Interactions between unarmed strikes, negative strength and an unconscious target

Consider this improbable yet possible scenario (which nonetheless came up at our table last night):

A PC is unconscious and currently making Death Saving Throws. A weak (8 Strength) and hostile NPC tries to punch the PC to kill it for good.

Attack rolls against an Unconscious character have advantage and any attack that hits the character is a Critical Hit if the attacker is within 5 feet of the character

The NPC rolls with advantage and beats the PC’s AC. It is therefore a critical hit.

If an Unconscious character takes damage while at 0 HP, they automatically fail one death saving throw, or 2 death saves if the damage is from a critical hit. Massive Damage can still outright kill the character so damage should still be rolled and if it equals or exceeds their max HP then they die

Ok, so that’s 2 failed Death Saving Throws for the PC! Let’s calculate the damage, just in case…

Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head–butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.

Here, 1 + STR = 0. The hit deals 0 damage. Does that even count as damage then?

Does the attack actually provoke failed Death Saving Throws? If so, how many? Can an unarmed strike even crit if there are no dice being thrown?

Proving that the Bellman-Ford algorithm contains negative circuit

Let $ D=(V,B), n=|V|$ be a directed graph. Then the graph contains a circuit of negative length from $ s$ if and only if $ f_n(v) \neq f_{n-1}(v),$ where $ v \in V,$ and $ f_k(v)=$ min$ \{l(P)|P$ is an $ s-v$ walk traversing at most $ k$ arcs }.

I do not understand what a $ s-v$ walk means and what is the meaning of the function $ f_n$ .

Can somebody help me prove the two directions of the above statement ? Many thanks.

Strongly connected subgraph that contains no negative cycles

Is there an algorithm that solves the following decision problem:

Given a strongly connected weighted directed graph G, defined by its transition matrix, is there a strongly connected spanning subgraph of G that has no negative cycles?

A strongly connected spanning subgraph of G is a strongly connected subgraph of G that shares the same vertexes with G. You can look to this paper for the definition of strongly connected spanning subgraph. In this paper they present an approximation for the minimum strongly connected subgraph problem, wich is different from the problem stated in this question.

A naive approach to this problem is to find a negative cycle of the graph using the Ford-Bellman or Floyd-Warshall algorithm, deleting an edge from this cycle, and repeating while the graph is still strongly connected. But this naive approach has poor time complexity because we will potentially run the Ford-bellman algorithm and check for strong connectivity many times — moreover I am unable to prove if this algorithm is correct in all instances.

I’m hoping to find experts here who can tell me if this decision problem can be solved in a polynomial time and what algorithm does so. Many thanks in advance.

What is dysfunctional, controversial, or negative about Epic skill checks?

I often see it said that the entire Epic Level Handbook should be dismissed as broken and frequently dysfunctional. However, outside of claims that the entire book is bad, I never see Epic skill checks listed as an example of something negative, controversial, or objectionable. The only near example that I can think of is Diplomancy, but that’s an issue that was largely inherited from Core. There are of course some absurd examples like the Arseplomancer, but Epic levels are all about performing absurd feats of skill.

This leads me to my question – it is frequently said that the entire Epic Level Handbook is bad, but what specifically is dysfunctional, controversial, or often seen as negative about Epic skill checks?

Minimum number of bits to represent negative number

Minimum number of bits required to represent $ (+32)_{base10}$ and $ (-32)_{base10}$ in signed two’s compliment form?

My attempt:

32 = 0100000 ( 1st zero – sign bit as positive)

So to represent +32 we need 7 bits

-32 = 1100000 (1st bit 1 – sign bit as negative)

So to represent -32 we need 7 bits

But answer is given as 6 bits. His reason – one 1 bit enough to represent negative number. I am confused. Please clarigy here

Also i have following Questions:-

Can we say number of bits required to represent a negative number is strictly less than( or less than equal to) number of bits required to represent that corresponding positive number?

how can we generalise minimum number of bits required to represent a given positive and negative number in signed magnitude representation, signed 1’s complement notation and signed two’s compliment notation.

I know that minimum number bits will be of order of logn to base 2. But exactly how much i am not able to think.

I know range of numbers in signed magnitude and signed one’s complement is $ -(2^{n-1} – 1) $ to $ +(2^{n-1} – 1) $ while range of numbers in signed two complement representation is $ -(2^{n-1}) $ to $ +(2^{n-1} – 1) $

Negative words in url/domain

I have added a negative word in ser and ran the project but still many links got built having the neg word in url and domain. I have tried running multiple projects but still happening the same.

Also in using domain extension skip filters like !edu!gov, still lots of redirects got build which dont have the edu or gov extensions.

Actually facing this from a long time but was trying to put some time in manual links removal but still I am reporting to get it checked. I hope it will be checked and worked on. Thanks

What are the smallest and biggest negative floating point numbers in IEEE 754 32 bit?

I am stuck with a question that asks for smallest and biggest negative floating point numbers in IEEE 754 32-bit (their representation and decimal numerical value from which one can approximate the precision of the number)? So -0, NaN and Infinity do not belong to negative rational numbers.

I have stumbled upon -3.403 x 10^38 and 2^-126. I came close to the first one actually. I tried to do some calculations but got kind of lost in the process as floating point representation is counter-intutive for me, especially when calculating negative numbers. Can someone help me to clarify my thought process for the calculations so that I can find the numbers?