## graphs – Fraction of matching not containing an edge

I am trying to prove the following statement (from book, page 317):

Let $$G(A,B,E)$$ be a bipartite graph, where $$A$$ and $$B$$ are the two disjoint sets of vertices s.t. $$|A|=|B|=n$$. Let the number of matchings of size $$kle n$$, be $$m_k$$. If $$|E|>k$$ then there exists an edge $$e$$, such that $$frac{m_{ne}}{m_k} ge frac{1}{n}$$, where $$m_{ne}$$ is the number of matchings of size $$k$$, that do not include/contain edge $$e$$.

The book gives a hint to use pigeonhole principle. But I am only able to get a weaker result.
Each matching of size $$k$$, contributes towards a matching of size $$k$$ not containing an edge, for $$|E|-k$$ edges. Thus as there are in total $$m_k$$ matchings, it can be seen as distributing $$(|E|-k)m_k$$
balls in $$|E|$$ bins. Thus by pigeonhole principle there is a bin (an edge) with at least $$frac{(|E|-k)cdot m_k}{|E|}$$ matchings which do not contain it. That is there is an edge $$e$$ such that
$$m_{ne} ge frac{(|E|-k)cdot m_k}{|E|}$$
$$frac{m_{ne}}{m_k} ge frac{(|E|-k)}{|E|} ge frac{1}{|E|} ge frac{1}{n^2}$$

How can I prove that the lower bound is at least $$frac{1}{n}$$ for some edge ?

## Unity Webgl build: fast in Chrome, slow in Firefox, Opera and Edge

Good day.

I’ve a Chrome ‘factory default’ settings that can Run my unity webgl app fast, without problem (between 40 and 60fps).

Same app run at 1 fps in others browsers: edge, firefox and opera.

What can I check to solve ?

Thanks

## tls – SSL self signed nginx Chrome ok, edge not ok

replaced IP and email

So, I made self signed nginx on centos using

https://www.digitalocean.com/community/tutorials/how-to-create-a-self-signed-ssl-certificate-for-nginx-on-centos-7

I ended up with three files

``````-rw-r--r--. 1 root root 1509 Apr 11 20:08 ./pki/tls/certs/nginx-selfsigned.crt
-rw-r--r--. 1 root root 424 Apr 11 20:36 ./pki/tls/certs/dhparam.pem
-rw-r--r--. 1 root root 1704 Apr 11 20:08 ./ssl/private/nginx-selfsigned.key
``````

