_io.c(1103): [client 192.168.1.1:63023] AH02001: Connection closed to child 3 with standard shutdown (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.856368 2019] [ssl:info] [pid 29120] [client 192.168.1.1:63039] AH01964: Connection to child 6 established (server www.MY_DOMAIN.net:443) [Fri Jan 18 04:19:26.856817 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(2139): [client 192.168.1.1:63039] AH02043: SSL virtual host for servername cloud.MY_DOMAIN.net found [Fri Jan 18 04:19:26.863787 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(2067): [client 192.168.1.1:63039] AH02041: Protocol: TLSv1.2, Cipher: ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits) [Fri Jan 18 04:19:26.865493 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(377): [client 192.168.1.1:63039] AH02034: Initial (No.1) HTTPS request received for child 6 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:27.153860 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(377): [client 192.168.1.1:63039] AH02034: Subsequent (No.2) HTTPS request received for child 6 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:27.297174 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(377): [client 192.168.1.1:63039] AH02034: Subsequent (No.3) HTTPS request received for child 6 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:27.436015 2019] [ssl:info] [pid 29134] [client 192.168.1.1:63040] AH01964: Connection to child 7 established (server www.MY_DOMAIN.net:443) [Fri Jan 18 04:19:27.436301 2019] [ssl:debug] [pid 29134] ssl_engine_kernel.c(2139): [client 192.168.1.1:63040] AH02043: SSL virtual host for servername tautulli.MY_DOMAIN.net found [Fri Jan 18 04:19:27.436335 2019] [core:debug] [pid 29134] protocol.c(2257): [client 192.168.1.1:63040] AH03155: select protocol from , choices=h2,http/1.1 for server tautulli.MY_DOMAIN.net [Fri Jan 18 04:19:27.439472 2019] [ssl:debug] [pid 29134] ssl_engine_kernel.c(2067): [client 192.168.1.1:63040] AH02041: Protocol: TLSv1.2, Cipher: ECDHE-RSA-CHACHA20-POLY1305 (256/256 bits) [Fri Jan 18 04:19:27.786856 2019] [watchdog:debug] [pid 29183] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:27.786966 2019] [proxy:debug] [pid 29183] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:27.786973 2019] [proxy:debug] [pid 29183] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:27.786988 2019] [proxy:debug] [pid 29183] proxy_util.c(1878): AH00931: initialized single connection worker in child 29183 for (*) [Fri Jan 18 04:19:28.787927 2019] [watchdog:debug] [pid 29186] mod_watchdog.c(565): AH02980: Watchdog: nothing configured? [Fri Jan 18 04:19:28.788027 2019] [proxy:debug] [pid 29186] proxy_util.c(1785): AH00925: initializing worker proxy:reverse shared [Fri Jan 18 04:19:28.788035 2019] [proxy:debug] [pid 29186] proxy_util.c(1827): AH00927: initializing worker proxy:reverse local [Fri Jan 18 04:19:28.788053 2019] [proxy:debug] [pid 29186] proxy_util.c(1878): AH00931: initialized single connection worker in child 29186 for (*) [Fri Jan 18 04:19:30.941966 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.16) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:30.983215 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.17) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:31.326812 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.18) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:31.372147 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.19) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:31.462389 2019] [ssl:debug] [pid 29120] ssl_engine_kernel.c(377): [client 192.168.1.1:63039] AH02034: Subsequent (No.4) HTTPS request received for child 6 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:33.877610 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.20) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:33.915044 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.21) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:34.368821 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.22) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:34.608589 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.23) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:34.660253 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.24) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:35.206134 2019] [ssl:debug] [pid 28735] ssl_engine_io.c(1103): [client 192.168.1.1:49536] AH02001: Connection closed to child 0 with standard shutdown (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:35.206771 2019] [ssl:debug] [pid 28658] ssl_engine_io.c(1103): [client 192.168.1.1:38116] AH02001: Connection closed to child 4 with standard shutdown (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:35.213859 2019] [ssl:debug] [pid 28807] ssl_engine_io.c(1103): [client 192.168.1.1:46554] AH02001: Connection closed to child 5 with standard shutdown (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:35.491299 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.25) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:35.567105 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.26) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:38.535059 2019] [ssl:debug] [pid 29115] ssl_engine_io.c(1103): [client 192.168.1.1:47190] AH02001: Connection closed to child 2 with standard shutdown (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:39.299918 2019] [ssl:debug] [pid 29114] ssl_engine_kernel.c(377): [client 192.168.1.1:47184] AH02034: Subsequent (No.27) HTTPS request received for child 1 (server cloud.MY_DOMAIN.net:443) [Fri Jan 18 04:19:40.777331 2019] [core:info] [pid 28514] AH00096: removed PID file /var/run/apache2/apache2.pid (pid=28514) [Fri Jan 18 04:19:40.777360 2019] [mpm_prefork:notice] [pid 28514] AH00169: caught SIGTERM, shutting down 

