Cancellation of inequalities in floating point arithmetic

In finite precision floating point arithmetic the associative property of addition is not satisfied. This is, it is not always the case that $ $ (a+b)+c=a+(b+c)$ $ Even $ a=(a+b)-b$ is not always true.

To prove that $ x+y<z$ is equivalent to $ x<z-y$ with real numbers we can add $ -y$ on both sides of $ x+y<z$ to get $ (x+y)-y<z-y$ and then from this $ x=x+(y-y)<z-y$ . But I can’t repeat the last step for floating point.

Question: Are the inequalities $ x+y<z$ and $ x<z-y$ equivalent in finite precision floating point arithmetic?

Would this Point Buy house rule for Maid character creation work at all?

Recently we’ve started a maid game here on the stack and we have a huge disparity of stats between the players, one of them has barely average stats, while some of the other players are pushing fours and sixes in abilities because of great rolls during generation. We have found that the standard rule that characters with good stats get fewer maid powers is insufficient.

Would a point buy system work in Maid RPG while still being able to attain the same level of play in Maid games? Using the favor base presented in the handbook I’ve come up with the following figures for point buy statistics. The standard array in Maid would be 1,1,2,2,3,3 or you could buy points at the following costs, with 200 starting favor:

0: 0 points
1: 10 points
2: 30 points
3: 60 points
4: 100 points

With the stipulation that any favor points not used during point buy are lost. Does a system like this function properly in the Maid system provided the Maid characteristics (Boyish, Sexy, Lolita, Pure, etc.) were rolled after (and only after) a character has distributed their points as they wish?

Intersection of line segments induced by point sets from fixed geometry

I am reading up on algorithms and at the moment looking at the below problem from Jeff Erickson’s book Algorithms.

Problem 14 snippet from Recursion chapter out of Algorithms book by Jeff Erickson

I solved (a) by seeing a relationship to the previous problem on computing the number of array inversions. However, I am struggling with problem (b) as I cannot see how to reduce the circle point arrangement to an arrangement of points and lines that would be an input to the problem posed in (a). Assuming I have something for (b), I also cannot see how one might resolve (c).

For part (b), clearly every point $ p = (x, y)$ satisfies $ x^2 + y^2 = 1$ but I do not see how I might be able to use this fact to do the reduction. The runtime I am shooting for of $ O(n \log^2 n)$ also seems to tell me the reduction is going to cost something non-trivial to do.

Can anyone have some further hints/insights that might help with part (b) and potentially even part (c)?

OpenVPN: test security from external point of view

How would I test an OpenVPN environment from external, kind of black box pentest. I have the public server-IP (port 1194, udp, tun).

I have found NO online ressources on how to do that, or whether some tools are available (e.g. for IPsec there is the ike-scan tools), nmap has no scripts for that, metasploit has no plugins, kali has no tools (only OpenVAS looks like it has a module, didnt try that yet).

Is there any way to test or analyse the security of OpenVPN from an external point of view?

Clustering a set of point by affine transform

We are given a set of $ n$ points on the plane $ a_i = \{x^a_i, y^a_i\}$ and $ b_i = \{x^b_i, y^b_i\}$ .

Assume that the points b are an affine transform of the points a, we can find a matrix $ M$ and vector $ t$ such that $ \sum_{i=0}^{n-1} ||M a_i + t – b_i ||^2$ is minimized, in fact, we can even do so analytically.

Assume however that the points a_i are composed of different subsets to which a different affine transform was applied.

Let $ \epsilon$ be a small, tolerance value. A partition $ \cup_{j=0}^m P_j = [1\ldots n] \wedge \forall j, k, P_j \cap P_k = \emptyset$ is said to be admissible iff

$ $ \forall j,~ \exists M_j, t_j,~ \forall i \in P_j,~ ||M_j a_i + t_j – b_i||^2 < \epsilon$ $

Simply speaking, we partition the points into different subsets each of which is sent to $ b$ with its own affine transform.

An admissible partition always exists because it’s always possible to sent a to b exactly if each point is given its own affine transform (in fact, every 3 points can be sent to any other 3 points).

We want to cut up the points in as few pieces as possible: an admissible partition is minimal when it has fewer or equal subsets than any other admissible partitions.

How would one go about finding an admissible partition? Heuristics and approximate solutions are welcome. One approach would be to consider the transformation defined by every triplet of points and try to cluster those together, but this requires looking at $ O(n^3)$ transforms.

Point Subdomain in Google Domains to Google Compute Instance running WordPress

I have installed wordpress (the bitnami multi-site version) to a compute instance from the marketplace. I’ve also recently moved my domain registration to domains.google.com. Everything is working fine with the top-level domain. I also set up a subdomain, wp.mydomain.com in the domains interface pointed to the static external IP I configured for the compute instance running wordpress. When I go to wp.mydomain.com it redirects me to http://.xip.io/.

How do I get this set up so that I stay on wp.mydomain.com instead of going to my ip address as the url?

Assuming I’m using Starbucks Wifi, is there a point of using a VPN if I want to remain anonymous?

Wouldn’t using Starbucks Wifi make me somewhat anonymous since my ip address would be the same as other users connected to the same network? Therefore, no need to use a VPN assuming I don’t want the website I’m connected to know my identify. Of course, the website can figure who I am assuming my browser fingerprints is unique. However, assuming I change my browser fingerprints every session, then I should be fine. Correct?

What is the highest hit point that one character can have?

By reading others questions like Highest damage in one melee attack and Highest AC possible.

How many hit points can a character have, and also highest achievable hit points possible in an instant?

Conditions :

We’re looking at a level 20 character and no multiclass.
Feats are allowed.
Magic items are those on the tables in the D&D 5th Edition DMG.
Spells, skills, feats and abilities available to a player character are eligible for use/consideration.
No other help from an ally.