Vitalik

3 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 ${0,1\dots89}$ (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 $x={0,1\dots98}$ . 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 $Z(x)=(x-x_1)*(x-x_2)*\dots*(x-x_n)$ 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 $Z(x) = (x-0)*(x-1)*\dots*(x-98)$ .
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

3 years ago

👏 Awesome post! When is part 3 coming?

Trent Lapinski

3 years ago

Very complex topic, great explanation

More on Web3 & Crypto

Nitin Sharma

2 years ago

Web3 Terminology You Should Know

The easiest online explanation.

Web3 is growing. Crypto companies are growing.

Instagram, Adidas, and Stripe adopted cryptocurrency.

Bitcoin and other cryptocurrencies made web3 famous.

Most don't know where to start. Cryptocurrency, DeFi, etc. are investments.

Since we don't understand web3, I'll help you today.

Let’s go.

1. Web3

It is the third generation of the web, and it is built on the decentralization idea which means no one can control it.

There are static webpages that we can only read on the first generation of the web (i.e. Web 1.0).

Web 2.0 websites are interactive. Twitter, Medium, and YouTube.

Each generation controlled the website owner. Simply put, the owner can block us. However, data breaches and selling user data to other companies are issues.

They can influence the audience's mind since they have control.

Assume Twitter's CEO endorses Donald Trump. Result? Twitter would have promoted Donald Trump with tweets and graphics, enhancing his chances of winning.

We need a decentralized, uncontrollable system.

And then there’s Web3.0 to consider. As Bitcoin and Ethereum values climb, so has its popularity. Web3.0 is uncontrolled web evolution. It's good and bad.

Dapps, DeFi, and DAOs are here. It'll all be explained afterwards.

2. Cryptocurrencies:

No need to elaborate.

Bitcoin, Ethereum, Cardano, and Dogecoin are cryptocurrencies. It's digital money used for payments and other uses.

Programs must interact with cryptocurrencies.

3. Blockchain:

Blockchain facilitates bitcoin transactions, investments, and earnings.

This technology governs Web3. It underpins the web3 environment.

Let us delve much deeper.

Blockchain is simple. However, the name expresses the meaning.

Blockchain is a chain of blocks.

Let's use an image if you don't understand.

The graphic above explains blockchain. Think Blockchain. The block stores related data.

Here's more.

4. Smart contracts

Programmers and developers must write programs. Smart contracts are these blockchain apps.

That’s reasonable.

Decentralized web3.0 requires immutable smart contracts or programs.

5. NFTs

Blockchain art is NFT. Non-Fungible Tokens.

Explaining Non-Fungible Token may help.

Two sorts of tokens:

These tokens are fungible, meaning they can be changed. Think of Bitcoin or cash. The token won't change if you sell one Bitcoin and acquire another.
Non-Fungible Token: Since these tokens cannot be exchanged, they are exclusive. For instance, music, painting, and so forth.

Right now, Companies and even individuals are currently developing worthless NFTs.

The concept of NFTs is much improved when properly handled.

6. Dapp

Decentralized apps are Dapps. Instagram, Twitter, and Medium apps in the same way that there is a lot of decentralized blockchain app.

Curve, Yearn Finance, OpenSea, Axie Infinity, etc. are dapps.

7. DAOs

DAOs are member-owned and governed.

Consider it a company with a core group of contributors.

8. DeFi

We all utilize centrally regulated financial services. We fund these banks.

If you have $10,000 in your bank account, the bank can invest it and retain the majority of the profits.

We only get a penny back. Some banks offer poor returns. To secure a loan, we must trust the bank, divulge our information, and fill out lots of paperwork.

DeFi was built for such issues.

Decentralized banks are uncontrolled. Staking, liquidity, yield farming, and more can earn you money.

Web3 beginners should start with these resources.

Ashraful Islam

4 years ago

Clean API Call With React Hooks


Photo by Juanjo Jaramillo on Unsplash

Calling APIs is the most common thing to do in any modern web application. When it comes to talking with an API then most of the time we need to do a lot of repetitive things like getting data from an API call, handling the success or error case, and so on.

