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Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

  • x+5
  • x^4
  • x^3+3x^2+3x+1
  • 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

  • A(0)+B(0)=C(0)
  • A(1)+B(1)=C(1)
  • A(2)+B(2)=C(2)
  • A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

  • 12+1=13
  • 10+8=18
  • 15+8=23
  • 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

  • A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
  • B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
  • C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

see part 3

(Edited)

Hackernoon

Hackernoon

4 years ago


👏 Awesome post! When is part 3 coming?

Trent Lapinski

Trent Lapinski

4 years ago

Very complex topic, great explanation

More on Web3 & Crypto

Yusuf Ibrahim

Yusuf Ibrahim

4 years ago

How to sell 10,000 NFTs on OpenSea for FREE (Puppeteer/NodeJS)

So you've finished your NFT collection and are ready to sell it. Except you can't figure out how to mint them! Not sure about smart contracts or want to avoid rising gas prices. You've tried and failed with apps like Mini mouse macro, and you're not familiar with Selenium/Python. Worry no more, NodeJS and Puppeteer have arrived!

Learn how to automatically post and sell all 1000 of my AI-generated word NFTs (Nakahana) on OpenSea for FREE!

My NFT project — Nakahana |

NOTE: Only NFTs on the Polygon blockchain can be sold for free; Ethereum requires an initiation charge. NFTs can still be bought with (wrapped) ETH.

If you want to go right into the code, here's the GitHub link: https://github.com/Yusu-f/nftuploader

Let's start with the knowledge and tools you'll need.

What you should know

You must be able to write and run simple NodeJS programs. You must also know how to utilize a Metamask wallet.

Tools needed

  • NodeJS. You'll need NodeJs to run the script and NPM to install the dependencies.
  • Puppeteer – Use Puppeteer to automate your browser and go to sleep while your computer works.
  • Metamask – Create a crypto wallet and sign transactions using Metamask (free). You may learn how to utilize Metamask here.
  • Chrome – Puppeteer supports Chrome.

Let's get started now!

Starting Out

Clone Github Repo to your local machine. Make sure that NodeJS, Chrome, and Metamask are all installed and working. Navigate to the project folder and execute npm install. This installs all requirements.

Replace the “extension path” variable with the Metamask chrome extension path. Read this tutorial to find the path.

Substitute an array containing your NFT names and metadata for the “arr” variable and the “collection_name” variable with your collection’s name.

Run the script.

After that, run node nftuploader.js.

Open a new chrome instance (not chromium) and Metamask in it. Import your Opensea wallet using your Secret Recovery Phrase or create a new one and link it. The script will be unable to continue after this but don’t worry, it’s all part of the plan.

Next steps

Open your terminal again and copy the route that starts with “ws”, e.g. “ws:/localhost:53634/devtools/browser/c07cb303-c84d-430d-af06-dd599cf2a94f”. Replace the path in the connect function of the nftuploader.js script.

const browser = await puppeteer.connect({ browserWSEndpoint: "ws://localhost:58533/devtools/browser/d09307b4-7a75-40f6-8dff-07a71bfff9b3", defaultViewport: null });

Rerun node nftuploader.js. A second tab should open in THE SAME chrome instance, navigating to your Opensea collection. Your NFTs should now start uploading one after the other! If any errors occur, the NFTs and errors are logged in an errors.log file.

Error Handling

The errors.log file should show the name of the NFTs and the error type. The script has been changed to allow you to simply check if an NFT has already been posted. Simply set the “searchBeforeUpload” setting to true.

We're done!

If you liked it, you can buy one of my NFTs! If you have any concerns or would need a feature added, please let me know.

Thank you to everyone who has read and liked. I never expected it to be so popular.

Henrique Centieiro

Henrique Centieiro

3 years ago

DAO 101: Everything you need to know

Maybe you'll work for a DAO next! Over $1 Billion in NFTs in the Flamingo DAO Another DAO tried to buy the NFL team Denver Broncos. The UkraineDAO raised over $7 Million for Ukraine. The PleasrDAO paid $4m for a Wu-Tang Clan album that belonged to the “pharma bro.”
DAOs move billions and employ thousands. So learn what a DAO is, how it works, and how to create one!

DAO? So, what? Why is it better?

