stay fit meaning的八卦，YOUTUBE和Yahoo名人娛樂都在討論

My sister, Michelle-Ann Iking's 3% chance of conceiving naturally was a success! Here's her story:

(My apologies as I've been overwhelmed with personal matters. I've only managed to get to my desk. So finally got around posting this).

This is the story behind my sister's pregnancy struggle and how she shared her journey over her Facebook page.

Because some may have not caught her LIVE session chat with me (https://www.facebook.com/daphneiking/videos/687743128744960/) , or read her lengthy post (as it's a private page);
she's allowed me to copy and paste it over my wall, in case you need to know more about her thought process on how AND why she focused on the 3% success probability. Read on.

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

Posted 10th May 2020.
FB Credit: Michelle-Ann Iking

A week ago today I celebrated becoming a mother to our second, long awaited child.

Please forgive this mother's LONG (self-indulgent) post, journalling what this significant milestone has meant for her personally, for her own fallible memory's sake as well as maybe to share one day with her son.

If all you were wondering was whether I had delivered and if mum and bub are OK, please be assured the whole KkLM family are thriving tremendously, and continue scrolling right along your Newsfeed 😁.

OUR 3% MIRACLE

All babies are miracles... and none more so than our precious Kiaen Aaryan (pronounced KEY-n AR-yen), whose name derives from Sanskrit origins meaning:

Grace of God
Spiritual
Kind
Benevolent

...words espousing the gratitude Kishore and I feel for Kiaen's arrival as our "3% miracle".

He was conceived, naturally, after 3 years of Kishore and I hoping, praying and 'endeavoring'... and only couples for whom the objective switches from pure recreation to (elusive) procreation will understand how this is less fun than it sounds ...

3 years during which time we had consensus from 3 different doctors that we, particularly I (with my advancing age etc etc) had only a 3% chance of natural conception and that our best hope for a sibling for our firstborn, Lara Anoushka, was via IVF.

Lara herself was an 'intervention baby', being one of the 20% of babies successfully conceived through the less intrusive IUI process, after a year and a half of trying naturally and already being told then my age was a debilitating factor.

We had tried another round of IUI for her sibling in 2017 when Lara was a year old. And that time we fell into the ranks of the 80% of would-be parents for whom it would be an exercise in futility... who would go home, comfort each other as best they could, while individually masking their own personal disappointment... hoping for the best, 'the next time around'...

So the improbability ratio of 97% against natural conception of our second baby, as concurred by the combined opinion of 3 medical professionals, was a very real, very daunting figure for us to have to mentally deal with.

Deep, DEEP, down in my heart however, though I had many a day of doubt... I kept a core kernel of faith that somehow, I would again experience the privilege of pregnancy, and again, have a chance at childbirth.

And so, the optimist in me would tell myself, "Well, there have to be people who fall in the 3% bucket... why shouldn't WE be part of the 3%?"

Those who know me well, understand my belief in the Law of Attraction, the philosophy of focusing your mind only on what you want to attract, not on what you don't want, and so even as Kishore and I prepared to go into significant personal debt to attempt IVF in the 2nd half of 2019, I marshalled a last ditch effort to hone in on that 3% chance of natural conception... through research coming across fertility supplements that I ordered from the US and sent to a friend in Singapore to redirect to me because the supplier would not deliver to Malaysia.

I made us as a couple take the supplements in the 3 month 'priming period' in the lead up to the IVF procedure - preconditioning our bodies for optimum results, if you will.

At the same time, I had invested in a sophisticated fertility monitor, with probes and digital sensors for daily tracking of saliva and other unmentionable fluid samples, designed to pinpoint with chemical accuracy my state of fertility on any given day.

(UPDATE: For those interested - I obtained the supplements and Ovacue Fertility Monitor from https://www.fairhavenhealth.com/. Though I had my supplies delivered to a friend in Singapore, and redirected to me here since the US site does not deliver to Malaysia, there are local distributors for these products, you will just have to research the trustworthiness of the vendors yourself...)