When calling tens of hundreds of API calls we always have to do those tedious tasks. We can handle those things efficiently by putting a higher level of abstraction over those barebone API calls, whereas in some small applications, sometimes we don’t even care.

The problem comes when we start adding new features on top of the existing features without handling the API calls in an efficient and reusable manner. In that case for all of those API calls related repetitions, we end up with a lot of repetitive code across the whole application.

In React, we have different approaches for calling an API. Nowadays mostly we use React hooks. With React hooks, it’s possible to handle API calls in a very clean and consistent way throughout the application in spite of whatever the application size is. So let’s see how we can make a clean and reusable API calling layer using React hooks for a simple web application.

I’m using a code sandbox for this blog which you can get here.

import "./styles.css";
import React, { useEffect, useState } from "react";
import axios from "axios";

export default function App() {
  const [posts, setPosts] = useState(null);
  const [error, setError] = useState("");
  const [loading, setLoading] = useState(false);

  useEffect(() => {
    handlePosts();
  }, []);

  const handlePosts = async () => {
    setLoading(true);
    try {
      const result = await axios.get(
        "https://jsonplaceholder.typicode.com/posts"
      );
      setPosts(result.data);
    } catch (err) {
      setError(err.message || "Unexpected Error!");
    } finally {
      setLoading(false);
    }
  };

  return (
    <div className="App">
      <div>
        <h1>Posts</h1>
        {loading && <p>Posts are loading!</p>}
        {error && <p>{error}</p>}
        <ul>
          {posts?.map((post) => (
            <li key={post.id}>{post.title}</li>
          ))}
        </ul>
      </div>
    </div>
  );
}

I know the example above isn’t the best code but at least it’s working and it’s valid code. I will try to improve that later. For now, we can just focus on the bare minimum things for calling an API.

Here, you can try to get posts data from JsonPlaceholer. Those are the most common steps we follow for calling an API like requesting data, handling loading, success, and error cases.

If we try to call another API from the same component then how that would gonna look? Let’s see.

500: Internal Server Error

Now it’s going insane! For calling two simple APIs we’ve done a lot of duplication. On a top-level view, the component is doing nothing but just making two GET requests and handling the success and error cases. For each request, it’s maintaining three states which will periodically increase later if we’ve more calls.

Let’s refactor to make the code more reusable with fewer repetitions.

Step 1: Create a Hook for the Redundant API Request Codes

Most of the repetitions we have done so far are about requesting data, handing the async things, handling errors, success, and loading states. How about encapsulating those things inside a hook?

The only unique things we are doing inside handleComments and handlePosts are calling different endpoints. The rest of the things are pretty much the same. So we can create a hook that will handle the redundant works for us and from outside we’ll let it know which API to call.

500: Internal Server Error

Here, this request function is identical to what we were doing on the handlePosts and handleComments. The only difference is, it’s calling an async function apiFunc which we will provide as a parameter with this hook. This apiFunc is the only independent thing among any of the API calls we need.

With hooks in action, let’s change our old codes in App component, like this:

500: Internal Server Error

How about the current code? Isn’t it beautiful without any repetitions and duplicate API call handling things?

Let’s continue our journey from the current code. We can make App component more elegant. Now it knows a lot of details about the underlying library for the API call. It shouldn’t know that. So, here’s the next step…

Step 2: One Component Should Take Just One Responsibility

Our App component knows too much about the API calling mechanism. Its responsibility should just request the data. How the data will be requested under the hood, it shouldn’t care about that.

We will extract the API client-related codes from the App component. Also, we will group all the API request-related codes based on the API resource. Now, this is our API client:

import axios from "axios";

const apiClient = axios.create({
  // Later read this URL from an environment variable
  baseURL: "https://jsonplaceholder.typicode.com"
});

export default apiClient;

All API calls for comments resource will be in the following file:

import client from "./client";

const getComments = () => client.get("/comments");

export default {
  getComments
};

All API calls for posts resource are placed in the following file:

import client from "./client";

const getPosts = () => client.get("/posts");

export default {
  getPosts
};

