Ciro Santilli @cirosantilli 34

In the context of an A* search, a heuristic function is said to be admissible if it does not overestimate the cost to reach the goal. Such functions can also be viewed as being "optimistic".

When using an admissible heuristic, A* is guaranteed to return a cost-optimal solution, i.e. the best path. Let's prove it by contradiction:

Assume that the algorithm returned a path, the cost of which is greater than the actual optimal path $P$. Let's call $C$ the cost of the path that was followed, and $C^{\ast }$ the cost of $P$, noting that $C^{\ast }<C$. First, we can safely assume that at least one node in $P$ was not expanded during the algorithm's execution (if all nodes of $P$ were expanded, then $P$ would have been chosen instead since that would lead to a lower path cost${}^{[1]}$). Without loss of generallity, let's take the first occurance of such unexpanded node and name it "n". By definition, $g(n)$ holds the least known cost to reach n starting from the origin. Let's name the actual cost from n to the destination $h^{\ast }(n)$ and define $g^{\ast }(n)$ as the cost of the optimal path from our origin to n. Since all previous nodes of the optimal path have already been expanded, we know that $g(n)=g^{\ast }(n)$. Here's what we've got:

Now note that $g^{\ast }(n)+h^{\ast }(n)$ is equal to "the cost to reach n following the optimal path" + "the cost to reach the goal starting from n, following the optimal path". That's just equal to the total cost of the optimal path! However, we know that $C^{\ast }<C$, so here's where the contradiction lies: If $f(n)$ really was less or equal to the length of the optimal path ($C^{\ast }$), then the A* algorithm would have expanded this node before trying to expand the destination since $f(destination)=C>f(n)$. A lower $f$ value would have always triggered an immediate expansion. $\square$

[1]: Remember than $h(n)$ (our heuristic) is just a hint to prioritize certain expansions over others. When everything is expanded however, $g(n)$ is the sole metric that will be considered, which will always lead to the optimal path being selected, that being $P$.

A common misconsception suggests that glass is a liquid of high viscosity. This not the case. Glass is its own distinct state of matter that doesn't coincide with any other classical one. Every liquid (except Helium) can be turned into glass, if a sufficiently rapid cooling takes place. This process is called vitrification. When a liquid is cooled (water for example) it normally goes through the process of crystallization. We say that the water is frozen as ice forms which has a very specific structure that is characterized by its stability (crystalline solid). If the cooling happens quickly enough, the water molecules don't have the opportunity to occupy the lowest energy sites and this is how the amorphous solids forms.

Annealing illustrates this phenomenon. When glass is cooled down in order to solidify, this process must be done during a specific time interval in order for the molecules to have enough time to position themselves in a more stable manner. If during the glass making process, the produced glass has been solidified too rapidly, then the stress present in the solid makes it too fragile to the point where it can rupture/shatter even during handling. By reheating the glass and slowly droping the temperature again, we ensure that the glass object has gained a much more stable structure.

As crystalline solids have a melting point, amorphous ones have a glass transition temperature which surprisingly depends on thermal history (how rapidly was the former liquid made into glass?). Around this temperature point, the viscosity of the glass increases rapidly and can be classified as a solid (under classical terms). It should be noted that the viscosity as well as other properties of the substance made into glass, present a continuous change as the temperature changes. This is not the case with "ordinary" freezing as liquid water turns spontaneously into a solid in a discontinuous manner (during the freezing process the temperature stays constant. Immediately below $0^{o}C$ all the water has turned into ice).

The glass state is metastable and its transition to a crystalline solid is thermodynamically favoured although kinetically inert.

