關於 math square ，我們在網路上蒐集到這些相關的討論、資訊與評價

其實唔止Matrix，所有數學系統裏面嘅 Zero 都勁有用，有用到好多時用咗都唔知，直到你去諗：如果無人發明「零」呢個數字，究竟點樣先至可以得到相同嘅效果？🧐⁣
⁣
例如：⁣
數量 — 你唔用零，點樣表達「無」？🤔⁣
機率 — 你唔用零，點樣表達「一定唔會發生」？🤭⁣
進制 — 你唔用零，點樣表達「極大嘅數字」？🤗⁣
⁣
分享一個冷知識畀你：據說「0」呢個符號係印度人發明，由無 0 去到有 0 足足花咗超過1000年，先至發明咗呢個窿出嚟😨⁣
⁣
我寫呢篇文章，就係想提醒你，記得「0」係好重要嘅，下次使用嘅時候，記得問清楚自己，眼前嘅 0 究竟係一個 #點樣嘅零 ？例如：⁣
⁣
Matrix嘅0 — 究竟dimension係幾多x幾多？係咪square matrix？⁣
Vector嘅0 — 你記唔記得加返個箭咀喺佢頭殼頂？⁣
⁣
若然你係M1同學，照樣睇埋呢篇M2專欄，我又問你一件事吖：⁣
Probability嘅0 — 例如P(A)=0係咪代表A就係empty set呢？歡迎作答～👇🏻⁣
⁣
-----------⁣
#M2技巧王 幫你避開考評陷阱，教你搶分技巧；M2 輕鬆攞 Lv 5+ 喇🌟⁣
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🎲賭Sir｜高階數學考試專家⁣
⁣
🎓21 項數學公開試．以一 Take 過考取完美戰績⁣
⁣
DSE：Math+M1+M2【5**】⁣
CE & AL：Math+A.Math+Pure+Applied【A】⁣
IAL：C12+C34+F1+F2+F3+M1+M2+M3+S1+S2+S3+D1【A】⁣
IGCSE：Mathematics+Further Pure Mathematics 【9】⁣
⁣
🖥最高人氣補習網紅・貼地教數別樹一格⁣
⁣
頻道 #杜氏數學 2016 年創辦，訂閱 65,000+，多條教學影片點擊 100,000+；2018 年獲出版社邀請，撰寫暢銷書《5**數學男人嫁得過》推廣「聰明應試」理念，並鼓勵年青人堅守自信。⁣
⁣
🧠以心理學、高效學習融入補習教育當中⁣
⁣
從中文大學風險管理學士畢業之後，鑽研超速學習法（Ultralearning）及教育心理學，將高效學方法先行用於自己身上，無間斷學習新知識；四年後重返校園，完成中文大學數學碩士（大數據分析）課程，期間考入門薩學會（Mensa），實證超速學習法。⁣
⁣
🏆座右銘⁣
⁣
好多人以為自己因為對數學無興趣，所以數學低分；事實剛好相反：因為自己數學低分，所以對數學無興趣。試諗下，若然你有歌神嘅聲線，你仲會對唱歌無興趣嗎？⁣
⁣
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#數學 #DSE #dser #math #maths #afterschool #dsemath #examskills #mathtutor #followme #2022DSE #2023DSE #2024DSE #tutor #mathtutor #DSEfighter #tutotial

