Lecture notes that were apparently very popular at Cornell University. In this period he was actively synthesizing the revolutionary bullshit Richard Feynman and Julian Schwinger were writing and making it understandable to the more general physicist audience, so it might be a good reading.
We shall not develop straightaway a correct theory including many particles. Instead we follow the historical development. We try to make a relativistic quantum theory of one particle, find out how far we can go and where we get into trouble.
These appear to be benchmarks that don't involve running anything concretely, just compiling and likely then counting gates:
See also: e-learning website.
Related ideas:
One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of .
Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.
As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.
The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.
For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.
The most important thing this project provides appears to be the
.onnx file format, which represents ANN models, pre-trained or not.Deep learning frameworks can then output such
.onnx files for interchangeability and serialization.Some examples:
- activatedgeek/LeNet-5 produces a trained
.onnxfrom PyTorch - MLperf v2.1 ResNet can use
.onnxas a pre-trained model
Here is a very direct description of the system:Code 1. "Sample Bitcoin transaction graph" illustrates these concepts:
- each transaction (transaction is often abbreviated "tx") has a list of inputs, and a list of outputs
- each input is the output of a previous transaction. You verify your identity as the indented receiver by producing a digital signature for the public key specified on the output
- each output specifies the public key of the receiver and the value being sent
- the sum of output values cannot obvious exceed the sum of input values. If it is any less, the leftover is sent to the miner of the transaction as a transaction fee, which is an incentive for mining.
- once an output is used from an input, it becomes marked as spent, and cannot be reused again. Every input uses the selected output fully. Therefore, if you want to use an input of 1 BTC to pay 0.1 BTC, what you do is to send 0.1 BTC to the receiver, and 0.9 BTC back to yourself as change. This is why the vast majority of transactions has two outputs: one "real", and the other change back to self.
tx0: magic transaction without any inputs, i.e. either Genesis block or a coinbase mining reward. Since it is a magic transaction, it produces 3 Bitcoins from scratch: 1 inout0and 2 inout1. The initial value was actually 50 BTC and reduced with time: Section "Bitcoin halving"tx1: regular transaction that takes:Since this is a regular transaction, no new coins are produced.tx2: regular transaction with a single input and a single output. It uses up the entire input, leading to 0 miner fees, so this greedy one might (will?) never get mined.tx3: regular transaction with two inputs and one output. The total input is 2.3, and the output is 1.8, so the miner fee will be 0.5
tx1 tx3
tx0 +---------------+ +---------------+
+----------+ | in0 | | in0 |
| out0 |<------out: tx0 out0 | +------out: tx1 out1 |
| value: 1 | +---------------+ | +---------------+
+----------+ | out0 | | | in1 |
| out1 |<-+ | value: 0.5 | | +----out: tx2 out0 |
| value: 2 | | +---------------+ | | +---------------+
+----------+ | | out1 |<-+ | | out1 |
| | value: 0.3 | | | value: 1.8 |
| +---------------+ | +---------------+
| |
| |
| |
| tx2 |
| +---------------+ |
| | in0 | |
+----out: tx0 out1 | |
+---------------+ |
| out0 |<---+
| value: 2 |
+---------------+Code 1.
Sample Bitcoin transaction graph
. Since every input must come from a previous output, there must be some magic way of generating new coins from scratch to bootstrap the system. This mechanism is that when the miner mines successfully, they get a mining fee, which is a magic transaction without any valid inputs and a pre-agreed value, and an incentive to use their power/compute resources to mine. This magic transaction is called a "coinbase transaction".
The key innovation of Bitcoin is how to prevent double spending, i.e. use a single output as the input of two different transactions, via mining.
For example, what prevents me from very quickly using a single output to pay two different people in quick succession?
The solution are the blocks. Blocks discretize transactions into chunks in a way that prevents double spending.
A block contains:
- a list of transactions that are valid amongst themselves. Notably, there can't be double spending within a block.People making transactions send them to the network, and miners select which ones they want to add to their block. Miners prefer to pick transactions that are:
- the ID of its parent block. Blocks therefore form a linear linked list of blocks, except for temporary ties that are soon resolved. The longest known list block is considered to be the valid one.
- a nonce, which is an integer chosen "arbitrarily by the miner"
For a block to be valid, besides not containing easy to check stuff like double spending, the miner must also select a nonce such that the hash of the block starts with N zeroes.