I had set an intention - in the 3 months of pre-IVF priming, I would consume what seemed like a pharmacy's worth of supplements, and track fertility religiously... in hopes that somehow, within the 3 month priming period, we would conceive naturally and potentially save ourselves a down payment on a new property... and this was just a projection on financial costs of IVF, not even considering the physical, emotional and mental toll it involves, with no guarantee of a baby at the end of it all...

It was a continuation of an intention embedded even with my first pregnancy, where all the big ticket baby items were consciously purchased for use by a future sibling, in gender neutral colours, in hopes that sibling would be a brother "for a balanced pair", though of course any healthy child would be a welcome blessing.

It was a very conscious determination to always skew my thoughts in service of what the end objective was. For example, when 3+year old Lara would innocently express impatience at not yet having a sibling, at one point suggesting that since we were "taking too long to give her a baby brother/sister", perhaps we should just "go buy a baby from a shop", instead of getting defensive or berating the baby that she herself was, we enlisted Lara's help to pray for her sibling... so in any place of worship, or sacred ground of any kind that we passed thereon, Lara would stop, close her eyes, bow her small head and place her tiny hands together in prayer, reciting earnestly, "Please God, please give me a baby brother or baby sister."

After months and months of watching Lara do this, in the constancy of her childlike chant, Kishore started feeling the pressure of possibly disappointing Lara if her prayer was not answered. Whereas for me, Lara's recitation of her simple wish became like a strengthening mantra, our collective intention imbued with greater power with each repetition, and the goal of a sibling kept very much in the forefront of our minds (hence our calling Lara our 'project manager' in this endeavour).

And somehow in the 2nd month of that 3 month period, a positive + sign appeared on one of the home pregnancy tests I had grown accustomed to taking - my version of the lottery tickets others keep buying in hopes of hitting the jackpot, with all the cyclical anticipation and more often than not, disappointment, that entails...

This time however I was not disappointed.

With God's Grace, (hence 'Kiaen', a variation of 'Kiaan' which means 'Grace of God'), my focus on our joining the ranks of the 3% had materialised.

It seems poetic then, that Kiaen chose to make his appearance on the 3rd May, ironically the same date that his paternal great-grandfather departed this world for the next... such that in the combined words of Kishore and his father Kai Vello Suppiah,

"The 1st generation Suppiah left on 3rd May and the 4th generation Suppiah arrived on 3rd May after 41yrs...
One leaves, another comes, the legacy lives on..."

***

KIAEN AARYAN SUPPIAH'S BIRTH STORY

On Sunday 3rd May, I was 40 weeks and 5 days pregnant.

The baby was, in my mind, very UN-fashionably late past his due date of 29th April, so as much as I had willed and 'manifested' the privilege of pregnancy, to say I was keen to be done with it all was an understatement.

In the weeks leading to up to my full term, I had experienced increasingly intense Braxton-Hicks 'practice contractions' - annoying for me for the discomfort involved, stressful for Kishore who was on tenterhooks with the false alarms, on constant alert for when we would actually need to leave home for the hospital.

Having become a Hypnobirthing student and advocate from my first pregnancy with Lara, and thus being equipped with
(1) a lack of fear about childbirth in general and
(2) a basic understanding of how all the sensations I would experience fit into the big picture of my body bringing our baby closer to us,
I was less stressed - content to wait for the baby to be "fully cooked" and come out whenever he was ready... though I wouldn't have minded at all if the cooking time ended sooner, rather than later.

With Lara, I had been somewhat 'forced' into an induced labour, even though she was not yet due, and that had resulted in a 5 DAY LABOUR, a Birth Story for another post, so I was not inclined to chemically induce labour, even though I was assured that for second time mothers, it would be 'much faster and easier'...