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

ใช้ AI ตรวจจับใบหน้าคนในรูป
สมัยนี้ดูจะธรรมดาเกินไป คงเห็นกันทำเยอะแล้ว
เรามาดูผลงานวิจัย AI อีกเวอร์ชั่นหนึ่ง
ใช้ตรวจจับอารมณ์คนขณะเรียลไทม์ได้ด้วย ... อะฮะไม่ธรรมดา
.
จาก paper ต้นฉบับ
"Real-time Convolutional Neural Networks for emotion and gender classification"
https://arxiv.org/abs/1710.07557
.
เทคนิคโดยย่อเขาจะใช้ Deep learning เป็นประเภท CNN
มาทำการตรวจจับ 2 อย่างในรูปภาพได้แก่
1) ตรวจสอบว่าเป็น เพศชาย เพศหญิง ...มีความแม่นยำสูง ถูกต้อง 96%
2) ตรวจจับอารมณ์คนได้แก่ ....แต่ความแม่นยำยังต่ำอยู่ ถูกแค่ 66%
.
ซึ่งอารมณ์คนที่จับได้ มี่ 8 อย่าง ดังนี้
“angry”, “disgust”, “fear”, “happy”,“sad”, “surprise”, “neutral”
แปลเป็นไทย
“ โกรธ”,“ รังเกียจ”,“ กลัว”,“ มีความสุข”,“ เศร้า”,“ แปลกใจ”,“ เป็นกลาง”
.
ซึ่งเทคนิคนี้สามารถตรวจจับภาพหน้าคนได้ทั้งแบบภาพนิ่ง
หรือเป็นภาพวีดีโอก็ได้
ในระดับเรียลไทม์ ....ขอบอกเลย
.
แต่เท่าที่ลองจับอารมณ์คน
ก็ยังเห็นผิดพลาดเยอะอยู่นะ
ถ้าคนสีหน้านิ่งเกิ๊นไป ก็ตรวจไม่ได้
ถือว่าปราบเซียนอยู่เหมือนกัน
.
คิดไปคิดมา เปลี่ยนมาตรวจจับหน้าคนในละครแทนดีกว่า
เลยไปเอามาจากละคร "น้ำตากามเทพ" ของจีทีเฮช
เหตุผลนักแสดงเรื่องนี้ เขาเล่นโอเวอร์แอคติ้ง เล่นใหญ่ดี
ผลปรากฏว่าตรวจจับได้ดีขึ้นเยอะ
(แต่ก็ยังมีผิดอยู่ เอ่อๆ บ้าง)
.

ทั้งนี้ในคลิปจะตรวจจับอารมณ์คนอย่างเดียว
จะเห็นเป็นกรอบสี่เหลี่ยมครอบหน้าคน
แล้วขึ้นข้อความบอกว่าสีหน้าอารมณ์ตอนนี้คืออะไร?
แต่ไม่ได้โชว์เพศชาย หรือหญิงให้ดูนะบอกก่อน
:
:
ใครสนใจอยากลองทำ
ก็เชิญดูโค้ดเขาตามนี้เลยครับ
มันเป็นของงานวิจัยเขาโดยตรง
https://github.com/oarriaga/face_classification/
.
ทั้งนี้โค้ดสามารถอ่านจากรูปภาพ
หรือจากกล้องเวบเคมก็ได้ ...ชีวิตดีดี
ภาษาที่ใช้เป็น python ครับผม
แต่เท่าที่ลองรัน ก็เจอผู้สร้างวางยา ยังมีบั๊กอยู่นะครับ ฮ่าาาา
:
ยังไงก็เอาไปศึกษาได้
หรือจะไปต่อยอด ....ทำให้เหนือกว่าเขาก็ได้ครับ
:
สำหรับวิธีติดตั้งและใช้งานภาษาไทย ผมเขียนไว้ที่นี้นะครับ
https://www.patanasongsivilai.com/…/real-time-emotion-detec…
:
หมายเหตุ ในคลิปผมใส่เสียงพูดตัวละครเข้าไป เพื่ออรรถรสในการชม
ติดตามคลิปนี้ได้ที่ youtube อีกที
https://youtu.be/fzgXTNXHOME
.
.
ขอแนะนำหนังสือ "AI ไม่ยาก เรียนรู้ด้วยเลขม. ปลาย"
เน้นพื้นฐานคณิตศาสตร์ระดับเด็กม. ปลาย
ไม่มีโค้ดดิ้งให้ปวดหัว
ก็สั่งซื้อได้ที่นี้ (ขออภัยยังไม่มีเล่มกระดาษขาย)
👉 https://www.mebmarket.com/web/index.php…
.
ส่วนตัวอย่างหนังสือ ก็ดูได้ที่
👉 https://www.dropbox.com/s/fg8l38hc0k9b…/chapter_example.pdf…
.
✍ เขียนโดย โปรแกรมเมอร์ไทย thai programmer
Use AI to detect faces in pictures
It seems too ordinary these days. We probably see a lot of people doing.
Let's see another version of AI research.
Use to detect real-time people's emotions too... Aha. Extraordinary.
.
From the original paper.
"Real-time Convolutional Neural Networks for emotion and gender classification"
https://arxiv.org/abs/1710.07557
.
Brief technique. He will use Deep learning as a CNN type.
Let's do 2 detections in the photo:
1) Check out male, female... High accuracy 96 % accurate
2) Emotional detection. People are.... but accuracy is still low. Only 66 % right.
.
The following 8 people who caught me.
“angry”, “disgust”, “fear”, “happy”,“sad”, “surprise”, “neutral”
Translate to Thai
′′ Angry "," disgusted "," afraid "," happy "," sad "," surprise "," neutral ′′
.
This technique can detect a human face in a slide way.
Or it can be a video.
In real time.... Let me tell you.
.
But I try to catch people's emotions.
Still see a lot of mistakes
If the face is too calm, I can't check.
It's considered a masterful defeat.
.
Think about it. Change to detect people in drama instead.
So I took it from GTH's ′′ Cupid Tears ′′ drama.
This actor reason he plays over action. He plays big.
Turns out a lot better detection
(but still wrong, well, some)
.