Finally, the App component looks like the following:

import "./styles.css";
import React, { useEffect } from "react";
import commentsApi from "./api/comments";
import postsApi from "./api/posts";
import useApi from "./hooks/useApi";

export default function App() {
  const getPostsApi = useApi(postsApi.getPosts);
  const getCommentsApi = useApi(commentsApi.getComments);

  useEffect(() => {
    getPostsApi.request();
    getCommentsApi.request();
  }, []);

  return (
    <div className="App">
      {/* Post List */}
      <div>
        <h1>Posts</h1>
        {getPostsApi.loading && <p>Posts are loading!</p>}
        {getPostsApi.error && <p>{getPostsApi.error}</p>}
        <ul>
          {getPostsApi.data?.map((post) => (
            <li key={post.id}>{post.title}</li>
          ))}
        </ul>
      </div>
      {/* Comment List */}
      <div>
        <h1>Comments</h1>
        {getCommentsApi.loading && <p>Comments are loading!</p>}
        {getCommentsApi.error && <p>{getCommentsApi.error}</p>}
        <ul>
          {getCommentsApi.data?.map((comment) => (
            <li key={comment.id}>{comment.name}</li>
          ))}
        </ul>
      </div>
    </div>
  );
}

Now it doesn’t know anything about how the APIs get called. Tomorrow if we want to change the API calling library from axios to fetch or anything else, our App component code will not get affected. We can just change the codes form client.js This is the beauty of abstraction.

Apart from the abstraction of API calls, Appcomponent isn’t right the place to show the list of the posts and comments. It’s a high-level component. It shouldn’t handle such low-level data interpolation things.

So we should move this data display-related things to another low-level component. Here I placed those directly in the App component just for the demonstration purpose and not to distract with component composition-related things.

Final Thoughts

The React library gives the flexibility for using any kind of third-party library based on the application’s needs. As it doesn’t have any predefined architecture so different teams/developers adopted different approaches to developing applications with React. There’s nothing good or bad. We choose the development practice based on our needs/choices. One thing that is there beyond any choices is writing clean and maintainable codes.

Amelie Carver

3 years ago

Web3 Needs More Writers to Educate Us About It

WRITE FOR THE WEB3

Why web3’s messaging is lost and how crypto winter is growing growth seeds

People interested in crypto, blockchain, and web3 typically read Bitcoin and Ethereum's white papers. It's a good idea. Documents produced for developers and academia aren't always the ideal resource for beginners.

Given the surge of extremely technical material and the number of fly-by-nights, rug pulls, and other scams, it's little wonder mainstream audiences regard the blockchain sector as an expensive sideshow act.

What's the solution?

Web3 needs more than just builders.

After joining TikTok, I followed Amy Suto of SutoScience. Amy switched from TV scriptwriting to IT copywriting years ago. She concentrates on web3 now. Decentralized autonomous organizations (DAOs) are seeking skilled copywriters for web3.

Amy has found that web3's basics are easy to grasp; you don't need technical knowledge. There's a paradigm shift in knowing the basics; be persistent and patient.

Apple is positioning itself as a data privacy advocate, leveraging web3's zero-trust ethos on data ownership.

Finn Lobsien, who writes about web3 copywriting for the Mirror and Twitter, agrees: acronyms and abstractions won't do.

Image screenshot from FLobsien’s Twitter feed

Web3 preached to the choir. Curious newcomers have only found whitepapers and scams when trying to learn why the community loves it. No wonder people resist education and buy-in.

Due to the gender gap in crypto (Crypto Bro is not just a stereotype), it attracts people singing to the choir or trying to cash in on the next big thing.

Last year, the industry was booming, so writing wasn't necessary. Now that the bear market has returned (for everyone, but especially web3), holding readers' attention is a valuable skill.

White papers and the Web3

Why does web3 rely so much on non-growth content?

Businesses must polish and improve their messaging moving into the 2022 recession. The 2021 tech boom provided such a sense of affluence and (unsustainable) growth that no one needed great marketing material. The market found them.

This was especially true for web3 and the first-time crypto believers. Obviously. If they knew which was good.

White papers help. White papers are highly technical texts that walk a reader through a product's details. How Does a White Paper Help Your Business and That White Paper Guy discuss them.

They're meant for knowledgeable readers. Investors and the technical (academic/developer) community read web3 white papers. White papers are used when a product is extremely technical or difficult to assist an informed reader to a conclusion. Web3 uses them most often for ICOs (initial coin offerings).

