How to effectively represent and generate 2D cellular automaton rules that are invariant under rotation and reflection of the input matrix?

Consider cellular automaton rules for a two-dimensional universe with two states, where a cell’s new state can depend on its previous state and the states of the cells in its Moore neighborhood. Such a rule can be modeled as a function that takes as input a 3 by 3 matrix of bits, and outputs a bit.

Such a rule can be represented easily using a string of 512 bits representing the output for each of the $ 2^{3 \times 3}$ input states. Since this representation is bijective, a rule can also be randomly generated by sampling 512 bits.

However, it is sometimes preferable for reasons of aesthetics and comprehensibility that the output of the rule be the same when the input matrix is rotated or flipped horizontally or vertically. The rule for Conway’s Game of Life is an example of a function satisfying this restriction.

Given a function $ r : 2^9 \to 2$ which does not necessarily obey this restriction, we can obtain a function that does by mapping the input to the lexicographically smallest matrix obtainable by reflecting or rotating it before passing to $ r$ . However, this provides little insight into the questions I am interested in:

  • How many functions obey this restriction?
  • How can they be compactly representing using a bit string?
  • How can they be efficiently randomly generated?

How to Under Volt CPU on Ubuntu?

Hello I was wondering if there’s anyway to Under volt CPU on ubuntu for better temperature? I know there are apps on win 10 like Throttlestop that do this, but i was not sure if the saves are written into bios so lptop stays under volt even after reboot and switchign OS to Ubuntu too. So if there’s anyone know a solution me and rest of people looking for this would appreciate this. Because it is a hot topic. Btw my specs : Inter Core i7-8750H CPU @ 2,20GHz

Creating a Sharepoint 2013 List with multiple rows under one column header using InfoPath 2013

I want to create an order form with 14 columns and as many rows as possible that will kick off a workflow. my challenge is creating a single List at one go to contain an X amount of rows with a single row of column headings(14) to be saved as a single list and can be editted later.

i am very new on infopath and still finding my way around sharepoint. please asisst.

Thanks,

Are models of computation closed under composition?

It’s common to ask whether a particular class of languages $ \mathcal{C} \subseteq \mathcal{P}(\Sigma^*)$ , for some alphabet $ \Sigma$ , is closed under complement, or union, or intersection, or concatenation, or the Kleene star. And those questions seem natural to me, because they’re essentially questions about the power of a model of computation that can decide precisely the languages in $ C$ . However, it seems just as natural to me – perhaps even more natural – to ask whether such a class is also closed under composition.

Here’s what I mean by that. If I fix some subset $ \mathcal{C} \subseteq \mathcal{P}(\Sigma^*)$ of “decidable” languages relative to some model of computation, for any (finite) $ \Sigma$ , then I have also fixed some subset $ \mathcal{F} \subseteq B^A$ of computable functions, for any languages $ A, B$ – because each function $ f : A \rightarrow B$ can be viewed as a function $ \bar{f} : A \times B \rightarrow \{0, 1\}$ . Given that, I would expect that for any reasonable model of computation, if $ f : A \rightarrow B$ and $ g : B \rightarrow C$ are computable, then $ g \circ f : A \rightarrow C$ should be as well. Put in terms of the corresponding languages, I’d expect that if $ L_f = \{(a, b) \in A \times B : f(a) = b\}$ and $ L_g = \{(b, c) \in B \times C : g(b) = c\}$ are decidable, then $ L_{g \circ f} = \{(a, c) : \exists b \in B s.t. f(a) = b \wedge g(b) = c\}$ should be decidable as well.

This seems to me like a natural question to ask of any class of languages. Is it in fact a reasonable question? If not, why? If it is, is there a better way to frame it, one that would make it more clear what we’re demanding?

Microsoft XboxOne and XboxOne S controller under Ubuntu (Wired USB)

I’ve got both Xbox One Controllers the Original (shiny plastic around guide button) and the Second Edition (smooth matt plastic to Guide button)

I am connecting these controllers via a USB cable. They are being detected by dmesg and lsusb gives me details about the attached device.

Doesn’t get any further than that.

I’ve tried installing the suggested profiles but nothings working.