That morning, I had a hunch *maybe* that day was the day, because in contrast to previous weeks' sensations of tightening, pressure and even spasms that were concentrated in the front of my abdomen and occasionally shot through my sides and legs, I felt period - like cramping in my lower back which I had not felt before throughout the pregnancy.

It was about 8am in the morning then, and my 'surges' were still relatively mild ('surges' being Hypnobirthing - speak for 'contractions', designed to frame them with the more positive connotations needed to counteract common language in which childbirth is presented as something that is unequivocally painful and traumatic, instead of the miraculous, powerful and natural phenomenon it actually is).

I recall (masochistically?) entertaining the thought of opting NOT to have an epidural JUST TO SEE WHAT IT WOULD BE LIKE...

I figured this would be the last time I would be pregnant and so it would be my 'last chance' to experience 'drug free labour' which, apart from the health benefits for baby and mother, might be *interesting* in a way that people who are curious about what getting a tattoo and skydiving and bungee jumping are like, might find these *interesting*...even knowing there will be pain and risk involved...

Since I have tried tattoos and skydiving (unfortunately not being able to squeeze in bungee-jumping while my life was purely my own to risk at no dependents' possible detriment) a similar curiousity about a no-epidural labour was on my mind...

In the absence of other signs of the onset of labour (like 'bloody show' or my waters breaking), I wanted to wait until the surges were coming every few minutes before we actually left the house for the hospital, not wanting to be one of those couples who rushed in too early and had interminable waits for the next stage in unfamiliar, clinical surroundings and/or were made to go home in an anti-climatic manner.

I was even calm enough through my surges to have the presence of mind to wash and blowdry my hair, knowing if I did deliver soon I would not be allowed this luxury for a while.

Around 9am I asked Kishore to prep for Lara and himself to be dressed and breakfasted so we could head to hospital soon, while I sent messages to family members on both sides informing them 'today might be the day.'

My mother, who had briefly served as a midwife before going back into general nursing and then becoming a nursing tutor, prophetically stated that if what I was experiencing was true labour, "the baby would be out by noon".

The pace in which my surges grew closer together was surprisingly quicker than I expected; and while I asked Lara to "Hurry up with breakfast" with only a tad more urgency than we normally tell her to do, little Missy being prone to dilly-dallying at meals, I probably freaked Kishore out when about 930am onwards, I had to instinctively get on my hands and knees a couple of times, eyes closed, trying to practice the Hypnobirthing breathing techniques I had revised to help along the process of my body birthing our child into the world.

I recall him saying a bit frantically as I knelt at our front door, doubled over as he waited for Lara to complete something or other, "Lara hurry up! Can't you see Mama is in so much pain and you are taking your own sweet time??!!"

SIDETRACK: Just the night before, Lara and I had watched a TV show in which a woman gave birth with the usual histrionics accompanying pop culture depictions of labour.

Lara watched the scene, transfixed.

I told her, simply and matter-of-factly, "That's what Mama has to do to get baby brother out Lara, and that's what I had to do for you also."

In most of interactions with my daughter, I have sought to equip her to face life's situations with calmness, truthful common sense, and ideally a minimum of drama.

Those who know the dramatic diva that Lara can be will know that this is a work-in-progress, but her response to me that night showed me some of my 'teachings' were sinking in:

She looked at me unfazed, "But Mama," she said. "You won't cry and scream like that lady, right? You will be BRAVE and stay calm, right?"
#nopressure.

So as we prepped to leave for the hospital I did indeed attempt to be that role model of calm for her, asking her only for her help in keeping very quiet,
"Because Mama needs to focus on bringing baby brother out and she needs quiet to concentrate...".

As we left the house at 10.11am, I texted Kishore's sister Geetha to please prep to pick up Lara from the hospital, and was grateful Kishore had the foresight to ask our gynae to prepare a letter for Geetha to show any police roadblocks between my in-laws' home in Subang Jaya and the hospital in Bangsar, this all happening under the Movement Control Order (MCO).

To Lara's credit, in the journey over to the hospital, she - probably sensing the gravity of the situation, sat very quietly in her seat at the back, and the silence was punctuated only by my occasional deep intakes of breath and some variation of my Ohmmm-like moans when the sensations were at their height.

By the time we got to Pantai Hospital at around 10.30am, my surges were strong enough I requested a wheelchair to assist me in getting to the labour ward, as I did not trust my own legs to support me... and Kishore would have to wait until Geetha had arrived to take Lara back to my in-laws' house before he himself could go up.

I slumped in the wheelchair and was wheeled up to the labour room with my eyes closed the whole time, trying to handle my surges.

I didn't even look up to see the attendant who pushed me... but did make the effort to thank him sincerely when he handed me over, with what seemed like a palpable sense of relief on his part, to the labour ward nurses.

The nurse attending me at Pantai was calm, steady and efficient. I answered some questions and changed into my labour gown while waiting for Kishore to come up, all the while managing the increasingly intense surges with my rusty Hypnobirthing breathing techniques.

By the time Kishore joined me at around 11am (I know these timings based on the timestamps of the 'WhatsApp live feed' of messages Kishore sent to his family), I was asking the nurse on duty, "How soon can I get an epidural??" thinking what crazy woman thought she could do this without drugs???!!!

The nurse checked my cervix dilation, I saw her bloodied glove indicating my mucous plug had dislodged, and she told me, "Well you are already at 7cm (which, for the uninitiated, is 70% of the way to the 10cm dilation needed for birthing), you are really doing well, if you made it this far without any drugs, if can you try and manage without it... I suspect within 2 hours or less you will deliver your baby and since it will take about that time for the anaesthesiologist to be called, epidural to be administered and kick in... it might all be for nothing... but of course the decision is completely up to you... "

So there I was, super torn, should I risk the sensations becoming worse... or risk the epidural becoming a waste?? And of course I was trying to decide this as my labour surges were coming at me stronger and stronger...

I was in such a dilemma...because as a 'recovering approval junkie' there was also a silly element of approval-seeking involved, ("The nurse thinks I can do this without drugs... maybe I CAN do this without drugs... Yay me!") mixed with that element of curiosity I mentioned earlier ("What if I actually CAN do this without drugs... plenty of other women have done it all over the world since time immemorial.. no big deal, how bad can it be...??") so then I thought I would use the financial aspect to be the 'tiebreaker' in my decision making...

I asked the nurse how much an epidural would cost and when she replied "Around MYR1.5k", I still remember Kishore's incredulous face as I asked the question, i.e."Seriously babe, you are gonna think about money right now? If you need the epidural TAKE IT, don't worry about the money!!!"... and while we are not rich by any stretch of the imagination, thankfully RM1.5k is not a quantum that made me swing towards a decision to "better save the money"...

So in the end, I guess my curiosity won out, and I turned down the epidural "just to see what it would be like and if I had it in me" (in addition of course to avoiding the side effects of any drugs introduced into my and the baby's body).

My labour occuring in the time of coronavirus, it was protocol for me to have a COVID19 test done, so the medical staff could apply the necessary precautions. I had heard from a friend Sharon Ruba that the test procedure was uncomfortable, so when the nurse came with the test kit as I was starting another surge, I asked, "Please can I just finish this surge before I do the test?" as I really didn't think I could multitask tackling multiple uncomfortable sensations in one go.

The COVID19 test involved what felt like a looong, skinny cotton bud being inserted into one nostril... I definitely felt more than a tickle as it went in and up, being told to take deep breaths by the nurse. Then she asked me to "Try to swallow" and I felt it go into my nasal cavities where I didn't think anything could go any further, but was proven wrong when she asked me to swallow again and the swab was probed even deeper. Then she warned me there would be some slight discomfort as she prepared to collect a sample... but at that point all I could think about was:

(i) I really don't have much of a choice
(ii) please let this be over before my next surge kicks in
(iii) if all the people breaking the MCO rules knew what it feels like to do this test maybe they won't put themselves at risk of the need to perform one...