So, this was my first attempt at the cert where I did not put Subject Alternative Name IP

``````openssl x509 -in 12.123.123.123.pem -text -noout
Certificate:
Data:
Version: 3 (0x2)
Serial Number:
Signature Algorithm: sha256WithRSAEncryption
Issuer: C = US, ST = CA, L = San Jose, O = "Bouncy Castles, Inc.", OU = Ministry of Water Slides, CN = 12.123.123.123, emailAddress = email@gmail.com
Validity
Not Before: Apr 11 20:08:00 2021 GMT
Not After : Apr 11 20:08:00 2022 GMT
Subject: C = US, ST = CA, L = San Jose, O = "Bouncy Castles, Inc.", OU = Ministry of Water Slides, CN = 12.123.123.123, emailAddress = email@gmail.com
Subject Public Key Info:
Public Key Algorithm: rsaEncryption
RSA Public-Key: (2048 bit)
Modulus:
00:c7:63:9d:f0:ce:34:af:6a:1c:9c:b7:b2:0c:6c:
43:3f:db:c8:e0:33:55:81:50:67:b1:50:01:02:ff:
6d:eb:2d:20:2f:6b:9c:6e:db:d5:a6:c7:1d:99:50:
87:98:19:97:d2:32:fb:9f:e7:4f:f9:90:a9:1c:10:
ec:b9:ac:f5:d4:48:1d:59:85:ab:d4:14:9a:1e:59:
5b:71:16:ff:23:8c:c1:63:87:19:f3:de:f4:75:30:
66:46:45:7b:fe:e2:25:9b:3f:99:9c:d0:d6:b9:03:
05:90:e6:51:b4:07:96:fd:a8:00:68:74:20:e7:fc:
0b:c9:2e:72:18:43:48:6e:f2:52:76:ae:90:c3:a4:
82:91:97:a5:5b:45:7a:dc:94:8c:b0:55:cc:01:d1:
8c:26:41:ae:90:b2:22:47:97:7e:35:94:a0:7d:78:
34:4f:45:df:f2:67:c4:a5:ab:b3:0c:dc:51:a6:55:
0b:64:b4:bf:0c:05:d4:0b:ee:79:62:5b:81:c7:99:
f1:fc:cc:fc:ff:b9:f4:46:82:0a:d6:09:f9:83:9f:
da:23:a8:ed:58:71:8f:67:9b:c0:33:de:44:b0:c4:
e9:cf:f6:bc:47:8c:6c:9d:9d:72:ff:5d:9f:c0:25:
6b:dd:be:bc:d9:61:3a:77:98:db:85:fb:d5:6d:29:
6e:d9
Exponent: 65537 (0x10001)
X509v3 extensions:
X509v3 Subject Key Identifier:
9C:84:63:6F:ED:22:1D:78:91:63:EF:0E:C0:79:33:FB:0D:7D:67:8F
X509v3 Authority Key Identifier:
keyid:9C:84:63:6F:ED:22:1D:78:91:63:EF:0E:C0:79:33:FB:0D:7D:67:8F

X509v3 Basic Constraints:
CA:TRUE
Signature Algorithm: sha256WithRSAEncryption
68:14:74:e8:3a:a4:48:f5:79:eb:08:d7:74:eb:5f:89:fc:8c:
ef:7a:09:d7:5c:a1:1f:99:80:dc:31:91:8b:02:33:8b:30:66:
01:37:7a:fa:b2:f5:7b:92:1a:c3:65:f3:41:b9:6e:67:e0:66:
ff:aa:e6:c9:16:66:39:1e:d0:2c:ac:67:65:6f:fc:4f:58:6f:
8a:bc:12:fd:17:80:29:82:5b:14:17:36:49:de:d9:0a:94:3c:
77:b8:15:78:1b:31:67:58:95:90:1a:aa:a2:32:bc:b9:0b:48:
00:ea:f1:8d:b6:73:bb:8d:2a:28:c7:49:83:2d:a6:f6:84:7d:
94:58:62:f9:9c:a2:7e:9b:93:64:07:d4:b7:c6:0c:5d:59:1b:
e9:5d:be:72:c3:5b:92:05:e2:62:49:b2:a9:c6:35:fe:87:37:
c4:16:20:c9:1b:1e:5e:8f:aa:91:c5:da:bf:49:0b:46:8f:d5:
bc:15:d9:b9:c9:e3:67:c8:1e:9b:d4:af:14:9c:24:ee:08:d4:
f4:f2:c6:d9:9d:d9:eb:cd:fd:21:c3:f5:e4:47:12:98:7c:fd:
55:e0:e1:2f:98:b1:f0:b7:9a:ec:ae:49:10:d3:43:df:de:aa:
eb:6f:67:7b

``````

which I imported in Windows 10 root cert store using

https://www.ssls.com/knowledgebase/how-to-import-intermediate-and-root-certificates-via-mmc/

Then when I went to chrome and edge it showed me

``````Your connection isn't private
Attackers might be trying to steal your information from 12.123.123.123 (for example, passwords, messages, or credit cards).
NET::ERR_CERT_AUTHORITY_INVALID
``````

I did some research and realized I did not specify

``````X509v3 Subject Alternative Name:
``````

anywhere. Then I followed

https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/6/html/deployment_guide/sssd-ldap-domain-ip

Here my command was failing

`````` sudo openssl x509 -req -in req.pem -out new_cert.pem -extfile /etc/pki/tls/openssl.cnf -extensions v3_ca -signkey /etc/pki/tls/certs/nginx-selfsigned.crt
Signature ok
subject=/C=US/ST=CA/L=San Jose/O=Bouncy Castles, Inc./OU=Ministry of Water Slides/CN=12.123.123.123/emailAddress=email@gmail.com
Getting Private key
140564642027408:error:0906D06C:PEM routines:PEM_read_bio:no start line:pem_lib.c:707:Expecting: ANY PRIVATE KEY

``````

I believe because it was expecting a keystore, and not a pub cert. So, I gave location of my private key and it worked.