A Decentralized Autonomous Organization (DAO). Some people like to also refer to it as Digital Autonomous Organization, but I prefer the former.
They are virtual organizations. In the real world, you have organizations or companies right? These firms have shareholders and a board. Usually, anyone with authority makes decisions. It could be the CEO, the Board, or the HIPPO. If you own stock in that company, you may also be able to influence decisions. It's now possible to do something similar but much better and more equitable in the cryptocurrency world.

This article informs you:

DAOs- What are the most common DAOs, their advantages and disadvantages over traditional companies? What are they if any?
Is a DAO legally recognized?
How secure is a DAO?
I’m ready whenever you are!

A DAO is a type of company that is operated by smart contracts on the blockchain. Smart contracts are computer code that self-executes our commands. Those contracts can be any. Most second-generation blockchains support smart contracts. Examples are Ethereum, Solana, Polygon, Binance Smart Chain, EOS, etc. I think I've gone off topic. Back on track.   Now let's go!
Unlike traditional corporations, DAOs are governed by smart contracts. Unlike traditional company governance, DAO governance is fully transparent and auditable. That's one of the things that sets it apart. The clarity!
A DAO, like a traditional company, has one major difference. In other words, it is decentralized. DAOs are more ‘democratic' than traditional companies because anyone can vote on decisions. Anyone! In a DAO, we (you and I) make the decisions, not the top-shots. We are the CEO and investors. A DAO gives its community members power. We get to decide.
As long as you are a stakeholder, i.e. own a portion of the DAO tokens, you can participate in the DAO. Tokens are open to all. It's just a matter of exchanging it. Ownership of DAO tokens entitles you to exclusive benefits such as governance, voting, and so on. You can vote for a move, a plan, or the DAO's next investment. You can even pitch for funding. Any ‘big' decision in a DAO requires a vote from all stakeholders. In this case, ‘token-holders'! In other words, they function like stock.

What are the 5 DAO types?

Different DAOs exist. We will categorize decentralized autonomous organizations based on their mode of operation, structure, and even technology. Here are a few. You've probably heard of them:

1. DeFi DAO

These DAOs offer DeFi (decentralized financial) services via smart contract protocols. They use tokens to vote protocol and financial changes. Uniswap, Aave, Maker DAO, and Olympus DAO are some examples. Most DAOs manage billions.

Maker DAO was one of the first protocols ever created. It is a decentralized organization on the Ethereum blockchain that allows cryptocurrency lending and borrowing without a middleman.
Maker DAO issues DAI, a stable coin. DAI is a top-rated USD-pegged stable coin.
Maker DAO has an MKR token. These token holders are in charge of adjusting the Dai stable coin policy. Simply put, MKR tokens represent DAO “shares”.

2. Investment DAO

Investors pool their funds and make investment decisions. Investing in new businesses or art is one example. Investment DAOs help DeFi operations pool capital. The Meta Cartel DAO is a community of people who want to invest in new projects built on the Ethereum blockchain. Instead of investing one by one, they want to pool their resources and share ideas on how to make better financial decisions.

Other investment DAOs include the LAO and Friends with Benefits.

3. DAO Grant/Launchpad

In a grant DAO, community members contribute funds to a grant pool and vote on how to allocate and distribute them. These DAOs fund new DeFi projects. Those in need only need to apply. The Moloch DAO is a great Grant DAO. The tokens are used to allocate capital. Also see Gitcoin and Seedify.

4. DAO Collector

I debated whether to put it under ‘Investment DAO' or leave it alone. It's a subset of investment DAOs. This group buys non-fungible tokens, artwork, and collectibles. The market for NFTs has recently exploded, and it's time to investigate. The Pleasr DAO is a collector DAO. One copy of Wu-Tang Clan's "Once Upon a Time in Shaolin" cost the Pleasr DAO $4 million. Pleasr DAO is known for buying Doge meme NFT. Collector DAOs include the Flamingo, Mutant Cats DAO, and Constitution DAOs. Don't underestimate their websites' "childish" style. They have millions.

5. Social DAO

These are social networking and interaction platforms. For example, Decentraland DAO and Friends With Benefits DAO.

What are the DAO Benefits?

Here are some of the benefits of a decentralized autonomous organization:

  • They are trustless. You don’t need to trust a CEO or management team
  • It can’t be shut down unless a majority of the token holders agree. The government can't shut - It down because it isn't centralized.
  • It's fully democratic
  • It is open-source and fully transparent.

What about DAO drawbacks?