Clearly, mpm_prefork sends Apache a SIGTERM, triggering the shut down. But I don’t understand what is causing this to occur. Is there another log file that I should be examining?

The contents of mpm_prefork.conf was originally set to default values. The server is never under a heavy load and I don’t see anything indicating that MaxClients is reached or anything of the sort. Despite this, I thought that perhaps the default settings were still to restrictive, so I have tried adjusting them to improve performance:

<IfModule mpm_prefork_module>   StartServers 2   MinSpareServers 2   MaxSpareServers 5   MaxClients 50   ServerLimit 50   MaxRequestsPerChild 100 </IfModule> 

Am I overlooking something? Any help or pointers are appreciated, thanks!

## Question about determining area of a right triangle, perimeter given, hypotenuse value given in terms of one of the legs.

Hello I have a question about a difficult problem.
The problem states:
Right Triangle- perimeter of 84, and the hypotenuse is 2 greater than the other leg. Find the area of this triangle.
I have tried different methods of solving this problem using Pythagorean Theorem and systems of equations, but cannot find any of the side lengths or the area of the right triangle. I looked for similar problems on StackExchange and around the internet, but could not find anything.
Does anyone know anything that could help find the side lengths of the triangle and the area as well?

Thanks,
William.

## In determining shape from line, what is special about the lines I’ve shown in these drawings by Ken Reid? [closed]

I’m interested in the way artists use lines to indicate shape in drawings. Strictly speaking, my question is about human vision — how our brains interpret certain lines — but I’m asking it here because those working in shape perception might be able to suggest an answer. It concerns what my visual system thinks it’s seeing in the arrowed parts of drawings such as these, and how this relates to the geometrical properties of the objects and their projection onto two dimensions:

Before continuing with the question, I should add that after I posted it, “D.W.” put it on hold without consulting me, on the grounds that it’s not about computer science. I refer him or her to http: //gfx.cs.princeton.edu/proj/ld3d/ , “Line Drawings of 3D Shapes”. To quote from the top of that page:

This site describes recent research on line drawings of 3D shapes, including studies on how artists create drawings and how people interpret drawings.

So far, this work involves two studies. The first, “Where Do People Draw Lines?,” investigates how artists’ drawings of 3D shapes correlate with the mathematical properties of the shapes, and known computer graphics line drawing techniques. The second, “How Well Do Line Drawings Depict Shape?,” examines how people interpret line drawings, both hand-drawn and computer-generated, and when depiction succeeds and fails.

Note the bit about how drawings correlate with the mathematical properties of the shapes drawn. This is related to the cues that humans and programs use to infer 3-d shape from 2-d projections, which in turn are related to the way that 3-d shapes look when projected onto 2-d surfaces. An excellent writeup of the latter topic is given in http: //www.gestaltrevision.be/pdfs/koenderink/Shape.pdf , “Shadows of Shape” by Jan Koenderink, a mathematician and psychologist known for his researches on visual perception, computer vision, and geometry. I hope what I’ve said in bold shows that my question is relevant to computing, but if not, D.W., please ask a computer-vision expert.

The drawings are by Ken Reid. He drew for the Beano and other comics, and was known for strips such as Frankie Stein, Queen of the Seas, and The Nervs. His faces were often grotesque, with protrusions such as chins and Adam’s apples standing out clearly despite being drawn with very few lines. There are examples of his work on Lew Stringer’s blog at http://lewstringer.blogspot.co.uk/2012/07/ken-reid-genius.html , and a copy of a The Nervs strip at http://1.bp.blogspot.com/_448y6kVhntg/RhIjT_1lF0I/AAAAAAAAA3I/KtvcxEIE3F8/s1600-h/nervs_pg1.jpg . What interests me is why the lines he drew are so effective. What is the visual system interpreting them as?