This was my final cert which I reimported into Windows trusted root cert store

``````\$ openssl x509 -in 12.123.123.123.crt -text -noout
Certificate:
Data:
Version: 3 (0x2)
Serial Number:
cf:78:d4:da:94:7e:aa:9f
Signature Algorithm: sha256WithRSAEncryption
Issuer: C = US, ST = CA, L = San Jose, O = "Bouncy Castles, Inc.", OU = Ministry of Water Slides, CN = 12.123.123.123, emailAddress = email@gmail.com
Validity
Not Before: Apr 11 22:00:24 2021 GMT
Not After : May 11 22:00:24 2021 GMT
Subject: C = US, ST = CA, L = San Jose, O = "Bouncy Castles, Inc.", OU = Ministry of Water Slides, CN = 12.123.123.123, emailAddress = email@gmail.com
Subject Public Key Info:
Public Key Algorithm: rsaEncryption
RSA Public-Key: (2048 bit)
Modulus:
00:c7:63:9d:f0:ce:34:af:6a:1c:9c:b7:b2:0c:6c:
43:3f:db:c8:e0:33:55:81:50:67:b1:50:01:02:ff:
6d:eb:2d:20:2f:6b:9c:6e:db:d5:a6:c7:1d:99:50:
87:98:19:97:d2:32:fb:9f:e7:4f:f9:90:a9:1c:10:
ec:b9:ac:f5:d4:48:1d:59:85:ab:d4:14:9a:1e:59:
5b:71:16:ff:23:8c:c1:63:87:19:f3:de:f4:75:30:
66:46:45:7b:fe:e2:25:9b:3f:99:9c:d0:d6:b9:03:
05:90:e6:51:b4:07:96:fd:a8:00:68:74:20:e7:fc:
0b:c9:2e:72:18:43:48:6e:f2:52:76:ae:90:c3:a4:
82:91:97:a5:5b:45:7a:dc:94:8c:b0:55:cc:01:d1:
8c:26:41:ae:90:b2:22:47:97:7e:35:94:a0:7d:78:
34:4f:45:df:f2:67:c4:a5:ab:b3:0c:dc:51:a6:55:
0b:64:b4:bf:0c:05:d4:0b:ee:79:62:5b:81:c7:99:
f1:fc:cc:fc:ff:b9:f4:46:82:0a:d6:09:f9:83:9f:
da:23:a8:ed:58:71:8f:67:9b:c0:33:de:44:b0:c4:
e9:cf:f6:bc:47:8c:6c:9d:9d:72:ff:5d:9f:c0:25:
6b:dd:be:bc:d9:61:3a:77:98:db:85:fb:d5:6d:29:
6e:d9
Exponent: 65537 (0x10001)
X509v3 extensions:
X509v3 Subject Alternative Name:
X509v3 Subject Key Identifier:
9C:84:63:6F:ED:22:1D:78:91:63:EF:0E:C0:79:33:FB:0D:7D:67:8F
X509v3 Authority Key Identifier:
keyid:9C:84:63:6F:ED:22:1D:78:91:63:EF:0E:C0:79:33:FB:0D:7D:67:8F

X509v3 Basic Constraints:
CA:TRUE
Signature Algorithm: sha256WithRSAEncryption
d4:b6:b0:a4:11:f0:38:f1:f2:4d:71:e5:c8:cf:5f:39:16:a9:
f6:10:72:ce:9c:98:4b:51:1e:20:e2:d1:34:87:15:3c:53:15:
68:11:f6:32:3d:ff:fd:41:da:ec:73:87:09:58:62:33:85:b7:
63:b6:7a:89:a7:d3:8d:aa:f2:e4:8e:77:9e:1e:1b:b8:10:35:
b6:0c:db:12:64:28:d2:b1:c2:4d:36:77:f1:e9:7a:27:92:39:
bf:6e:6e:38:25:94:f3:4b:d1:73:18:78:2d:af:8e:fa:c4:a4:
ef:5b:b2:19:08:67:fb:4f:a0:96:d9:56:e2:c0:6f:a4:93:fa:
d3:44:2c:f3:15:80:1b:ee:8e:f9:83:69:fb:d9:8d:16:d5:e5:
94:0c:84:92:95:ee:82:6d:43:32:08:c2:fc:69:69:e3:20:12:
6d:2c:1f:5e:5d:cc:c9:09:33:36:05:7d:9d:ee:89:23:90:0f:
45:79:70:6e:ab:41:a6:b0:bc:c4:4e:7c:44:11:c9:6f:8e:41:
53:8f:7b:93:e0:66:20:a7:2a:d2:39:32:1e:39:9a:0f:78:a4:
af:cc:ed:40
``````