White papers for web3 education help newcomers learn about the web3 industry's components. It's like sending a first-grader to the Annotated Oxford English Dictionary to learn to read. It's a reference, not a learning tool, for words.

Newcomers can use platforms that teach the basics. These included Coinbase's Crypto Basics tutorials or Cryptochicks Academy, founded by the mother of Ethereum's inventor to get more women utilizing and working in crypto.

Discord and Web3 communities

Discord communities are web3's opposite. Discord communities involve personal communications and group involvement.

Online audience growth begins with community building. User personas prefer 1000 dedicated admirers over 1 million lukewarm followers, and the language is much more easygoing. Discord groups are renowned for phishing scams, compromised wallets, and incorrect information, especially since the crypto crisis.

White papers and Discord increase industry insularity. White papers are complicated, and Discord has a high risk threshold.

Web3 and writing ads

Copywriting is emotional, but white papers are logical. It uses the brain's quick-decision centers. It's meant to make the reader invest immediately.

Not bad. People think sales are sleazy, but they can spot the poor things.

Ethical copywriting helps you reach the correct audience. People who gain a following on Medium are likely to have copywriting training and a readership (or three) in mind when they publish. Tim Denning and Sinem Günel know how to identify a target audience and make them want to learn more.

In a fast-moving market, copywriting is less about long-form content like sales pages or blogs, but many organizations do. Instead, the copy is concise, individualized, and high-value. Tweets, email marketing, and IM apps (Discord, Telegram, Slack to a lesser extent) keep engagement high.

What does web3's messaging lack? As DAOs add stricter copyrighting, narrative and connecting tales seem to be missing.

Web3 is passionate about constructing the next internet. Now, they can connect their passion to a specific audience so newcomers understand why.

Jenn Leach

3 years ago

I created a faceless TikTok account. Six months later.

Follower count, earnings, and more

I created my 7th TikTok account six months ago. TikTok's great. I've developed accounts for Amazon products, content creators/brand deals education, website flipping, and more.

Introverted or shy people use faceless TikTok accounts.

Maybe they don't want millions of people to see their face online, or they want to remain anonymous so relatives and friends can't locate them.

Going faceless on TikTok can help you grow a following, communicate your message, and make money online.

Here are 6 steps I took to turn my Tik Tok account into a $60,000/year side gig.

From nothing to $60K in 6 months

It's clickbait, but it’s true. Here’s what I did to get here.

Quick context:

I've used social media before. I've spent years as a social creator and brand.

I've built Instagram, TikTok, and YouTube accounts to nearly 100K.

How I did it

First, select a niche.

If you can focus on one genre on TikTok, you'll have a better chance of success, however lifestyle creators do well too.

Niching down is easier, in my opinion.

Examples:

Travel
Food
Kids
Earning cash
Finance

You can narrow these niches if you like.

During the pandemic, a travel blogger focused on Texas-only tourism and gained 1 million subscribers.

Couponing might be a finance specialization.

One of my finance TikTok accounts gives credit tips and grants and has 23K followers.

Tons of ways you can get more specific.

Consider how you'll monetize your TikTok account. I saw many enormous TikTok accounts that lose money.

Why?

They can't monetize their niche. Not impossible to commercialize, but tough enough to inhibit action.

First, determine your goal.

In this first step, consider what your end goal is.

Are you trying to promote your digital products or social media management services?

You want brand deals or e-commerce sales.

This will affect your TikTok specialty.

This is the first step to a TikTok side gig.

Step 2: Pick a content style

Next, you want to decide on your content style.

Do you do voiceover and screenshots?

You'll demonstrate a product?

Will you faceless vlog?

Step 3: Look at the competition

Find anonymous accounts and analyze what content works, where they thrive, what their audience wants, etc.

This can help you make better content.

Like the skyscraper method for TikTok.

Step 4: Create a content strategy.

Your content plan is where you sit down and decide:

How many videos will you produce each day or each week?
Which links will you highlight in your biography?
What amount of time can you commit to this project?

You may schedule when to post videos on a calendar. Make videos.