In the clip, I will detect emotion only.
I will see it as a square frame in front of people.
So what's the current expressions?
But I didn't show you male or female. I told you first.
:
:
Who is interested in trying it
Let's see his code according to this.
It belongs to his research directly.
https://github.com/oarriaga/face_classification/
.
The code can be read from pictures
Or from the web camera... Life is good.
The language used as python.
But as far as I try, I have found a poisoning creator. There is still a buck. Haha.
:
I can study it anyway.
Or you can go to the top.... You can do it above other people.
:
For how to install and use Thai language, I wrote this here.
https://www.patanasongsivilai.com/blog/real-time-emotion-detection-ai
:
Note in the clip, I put character voice in for the taste of watching.
Follow this clip on YouTube again.
https://youtu.be/fzgXTNXHOME
.
.
Introducing the book ′′ AI. It's not difficult to learn with university numbers. The end ′′
Focusing on the base of math. Level of middle school kids. The end.
No code to get headache
You can order here. (Sorry, no paper book for sale)
👉 https://www.mebmarket.com/web/index.php?action=BookDetails&data=YToyOntzOjc6InVzZXJfaWQiO3M6NzoiMTcyNTQ4MyI7czo3OiJib29rX2lkIjtzOjY6IjEwODI0NiI7fQ
.
Personal like a book. You can see it.
👉 https://www.dropbox.com/s/fg8l38hc0k9b0md/chapter_example.pdf?dl=0
.
✍ Written by Thai programmer thai coderTranslated

?杜氏數學 官方網站： http://www.HermanToMath.com
?賭Sir 幫你急救 DSE 數學： https://hermantomath.skx.io/courses/6328693527937024
----------
賭Sir語錄?學習知識 不宜揀飲擇食
賭Sir語錄?包拗頸法則 e.g. 唔恐慌！唔飲喜茶！唔睇賀歲片！
----------
⚡快速跳播目錄：
02:37 ?Hypothesis Testing原理?
11:42 ?戀愛統計學應用?
----------
?️賭Sir是杜氏數學Herman To Math的始創人
?全港唯一「完爆」【DSE Core+M1+M2】、【IAL 12科Maths】、【AL Pure+Applied】、【CE Maths+A.Maths】的數學導師
?全港第一最多訂閱粉絲的數學教育YouTuber
?YouTube觀看次數超越700萬、訂閱粉絲超過50000人
----------
? Mensa Club member
? 中文大學 數學碩士畢業（Big Data stream）
? 中文大學 風險管理學士畢業
----------
?流行文學作家，出版著作：
《賭波男人嫁得過》?（2018）
《碌葛男人嫁得過》?（2018）
《5**數學男人嫁得過》?（2019）
《YouTuber新手到網紅》?（2019）
《賭馬男人嫁得過》?（2020）
----------
?YouTuber Go網絡課程 全港最平+獨家 報讀優惠：
http://hermantomath.blogspot.com/2019/03/youtuber-go-link.html