Now it works on my chrome, but on edge it still gives the same errors:

``````Your connection isn't private
Attackers might be trying to steal your information from 12.123.123.123 (for example, passwords, messages, or credit cards).
NET::ERR_CERT_AUTHORITY_INVALID
``````

Also on chrome it shows me a circled (i) instead of a green padlock.

``````openssl x509 -req -in req.pem -out new_cert.pem -extfile ./openssl.cnf -extensions v3_ca -signkey old_cert.pem
``````

I though the signkey is public key. Is that correct, but for the self signed cert it is the private key?
Basically to sign means, to generate a hash and encrypt it with a RSA key. We cannot use the public key to sign a root certificate because we will be sending the public key to client and they can use the key to decrypt the messages, hence the root has to be signed with private key.
If it was some inter mediate cert, I could have used the server cert of the intermediate CA, which contains its public keys?

## transactions – I used edge wallet to send my bitcoin from my wallet to my cash app but i used a low fee soo its been unconfirmed for 10 days what can i do?

So it looks like your transaction does not have RBF (Replace-by-Fee) enabled, so you won’t be able to bump your fee in a replacement transaction.

And there’s no change output, so it seems you sent all your money in one go, so you wouldn’t be able to do a CPFP (Child-Pays-for-Parent) transaction.

One suggestion is to use ViaBTC’s Transaction Accelerator service. You can pay them in Bitcoin Cash to have them include your transaction in the next block they mine. So, you’ll lose money still by paying for the service, but your transaction would be confirmed sooner.

## co.combinatorics – Fastest algorithm to construct a proper edge \$(Delta(G)+1)\$-coloring of a simple graph

A proper edge coloring is a coloring of the edges of a graph so that adjacent edges receive distinct colors. Vizing’s theorem states that every simple graph $$G$$ has a proper edge coloring using at most maximum degree plus one colors. In (1), the authors showed that there is an $$O(mn)$$-time algorithm to construct a proper edge $$(Delta(G)+1)$$-coloring of a simple graph whth $$m$$ edges and $$n$$ vertices. I wonder whether there is a faster algorithm to construct such an edge coloring.

(1) J. Misra, and D. Gries. A constructive proof of Vizing’s theorem.Inform. Process. Lett.41(3)131–133 (1992)

## Brighter irregular edge of a Polaroid photo

I use Polaroid OneStep 2 with Color i-Type film packs.

Sometimes, at the bottom edge of the image, not fully developed irregular areas appear as the medium inside has not been properly distributed. Only the bottom edge is a problematic one, the rest of the photo is fine.

It does not seem to be related to the temperature the photos were taken in. Also, it has been happening with multiple packs, so it might not be the case either, I think. I try to keep the rollers clean every time I insert a new one.

What may be the cause of that? Below you can find a photo of the issue I’m talking about. See the bottom edge of the pictures, especially the second one.

## Why is there a bright edge in my photos even though my studio lights provide even coverage?

You haven’t told us exactly which Paul Buff Alien Bees flashes you’re using, but many studio flashes take longer to release their energy than most speedlights do. For the most part, camera’s flash sync (X-sync) ratings are based on using the camera with that brand of camera’s in-house speedlight selection sitting directly on the hot shoe or using the camera’s built-in popup flash. This is particularly the case with cameras that do not have a PC port¹ used to send a “fire” signal to external flashes without using the hot shoe connection.

