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

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

Key techniques for leveling mana origin magic:

In order to achieve the level evaluation method of mana origin magic, it is necessary to apply a variety of numerical tools and mathematical algorithms to analyze and process the data obtained from actual tests, and find a universal formula that can be used to analyze the correlation of various data types.

So, for practical reasons, this section will cover the mana flow node, the annealing equation, the posture of the duplex pair at the mana flow node, and the universal formula for rating mana origin magic.

Mana flow node:

The mana flow node is the key to whether a caster can successfully cast a spell and what color mana spell is cast. As we all know, mana flow nodes have five degrees of freedom: red, white, green, blue, and black.

Thanks to the popularity of flexible control spellcasting, we were able to reduce the cost of mana flow when controlling the flow of single or multiple mana, and the mana flow through the mana flow node was smoother and the risk of mana burn was reduced—thanks to my classmate Victor. The technology he invented is truly a boon to all spellcasters.

Annealing formula:

The annealing equation is a heuristic search calculation based on the annealing method, and we would like to thank Scorpius Cook, senior accountant of the Orzhov Chamber of Commerce, who discovered it. This calculation was originally used to estimate the population, but I found value in this equation that had been buried for many years.

The simple principle of this equation is to start with an initial node and then pick up another new node in the adjacent area of that node (both before and after). This new node generated will accept the Monte Carlo method discovered by Mr. Monte Carlo and the Marpus criterion discovered by Mr. Mapps.

The annealing equation is actually an equation to solve the optimal solution of a problem, based on its characteristics, we first need to construct a nonlinear cost function, and then anneal it to achieve the optimization purpose.

Let's assume that the state of the previous node is a, then its state becomes b after adding a certain random perturbation. Correspondingly, the result of its state is B1, which is described as the probability of receiving this perturbation p as 1 plus the mana constant ε negative B1 minus A1 multiplied by the reciprocal of temperature t.

Amazingly, we were able to see that the formula looked incredibly beautiful under the glow of mana. After the state transfer, if the energy decreases, then the act of this transfer will be accepted; If the energy becomes larger, it means that the node of this calculation deviates from the global optimal position.

However, in this formula, we will not discard this result right away. Because of all the different factors that affect mana flow, we can't deny that there are less than good nodes. You know, for a spell's path, the local optimal is not necessarily the global optimum. Spellcasters often try to minimize the distance between each mana flow node when casting spells, theorizing that the smallest sum must be the smallest.

Wrong! Miss by a mile! We know that the valves and flow of the mana flow node are not fixed, they always fluctuate within a certain range with the mana tide. Capers who can observe this subtle change tend to be better - their spells are completed quickly and well, compared to other casters who can't master the method.

That said, being able to go for every mana flow node to be perfect may have a negative impact on the full release of the spell, either slower, less powerful, or more mana burn.

Therefore, there is value in not throwing away nodes that are not good enough right away. However, it is not to accept all the nodes that are not good enough, but to judge them by the acceptance probability p. When the ε is less than p, the transfer will also be accepted, otherwise, it will not be accepted, and the node will be discarded and re-stated.

One of the main parameters of the iterative process of the control equation is the temperature t. After multiple transformations of the equation, the global optimal node of temperature t for the optimization problem can be obtained. By gradually decreasing the value of t, that is, gradually cooling and annealing, when the temperature is close to 0, the optimal node of the whole problem is obtained.

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

"Give me the order, and everyone will form a team at once! The wounded soldiers are in front, and the non-wounded soldiers are in the back! Prapi Bolton ordered. Hearing this order, all the wounded soldiers turned to ashes. Prapi Bolton was known for his ruthlessness, and if a wounded soldier would be a stumbling block in a retreat or attack, he would not hesitate to use the Overseers to drive them into battle or leave them to fend for themselves. Of course, there is also the case of a war against the kingdom of Ahmad more than a decade ago, when Prapi Bolton trampled more than 800 wounded soldiers directly on the muddy road, and the flesh of these wounded soldiers turned into the iron hooves of war horses and the sludge under the wheels of supply vehicles.

However, even so, the wounded soldiers did not flee, but consciously lined up (of course, the ones who could still move). Because they knew that if they didn't line up, Prapi would immediately call the Overseers, and the Overseers' knives would cut their necks one by one.

But in the end, on the other hand, Prapi still gave these poor guys a "way out". If, after the order, the wounded survived to the end of the war, they were allowed to return home and end their military service. And their children are no longer required to do military service.

You must know that the reason why the army of the Tangenis Command has been able to maintain such a high level of quantity and quality is not unrelated to the brutal rule practiced by Gegit and his lackeys.

The people of Tangorness are all under this reign of terror. Gaget demanded that all of them, young and old, be required to serve in the military for a period of five years. The farmer and orchard that were abandoned during this period will not be compensated by Gagette. The only preferential policy he gives you is that when you go to the military, your family will not be killed by the executioners sent by the local executive.

Of course, for retired and wounded soldiers, Gage also gave benefits - he exempted these families from all taxes for three years, and in the next ten years, the taxes were reduced by a fifth, and after ten years they were no longer valid. For the valiant, Gage did not hesitate to flank knights or promote them to non-commissioned officers. Thus, while its brutality caused some of the Tangnis to flee, some of them were threatened or enticed.

"The wounded soldiers are ready to eat, pay attention, you have to eat enough, because this may be your last meal, you know what that means." Prapi picked up a wooden bowl and stirred it in the porridge full of oats and meat batter.

Having eaten and drunk to his heart's content, Prapi ordered the healthy soldiers to eat. After a brief trimming, he gave the order to attack.

"All the lightly injured are attacking head-on, and the seriously injured are responsible for carrying the assistive devices. Listen up, able-bodied guys, for when the wounded attack on the Ivory, you must go around to the cliff behind the Ivory. You'll have to climb the cliffs behind the Ivory at night, and then quickly storm the walls. Of course, this can be done with only a small number of people, and for the rest, I ask you to march behind the wounded soldiers and erect the siege ladder. Speaking of this, he looked at the wounded soldiers in the formation, there were many lightly wounded, and they could still fight. Seeing this, he nodded with satisfaction, and then continued: "Wounded soldiers, you also have a chance to live, I don't care if you rush to the city wall or not, if you survive until the end of the war, you can be immediately sent back to Tangenness to enjoy the treatment of retired soldiers, and if you make meritorious contributions, you can also receive more rewards." Do you maggots get it? ”

The wounded soldiers did not respond, but nodded silently. However, visible to the naked eye, there is a little more color in their dead gray eyes, which is hope, fantasy, joy, and greed.

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

"The moon is so hazy tonight, and the weather seems to be gloomy, but it is beautiful." Mirialia said to Lily Bones.

Lily gestured disappretently, signaling Milia Khan not to care, this glorious moment of victory, all you need to do is drink.

"Hopefully nothing happens tonight, it's not a good night." Mirialia said worriedly.

"Don't be so pessimistic, Khan, if you want me to say, although the little man Prapi can't swallow this breath, he probably won't come to attack today, we can sleep well, after all, he just lost the battle." Mark said the same.

"I'd rather suggest that the sentry should not be abolished, and that it would be better to send more of them. If the enemy takes advantage of the darkness to attack the city, we can react as soon as possible. Wenner said.

"What if Prapi is trying to seduce us? We have just finished a terrible battle, we are tired, the soldiers need to rest, if we don't sleep tonight, then how will we deal with them if they come to attack the city tomorrow? Mark said that Lily agreed with her husband's statement.