We've been saying DAOs are the bomb? But are they really the shit? What could go wrong with DAO?
DAOs may contain bugs. If they are hacked, the results can be catastrophic.
No trade secrets exist. Because the smart contract is transparent and coded on the blockchain, it can be copied. It may be used by another organization without credit. Maybe DAOs should use Secret, Oasis, or Horizen blockchain networks.

Are DAOs legally recognized??

In most counties, DAO regulation is inexistent. It's unclear. Most DAOs don’t have a legal personality. The Howey Test and the Securities Act of 1933 determine whether DAO tokens are securities. Although most countries follow the US, this is only considered for the US. Wyoming became the first state to recognize DAOs as legal entities in July 2021 after passing a DAO bill. DAOs registered in Wyoming are thus legally recognized as business entities in the US and thus receive the same legal protections as a Limited Liability Company.

In terms of cyber-security, how secure is a DAO?

Blockchains are secure. However, smart contracts may have security flaws or bugs. This can be avoided by third-party smart contract reviews, testing, and auditing

Finally, Decentralized Autonomous Organizations are timeless. Let us examine the current situation: Ukraine's invasion. A DAO was formed to help Ukrainian troops fighting the Russians. It was named Ukraine DAO. Pleasr DAO, NFT studio Trippy Labs, and Russian art collective Pussy Riot organized this fundraiser. Coindesk reports that over $3 million has been raised in Ethereum-based tokens. AidForUkraine, a DAO aimed at supporting Ukraine's defense efforts, has launched. Accepting Solana token donations. They are fully transparent, uncensorable, and can’t be shut down or sanctioned.
DAOs are undeniably the future of blockchain. Everyone is paying attention. Personally, I believe traditional companies will soon have to choose between adapting or being left behind.

Long version of this post: https://medium.datadriveninvestor.com/dao-101-all-you-need-to-know-about-daos-275060016663

Isobel Asher Hamilton

Isobel Asher Hamilton

3 years ago

$181 million in bitcoin buried in a dump. $11 million to get them back

$181 million in bitcoin buried in a dump

James Howells lost 8,000 bitcoins. He has $11 million to get them back.

His life altered when he threw out an iPhone-sized hard drive.

Howells, from the city of Newport in southern Wales, had two identical laptop hard drives squirreled away in a drawer in 2013. One was blank; the other had 8,000 bitcoins, currently worth around $181 million.

He wanted to toss out the blank one, but the drive containing the Bitcoin went to the dump.

He's determined to reclaim his 2009 stash.

Howells, 36, wants to arrange a high-tech treasure hunt for bitcoins. He can't enter the landfill.

James Howells lost 8,000 bitcoins

Newport's city council has rebuffed Howells' requests to dig for his hard drive for almost a decade, stating it would be expensive and environmentally destructive.

I got an early look at his $11 million idea to search 110,000 tons of trash. He expects submitting it to the council would convince it to let him recover the hard disk.

110,000 tons of trash, 1 hard drive

Finding a hard disk among heaps of trash may seem Herculean.

Former IT worker Howells claims it's possible with human sorters, robot dogs, and an AI-powered computer taught to find hard drives on a conveyor belt.

His idea has two versions, depending on how much of the landfill he can search.

His most elaborate solution would take three years and cost $11 million to sort 100,000 metric tons of waste. Scaled-down version costs $6 million and takes 18 months.

He's created a team of eight professionals in AI-powered sorting, landfill excavation, garbage management, and data extraction, including one who recovered Columbia's black box data.

The specialists and their companies would be paid a bonus if they successfully recovered the bitcoin stash.

Howells: "We're trying to commercialize this project."

Howells claimed rubbish would be dug up by machines and sorted near the landfill.

Human pickers and a Max-AI machine would sort it. The machine resembles a scanner on a conveyor belt.

Remi Le Grand of Max-AI told us it will train AI to recognize Howells-like hard drives. A robot arm would select candidates.

Howells has added security charges to his scheme because he fears people would steal the hard drive.

He's budgeted for 24-hour CCTV cameras and two robotic "Spot" canines from Boston Dynamics that would patrol at night and look for his hard drive by day.

Howells said his crew met in May at the Celtic Manor Resort outside Newport for a pitch rehearsal.

Richard Hammond's narrative swings from banal to epic.

Richard Hammond filmed the meeting and created a YouTube documentary on Howells.

Hammond said of Howells' squad, "They're committed and believe in him and the idea."

Hammond: "It goes from banal to gigantic." "If I were in his position, I wouldn't have the strength to answer the door."

Howells said trash would be cleaned and repurposed after excavation. Reburying the rest.

"We won't pollute," he declared. "We aim to make everything better."

The Newport, Wales, landfill from the air. Darren Britton / Wales News

After the project is finished, he hopes to develop a solar or wind farm on the dump site. The council is unlikely to accept his vision soon.

A council representative told us, "Mr. Howells can't convince us of anything." "His suggestions constitute a significant ecological danger, which we can't tolerate and are forbidden by our permit."

Will the recovered hard drive work?

The "platter" is a glass or metal disc that holds the hard drive's data. Howells estimates 80% to 90% of the data will be recoverable if the platter isn't damaged.

Phil Bridge, a data-recovery expert who consulted Howells, confirmed these numbers.

If the platter is broken, Bridge adds, data recovery is unlikely.

Bridge says he was intrigued by the proposal. "It's an intriguing case," he added. Helping him get it back and proving everyone incorrect would be a great success story.

Who'd pay?

Swiss and German venture investors Hanspeter Jaberg and Karl Wendeborn told us they would fund the project if Howells received council permission.

Jaberg: "It's a needle in a haystack and a high-risk investment."

Howells said he had no contract with potential backers but had discussed the proposal in Zoom meetings. "Until Newport City Council gives me something in writing, I can't commit," he added.

Suppose he finds the bitcoins.

Howells said he would keep 30% of the data, worth $54 million, if he could retrieve it.

A third would go to the recovery team, 30% to investors, and the remainder to local purposes, including gifting £50 ($61) in bitcoin to each of Newport's 150,000 citizens.

Howells said he opted to spend extra money on "professional firms" to help convince the council.

What if the council doesn't approve?

If Howells can't win the council's support, he'll sue, claiming its actions constitute a "illegal embargo" on the hard drive. "I've avoided that path because I didn't want to cause complications," he stated. I wanted to cooperate with Newport's council.

Howells never met with the council face-to-face. He mentioned he had a 20-minute Zoom meeting in May 2021 but thought his new business strategy would help.

He met with Jessica Morden on June 24. Morden's office confirmed meeting.

After telling the council about his proposal, he can only wait. "I've never been happier," he said. This is our most professional operation, with the best employees.

The "crypto proponent" buys bitcoin every month and sells it for cash.

Howells tries not to think about what he'd do with his part of the money if the hard disk is found functional. "Otherwise, you'll go mad," he added.


This post is a summary. Read the full article here.

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Scott Galloway

Scott Galloway

3 years ago

First Health

ZERO GRACE/ZERO MALICE

Amazon's purchase of One Medical could speed up American healthcare

The U.S. healthcare industry is a 7-ton seal bleeding at sea. Predators are circling. Unearned margin: price increases relative to inflation without quality improvements. Amazon is the 11-foot megalodon with 7-inch teeth. Amazon is no longer circling... but attacking.

In 2020 dollars, per capita U.S. healthcare spending increased from $2,968 in 1980 to $12,531. The result is a massive industry with 13% of the nation's workers and a fifth of GDP.

Doctor No

In 40 years, healthcare has made progress. From 73.7 in 1980 to 78.8 in 2019, life expectancy rose (before Covid knocked it back down a bit). Pharmacological therapies have revolutionized, and genetic research is paying off. The financial return, improvement split by cost increases, is terrible. No country has expense rises like the U.S., and no one spends as much per capita as we do. Developed countries have longer life expectancies, healthier populations, and less economic hardship.

Two-thirds of U.S. personal bankruptcies are due to medical expenses and/or missed work. Mom or Dad getting cancer could bankrupt many middle-class American families. 40% of American adults delayed or skipped needed care due to cost. Every healthcare improvement seems to have a downside. Same pharmacological revolution that helped millions caused opioid epidemic. Our results are poor in many areas: The U.S. has a high infant mortality rate.

Healthcare is the second-worst retail industry in the country. Gas stations are #1. Imagine walking into a Best Buy to buy a TV and a Blue Shirt associate requests you fill out the same 14 pages of paperwork you filled out yesterday. Then you wait in a crowded room until they call you, 20 minutes after the scheduled appointment you were asked to arrive early for, to see the one person in the store who can talk to you about TVs, who has 10 minutes for you. The average emergency room wait time in New York is 6 hours and 10 minutes.

If it's bad for the customer, it's worse for the business. Physicians spend 27% of their time helping patients; 49% on EHRs. Documentation, order entry, billing, and inbox management. Spend a decade getting an M.D., then become a bureaucrat.

No industry better illustrates scale diseconomies. If we got the same return on healthcare spending as other countries, we'd all live to 100. We could spend less, live longer and healthier, and pay off the national debt in 15 years. U.S. healthcare is the worst ever.

What now? Competition is at the heart of capitalism, the worst system of its kind.

Priority Time

Amazon is buying One Medical for $3.9 billion. I think this deal will liberate society. Two years in, I think One Medical is great. When I got Covid, I pressed the One Medical symbol on my phone; a nurse practitioner prescribed Paxlovid and told me which pharmacies had it in stock.

Amazon enables the company's vision. One Medical's stock is down to $10 from $40 at the start of 2021. Last year, it lost $250 million and needs cash (Amazon has $60 billion). ONEM must grow. The service has 736,000 members. Half of U.S. households have Amazon Prime. Finally, delivery. One Medical is a digital health/physical office hybrid, but you must pick up medication at the pharmacy. Upgrade your Paxlovid delivery time after a remote consultation. Amazon's core competency means it'll happen. Healthcare speed and convenience will feel alien.

It's been a long, winding road to disruption. Amazon, JPMorgan, and Berkshire Hathaway formed Haven four years ago to provide better healthcare for their 1.5 million employees. It rocked healthcare stocks the morning of the press release, but folded in 2021.

Amazon Care is an employee-focused service. Home-delivered virtual health services and nurses. It's doing well, expanding nationwide, and providing healthcare for other companies. Hilton is Amazon Care's biggest customer. The acquisition of One Medical will bring 66 million Prime households capital, domain expertise, and billing infrastructure. Imagine:

"Alexa, I'm hot and my back hurts."

"Connecting you to a Prime doctor now."

Want to vs. Have to

I predicted Amazon entering healthcare years ago. Why? For the same reason Apple is getting into auto. Amazon's P/E is 56, double Walmart's. The corporation must add $250 billion in revenue over the next five years to retain its share price. White-label clothes or smart home products won't generate as much revenue. It must enter a huge market without scale, operational competence, and data skills.

Current Situation

Healthcare reform benefits both consumers and investors. In 2015, healthcare services had S&P 500-average multiples. The market is losing faith in public healthcare businesses' growth. Healthcare services have lower EV/EBITDA multiples than the S&P 500.

Amazon isn't the only prey-hunter. Walmart and Alibaba are starting pharmacies. Uber is developing medical transportation. Private markets invested $29 billion in telehealth last year, up 95% from 2020.

The pandemic accelerated telehealth, the immediate unlock. After the first positive Covid case in the U.S., services that had to be delivered in person shifted to Zoom... We lived. We grew. Video house calls continued after in-person visits were allowed. McKinsey estimates telehealth visits are 38 times pre-pandemic levels. Doctors adopted the technology, regulators loosened restrictions, and patients saved time. We're far from remote surgery, but many patient visits are unnecessary. A study of 40 million patients during lockdown found that for chronic disease patients, online visits didn't affect outcomes. This method of care will only improve.

Amazon's disruption will be significant and will inspire a flood of capital, startups, and consumer brands. Mark Cuban launched a pharmacy that eliminates middlemen in January. Outcome? A 90-day supply of acid-reflux medication costs $17. Medicare could have saved $3.6 billion by buying generic drugs from Cuban's pharmacy. Other apex predators will look at different limbs of the carcass for food. Nike could enter healthcare via orthopedics, acupuncture, and chiropractic. LVMH, L'Oréal, and Estée Lauder may launch global plastic surgery brands. Hilton and Four Seasons may open hospitals. Lennar and Pulte could build "Active Living" communities that Nana would leave feet first, avoiding the expense and tragedy of dying among strangers.

Risks

Privacy matters: HIV status is different from credit card and billing address. Most customers (60%) feel fine sharing personal health data via virtual technologies, though. Unavoidable. 85% of doctors believe data-sharing and interoperability will become the norm. Amazon is the most trusted tech company for handling personal data. Not Meta: Amazon.

What about antitrust, then?