?無限操數王(epractice) 全港最平+獨家 優惠(可同時使用)：
?50%OFF 半價優惠碼：MC83-AI93-NFW0-331E
?25%OFF 額外邀請碼：J7N9-RDRP-NFAH-OH13
官方網頁：https://www.dsemth.com/

?教你「教外國人學廣東話」賺錢課程：https://forms.gle/BGEqVnSLcDr941HUA

?成為杜氏數學電視台的股東：https://www.youtube.com/channel/UCH2t6jvINIOeYzBQR0iI5kw/join

?跟我的靚女老師Abby學英文 + 送你USD$10優惠：https://italki.com/teacher/5422298?ref=6BDcd0

?跟我的靚仔老師Connor學英文 + 送你USD$10優惠：https://www.italki.com/teacher/5984357?ref=6BDcd0

?Tidebit全港最穩妥的比特幣(Bitcoin)交易所：http://bit.ly/2LIWA4J

?Uber免費送你$25優惠：https://www.uber.com/invite/2utyzr

?Trip.com送你酒店8％折扣優惠： http://t.trip.com/FTTE3b0
----------
賭Sir考試戰績:

新制中六DSE: (2016 M2 + 2017 M1)
?數學必修 (Mathematics) 一take過 奪5**
?數學延伸M1 (Calculus and Statistics) 一take過 奪5**
?數學延伸M2 (Algebra and Calculus) 一take過 奪5**

國際高考International Advanced Level: (2017 + 2018)
?Core Math 1 2 一take過 奪A
?Core Math 3 4 一take過 奪A
?Further Pure Math 1 一take過 奪A
?Further Pure Math 2 一take過 奪A
?Further Pure Math 3 一take過 奪A
?Mechanics 1 一take過 奪A
?Mechanics 2 一take過 奪A
?Mechanics 3 一take過 奪A
?Statistics 1 一take過 奪A
?Statistics 2 一take過 奪A
?Statistics 3 一take過 奪A
?Decision Math 1 一take過 奪A

舊制中七高考: (2011)
?純粹數學 (Pure Mathematics) 一take過 奪A
?應用數學 (Applied Mathematics) 一take過 奪A

舊制中五會考: (2009)
?數學 (Mathematics) 一take過 奪A
?附加數學 (Additional Mathematics) 一take過 奪A

#sorry廢up耐咗 #大學生必學 #室外補習都有錄影

?杜氏數學 官方網站： http://www.HermanToMath.com
?賭Sir 幫你急救 DSE 數學： https://hermantomath.skx.io/courses/6328693527937024
----------
?記得睇埋另一集：
https://youtu.be/5ANn3nQVu6w
----------
?‍♀️7科5**狀元Melody Tam：
https://www.youtube.com/channel/UCJ29RUajHhET4mPA-hyxesQ
----------
?️賭Sir是杜氏數學Herman To Math的始創人
?全港唯一「完爆」【DSE Core+M1+M2】、【IAL 12科Maths】、【AL Pure+Applied】、【CE Maths+A.Maths】的數學導師
?全港第一最多訂閱粉絲的數學教育YouTuber
?YouTube觀看次數超越700萬、訂閱粉絲超過50000人
----------
? Mensa Club member
? 中文大學 數學碩士畢業（Big Data stream）
? 中文大學 風險管理學士畢業
----------
?流行文學作家，出版著作：
《賭波男人嫁得過》?（2018）
《碌葛男人嫁得過》?（2018）
《5**數學男人嫁得過》?（2019）
《YouTuber新手到網紅》?（2019）
《賭馬男人嫁得過》?（2020）
----------
?YouTuber Go網絡課程 全港最平+獨家 報讀優惠：
http://hermantomath.blogspot.com/2019/03/youtuber-go-link.html

?無限操數王(epractice) 全港最平+獨家 優惠(可同時使用)：
?50%OFF 半價優惠碼：MC83-AI93-NFW0-331E
?25%OFF 額外邀請碼：J7N9-RDRP-NFAH-OH13
官方網頁：https://www.dsemth.com/

