Michael Donawan's Graduation Thesis of the Holy Falcon Empire Wizarding Academy (3):

"Research on the Rating Method of Mana Origin Magic" - Michael Donawan.

The steps to implement the annealing equation are as follows:

1. Return to the source. Given the interval of change for each mana flow node in the equation, an initial node is randomly selected within those intervals, and the corresponding initial value of the "source" energy is calculated based on this initial node. In the equation, set the initial temperature and the end temperature of the iteration. The threshold for the probability of accepting a new node in each iteration is ε mana constant. The cooling law in each iteration is set as the product of the initial node temperature and the annealing coefficient as the new node temperature.

2. Add random perturbations. At a certain annealing temperature, perform a random perturbation of the mana flow node at the current temperature value, causing it to create a new node at a new node inclination. Once a new node is obtained, its corresponding "source" energy value is calculated.

3. If the energy of the change is less than 0, the new mana flow node is accepted, otherwise the acceptance probability P is used to determine whether the new node is accepted. If p is greater than ε, the new node is accepted, otherwise the new node and its calculation process are discarded, and the perturbation is re-increased from the previous "source" energy value and the new node is calculated.

4. Repeat steps 2 and 3 at a certain temperature.

5. Annealing gradually according to the cooling law.

6. Repeat iterations 2 through 5 until the equation converges to a temperature close to 0. At this point, you get the complete mana flow node and its trajectory. Add up the mana flow required by these trajectories to get the mana source flow for the entire spell.

Doublet pair of valve poses at the mana flow node:

A double pair is a number made up of two tuple pairs. Pairs of numbers that exist in tuple pairs are virtual mana units orthogonal to each other. It is characterized by the fact that they do not exist alone and cannot be perceived alone. When the pair is split, the mana flow disappears, but when they are combined, a tuple pair represents a negative unit of mana flow. Or to put it another way, it's the flow of mana in mana burn.

In the reference frame of a mana flow node, the valve of its flow spirals around the pivot point. If the valve is in such a way that it resonates with a certain resonance with the pivot point, then the mapping of the frequency can be represented by two tuple pairs. And over time, we were able to figure out where and in what position the mana flow valve was in a mana flow node.

Based on this valve, we can construct a mana flow valve that tends to the next mana flow node, which can be used in our annealing formula without even having to change the formula. Thanks to the cultivator Taixu Dao Master of the Qin'a Empire, he invented this tuple pair that was originally used to calculate the "Heavenly Dao Cycle" pursued by cultivators. I have a hunch that the "Heavenly Dao Cycle" in the mouths of the cultivators of the Qin'a Empire has something in common with the tidal fluctuations of our mana. Elsa's mana has a tidal phenomenon, and we, as creatures that can invoke mana, naturally have a tidal phenomenon in our bodies, and I think this tidal phenomenon is the valve.

The four numbers in a triplet pair should satisfy a relationship where their sum should equal 1 so that their representation in the rotation matrix can be translated into mana flow node valve frequencies.

When we have this valve frequency, we can bring in the annealing equation to calculate. In addition to being able to get the global optimal mana flow node and its mana flow sum, we can also use AHP analytic hierarchy process to get the best choice for the entire cast path.

Know that the best way to cast a spell is not set in stone. Experienced spellcasters will change their cast path based on their status, enemy status, and the frequency of the mana tide in the world of Elsa, allowing them to be cast easily and efficiently in any situation.

-------------------------------------------------------------------------------------------------------------------------------------

"General Napolion, the statistics are out." A non-commissioned officer holds a roster and sketches on it, with casualty figures for each unit written next to it.

"Tell me first, and then go back, I estimate that the loss will not be small, it is estimated that there will be about 300 people, if you go in and report like this, Chief Foster will scold you for squirting blood, and in anger, he may send you to the death squad." Napolion said to the non-commissioned officer that he did not want a good non-commissioned officer to be punished for such a trivial matter, or even lose his life—it was not worth it, and there was no honor to speak of.

"112 people died, 22 were missing, 176 were seriously injured, 391 were slightly injured, 68 tents were lost, 8 trebuchets were lost, 3 of which were completely damaged and needed to be re-erected." The non-commissioned officer sighed, flipped through the roster, and said listlessly.

"The loss is indeed too great, what happened to the black wolf bird?" Napolion reached out and pressed it to his temple, stroking his unconsciously twitching tendons.

"The bird went berserk at our camp for some reason, but we killed it. Ay! This damn natural disaster, our luck doesn't seem to be good. The non-commissioned officer said.

"Go, come with me to see the brute's corpse, I think something is not quite right—it's so coincidental that I suspect someone is playing tricks, and it's the Zamir maggots who lured her here. The Zamir maggot is all too familiar with the Mist Forest, just like his own backyard. Napolion said.

"I'll show you the way! Sir! The sergeant made a gesture of please, and led Napolion to the corpse of the black wolfbird.

The body of the black wolf bird was lying on the ground, her tail had been cut off, one eye had been shot blind, and blood was still oozing out. Her back armor had been hit hard and was covered in cracked lines.

Napolion took a closer look. He first looked at the head of the black wolf bird, "Who shot her eyes blind?" He asked.

"Commander of the Guillotine Legion, Delix - he is a strong man, and in addition to using a sword, he is also good at archery. Before military service was a hunter. A non-commissioned officer who manages the army roster replied.

"Reward him, ask him if he would like to extend his service, and if he answers in the affirmative, promote him to non-commissioned officer, and let him manage a squad of archers." Napolion commanded.

The non-commissioned officer in charge of managing the roster was somewhat embarrassed, and he was not sure if his commander would be able to bypass the orders of the highest commander of Foster and appoint non-commissioned officers directly in wartime. Hence his hesitation.

"Rest assured, Chief Foster will agree, it should be said that he doesn't care about such a thing—as long as he can win the battle, he doesn't care about the process. And, you see, the black wolf bird has eyelids, and the angle of this arrow is very tricky, and it is shot directly from the angle below. You know, it's not easy to shoot from the bottom up, the angle is very small. However, you see, the black wolf bird had so much blood that the tail feathers of the entire arrow were almost submerged into the eye socket, which showed that the archer's arrow was powerful and full of confidence. Napolion patiently explained, trying to reassure the non-commissioned officer who was in charge of the roster.

The non-commissioned officer had no choice but to nod and write it down.

"Oh! What a blow! What was this struck by? He asked, pointing to the cracked back armor that had sunken down the black wolfbird's back.

"Nature is trebuchet. A trebuchet operator unleashed this attack, which was the only one that hit. ”

"Very good, commend him, reward him with a silver wolf and a small barrel of wine. You see, this blow was a blow to the beast. Strangely, though, she didn't bleed from the broken tail, so I guess we didn't do it, right? ”

"Yes, you are absolutely right, Sir Naborion. It's really not our fault, the bird broke into the camp without its tail, which is suspicious. ”

"Yes, it's suspicious. The bird was female, and her tail feathers were open, apparently just finished giving birth, and she was already very aggressive, and she was likely to retaliate if someone violated her territory. Black wolf birds are creatures that males are lazy and they don't chase prey and enemies all the time. But females are different, they will chase their enemies to death - either the enemy dies, or the enemy lives, and she dies. Naborion explained.

"By the way, there's one thing I forgot to report to you! At first I thought it was a small incident, but now I suspect it has something to do with the bird. The non-commissioned officer said.

"Tell me about it!"

"The Zamir scouts had touched the edge of the sentry before, but they had not attacked. They just threw dung and stones at our camp gates from afar, which was more like a humiliation and provocation to us. I thought there might be a conspiracy in this, so I didn't let the sentry and the troops attack. I don't think we're going to be able to do any real damage if we just provoke us, but if we get provoked and go out of the camp to hunt down the maggots, we risk being ambushed. The non-commissioned officer spoke his mind.

"You're doing the right thing, you're being cautious. The enemy's provocation indicates that they are looking for an opportunity to induce us to engage in contact warfare with them in the forest, and for the Zanmir locals who are familiar with the terrain, it is entirely possible to disrupt our deployment by guerrilla means and annihilate our pursuit team. This shows that the enemy does not have the determination, willingness, and ability to fight us head-on. But let's go ahead and hear what you think. ”

"Yes, sir. I think it's a serial calculation, if I attack, I'll be ambushed, and if I don't, I'll be attacked by the black wolf birds they attracted. I judge this way because of their-throwing behavior. I suddenly remembered that the black wolf bird's eggs smelled like this kind of dung, and it was very strong. You said it was a female who had just given birth, and if I did, I would send a local who knew the woods as a scout, steal the eggs, run away, and then project the eggs into the camp through the slings—it would be strange if the beast didn't make a fuss. ”

"Looks like we've found the truth of the matter." Napolion said with his hands on his chest.

"Are you going to find out the truth of the matter so that you can report it to High Commander Foster?" The non-commissioned officer asked.

"Of course not, young man, I just want to know the truth. You go and have the head of the beast cut off and send it to Chief Foster, saying that you have gone hunting, and this honor must be given only to the highest officer. Remember, don't talk about the truth of the matter, and don't talk about our losses. Napolion said meaningfully.

The soldier snapped and immediately said, "I think I understand what you mean, sir. ”