Proof-of-inclusion: Merkle Tress, derivation paths

My assumption is that when transaction proof of inclusion occurs, it takes place only at full nodes, since this may happen when a block is mined (as a node has to evict transactions from its mempool to make sure the same txns aren’t added in their candidate block) and when someone queries a block explorer and the full nodes hold all the transactions (needed for merkle proofs). Is this true?

In these cases then, wouldn’t it be quicker to just search through the transactions for a match instead of doing merkle proofs? How does a node know which block a TX is in? The transaction data doesn’t contain what block it is in, so does a node start scanning the chain downwards?

When someone queries a proof-of-inclusion, a bitfield is constructed as a derivation path down to the leaf in question. For this to work, I assume that for each merkle root, is a mapping, and the associates nodes and all transactions. Doesn’t this defeat the purpose of a merkle tree then, still needing to hold all information + more? So is it just to summarise the transaction data in a block header to add some more entropy to a block hash?

If only the root and leaf are known, how is a derivation path found?

Is it so that that a light clients queries full nodes on who construct the merkle tree on the fly, providing a tree which the light client can then perform proof of inclusion?

I know I am missing something. Could someone please fill me in here? Thank you.

PS: Apologies for the long drawn out question.

How can I draw orbit paths for a solar system?

I’m trying to make the orbital paths visible for my solar system simulation game. I have most around with trail renderers and solid line sprite but not achieving the desired look I want. I’m hoping to get something where the path is alway present but darker directly behind where the planet currently is, and lighter and more transparent ahead of where it’s going. This effect is achieved in the game Worbital. worbital example here

If anyone could point me in the right direction how I can achieve this I would be much appreciated.

graphs – An algorithm to find differences between routing paths

I need to come up with an algorithm that finds differences in sequence of each product’s routing (or sequence of processes).
There are several processes aligned with together and each process’s been operated under specified equipment.

For example,

if there are four processes(A – B – C – D) until to the final product, the routing for each product can be shown below:

Process A B C D
Product1 a1 b3 c3 d2
product2 a2 b1 c2 d1
product3 a1 b2 c1 d1
product4 a1 b1 c2 d3
product5(defect) a2 b4 c3 d2
product6 a1 b3 c2 d3
product7 a1 b2 c2 d3

If it turned out product 5 to be a defect product, we may conclude that in B process, the equipment b4 has most likely caused an issue to the product5.

Approach 1:

I label-encoded to each equipment by column to implement machine learning model and calculate shapley scores for each column to see what process caused an issue. The problem is that some cases there are few defective products which causes an extreme data imbalance between normal and faulty products’ routing

If you could suggest feasible algorithms what would it be?

Does unaliasing have an effect to the security of a shell script which just uses full paths?

Recently I had a discussion about code security. Someone argued that one should set PATH, IFS, umask in a script and delete existing aliases (by using unalias) to improve the security or to mitigate weaknesses.

The script itself is used to generate invoices. So it reads an INI file, creates a LaTeX file and generates PDF output. The code in question is:

unset -f command
unset -f unalias
unalias -a

In my opinion this has no effect regarding security. The script just uses what is there. So if someone set an alias, it was either the user or a sysadmin. They should know what they’re doing.

Is it useful to use unalias for this script and does it improve the security?

programming languages – Can SE be divided into several separate career paths with separate skillsets?

programming languages – Can SE be divided into several separate career paths with separate skillsets? – Software Engineering Stack Exchange

graphs – Find an algorithm which returns the weight of a lightest path between all paths with a weight divided by three

Question: Find an algorithm which returns the weight of a lightest path between all paths with a weight divided by three in a graph with natural weights of the edges.

My instructor has given me a hint of doing calculations modulo three and creating a new graph and applying Dijkstra’s algorithm on it.

I have no idea how to solve this question and I would be happy to get your help.

Thank you

Unity: NavMeshAgent fails to find paths in certain areas in NavMesh

I’ve been using Unity for about 2 days, and I have a scene with a navmesh. I can click on the NavMesh and get the NavMeshAgents to move to that position most of the time. However, there is a region of the NavMesh where it fails to generate a path to. I technically have two NavMeshes, because I have two different sized NavMeshAgents, but both fail in the same region. Since I’m very new to Unity, I don’t know how to diagnose this, much less fix it. How should I go about learning more about this problem?

EDIT: I can path through the affected area, as long as the destination point is on the other side of it. Also, when I put a cube in the middle of the affected area and rebake the NavMesh, the problem area moves to a new location, so it must have something to do with the geometry.

eulerian paths – For every nondeterministic Turing machine, must there exist an equivalent deterministic one that runs in no more than twice the time?

If this were the case, then we would have P=NP, since then any polynomial-time NTM could be made into a polynomial-time DTM.

Also, it is known that an NTM in time n can do more than a DTM in time n, that is, DTIME$(n)subsetneq{}$NTIME$(n)$, see

However, you asking whether NTIME$(f(n))$ is contained in DTIME$(2f(n))$. For any $finomega(n)$, one has DTIME$(2f(n))$=DTIME$(f(n))$, so your question boils down to whether NTIME$(f(n))supsetneq{}$DTIME$(f(n))$. This question seems open.

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