?教你「教外國人學廣東話」賺錢課程：https://forms.gle/BGEqVnSLcDr941HUA

?成為杜氏數學電視台的股東：https://www.youtube.com/channel/UCH2t6jvINIOeYzBQR0iI5kw/join

?跟我的靚女老師Abby學英文 + 送你USD$10優惠：https://italki.com/teacher/5422298?ref=6BDcd0

?送你USD$10優惠學英文：
https://italki.com/i/6BDcd0?hl=en-us

?Tidebit全港最穩妥的比特幣(Bitcoin)交易所：http://bit.ly/2LIWA4J

?Uber免費送你$25優惠：https://www.uber.com/invite/2utyzr

?Trip.com送你酒店8％折扣優惠： http://t.trip.com/FTTE3b0
----------
賭Sir考試戰績:

新制中六DSE: (2016 M2 + 2017 M1)
?數學必修 (Mathematics) 一take過 奪5**
?數學延伸M1 (Calculus and Statistics) 一take過 奪5**
?數學延伸M2 (Algebra and Calculus) 一take過 奪5**

國際高考International Advanced Level: (2017 + 2018)
?Core Math 1 2 一take過 奪A
?Core Math 3 4 一take過 奪A
?Further Pure Math 1 一take過 奪A
?Further Pure Math 2 一take過 奪A
?Further Pure Math 3 一take過 奪A
?Mechanics 1 一take過 奪A
?Mechanics 2 一take過 奪A
?Mechanics 3 一take過 奪A
?Statistics 1 一take過 奪A
?Statistics 2 一take過 奪A
?Statistics 3 一take過 奪A
?Decision Math 1 一take過 奪A

舊制中七高考: (2011)
?純粹數學 (Pure Mathematics) 一take過 奪A
?應用數學 (Applied Mathematics) 一take過 奪A

舊制中五會考: (2009)
?數學 (Mathematics) 一take過 奪A
?附加數學 (Additional Mathematics) 一take過 奪A

#記得讚好 #記得訂閱 #記得去Melody頻道睇埋另一集

HKDSE Mathematics 數學天書 訂購表格及方法︰ http://goo.gl/forms/NgqVAfMVB9
課程簡介︰ https://youtu.be/Rgm7yUVG9cY
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DSE 數學 Core 天書 A 第1堂 (共2小時45分鐘) https://www.youtube.com/playlist?list=PLzDe9mOi1K8p2A7HMhwz4udhLJTQt9p2b
DSE 數學 Core 天書 A 第2堂 (共2小時8分鐘) https://youtu.be/SGeMFO9tips?list=PLzDe9mOi1K8p2A7HMhwz4udhLJTQt9p2b
DSE 數學 Core 天書 A 第3堂 (共2小時4分鐘) https://youtu.be/-z_sjshGWEs?list=PLzDe9mOi1K8p2A7HMhwz4udhLJTQt9p2b
DSE 數學 Core 天書 A 第4堂 (共3小時17分鐘) https://youtu.be/1yWKUMSE5fU?list=PLzDe9mOi1K8p2A7HMhwz4udhLJTQt9p2b
Past Paper Demo (太多，無法估計) https://youtu.be/41cdF_BqxME?list=PLzDe9mOi1K8p2A7HMhwz4udhLJTQt9p2b
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DSE 數學 Core 天書 A 的內容:
1 -- Number system 數系
2 -- Estimation and Error 估算及誤差
3 -- Quadratic Equation 二次方程
4 -- Function and Graph 函數及圖像
5 -- Exponential (Index) and Logarithm 指數及對數
6 -- More about Graphs 進階圖像
7 -- Numeral systems 進制系統
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HKDSE 數學 Core 各天書 的內容︰ https://www.facebook.com/hy.publishing/photos/a.312736375489291.68655.198063650289898/933817946714461/?type=3&theater
HKDSE 數學 Core 特別快車班
28堂 (共7本天書) 完成整個 HKDSE 數學 Core
(中一至中六) 要考的所有課題，
適合任何考 HKDSE 的同學上課 (中四至中六都合適)

(p.s. Herman Yeung 所有天書，中英對照)
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