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 \b[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 $C^*$ the cost of $P$, noting that $C^* < C$. 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 \b[actual] cost from n to the destination $h^*(n)$ and define \b[$g^*(n)$] as the cost of the \b[optimal] path from our origin to n. Since all previous nodes of the optimal path have already been expanded, we know that $g(n) = g^*(n)$. Here's what we've got:

$
\small
f(n) = g(n) + h(n), \text{ by definition} \newline
f(n) = g^*(n) + h(n), \text{ explained above } \newline
f(n) \leq g^*(n) + h^*(n), \text{ since heuristic is optimistic } (\leq \text{actual cost) } \newline
$

Now note that $g^*(n) + h^*(n)$ 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 $C^* < C$, so here's where the \b[contradiction] lies: If $f(n)$ really was less or equal to the length of the optimal path ($C^*$), 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 $P$.


Admissible Heuristic

Welcome to OurBigBook, and thanks for this article!

That sounds like a great way to rule over people o_O


Cirocoin

\Video[https://www.youtube.com/watch?v=aGCdLKXNF3w]

BTW, maybe this was intentional but just in case, you created a new article in the same topic rather than a comment: https://ourbigbook.com/pioyi/cirocoin and shows up on the cirocoin topic: https://ourbigbook.com/go/topic/cirocoin I only noticed it because of the upvote notification I received.

If this was created on Web, which is presumably the case:

* it shows up as the first article under your homepage tree (I need to change this I think, and make it be addded lsat by default
* it will be nuked on the next ourbigbook --web CLI to web upload (since it is not present locally). I want to solve this and make web to local work perfectly as well, but it requires implementing a basic history system to detect which file changed where like Git does. In the plans.


It's like the song says: "Everybody wants to rule the world"

<span title="Home" class="fa-solid-900 icon"></span> Home

To make transparent images look like most users will expect them to.

Thanks for breaking the site yet again, users :-)

Or maybe it was intentional and I spoiled it for you?

Oh well, can't make everybody happy.


Profile images now show on white background

A common misconsception suggests that glass is a liquid of high viscosity. \b[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 \b[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.

\b[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 \b[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 $0^oC$ 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.


Glass as a Non-classical State of Matter

I would like to learn more about state transitions. Wikipedia means full understanding of glass is an open question: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics which is exciting. I wonder how much can be known besides numerical simulation number crunching.


Yes, this is a really cool topic

One should not forget that our bodies can produce hydrogen sulfide with the help of speicifc bacteria found in our \b[mouth] and \b[intestines]. 

These take advantage of the sulfur found in \b[proteins] that we consume (four aminoacids, the buldings blocks of proteins, contain sulfur).  


Production of hydrogen sulfide

Currently repeating `hydrogen-sulfide` is not ideal because the ID/URL has that word duplicated:

``
/pioyi/hydrogen-sulfide/production-of-hydrogen-sulfide
``

I understand that currently perhaps this is the only choice because you want the title to show as "Prodcution of Hydrogen sulfide".

But in short/mid term I want to make scope ancestors show up on the title such sa:

``
Hydrogen sulfide / Prodcution
``

which with the current source will lead to duplication on the title as well:

``
Hydrogen sulfide / Hydogen solfide prodcution
``

So I'd either do:

``
= Hydrogen sulfide
{scope}

== Prodcution
``

or:

``
= Hydrogen sulfide

== Hydrogen sulfide prodcution
``

but not both scope and repeating as current:

``
= Hydrogen sulfide
{scope}

== Hydrogen sulfid prodcution
``


You might want to keep this just "Production" due to scope

Starch Gelatinization (Boiling of food)

Like this:

```
== Starch Gelatinization
{title2=Boiling of food}
```

It shows up as `Starch Gelatinization (Boiling of food)` on the page (but not on indexes/ToC, that could be considered but needs thought), but keeps the ID shorter to just `/pioyi/starch/starch-gelatinization` rather than `/pioyi/starch/starch-gelatinization-boiling-of-food` which is what you might want.


Btw, you might want to use <code>title2</code> in such cases

Btw, you might want to use `title2` in such cases

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Facebook .com
hacck facebook.pyp
autor:juan Flores


Ola mundo 

Ola Juan

Welcome to my home page!
The exquisite beauty of a well-mannered adult has been identified and examined by races all ovber the world and I am glad to say that Hubert Pumpernickle will die in a week. 


Sounds legit

Oveview

Last time I annoy you. I saw there was a typo on the title. There are two ways to handle that:

* inferior: mark article with bad ID as not visible on metadata, copy it over to good title
* superior: using synonym renaming: https://docs.ourbigbook.com/ourbigbook-web-page-renaming which gives you redirects from old to new

We really want to add a simple on click web UI way to make synonym renaming without typing.