Amazon should be required to spin off AWS and/or Amazon Fulfillment and banned from promoting its own products. It should be allowed to acquire hospitals. One Medical's $3.9 billion acquisition is a drop in the bucket compared to UnitedHealth's $498 billion market valuation.

Antitrust enforcement shouldn't assume some people/firms are good/bad. It should recognize that competition is good and focus on making markets more competitive in each deal. The FTC should force asset divestitures in e-commerce, digital marketing, and social media. These companies can also promote competition in a social ill.

U.S. healthcare makes us fat, depressed, and broke. Competition has produced massive value and prosperity across most of our economy.

Dear Amazon … bring it.

Sammy Abdullah

Sammy Abdullah

3 years ago

SaaS payback period data

It's ok and even desired to be unprofitable if you're gaining revenue at a reasonable cost and have 100%+ net dollar retention, meaning you never lose customers and expand them. To estimate the acceptable cost of new SaaS revenue, we compare new revenue to operating loss and payback period. If you pay back the customer acquisition cost in 1.5 years and never lose them (100%+ NDR), you're doing well.

To evaluate payback period, we compared new revenue to net operating loss for the last 73 SaaS companies to IPO since October 2017. (55 out of 73). Here's the data. 1/(new revenue/operating loss) equals payback period. New revenue/operating loss equals cost of new revenue.

Payback averages a year. 55 SaaS companies that weren't profitable at IPO got a 1-year payback. Outstanding. If you pay for a customer in a year and never lose them (100%+ NDR), you're establishing a valuable business. The average was 1.3 years, which is within the 1.5-year range.

New revenue costs $0.96 on average. These SaaS companies lost $0.96 every $1 of new revenue last year. Again, impressive. Average new revenue per operating loss was $1.59.

Loss-in-operations definition. Operating loss revenue COGS S&M R&D G&A (technical point: be sure to use the absolute value of operating loss). It's wrong to only consider S&M costs and ignore other business costs. Operating loss and new revenue are measured over one year to eliminate seasonality.

Operating losses are desirable if you never lose a customer and have a quick payback period, especially when SaaS enterprises are valued on ARR. The payback period should be under 1.5 years, the cost of new income < $1, and net dollar retention 100%.

Sofien Kaabar, CFA

Sofien Kaabar, CFA

3 years ago

How to Make a Trading Heatmap

Python Heatmap Technical Indicator

Heatmaps provide an instant overview. They can be used with correlations or to predict reactions or confirm the trend in trading. This article covers RSI heatmap creation.

The Market System

Market regime:

  • Bullish trend: The market tends to make higher highs, which indicates that the overall trend is upward.

  • Sideways: The market tends to fluctuate while staying within predetermined zones.

  • Bearish trend: The market has the propensity to make lower lows, indicating that the overall trend is downward.

Most tools detect the trend, but we cannot predict the next state. The best way to solve this problem is to assume the current state will continue and trade any reactions, preferably in the trend.

If the EURUSD is above its moving average and making higher highs, a trend-following strategy would be to wait for dips before buying and assuming the bullish trend will continue.

Indicator of Relative Strength

J. Welles Wilder Jr. introduced the RSI, a popular and versatile technical indicator. Used as a contrarian indicator to exploit extreme reactions. Calculating the default RSI usually involves these steps:

  • Determine the difference between the closing prices from the prior ones.

  • Distinguish between the positive and negative net changes.

  • Create a smoothed moving average for both the absolute values of the positive net changes and the negative net changes.

  • Take the difference between the smoothed positive and negative changes. The Relative Strength RS will be the name we use to describe this calculation.

  • To obtain the RSI, use the normalization formula shown below for each time step.

GBPUSD in the first panel with the 13-period RSI in the second panel.

The 13-period RSI and black GBPUSD hourly values are shown above. RSI bounces near 25 and pauses around 75. Python requires a four-column OHLC array for RSI coding.