5. Create videos.

No video gear needed.

Using a phone is OK, and I think it's preferable than posting drafts from a computer or phone.

TikTok prefers genuine material.

Use their app, tools, filters, and music to make videos.

And imperfection is preferable. Tik okers like to see videos made in a bedroom, not a film studio.

Make sense?

When making videos, remember this.

I personally use my phone and tablet.

Step 6: Monetize

Lastly, it’s time to monetize How will you make money? You decided this in step 1.

Time to act!

For brand agreements

Include your email in the bio.
Share several sites and use a beacons link in your bio.
Make cold calls to your favorite companies to get them to join you in a TikTok campaign.

For e-commerce

Include a link to your store's or a product's page in your bio.

For client work

Include your email in the bio.
Use a beacons link to showcase your personal website, portfolio, and other resources.

For affiliate marketing

Include affiliate product links in your bio.
Join the Amazon Influencer program and provide a link to your storefront in your bio.

$60,000 per year from Tik Tok?

Yes, and some creators make much more.

Tori Dunlap (herfirst100K) makes $100,000/month on TikTok.

My TikTok adventure took 6 months, but by month 2 I was making $1,000/month (or $12K/year).

By year's end, I want this account to earn $100K/year.

Imagine if my 7 TikTok accounts made $100K/year.

7 Tik Tok accounts X $100K/yr = $700,000/year

Wayne Duggan

3 years ago

What An Inverted Yield Curve Means For Investors

The yield spread between 10-year and 2-year US Treasury bonds has fallen below 0.2 percent, its lowest level since March 2020. A flattening or negative yield curve can be a bad sign for the economy.

What Is An Inverted Yield Curve?

In the yield curve, bonds of equal credit quality but different maturities are plotted. The most commonly used yield curve for US investors is a plot of 2-year and 10-year Treasury yields, which have yet to invert.

A typical yield curve has higher interest rates for future maturities. In a flat yield curve, short-term and long-term yields are similar. Inverted yield curves occur when short-term yields exceed long-term yields. Inversions of yield curves have historically occurred during recessions.

Inverted yield curves have preceded each of the past eight US recessions. The good news is they're far leading indicators, meaning a recession is likely not imminent.

Every US recession since 1955 has occurred between six and 24 months after an inversion of the two-year and 10-year Treasury yield curves, according to the San Francisco Fed. So, six months before COVID-19, the yield curve inverted in August 2019.

Looking Ahead

The spread between two-year and 10-year Treasury yields was 0.18 percent on Tuesday, the smallest since before the last US recession. If the graph above continues, a two-year/10-year yield curve inversion could occur within the next few months.

According to Bank of America analyst Stephen Suttmeier, the S&P 500 typically peaks six to seven months after the 2s-10s yield curve inverts, and the US economy enters recession six to seven months later.

Investors appear unconcerned about the flattening yield curve. This is in contrast to the iShares 20+ Year Treasury Bond ETF TLT +2.19% which was down 1% on Tuesday.

Inversion of the yield curve and rising interest rates have historically harmed stocks. Recessions in the US have historically coincided with or followed the end of a Federal Reserve rate hike cycle, not the start.

Sofien Kaabar, CFA

2 years ago

Innovative Trading Methods: The Catapult Indicator

Python Volatility-Based Catapult Indicator

As a catapult, this technical indicator uses three systems: Volatility (the fulcrum), Momentum (the propeller), and a Directional Filter (Acting as the support). The goal is to get a signal that predicts volatility acceleration and direction based on historical patterns. We want to know when the market will move. and where. This indicator outperforms standard indicators.

Knowledge must be accessible to everyone. This is why my new publications Contrarian Trading Strategies in Python and Trend Following Strategies in Python now include free PDF copies of my first three books (Therefore, purchasing one of the new books gets you 4 books in total). GitHub-hosted advanced indications and techniques are in the two new books above.

The Foundation: Volatility

The Catapult predicts significant changes with the 21-period Relative Volatility Index.

The Average True Range, Mean Absolute Deviation, and Standard Deviation all assess volatility. Standard Deviation will construct the Relative Volatility Index.

Standard Deviation is the most basic volatility. It underpins descriptive statistics and technical indicators like Bollinger Bands. Before calculating Standard Deviation, let's define Variance.