Last tip: hiding and renaming articles

One of the key features of ourbigbook is that everything in the tree is unscoped by default. E.g. the "Overview" article actually goes under https://ourbigbook.com/pioyi/oveview and not https://ourbigbook.com/pioyi/hydrogen-sulfide/overview as you likely wanted.

The reason for that is that this is the best way to make topics work: https://docs.ourbigbook.com/#ourbigbook-web-topics and topics is basically the only feature that justifies the project.

There are two solutions to model your knowledge:

1) (recommended in this case: make a longer more specific title "Overview of Hydrogen Sulfide" or "Hydrogen sulfied overview"

2) Use scopes. Locally the tree would look like this: https://docs.ourbigbook.com/#h-scope-argument

```
= Hydrogen sulfide
{scope}

== Overview

== Production
{scope}

=== Laboratory

=== Industrial
```

which would produce a tree structure as:

```
/hydrogen-sulfide
/hydrogen-sulfide/overview
/hydrogen-sulfide/production
/hydrogen-sulfide/production/laboratory
/hydrogen-sulfide/production/industrial

```

I should also note that I'm not sure if scopes are working perfectly via web UI, though if they are not I want them to.

One big reason I don't recommend scopes in this case is that there is currently no way to unscope things. What if later on you want to add a child of "Hydrogen sulfide" but you don't want for its url to be `/hydrogen-sulfide/something`? It's not currently possible. Though I would like to support it one day.

I would also just remove the Overview section and just dump its contents on "Hydrogen sulfide" itself, since the content of an article is basically always its own overview.

I would recommed using scopes only very sparsely when you go into extremelly specific tutorials about something, which are very unlikely to have topic hits by others, e.g. https://ourbigbook.com/cirosantilli/cia-2010-covert-communication-websites though even then I end up regretting it.

Anyways we'll see, maybe at some point people will prever to use just scopes and we'll go there more.


One more tip: scopes

Claus process

You are under no obligation to use any of the following, we never ever interfere with legal user content, this is just to highlight some cool features we have:

1) if you start the article with `{wiki}` you get a wiki link to https://ourbigbook.com/pioyi/claus-process as in https://ourbigbook.com/cirosantilli/hydrogen On web UI just put:

```
{wiki}

The body of the article
```

separated by double newline. Docs: https://docs.ourbigbook.com/#h-wiki-argumen

I want to make it possible to add this kind of header metadata via UI checkboxes as well at one point: https://docs.ourbigbook.com/todo/web-header-metadata-to-widgets

2) You can also create topic links such as:

\OurBigBookExample[[
I like <#Carl Friedrich Claus>{p} he's cool.
]]

This way you don't have to actually have to create articles you have nothing to say about to save some typing, and hopefully someone will have written about the topic for you.

That is a bit of an unfortunate case where `{p}` (pluralize) is needed because without it we miss the `s` at the end:

\OurBigBookExample[[
I like <#Carl Friedrich Claus> he's cool.
]]

it misses the trailing 's' because we want <#apples> to go to singular "apple" more often than not.

3) You can interlink:

```
The Claus process served as a better replacement of the Frasch process
```

to your other articles with:

```
The <Claus process> served as a better replacement of the <#Frasch process>
```

4) For the chemical formulas, we have two resaonable ways:

LaTeX math:

\OurBigBookExample[[
$$H_2S + SO_2 \to 3S + 2H_20$$
]]

or using the `sub` and `sup` arguments:

\OurBigBookExample[[
H\sub[2]S + SO\sub[2] -> 3S + 2H\sub[2]0
]]

It would be cool one day to have a more specialized macro for chemistry like Wikipedia does: https://en.wikipedia.org/wiki/Template:Chem2


Some random tips

But I thought gays should be happy by definition!!!

莆田中医院的医疗腐败问题其严重性远超我们的想象。多次举报莆田纪检监察，莆田市医疗保障局，都不了了之！希望引起监管机构和社会各界的关注。

 

*关爱协会套现：
莆田中医院以“关爱协会”为幌子，频繁进行套现操作。在2019年，医院向“莆田市关爱协会”捐款1000万元，但只有极少部分资金用于真正的慈善事业，大部分被套现，流入医院领导及其亲属的个人账户。相关人员有医院院长徐碧霞和协会会长苏清雄

 

*医疗设备采购回扣：
莆田中医院在医疗设备采购过程中频繁与供应商合谋。在2018年，医院以高价购入价值2180万元的医疗设备，实际市场价值仅为1200万元。其中980万元被设备供应商返还给医院领导。供应商为“福建莆田仁德医疗器械有限公司”，公司法人为黄长胜