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A scribe is a person who serves a professional copyist. The work of scribes can involve copying manuscripts and other texts as well as secretarial and administrative duties such as the taking of dictation and keeping of business, judicial and historical records for kings, nobles, temples and cities. The profession has developed into public servants, journalists, accountants, bookkeepers, typists, and lawyers. One of the most important professionals in ancient Egypt was a person educated in the arts of writing and arithmetic. Scribes were considered part of the royal court, were not conscripted into the army, did not have to pay taxes and were exempt from the heavy manual labor required of the lower classes. Sons of scribes were brought up in the same scribal tradition, sent to school and inherited their fathers' positions upon entering the civil service. Much of what is known about ancient Egypt is due to the activities of its scribes and the officials. Monumental buildings were erected under their supervision, administrative and economic activities were documented by them, and stories from Egypt's lower classes and foreign lands survive due to scribes putting them in writing. In addition to accountancy and governmental politicking, the scribal professions branched out into literature. The first storeis were probably religious text. Other genres evolved, such as wisdom literature, which were collections of the philosophical sayings from wise men. These contain the earliest recordings of societal thought and exploration of ideas in some length and detail. In the Middle Ages, every book was made by hand. Specially trained scribes had to carefully cut sheets of parchment, make the ink, write the script, bind the pages and create a cover to protect the script. This was all accomplished in a writing room called a scriptorium which was kept very quiet so scribes could maintain concentration. A large scriptorium may have up to 40 scribes working. Scribes woke to morning bells before dawn and worked until the evening bells, with a lunch break in between. They worked every day except for the Sabbath. Scribes were only able to work in daylight, due to the expense of candles. The scribe was a common job in medieval European towns during the 10th and 11th centuries. Many were employed at scriptoria owned by local schoolmasters or lords. These scribes worked under deadlines to complete commissioned works such as historic chronicles or poetry. These scribes would meticulously record the information presented in the texts, but not mindlessly. In the case of herbals, for instance, there is evidence that the monks improved upon some texts, retracted textual errors, and made the text particularly relevant to the area in which they lived. Some scribes even went so far as to grow some of the plants included in the texts. They had little room or patience to disseminate the imaginary plants. The writers truly restricted themselves to only include practical information. Meanwhile, in the case of bestiaries, the scribes generally copied and cited previous texts to pass them on. Unlike the herbals, the scribes could not grow an animal in their garden, so largely the information taken from the bestiaries was taken at face value. In the 13th century, Paris was the first city to have a large commercial trade of manuscripts, with book producers being commissioned to make specific books for specific people. Paris had a large enough population of wealthy literate persons to support the livelihood of people producing manuscripts. Wait, why the paragraph break doesnt work at all?

I can not join your movement because I really have more reasons than other ones. For privacy, I can't explain that. And, For me, I know that for the current situations in China, I can't do anything. For China, I think only solution is revolution not reform. The protesters will die with nobody know that without tech. People could try, but it is a Way of Sacrifice. space.bilibili.com/355027238/dynamic chinadigitaltimes.net/chinese/667881.html According the report, this organization help programthink arrested. I research that for some days, and the evidences express its correctness. 净网志愿者协会, may one day you will be captured by them. But you are foreigner, they don't have a way to do that. 净网志愿者协会, it is a semi-official organization but with high-tech hacker technology. You know, in China, high-tech hackers will not be an offical. Because it is a semi-official organization with many young little-pink engineer, the tracking for programthink, it could be done. They are actually not wumao, but they may be more formidable opponent. But you live aboard, they can't do anything and officals will not always listen their views. Why do I think its claim for programthink's arrest is credible? Because some inference. The organization says programthink is 马勇康. github.com/programthink/zhao/issues/418 one year passed, 2022/05, offical media(only media) say 马某某，煽动分裂国家、煽动颠覆国家政权 baijiahao.baidu.com/s?id=1731886110528251526&wfr=spider&for=pc the 马 first name only has 1% population in China. Coincidence? And according the report's keyword: 浙江温州, 科技有限公司，“洗脑”，“人生导师”，顽固 just like a copycat keyword for programthink blog and it conforms characteristics. and the organization say 马勇康 is 山东人, the offical media say he is 浙江人 According the data in the website or anywhere: www.23mofang.com/ancestry/library-surname/5f34ee9eff5a3344d6a8aabe 浙江(ZheJiang province) have less 马 than 山东. And programthink family's post say programthink lastly has a business travel to a city in eastern China, you see 温州，浙江，上海，all keyword is about the eastern China. 温州 is a interesting keyword, if you search programthink's issues, it has a strange 温州 people, but no other Zhejiang province's county. And other crime such as 政治纲领, as I know for CCP cop, they need some more outstanding achievement. 继续调查中，because the CCP cop needs more news by the mouth even it is not neutral. And, it is possible that programthink think he could take the all blames on his shoulder maybe. These inference may is only inference by brain ———— we never know what is a truth. www.bilibili.com/video/BV14S4y1T7RT/?spm_id_from=333.999.0.0 净网志愿者协会 mentions programthink in the video. I only know that they may be the not many real high-tech little-pink and hackers and really can do that. They are more terrible cop, even sometimes, gov will not listen them. I don't know in 2022 the organizations like it will do what. Sometimes I think what is better? For my reasons I know I couldn't join yours. And I can't keep "doublethink"(ps: I'm not an official, official never doublethink). The only difference between China and 1984 may is the war is peace. China gov officials say China love peace, and in fact, CCP indeed take less war than other countries. But it is Chinese nature, may CCP also keep something. CCP is not worse like Russia, so it is more difficult, for any reform. And reform may not work too fast or really work, only revolution.

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