Variance is the squared deviations from the mean (a dispersion measure). We take the square deviations to compel the distance from the mean to be non-negative, then we take the square root to make the measure have the same units as the mean, comparing apples to apples (mean to standard deviation standard deviation). Variance formula:

As stated, standard deviation is:

# The function to add a number of columns inside an array
def adder(Data, times):
    
    for i in range(1, times + 1):
    
        new_col = np.zeros((len(Data), 1), dtype = float)
        Data = np.append(Data, new_col, axis = 1)
        
    return Data

# The function to delete a number of columns starting from an index
def deleter(Data, index, times):
    
    for i in range(1, times + 1):
    
        Data = np.delete(Data, index, axis = 1)
        
    return Data
    
# The function to delete a number of rows from the beginning
def jump(Data, jump):
    
    Data = Data[jump:, ]
    
    return Data

# Example of adding 3 empty columns to an array
my_ohlc_array = adder(my_ohlc_array, 3)

# Example of deleting the 2 columns after the column indexed at 3
my_ohlc_array = deleter(my_ohlc_array, 3, 2)

# Example of deleting the first 20 rows
my_ohlc_array = jump(my_ohlc_array, 20)

# Remember, OHLC is an abbreviation of Open, High, Low, and Close and it refers to the standard historical data file

def volatility(Data, lookback, what, where):
    
  for i in range(len(Data)):

     try:

        Data[i, where] = (Data[i - lookback + 1:i + 1, what].std())
     except IndexError:
        pass
        
  return Data

The RSI is the most popular momentum indicator, and for good reason—it excels in range markets. Its 0–100 range simplifies interpretation. Fame boosts its potential.

The more traders and portfolio managers look at the RSI, the more people will react to its signals, pushing market prices. Technical Analysis is self-fulfilling, therefore this theory is obvious yet unproven.

RSI is determined simply. Start with one-period pricing discrepancies. We must remove each closing price from the previous one. We then divide the smoothed average of positive differences by the smoothed average of negative differences. The RSI algorithm converts the Relative Strength from the last calculation into a value between 0 and 100.

def ma(Data, lookback, close, where): 
    
    Data = adder(Data, 1)
    
    for i in range(len(Data)):
           
            try:
                Data[i, where] = (Data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                pass
            
    # Cleaning
    Data = jump(Data, lookback)
    
    return Data
def ema(Data, alpha, lookback, what, where):
    
    alpha = alpha / (lookback + 1.0)
    beta  = 1 - alpha
    
    # First value is a simple SMA
    Data = ma(Data, lookback, what, where)
    
    # Calculating first EMA
    Data[lookback + 1, where] = (Data[lookback + 1, what] * alpha) + (Data[lookback, where] * beta)    
 
    # Calculating the rest of EMA
    for i in range(lookback + 2, len(Data)):
            try:
                Data[i, where] = (Data[i, what] * alpha) + (Data[i - 1, where] * beta)
        
            except IndexError:
                pass
            
    return Datadef rsi(Data, lookback, close, where, width = 1, genre = 'Smoothed'):
    
    # Adding a few columns
    Data = adder(Data, 7)
    
    # Calculating Differences
    for i in range(len(Data)):
        
        Data[i, where] = Data[i, close] - Data[i - width, close]
     
    # Calculating the Up and Down absolute values
    for i in range(len(Data)):
        
        if Data[i, where] > 0:
            
            Data[i, where + 1] = Data[i, where]
            
        elif Data[i, where] < 0:
            
            Data[i, where + 2] = abs(Data[i, where])
            
    # Calculating the Smoothed Moving Average on Up and Down
    absolute values        
                             
    lookback = (lookback * 2) - 1 # From exponential to smoothed
    Data = ema(Data, 2, lookback, where + 1, where + 3)
    Data = ema(Data, 2, lookback, where + 2, where + 4)
    
    # Calculating the Relative Strength
    Data[:, where + 5] = Data[:, where + 3] / Data[:, where + 4]
    
    # Calculate the Relative Strength Index
    Data[:, where + 6] = (100 - (100 / (1 + Data[:, where + 5])))  
    
    # Cleaning
    Data = deleter(Data, where, 6)
    Data = jump(Data, lookback)

    return Data

EURUSD in the first panel with the 21-period RVI in the second panel.

def relative_volatility_index(Data, lookback, close, where):

    # Calculating Volatility
    Data = volatility(Data, lookback, close, where)
    
    # Calculating the RSI on Volatility
    Data = rsi(Data, lookback, where, where + 1) 
    
    # Cleaning
    Data = deleter(Data, where, 1)
    
    return Data

The Arm Section: Speed

The Catapult predicts momentum direction using the 14-period Relative Strength Index.