Neither of which are being detected in Game or in Steam menus or showing up in the /dev/input list

$  > /dev/input/by-id usb-Logitech_Logitech_G930_Headset-event-if03 usb-Logitech_Trackball-event-mouse usb-Logitech_Trackball-mouse usb-Mad_Catz_Saitek_Pro_Flight_X-56_Rhino_Stick-event-joystick usb-Mad_Catz_Saitek_Pro_Flight_X-56_Rhino_Stick-joystick usb-Microsoft_Natural®_Ergonomic_Keyboard_4000-event-kbd usb-Microsoft_Natural®_Ergonomic_Keyboard_4000-if01-event-kbd usb-Oculus_VR_Rift_Sensor_WMTD303A3011WY-event-if00 
$  > dmesg [  389.625051] usb 3-13: new full-speed USB device number 15 using xhci_hcd [  389.774252] usb 3-13: New USB device found, idVendor=045e, idProduct=02ea, bcdDevice= 3.01 [  389.774255] usb 3-13: New USB device strings: Mfr=1, Product=2, SerialNumber=3 [  389.774258] usb 3-13: Product: Controller [  389.774260] usb 3-13: Manufacturer: Microsoft [  389.774261] usb 3-13: SerialNumber: 3032363030303235393132373233 [  429.862555] usb 3-13: USB disconnect, device number 15 
drevilish@Linsair:~$   lsusb -d 045e:02ea -v  Bus 003 Device 018: ID 045e:02ea Microsoft Corp. Xbox One S Controller Couldn't open device, some information will be missing Device Descriptor:   bLength                18   bDescriptorType         1   bcdUSB               2.00   bDeviceClass          255 Vendor Specific Class   bDeviceSubClass        71    bDeviceProtocol       208    bMaxPacketSize0        64   idVendor           0x045e Microsoft Corp.   idProduct          0x02ea Xbox One S Controller   bcdDevice            3.01   iManufacturer           1    iProduct                2    iSerial                 3    bNumConfigurations      1   Configuration Descriptor: 
Linux Hostname 5.3.0-12-generic #13-Ubuntu SMP Tue Sep 17 12:35:50 UTC 2019 x86_64 x86_64 x86_64 GNU/Linux 

Undead under Undead Anatomy

If a Lich, Vampire, or some other undead casts Undead Anatomy on itself, does the spells effect hold true?

In this form, you detect as an undead creature (such as with detect undead, but not with magic that reveals your true form, such as true seeing) and are treated as undead for the purposes of channeled energy, cure spells, and inflict spells, but not for other effects that specifically target or react differently to undead (such as searing light).

How does document set permissions to files under it? – SharePoint 2013

How does the Doc Set permissions work.I have created a some document sets which i have assigned unique users to and then added some files under the document set. I taught with this approach users would only see there folder in the document set as i have locked the document set/folder with unique permissions but it seems users cant see the files under the document sets and no access to files.

Any ideas

How Ubuntu 16 instance under AWS upgrade to 18.04 ?

Hello,
I have Ubuntu 16 instance under AWS
and on login to its console I see message:

New release '18.04.2 LTS' available. Run 'do-release-upgrade' to upgrade to it. 
Code (markup):

I tried to run it following messages in commands :

Last login: Fri Sep 6 06:39:22 2019 from 213.109.234.130 ubuntu@ip-NN-NNN-NN-NNN:~$   clear ubuntu@ip-NN-NNN-NN-NNN:~$   sudo apt-get update Hit:1 http://us-east-2.ec2.archive.ubuntu.com/ubuntu xenial InRelease Hit:2...
Code (markup):

How Ubuntu 16 instance under AWS upgrade to 18.04 ?

Can’t use Win+E / Mod4+E shortcut under Ubuntu 18.04

I am having problems in Ubuntu-MATE 18.04 to use the WindowsE shortcut alias Mod4+E to start caja (the standard “File Explorer” of MATE).

  • this worked flawlessly on multiple Ubuntu-MATE 16.x machines.
  • also: SHIFT+Mod4+E does work(!)

Who or what captures my WinE under 18.x?

I don’t see any occupancy in the normal keyboard shortcuts list…

(PS: If you wonder, why I have to use parameters with caja, that’s explained here)

enter image description here