import numpy as np
def add_column(data, times):
    
    for i in range(1, times + 1):
    
        new = np.zeros((len(data), 1), dtype = float)
        
        data = np.append(data, new, axis = 1)
    return data
def delete_column(data, index, times):
    
    for i in range(1, times + 1):
    
        data = np.delete(data, index, axis = 1)
    return data
def delete_row(data, number):
    
    data = data[number:, ]
    
    return data
def ma(data, lookback, close, position): 
    
    data = add_column(data, 1)
    
    for i in range(len(data)):
           
            try:
                
                data[i, position] = (data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                
                pass
            
    data = delete_row(data, lookback)
    
    return data
def smoothed_ma(data, alpha, lookback, close, position):
    
    lookback = (2 * lookback) - 1
    
    alpha = alpha / (lookback + 1.0)
    
    beta  = 1 - alpha
    
    data = ma(data, lookback, close, position)
    data[lookback + 1, position] = (data[lookback + 1, close] * alpha) + (data[lookback, position] * beta)
    for i in range(lookback + 2, len(data)):
        
            try:
                
                data[i, position] = (data[i, close] * alpha) + (data[i - 1, position] * beta)
        
            except IndexError:
                
                pass
            
    return data
def rsi(data, lookback, close, position):
    
    data = add_column(data, 5)
    
    for i in range(len(data)):
        
        data[i, position] = data[i, close] - data[i - 1, close]
     
    for i in range(len(data)):
        
        if data[i, position] > 0:
            
            data[i, position + 1] = data[i, position]
            
        elif data[i, position] < 0:
            
            data[i, position + 2] = abs(data[i, position])
            
    data = smoothed_ma(data, 2, lookback, position + 1, position + 3)
    data = smoothed_ma(data, 2, lookback, position + 2, position + 4)
    data[:, position + 5] = data[:, position + 3] / data[:, position + 4]
    
    data[:, position + 6] = (100 - (100 / (1 + data[:, position + 5])))
    data = delete_column(data, position, 6)
    data = delete_row(data, lookback)
    return data

Make sure to focus on the concepts and not the code. You can find the codes of most of my strategies in my books. The most important thing is to comprehend the techniques and strategies.

My weekly market sentiment report uses complex and simple models to understand the current positioning and predict the future direction of several major markets. Check out the report here:

Using the Heatmap to Find the Trend

RSI trend detection is easy but useless. Bullish and bearish regimes are in effect when the RSI is above or below 50, respectively. Tracing a vertical colored line creates the conditions below. How:

  • When the RSI is higher than 50, a green vertical line is drawn.

  • When the RSI is lower than 50, a red vertical line is drawn.

Zooming out yields a basic heatmap, as shown below.

100-period RSI heatmap.

Plot code:

def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)  
        if sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

100-period RSI heatmap.

Call RSI on your OHLC array's fifth column. 4. Adjusting lookback parameters reduces lag and false signals. Other indicators and conditions are possible.

Another suggestion is to develop an RSI Heatmap for Extreme Conditions.

Contrarian indicator RSI. The following rules apply:

  • Whenever the RSI is approaching the upper values, the color approaches red.

  • The color tends toward green whenever the RSI is getting close to the lower values.

Zooming out yields a basic heatmap, as shown below.

13-period RSI heatmap.

Plot code:

import matplotlib.pyplot as plt
def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
        if sample[i, second_panel] > 80 and sample[i, second_panel] < 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'darkred', linewidth = 1.5)  
        if sample[i, second_panel] > 70 and sample[i, second_panel] < 80:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'maroon', linewidth = 1.5)  
        if sample[i, second_panel] > 60 and sample[i, second_panel] < 70:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'firebrick', linewidth = 1.5) 
        if sample[i, second_panel] > 50 and sample[i, second_panel] < 60:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 40 and sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 30 and sample[i, second_panel] < 40:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'lightgreen', linewidth = 1.5)
        if sample[i, second_panel] > 20 and sample[i, second_panel] < 30:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'limegreen', linewidth = 1.5) 
        if sample[i, second_panel] > 10 and sample[i, second_panel] < 20:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'seagreen', linewidth = 1.5)  
        if sample[i, second_panel] > 0 and sample[i, second_panel] < 10:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

13-period RSI heatmap.

Dark green and red areas indicate imminent bullish and bearish reactions, respectively. RSI around 50 is grey.

Summary

To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation.

Technical analysis will lose its reputation as subjective and unscientific.

When you find a trading strategy or technique, follow these steps:

  • Put emotions aside and adopt a critical mindset.

  • Test it in the past under conditions and simulations taken from real life.

  • Try optimizing it and performing a forward test if you find any potential.

  • Transaction costs and any slippage simulation should always be included in your tests.

  • Risk management and position sizing should always be considered in your tests.

After checking the above, monitor the strategy because market dynamics may change and make it unprofitable.