EURUSD in the first panel with the 14-period RSI in the second panel.

As a reminder, the RSI ranges from 0 to 100. Two levels give contrarian signals:

A positive response is anticipated when the market is deemed to have gone too far down at the oversold level 30, which is 30.
When the market is deemed to have gone up too much, at overbought level 70, a bearish reaction is to be expected.

Comparing the RSI to 50 is another intriguing use. RSI above 50 indicates bullish momentum, while below 50 indicates negative momentum.

The direction-finding filter in the frame

The Catapult's directional filter uses the 200-period simple moving average to keep us trending. This keeps us sane and increases our odds.

Moving averages confirm and ride trends. Its simplicity and track record of delivering value to analysis make them the most popular technical indicator. They help us locate support and resistance, stops and targets, and the trend. Its versatility makes them essential trading tools.

EURUSD hourly values with the 200-hour simple moving average.

This is the plain mean, employed in statistics and everywhere else in life. Simply divide the number of observations by their total values. Mathematically, it's:

We defined the moving average function above. Create the Catapult indication now.

Indicator of the Catapult

The indicator is a healthy mix of the three indicators:

The first trigger will be provided by the 21-period Relative Volatility Index, which indicates that there will now be above average volatility and, as a result, it is possible for a directional shift.
If the reading is above 50, the move is likely bullish, and if it is below 50, the move is likely bearish, according to the 14-period Relative Strength Index, which indicates the likelihood of the direction of the move.
The likelihood of the move's direction will be strengthened by the 200-period simple moving average. When the market is above the 200-period moving average, we can infer that bullish pressure is there and that the upward trend will likely continue. Similar to this, if the market falls below the 200-period moving average, we recognize that there is negative pressure and that the downside is quite likely to continue.

lookback_rvi = 21
lookback_rsi = 14
lookback_ma  = 200
my_data = ma(my_data, lookback_ma, 3, 4)
my_data = rsi(my_data, lookback_rsi, 3, 5)
my_data = relative_volatility_index(my_data, lookback_rvi, 3, 6)

Two-handled overlay indicator Catapult. The first exhibits blue and green arrows for a buy signal, and the second shows blue and red for a sell signal.

The chart below shows recent EURUSD hourly values.

def signal(Data, rvi_col, signal):
    
    Data = adder(Data, 10)
        
    for i in range(len(Data)):
            
        if Data[i,     rvi_col] < 30 and \
           Data[i - 1, rvi_col] > 30 and \
           Data[i - 2, rvi_col] > 30 and \
           Data[i - 3, rvi_col] > 30 and \
           Data[i - 4, rvi_col] > 30 and \
           Data[i - 5, rvi_col] > 30:
               
               Data[i, signal] = 1
                           
    return Data

Signals are straightforward. The indicator can be utilized with other methods.

my_data = signal(my_data, 6, 7)

Lumiwealth shows how to develop all kinds of algorithms. I recommend their hands-on courses in algorithmic trading, blockchain, and machine learning.

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.

After you find a trading method or approach, follow these steps:

Put emotions aside and adopt an analytical perspective.
Test it in the past in conditions and simulations taken from real life.
Try improving it and performing a forward test if you notice any possibility.
Transaction charges and any slippage simulation should always be included in your tests.
Risk management and position sizing should always be included in your tests.

After checking the aforementioned, monitor the plan because market dynamics may change and render it unprofitable.

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Innovative Trading Methods: The Catapult Indicator

The Foundation: Volatility

The Arm Section: Speed

The direction-finding filter in the frame

Indicator of the Catapult

Summary