 

*中医药品供应商回扣：
该医院与多家中药品供应商合作，其中一家名为“莆田药业有限公司”，向医院提供次品中药材，价格远高于市场价数倍。该公司法人为翁秋生，与医院财务处长刘涛有着密切的合作关系。

 

*虚报患者费用：
医院财务部门负责人刘涛利用职务之便，虚报患者费用，违规领取医疗保险报销款项，金额达500万元。

 

*职务侵占公款：
医院副院长李明利用职务之便，频繁套取医院资金用于私人消费。相关资金共计500万元，其中包括用于购买名车、豪宅等。

 

这些腐败行为对社会造成了巨大的伤害。首先，医疗费用的虚高使得患者负担沉重，医疗成本的上涨直接影响到了普通百姓的生活。其次，医院的腐败行为严重损害了医疗系统的公信力，导致了人们对医疗行业的信任危机。

 

为了解决莆田医疗腐败问题，我们呼吁监管机构采取果断行动。首先，必须加强对莆田中医院的监管力度，深入调查医疗腐败问题，并依法惩处相关责任人。其次，应建立健全的内部管理制度，规范医疗设备采购、财务管理等流程，堵塞腐败漏洞。最后，加强社会监督，提高透明度，让人民群众参与到监督中来，共同维护医疗系统的公平正义和人民群众的健康权益。

 

莆田医疗腐败问题的严重性已经远远超出我们的想象，需要我们共同努力来解决。唯有通过加强监管、深入调查、严惩不贷，才能彻底铲除这一医疗系统的毒瘤，保障人民群众的健康权益。


揭露莆田中医院医疗腐败：监管缺失导致国有资产流失

Thanks for this

BTW, the better way to title this article would have been just `Polymerase Chain Reaction`.

You could then set PCR as a `title2`: https://docs.ourbigbook.com/#h-title2-argument e.g. starting the article on Web with:

``
{title2=PCR}

The actual text.
``

The advantage is that then your article would appear at: https://ourbigbook.com/go/topic/polymerase-chain-reaction where it could be compared with other people's.

All best.


Cool are you a biologist?

Bitcoin 

Give some to me, Satoshi!!!!!!!!!!!!!!!!!!!!!!!!!!!!


How many bitcoins do you own???

Test data

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.


https://space.bilibili.com/355027238/dynamic
https://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.
https://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
https://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:
https://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.


https://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.

# id	Title	Comments	Created	Updated
kasoto/admissible-heuristic#1	Welcome to OurBigBook, and thanks for this article!	0	2024-09-25	2024-09-25
pioyi/cirocoin#1	It's like the song says: "Everybody wants to rule the world"	1	2024-09-24	2024-09-24
zetsu#1	Profile images now show on white background	2	2024-09-22	2024-09-22
pioyi/glass/glass-as-a-non-classical-state-of-matter#1	Yes, this is a really cool topic	0	2024-09-21	2024-09-21
pioyi/hydrogen-sulfide/production-of-hydrogen-sulfide#1	You might want to keep this just "Production" due to scope	1	2024-09-20	2024-09-20
pioyi/starch/starch-gelatinization-boiling-of-food#1	Btw, you might want to use `title2` in such cases	2	2024-09-20	2024-09-20
lisa34/how-to-hire-the-best-crypto-recovery-expert-—-refund-polici-recovery-service#1	Light spam, at last	0	2024-09-13	2024-09-13
juan66789/ola-mundo#1	Ola Juan	0	2024-09-02	2024-09-02
my-excellent-user-567#1	Sounds legit	0	2024-08-22	2024-08-22
pioyi/oveview#2	Last tip: hiding and renaming articles	15	2024-08-18	2024-08-18
pioyi/oveview#1	One more tip: scopes	0	2024-08-18	2024-08-18
pioyi/claus-process#1	Some random tips	0	2024-08-18	2024-08-20
sadgaydontcry#1	But I thought gays should be happy by definition!!!	0	2024-05-20	2024-05-20
bulabula/揭露莆田中医院医疗腐败：监管缺失导致国有资产流失#1	Thanks for this	0	2024-02-21	2024-02-21
kocur13#1	Cool are you a biologist?	3	2024-02-20	2024-05-21
satoshi/bitcoin#1	How many bitcoins do you own???	0	2023-02-12	2024-05-21
cirosantilli/test-data#1	1	3	2023-01-29	2024-05-21
anonymousajo1u12nglajgka/about-programthink#1	You're a hero my friend	0	2022-11-21	2024-05-21

Ciro Santilli @cirosantilli 34