The images above are from the above-linked strip. In the first image, the back of the knee, there’s an upward-curving line above a short vertical above two downward-curving lines. The higher downward-curving line is presumably the contour of the lower leg. It’s less obvious what the downward-curving line below it is, or whether it corresponds to any physical feature. Nevertheless, it certainly helps in giving a sense of three-dimensional form.

Similarly, in the second image, some of the three upward-curving lines could be folds where the chin presses back against itself. But is the visual system interpreting them all as folds? I don’t know, but again, they readily give a sense of form. Another example is here, from the very first frame in that strip:

As I said at the start, those working in shape perception might have an answer. I’d also be interested to hear from anyone whose vision programs happen to fit Reid’s conventions so well that they can actually deduce from those drawings the shapes he intended.

By the way, I and other readers have noticed that Reid’s drawings seem very “intense”. As one reader commented in a blog, “they seem to enter the subconscious and stick there for the rest of your life”. Why? That’s probably outside the scope of computer vision, but not necessarily. It might be that some classes of line, e.g. closely-spaced lines curving around a cylinder, happen to affect us particularly strongly. So it would be useful to know if there’s something special about the geometry of Reid’s lines.

## Determining properties of linear code from generator matrix

I have a problem in error-correcting codes.

Say we have a generator matrix of a linear binary code

$$g=\begin{pmatrix} 10011 \ 01101 \end{pmatrix}$$

Q1: How many different codeword do we have? How many code bits can the code correct?

Say the generator matrix of a $$(6,2)$$ binary code is $$g=\begin{pmatrix} 101001\ 011111 \end{pmatrix}$$

Q2: How many errors can it guarantee to detect?

My try:

For Q1:

The way I find the number of codeword is count the number of rows in $$g$$ and raise it as a power to 2. So the answer is $$2^2=4$$.

For detecting and correcting I’m not sure, should I find the hamming distance and subtract 1?

I hope someone can explain to me how I can find the number bits I can detect and correct.

## Can You List the Names of Some Algorithms For Determining the Intersection of Two Context Free Grammars?

Suppose we have two sets of strings XS and YS such that set XS is described by grammar GX and YS is described by grammar GY.

We want an algorithm which accepts GX and Gy as inputs. The algorithm will return true if the intersection of sets XS and YS is non-empty and will return false otherwise. We do not need to know exactly what the intersection is. It is possible that the intersection set is massive, so returning a container of all elements is unreasonable. Describing the intersection as a grammar is okay as long as it’s apparent whether the grammar actually describes a non-empty set of string or not.

Just the name of the algorithm is fine if a Google search using that name will bring up the result. If the algorithm is obscure, additional information would be helpful.

## Is my algorithm for determining whether a ipv4 is public or private correct?

I have just created a function which checks whether a ipv4 is public or not. I have heavily tested it yet since it is kind of practically impossible to do so (because I do not know whether to start).

I was hoping if you could check it and let me know if it is correct, and if not where did i go wrong?

My algorithm is based on an article from this website.

Public IP addresses will be issued by an Internet Service Provider and will have number ranges from 1 to 191 in the first octet, with the exception of the private address ranges that start at 10.0.0 for Class A private networks and 172.16.0 for the Class B private addresses.

struct IpAddress {     uint8_t oct1;     uint8_t oct2;     uint8_t oct3;     uint8_t oct4; };  bool isIpPublic(const IpAddress &ip){     if (ip.oct1 >= 1 && ip.oct1 <= 191){            // not class C         if (ip.oct1 != 10){                         // not class A (all of class A is private)             if (ip.oct1 != 172 && ip.oct2 != 16){   // not class B (172.16.x.x is private)                 return true;             }         }     }      return false; } 

## Determining USB device port

lsusb | grep UART 

returns:

Bus 001 Device 006: ID 10c4:ea60 Cygnal Integrated Products, Inc. CP210x UART Bridge / myAVR mySmartUSB light 

How can I confirm that the device is at: /dev/ttyUSB0 without unplugging the USB device?

ls /dev/tty* | grep USB 

returns /dev/ttyUSB0 only when the device is plugged in, which seems to confirm the USB port location. I am seeking a confirmation process does not involve unplugging the USB device.

## Determining the line of symmetry

If f(x) is the image of the reflection of g(x), how do you determine the line of symmetry from the two equations?