In many cases, this means you must shoot with an exposure time longer (“slower shutter speed”) than your camera’s flash sync setting (X-sync speed). If you use an exposure time shorter than the time it takes the flash to fully fire, the second shutter curtain of your camera will begin closing before the flashes have produced all of its light. The parts of the sensor covered by the second shutter curtain as it is closing will be dimmer than the parts of the frame not covered by the second curtain until after the flash has released most or all of its energy.

Your Canon EOS Rebel T3/1100D has a flash sync setting of 1/200 seconds. That is equal to 5 micro-seconds. The Alien Bees B1600, for example, has a T.1 flash duration at full power of 1/300 second, or 3.333 microseconds. So far so good. The flash can release 90% of it’s burst of light in a shorter time than the camera’s X-sync speed. But then you have to factor in the delay between the time your camera signals the Cactus transmitter to “fire” the flash and the time the Cactus receiver(s) tells the flash(es) to “fire”. If there is any appreciable delay, then at 1/200 seconds your second shutter curtain will begin closing before the flash has released all of its light.

One thing I would check is to be sure you haven’t accidentally dialed in some delay in your Cactus V6 II transmitter’s settings. Anything greater than a delay of 1.67 microseconds (5ms minus 3.33ms) will mean the flash begins firing too late to complete its burst of light before your second shutter curtain is closing. In practice any delay dialed in would need to be shorter than that, because it takes time for the radio trigger’s microprocessors to react to the camera’s “fire” signal, to then send the radio pulse to “fire”, which is an encoded radio signal that has a more than instantaneous length to it, and then for the receiver(s) microprocessors to decode that signal and send the “fire” command to the flash(es) to which it is connected.

As a proof of concept that the shutter curtain beginning to close before the flash reaches T.1 is the root cause of your issue, take a few test shots with increasingly longer exposure times – 1/200, 1/160, 1/125, 1/100, 1/60, 1/30, etc. – and see if the bright area on one side of the frame gets increasing wider towards the “far” side from where you are currently getting the bright strip.

¹ PC in the context of flash photography has nothing to do with a personal computer. It is an abbreviation of Prontor/Compur. Prontor has its origins in the Italian word pronto (quick) and was a brand of shutter produced by Alfred Gauthier in the 1950s. Compur, derived from the word compound, was the shutter brand of the Deckel Company. Both companies were based in Germany and both counted Zeiss as an influential stockholder when they introduced the standard 1/8″-inch coaxial connector for shutter/flash synchronization.

## edge – how to remove vertical scrollbars from named ranges displayed using the excel web part

This issue does not occur when displaying embedded charts but manifests when referencing named ranges. A scrollbar appears to the right hand side of the zone that appears unrelated to the size of the webpart or the zone.

This issue is evident in Edge however it does not manifest in IE. But as IE is depreciated this is now a problem for us and creates a mess on many of our site pages.

Can anyone help ?

## vpn – With direct and private peering becoming the norm in IXS and Edge Networks, is that not more difficult to MITM?

Massive transit providers like m247, cdn77 etc have their pops all over the world, and more and more the Tier 1 ISP’s are being bypassed and networks are privately connecting to each other via direct peering in colocation centers. In such a scenario, is using a VPN to obfuscate MITM or traffic netflow analysis more difficult to a nation state adversary?
My specic question is as follows: Are the citizens of the world more secure when the data takes fewer hops from source to destination due to private peering in 2021? If the traffic is going over less routers, and the volume of traffic is increasing, is that not a hard problem to do correlation attacks?

## windows 10 – Why does (Chromium) Microsoft Edge get to skip past Default App’s screen? When every other app can’t?

Most browsers on launch check if they are the ‘default browser’ & when they are not they prompt you to make them the default (‘pick me pick me!‘). In Chrome when you click ‘Set as default’ in Windows 10 you are brought to the Settings, Default Apps screen in which you can set the default browser.

(Chromium) Microsoft Edge has the same prompt, but lo & behold it doesn’t bring you to the ‘Default Apps’ screen. I’m quite sure Windows 10 changed the app-association rules so only users controlled, but why is Microsoft breaking its own rules? Is it a ‘do as a say, not as I do?‘ thing. Has anyone else noticed this or brought it to Microsoft’s attention? Hasn’t Microsoft gotten in trouble for things like this before because it violated some EU law?