In full disclosure as I was transferred into the actual delivery room at some point after 11am, another nurse offered me 'laughing gas' to ostensibly take some of the edge off... I took the self-operated breathing nozzle passed to me but don't recall it making any difference to my sensations..so didn't use it much as it seemed pretty pointless.

I recall some measure of relief when I heard my gynae Dr. Paul entering the room, greeting Kishore and me, and telling us it was going well and it wouldn't be long now and he would see us again shortly.

From my previous labour with Lara I knew the midwives pretty much take you 90% of the way through the labour and when the Dr is called in you are really at the home stretch, so was very relieved to hear his voice though knowing he would leave and come back later meant it wasn't quite over yet.

I do remember realising when I had crossed the Thinning and Opening Phase of labour to the Birthing Phase, by the change in sensations... it is still amazing to me that as the Hypnobirthing book mentioned, having this knowledge I was instinctively able to switch breathing techniques for the next stage of labour .

Was my opting against epidural the right choice for me?

Overall? Yes.

Don't get me wrong.

I *almost* regretted the decision several times during active labour... especially when I felt my body being taken over by an overwhelming compulsion to push that did not seem conscious and was accompanied by involuntary gutteral moans where I literally just thought to myself, "I surrender, God do with me what you will..." (super dramatic I know but VERY real at the time...).

I think I experienced 3-4 such natural explusive reflexes (?), rhythmically pushing the baby down the birth path, one of which was accompanied by what felt like a swoosh of water coming out of a hose with a diameter the size of a golf ball... this was when I realised my water had finally broken...

The nurses kept instructing me to do different things, to keep breathing, to move to my side, then to move to the middle, to raise my feet... and when I didn't comply, Kishore (who was with me throughout both my labours) tried to help them by repeating the instructions prefaced with "Sayang..." but I basically ignored all the intructions because I felt I had no capacity to direct any part of my body to do anything and someone else would have to physically manoeuvre that body part themselves.

When I heard Dr. Paul's voice again and the flurry of commotion surrounding his presence, I knew the time was close... and when I heard the nurse say to Kishore, "Sir, these are your gloves, for when you cut the baby's cord", it was music to my ears...

I'm very, VERY grateful Kiaen slid out after maybe the 4th of those involuntary pushes... the wave of RELIEF when he came out so quickly... it still boggles my mind that my mother was essentially right and as his birth time was 12.02pm, it was *only* about 1.5 hours between our arrival at the hospital and his arrival into the world.

Kiaen was placed on my chest for skin to skin bonding and remained there for a considerable time.

For our short stay in the hospital he would be with us in my maternity ward number C327... another trivially serendipitous sign for me because he was born on the 3rd (May) and our wedding anniversary is 27th (July).

I was discharged the following day 4th May at about 5.30pm, after I got an all clear on COVID19 and a paediatric surgeon did a small procedure on Kiaen to address a tongue-tie that would affect his breastfeeding latch... making the entire duration of our stay about 31 hours.

I have taken the time and effort to record all this down so that whenever life's challenges threaten to get me down I can remind myself, "Ignore the 97% failure probability, focus on the 3% success probability".

Also that the human condition is miraculous and it is such a privilege to experience it.

To our son Kiaen Aaryan, thank you for coming into our lives and choosing us as your parents.

Even though Papa and I are both zombies trying to settle into a night time feeding routine with you, I look forward to spending not only all future Mother's Days, but every day, with you and your Akka...

And last but not least, to my husband Kishore...without whom none of this would be possible - we did it sayang, I love you ❤️

Photo credit: Stayhome session with Samantha Yong Photography (http://samanthayong.com/)

📜 [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.

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