For example, considering the transactions from Code 1. "Sample Bitcoin transaction graph", the block structure shown at Code 2. "Sample Bitcoin blockchain" would be valid. In it
block0 contains two transactions: tx0 and tx1, and block1 also contains two transactions: tx2 and tx3. block0 block1 block2
+------------+ +--------------+ +--------------+
| prev: |<----prev: block0 |<----prev: block1 |
+------------+ +--------------+ +--------------+
| txs: | | txs: | | txs: |
| - tx0 | | - tx2 | | - tx4 |
| - tx1 | | - tx3 | | - tx5 |
+------------+ +--------------+ +--------------+
| nonce: 944 | | nonce: 832 | | nonce: 734 |
+------------+ +--------------+ +--------------+
Code 2.
Sample Bitcoin blockchain
. nonces are on this example arbitrary chosen numbers that would lead to a desired hash for the block.block0 is the Genesis block, which is magic and does not have a previous block, because we have to start from somewhere. The network is hardcoded to accept that as a valid starting point.Now suppose that the person who created Clearly, this transaction would try to spend Notably, it is not possible that
tx2 had tried to double spend and also created another transaction tx2' at the same time that looks like this: tx2'
+---------------+
| in0 |
| out: tx0 out1 |
+---------------+
| out0 |
| value: 2 |
+---------------+tx0 out1 one more time in addition to tx2, and should not be allowed! If this were attempted, only the following outcomes are possible:block1containstx2. Then whenblock2gets made, it cannot containtx2', becausetx0 out1was already spent bytx2block1containstx2'.tx2cannot be spent anymore
block1 contains both tx2 and tx2', as that would make the block invalid, and the network would not accept that block even if a miner found a nonce.Since hashes are basically random, miners just have to try a bunch of nonces randomly until they find one that works.
The more zeroes, the harder it is to find the hash. For example, on the extreme case where N is all the bits of the hash output, we are trying to find a hash of exactly 0, which is statistically impossible. But if e.g. N=1, you will in average have to try only two nonces, N=2 four nonces, and so on.
The value N is updated every 2 weeks, and aims to make blocks to take 10 minutes to mine on average. N has to be increased with time, as more advanced hashing hardware has become available.
Once a miner finds a nonce that works, they send their block to the network. Other miners then verify the block, and once they do, they are highly incentivized to stop their hashing attempts, and make the new valid block be the new parent, and start over. This is because the length of the chain has already increased: they would need to mine two blocks instead of one if they didn't update to the newest block!
Therefore if you try to double spend, some random miner is going to select only one of your transactions and add it to the block.
They can't pick both, otherwise their block would be invalid, and other miners wouldn't accept is as the new longest one.
Then sooner or later, the transaction will be mined and added to the longest chain. At this point, the network will move to that newer header, and your second transaction will not be valid for any miner at all anymore, since it uses a spent output from the first one that went in. All miners will therefore drop that transaction, and it will never go in.
The goal of having this mandatory 10 minutes block interval is to make it very unlikely that two miners will mine at the exact same time, and therefore possibly each one mine one of the two double spending transactions. When ties to happen, miners randomly choose one of the valid blocks and work on top of it. The first one that does, now has a block of length L + 2 rather than L + 1, and therefore when that is propagated, everyone drops what they are doing and move to that new longest one.
Bought around: 2017-09.
TEFAL Multicook 8in1 RK302E15 MultiCooker - 4 Portions / 5L.
Likely bought from: www.johnlewis.com/tefal-rk302e15-8-in-1-multi-cooker/p231378165
How to open videos: can't find any, but the hard part (remove top lid) was the same as the video for joyoung rice cooker (2014), can be done by inserting a thin metal and going around it.
Bottom opens by taking off a single screw on the bottom and pulling it out (not obvious, a little bit of force).
2021-01: while making congee it overflowed without us noticing it, and next time we were going to cook something, it started to burn bits of congee that stuck to the heat plate. Opened it up and tried to clean everything.
2020-03: E01 error, looked up on manual and it is a top wire broken, opened up and confirmed one of the three wires going up broken, exactly like the previous one joyoung rice cooker (2014). Managed to fix easily with heat gun and Solder Seal Heat Shrink, no soldering iron, that thing is amazing: www.amazon.co.uk/dp/B085415G8N Let's see how long it lasts.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact