text:
# Mimic layout of paracolumned document in TOC

I have an unusual document layout where two sections about closely related subjects are set side-by-side. I would like the sections and subsections to be displayed in the same parallel way in the table of contents, like so:

(I know the section numbering repeats, but that I can fix and isn't really part of the question.)

This is not what my table of contents currently looks like. I had thought I could get what I wanted by redefining \switchcolumn to, when it is expanded, also write a \switchcolumn to the TOC. This is the only difference between the Paracol environment used in the MWE and the normal paracol

\documentclass{article}
\usepackage{kantlipsum,hyperref,paracol}
\makeatletter
\def\switchcolumn@i[#1]{
}
\newcommand\switchcolumn@ii{
}
\newenvironment{Paracol}[1]{%
\begin{paracol}{#1}
\let\oldswitchcolumn\switchcolumn
\def\switchcolumn{\kernel@ifnextchar[{\switchcolumn@i}{\switchcolumn@ii}}
}
\end{paracol}
}
\makeatother
\begin{document}
\tableofcontents
\begin{Paracol}{2}
\begin{column*}
\section{Trees}
\subsection{Silviculture of the Foo Tree}
\subsubsection{Habitat} \kant[1-2]
\subsubsection{Uses} \kant[3]
\subsubsection{Growth} \kant[4-5]
\end{column*}

\begin{column}
\section{Pests}
\subsection{Pests of the Foo Tree}
\subsubsection{Rats} \kant[1-2]
\subsubsection{Cats} \kant[3]
\subsubsection{Hats} \kant[4]
\end{column}

\begin{column*}
\subsection{Silviculture of the Bar Tree}
\end{column*}

\begin{column}
\subsection{Pests of the Bar Tree}
\end{column}
\begin{column*}Lorem ipsum dolor sit...
\subsubsection{Habitat} \kant[5]
\subsubsection{Uses} \kant[6]
\end{column*}
%An image spanning the width of the page
\begin{nthcolumn}{0}%Continuation of bar tree silvics
\subsubsection{Growth} \kant[7]
\end{nthcolumn}

\begin{column} Lorem ipsum dolor sit...
\subsubsection{Pigs} \kant[6]
\subsubsection{Wigs} \kant[7]
\end{column}

\end{Paracol}
\end{document}

Unfortunately, I do not think the \switchcolumns are not expanded in the order I expected, resulting in the following, messy TOC.

\begin {paracol}{2}
\contentsline {section}{\numberline {1}Trees}{1}{section.1}
%Many more \contentslines from sections in both columns.
\contentsline {subsubsection}{\numberline {1.1.3}Hats}{3}{subsubsection.1.1.3}
\switchcolumn *
\contentsline {subsection}{\numberline {1.2}Pests of the Bar Tree}{3}{subsection.1.2}
\switchcolumn *
\switchcolumn
\contentsline {subsection}{\numberline {1.2}Silviculture of the Bar Tree}{4}{subsection.1.2}
\switchcolumn
\contentsline {subsubsection}{\numberline {1.2.1}Pigs}{4}{subsubsection.1.2.1}
%More \contentslines
\end {paracol}
\contentsline {subsubsection}{\numberline {1.2.2}Uses}{6}{subsubsection.1.2.2}
\switchcolumn [0]
\contentsline {subsubsection}{\numberline {1.2.3}Growth}{6}{subsubsection.1.2.3}
\switchcolumn

I'm not really sure how to fix this. If I wanted the contents to align only at the \section entries in the TOC I could redefine \addtocontents to add the TOC commands to a \leftcontents and \rightcontents macro and then use those to add the contents at the very end. But since I want them aligned at the subsection level, this would produce something like

    \begin{paracol}{2}
\begin{column}\contentsline {section}{\numberline {1}Trees}{1}{section.1}\end{column}
\begin{column}\contentsline {subsection}{\numberline {1.1}Silviculture of the Foo Tree}{1}{subsection.1.1}\end{column}
%etc.
\begin{column*}\contentsline {section}{\numberline {1}Pests}{1}{section.1}\end{column*}
\begin{column*}\contentsline {subsection}{\numberline {1.1}Pests of the Foo Tree}{1}{subsection.1.1}\end{column*}
\end{paracol}

Which would still come out wrong.

Perhaps you can achieve something with package tableof.

For some reason I had to comment out all uses of kantlipsum in the example, as this had a strange influence on the mixture paracol+tableof (which I did not try to understand).

In the code below you could patch column and column* environments to have the \TAGLEFT and \TAGRIGHT automatically inserted.

\documentclass[a4paper]{article}
\usepackage{geometry}
\usepackage{kantlipsum,hyperref,paracol}
\usepackage{tableof}
\AtBeginDocument{\tofOpenTocFileForWrite}% see tableof doc, section 2.5

\def\TAGLEFT{\toftagstop{right}\toftagstart{left}}
\def\TAGRIGHT{\toftagstop{left}\toftagstart{right}}
\def\TAGLEFTRIGHT{\toftagstart{left}\toftagstart{right}}

\begin{document}\thispagestyle{empty}
\begin{paracol}{2}
\begin{column*}
\tableof{left}
\end{column*}
\begin{column}
\tableof{right}
\end{column}
\end{paracol}

% \tablenotof{left,right}

\begin{paracol}{2}

\begin{column*}
\TAGLEFT
\section{Trees}
\subsection{Silviculture of the Foo Tree}
\subsubsection{Habitat} %\kant[1-2]
\subsubsection{Uses}    %\kant[3]
\subsubsection{Growth}  %\kant[4-5]
\end{column*}

\begin{column}
\TAGRIGHT
\section{Pests}
\subsection{Pests of the Foo Tree}
\subsubsection{Rats} %\kant[1-2]
\subsubsection{Cats} %\kant[3]
\subsubsection{Hats} %\kant[4]
\end{column}

\begin{column*}
\TAGLEFT
\subsection{Silviculture of the Bar Tree}
\end{column*}

\begin{column}
\TAGRIGHT      \subsection{Pests of the Bar Tree}
\end{column}

\begin{column*}
\TAGLEFT
Lorem ipsum dolor sit...
\subsubsection{Habitat} %\kant[5]
\subsubsection{Uses}    %\kant[6]
\end{column*}

%An image spanning the width of the page
\begin{nthcolumn}{0}%Continuation of bar tree silvics
\TAGLEFT
\subsubsection{Growth} %\kant[7]
\end{nthcolumn}

\begin{column} Lorem ipsum dolor sit...
\TAGRIGHT
\subsubsection{Pigs} %\kant[6]
\subsubsection{Wigs} %\kant[7]
\end{column}
\end{paracol}
\end{document}

The parallelism of the two TOCs will continue only if they have the same number of sections, subsections, etc...


text:
# Starting to visualise the smart home

Recently I posted a survey on our Facebook page asking for input on future topics. Overwhelmingly the favourite topic was “visibility and dashboards”, so I started to plan out what that content might look like.

At the same time, I posted to the PiHole sub-reddit that I’d managed to integrate data from PiHole with my existing monitoring setup, which led to a number of calls for me to document my setup.

This mini-series of blog posts will cover all of these subjects, starting with building out a “home server” that can be used to run additional services needed to display dashboards and the like, and running right through the software I use to come up with a dashboard like the one at the top of this post.

This first post will lay out the tech stack and hardware that I’m using, then future posts will look at each of the components in turn until we have a dashboard up and running!

## The Hardware

When I built my home server, I had a fixed budget and the best custom-build I could get was the following specification:

• AMD Ryzen 5 2600 CPU
• 16G RAM
• 256G nVME drive for the Operating System
• 1TB SSD for “storage”
• Nvidia GT710 Graphics Card for both display output and to explore CUDA-based data analysis/machine learning

I originally ran CentOS Linux on the server, however recently I rebuilt it to use Arch Linux. I’ve been using Linux for over 20 years, so don’t be scared by this - you could easily achieve the same on Ubuntu or another flavour of Linux!

Alongside the server, I also have a number of Raspberry Pi computers for various projects, however two of them are reserved for PiHole - a network-wide DNS filter and ad-blocker, and it is those two that we’ll focus on during this series.

## The Software Stack

The network is made up of numerous software services that deal with DNS, Service Discovery, Secrets Management, and Container Orchestration, with a monitoring layer over the top of this.

If you think of your home infrastructure as a pyramid, we start with the network at the bottom, then DNS, then service discovery, then container orchestration and monitoring, with the applications on top of that.

### The Hashicorp Holy Trinity

Hashicorp write some of the most advanced tools out there for managing system and platform deployments, from vagrant to run multiple virtual machines on local laptops and Packer for building VM’s, containers, and cloud images right through to Terraform for deploying across multiple cloud platforms, Nomad for container orchestration (similar to Kubernetes) and Consul & Vault for service discovery and secrets management.

Three of these tools (Consul, Vault, and Nomad) will form the heart of our setup because when they are used together they can do amazing things!

#### Consul

Consul is a platform dedicated to service discovery. Applications and services can register with Consul via the API or agent, and those services and nodes appear in DNS.

As an example, if we register a postgresql database server as a service called pgsql with Consul, as soon as the health checks pass we’ll be able to access that server at pgsql.service.consul. (We can change the domain name, and we’ll look at how we do that when we get to the Consul section of this series!).

It’s not just services though, any host running the Consul agent and connected to the cluster can act as a DNS relay and will also register itself at <node_name>.node.consul, so if our host running Postgresql is called caliban then we’ll end up with two DNS entries in Consul:

• pgsql.service.consul for the service
• caliban.node.consul for the host itself

The great thing about Consul is that it talks really nicely to Nomad, so containers that are deployed using Nomad are automatically registered with Consul and appear in DNS within seconds of being launched.

Nomad is what we’ll use to orchestrate our containers. Nomad is similar to the darling of the DevOps and SRE world Kubernetes, although I find it far simpler to get up and running whilst providing all of the features that I’d want from an orchestration platform.

We’re still going to be using Docker under the hood, however Nomad allows us to describe how we want to deploy a service in a way that also allows us to pull secrets from Vault and register with Consul.

We’ll dig into some examples later in the series, however for now it’s worth checking out the materials on Hashicorp’s Learning Portal if you want to understand more about how Nomad works.

#### Vault

Vault is the final piece of the puzzle when it comes to our Hashicorp Triumvirate and will deal with “secrets management”. Initially this could be seen as overkill, however we’ll install it now because it can integrate with all kinds of other platforms to allow for security features such as auto-rotation of database passwords and even SSH access!

Again, we’ll go into more detail in future posts, and Hashicorp’s Learning Portal is the best place to look for more information on how all three of these bits of software hang together.

### Other software

Aside from the Linux Operating System, we’ll also be leaning heavily on PiHole for DNS and ad-blocking, FluentD and Fluent-Bit for log collection, Loki for log storage, Prometheus for metrics collection, and Grafana for data visualisation.

We’ll cover these in a couple of posts around logging and monitoring towards the end of the series.

### The setup

I’d like to end this post with a quick image to show how DNS in particular will flow through the platform, but also how the network components are connected.

If you’ve already read my mini-series on building a stable network you’ll know that I use the Ubiquiti Unifi platform for my network, so we’ll be integrating with those but I’ll make sure to add more generic instructions or alternatives where I can for those of you using other kit.

In the diagram above, a DNS request starts with the network client (the laptop, tablet, phone, or IoT device) which sends the request to PiHole. PiHole blocks any requests for hosts that are on the blocklist (this could be adverts, adult content, social media, or anything else you want to remove from your network) and then passes the request on to Consul.

Consul does a check to see if it can resolve the request against any of its nodes or services, and then if that fails it passes it upstream via the Unifi Security Gateway (USG) to an external service such as Google or OpenDNS.

This gives us the ability to block unwanted content whilst still accessing our local services and nodes and the wider world.

In the next part of this series, we’ll look at installing Consul and Vault, so be sure to like and follow our social media channels or subscribe to our RSS feed!

format: plain


text:
# Why is AES not a Feistel cipher?

I am studying for an exam right now. And I wanted to make sure I got this point correct.

AES is not a Feistel cipher because the operations in AES are not invertible.

Is the above statement correct? If not, why isn't it a Feistel cipher?

• If the operations were not invertible we wouldn't be able to decrypt anything. Read the links in Reid's answer and try to memorize the schematics and what a Feistel network looks like. That's very different from a simple sub-perm network (link also in Reid's answer). A Feistel cipher is a cipher that uses a Feistel structure in its design - AES does not. – rath Sep 28 '13 at 6:36
• @rath you would not be able to decrypt anything if the cipher was not augmented with a mode that only requires one way encryption such as CTR mode – Maarten Bodewes Sep 28 '13 at 12:51
• @rath Besides my previous comment, it is very possible to use constructions that are not invertible for a construction that - in total - isn't. As prime example the sub key derivation may well be non-invertible. – Maarten Bodewes Jun 9 '16 at 13:38

Well, AES is not a Feistel cipher because it's a substitution-permutation network instead. If I were taking a test that asked me why AES was not a Feistel cipher, this would be my argument: namely, that the structure of substitution-permutation networks is fundamentally different from that of Feistel networks. (Here one could elaborate on invertibility and other differences.)

That said, your statement is not correct. In a Feistel cipher, the round function is not necessarily invertible (DES's round function is not), but in AES, like any substitution-permutation network, the rounds are invertible. This is a property of the construction itself.

By definition, a Feistel network uses a series of rounds that split the input block into two sides, uses one side to permute the other side, then swaps the sides. As always, Wikipedia has a nice diagram.

AES doesn't do this. Performing a round necessarily permutes the entire state. Each round consists of the SubBytes, ShiftRows, MixColumns, and AddRoundKey steps, none of which behave in a Feistel network-like manner:

• SubBytes performs byte-wise substitution from a constant table, no byte's value influences another byte's permuted value.
• ShiftRows permutes 4-byte words at a time using only those 4 bytes, no byte from another word influences their permuted output.
• MixColumns permutes 4-byte words at a time using only those 4 bytes, no byte from another word influences their permuted output.
• AddRoundKey is a permutation using the derived round key, no byte's value influences another byte's permuted value.

So only the ShiftRows and MixColumns steps even allow a byte to influence the permutation of any other bytes in the state, and in both of those steps a given byte only influences the permutation of other bytes when it itself is also being permuted.

None of that matches the "split the block into A and B and use A to permute B" style of a Feistel network.

The simple answer is "Because its an SPN cipher".

What is difference between Feistel and SPN?

SPN operates on whole data in one round, where as Feistel divides data into N parts where N>=2 , then operate upon X parts where 0

Image Sources: FEISTEL, SPN

In balanced, data is divided in Two parts i.e N = 2, and X=1 (example is camellia cipher) In Unbalanced, data is divided in more than two parts, i.e N > 2, (example is SMS4 cipher)

SPN has to be invertible, otherwise decryption will not be possible. where as in Feistel cipher, the F function can be invertible or non-invertible. And you will still be able to get encryption and decryption.

Another beauty of Feistel Cipher is that code for Encryption and Decryption is same, you only need to use the round keys in reverse order. (even if your F function is invertible, you need not to write its inversion in the code)

One more point to note is, in Feistel your F function can be a simple SPN.

• Comments are not for extended discussion; this conversation has been moved to chat. – e-sushi Dec 17 '17 at 13:12


text:
A friend of mine recently had an interview for a software engineering position. They later recounted to me the content of the technical questions that they had been asked. Some had been pretty standard:

• “What’s the difference between concurrency and parallelism?" – a reasonable question given that Go was the company’s language of choice.
• “What’s the difference between a method and a function?" – a little more strange, in my opinion, since the difference is of little practical use.

But then, they recounted a rather interesting question:

How many values does a bool have?

Innocuous at first, isn’t it? Probably a bit simpler, in fact, than the questions about methods and functions, concurrency and parallelism. It’s plausible that a candidate has not done much concurrent or parallel programming in their life, or that they came from a language in which functions were rare and methods were ubiquitous. It’s not plausible, on the other hand, that a candidate applying to a software engineering position has not encountered booleans.

If you’re genuinely unsure about the answer to the question, I think there’s no reason for me to mess with you. The simple answer to the question – as far as I know – is that a boolean has two values. They are true and false in Java, or True and False in Haskell, and 1 and 0 in C. A boolean value is either true or false.

So, what’s there to think about? There are a few things, ackshually. Let’s explore them, starting from the theoretical perspective.

### Types, Values, and Expressions

Boolean, or bool, is a type. Broadly speaking, a type is a property of something that defines what the something means and what you can do with it. That something can be several things; for our purposes, it can either be an expression in a programming language (like those in the form fact(n)) or a value in that same programming language (like 5).

Dealing with values is rather simple. Most languages have finite numbers, usually with $2^{32}$ values, which have type int, i32, or something in a similar vein. Most languages also have strings, of which there are as many as you have memory to contain, and which have the type string, String, or occasionally the more confusing char*. Most languages also have booleans, as we discussed above.

The deal with expressions is a more interesting. Presumably expressions evaluate to values, and the type of an expression is then the type of values it can yield. Consider the following snippet in C++:

int square(int x) {
return x * x;
}

Here, the expression x is known to have type int from the type signature provided by the user. Multiplication of integers yields an integer, and so the type of x*x is also of type int. Since square(x) returns x*x, it is also of type int. So far, so good.

int meaningOfLife() {
return meaningOfLife();
}

No, wait, doesn’t say “stack overflow” just yet. That’s no fun. And anyway, this is technically a tail call, so maybe our C++ compiler can avoid growing the stack. And indeed, flicking on the -O2 flag in this compiler explorer example, we can see that no stack growth is necessary: it’s just an infinite loop. But meaningOfLife will never return a value. One could say this computation diverges.

Well, if it diverges, just throw the expression out of the window! That’s no int! We only want real ints!

And here, we can do that. But what about the following:

inf_int collatz(inf_int x) {
if(x == 1) return 1;
if(x % 2 == 0) return collatz(x/2);
return collatz(x * 3 + 1);
}

Notice that I’ve used the fictitious type inf_int to represent integers that can hold arbitrarily large integer values, not just the 32-bit ones. That is important for this example, and I’ll explain why shortly.

The code in the example is a simulation of the process described in the Collatz conjecture. Given an input number x, if the number is even, it’s divided in half, and the process continues with the halved number. If, on the other hand, the number is odd, it’s multiplied by 3, 1 is added to it, and the process continues with that number. The only way for the process to terminate is for the computation to reach the value 1.

Why does this matter? Because as of right now, nobody knows whether or not the process terminates for all possible input numbers. We have a strong hunch that it does; we’ve checked a lot of numbers and found that the process terminates for them. This is why 32-bit integers are not truly sufficient for this example; we know empirically that the function will terminate for them.

But why does this matter? Well, it matters because we don’t know whether or not this function will diverge, and thus, we can’t ‘throw it out of the window’ like we wanted to with meaningOfLife! In general, it’s impossible to tell whether or not a program will terminate; that is the halting problem. So, what do we do?

It turns out to be convenient – formally – to treat the result of a diverging computation as its own value. This value is usually called ‘bottom’, and written as $\bot$. Since in most programming languages, you can write a nonterminating expression or function of any type, this ‘bottom’ is included in all types. So in fact, the possible values of unsigned int are $\bot, 0, 1, 2, …$ and so on. As you may have by now guessed, the same is true for a boolean: we have $\bot$, true, and false.

You may be thinking:

Now he’s done it; he’s gone off the deep end with all that programming language theory. Tell me, Daniel, where the heck have you ever encountered $\bot$ in code? This question was for a software engineering interview, after all!

You’re right; I haven’t specifically seen the symbol $\bot$ in my time programming. But I have frequently used an equivalent notation for the same idea: undefined. In fact, here’s a possible definition of undefined in Haskell:

undefined = undefined

Just like meaningOfLife, this is a divergent computation! What’s more is that the type of this computation is, in Haskell, a. More explicitly – and retreating to more mathematical notation – we can write this type as: $\forall \alpha . \alpha$. That is, for any type $\alpha$, undefined has that type! This means undefined can take on any type, and so, we can write:

myTrue :: Bool
myTrue = True

myFalse :: Bool
myFalse = False

myBool :: Bool
myBool = undefined

In Haskell, this is quite useful. For instance, if one’s in the middle of writing a complicated function, and wants to check their work so far, they can put ‘undefined’ for the part of the function they haven’t written. They can then compile their program; the typechecker will find any mistakes they’ve made so far, but, since the type of undefined can be anything, that part of the program will be accepted without second thought.

The language Idris extends this practice with the idea of typed holes, where you can leave fragments of your program unwritten, and ask the compiler what kind of thing you need to write to fill that hole.

### Java and null

Now you may be thinking:

This whole deal with Haskell’s undefined is beside the point; it doesn’t really count as a value, since it’s just a nonterminating expression. What you’re doing is a kind of academic autofellatio.

Alright, I can accept this criticism. Perhaps just calling a nonterminating function a value is far-fetched (even though in denotational semantics we do extend types with $\bot$). But denotational semantics are not the only place where types are implicitly extend with an extra value; let’s look at Java.

In Java, we have null. At the core language level, any function or method that accepts a class can also take null; if null is not to that function or method’s liking, it has to explicitly check for it using if(x == null).

This null value does not at first interact with booleans. After all, Java’s booleans are not classes. Unlike classes, which you have to allocate using new, you can just throw around true and false as you see fit. Also unlike classes, you simply can’t assign null to a boolean value.

The trouble is, the parts of Java dealing with generics, which allow you to write polymorphic functions, can’t handle ‘primitives’ like bool. If you want to have an ArrayList of something, that something must be a class. But what if you really do want an ArrayList of booleans? Java solves this problem by introducing ‘boxed’ booleans: they’re primitives wrapped in a class, called Boolean. This class can then be used for generics.

But see, this is where null has snuck in again. By allowing Boolean to be a class (thereby granting it access to generics), we’ve also given it the ability to be null. This example is made especially compelling because Java supports something they call autoboxing: you can directly assign a primitive to a variable of the corresponding boxed type. Consider the example:

Boolean myTrue = true;
Boolean myFalse = false;
Boolean myBool = null;

Beautiful, isn’t it? Better yet, unlike Haskell, where you can’t really check if your Bool is undefined (because you can’t tell whether a non-terminating computation is as such), you can very easily check if your Boolean is true, false, or null:

assert myTrue != myFalse;
assert myFalse != myBool;
assert myTrue != myBool;

We’re okay to use != here, instead of equals, because it so happens each boxed instance of a boolean value refers to the same Boolean object. In fact, this means that a Boolean variable can have exactly 3 values!

### C and Integers

Oh the luxury of having a type representing booleans in your language! It’s almost overly indulgent compared to the spartan minimalism of C. In C, boolean conditions are represented as numbers. You can perhaps get away with throwing around char or short int, but even then, these types allow far more values than two!

unsigned char test = 255;
while(test) test -= 1;

This loop will run 255 times, thereby demonstrating that C has at least 255 values that can be used to represent the boolean true.

There are other languages with this notion of ‘truthy’ and ‘falsey’ values, in which something not exactly true or false can be used as a condition. However, some of them differ from C in that they also extend this idea to equality. In JavaScript:

console.assert(true == 1)
console.assert(false == 0)

Then, there are still exactly two distinct boolean values modulo ==. No such luck in C, though! We have 256 values that fit in unsigned char, all of which are also distinct modulo ==. Our boolean variable can contain all of these values. And there is no respite to be found with enums, either. We could try define:

enum bool { TRUE, FALSE };

Unfortunately, all this does is define bool to be a numeric type that can hold at least 2 distinct values, and define numeric constants TRUE and FALSE. So in fact, you can still write the following code:

enum bool b1 = TRUE;
enum bool b2 = FALSE;
enum bool b3 = 15;

And so, no matter how hard you try, your ‘boolean’ variable can have many, many values!

### Conclusion

I think that ‘how many values does a boolean have’ is a strange question. Its purpose can be one of two things:

• The interviewer expected a long-form response such as this one. This is a weird expectation for a software engineering candidate - how does knowing about $\bot$, undefined, or null help in creating software, especially if this information is irrelevant to the company’s language of choice?
• The interviewer expected the simple answer. In that case, my previous observation applies: what software engineering candidate has not seen a boolean in their time programming? Surely candidates are better screened before they are offered an interview?

Despite the question’s weirdness, I think that the resulting investigation of the matter – outside of the interview setting – is useful, and perhaps, in a way, enlightening. It may help one understand the design choices made in their language of choice, and how those choices shape the code that they write.

That’s all I have! I hope that you found it interesting.


text:
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Let $f$ be the function defined by $f(x) = 2x^2 + 4x - 16$. Let $g$ be the function defined by \begin{align} g(x) &= 2(x+1)^2 - 18 . \end{align} Verify...

Non-profit Tax ID # 203478467


text:
source

# Auto-Encoding Gaussian Mixture Model¶

## Overview¶

The Auto-Encoding Gaussian Mixture Model (AEGMM) Outlier Detector follows the Deep Autoencoding Gaussian Mixture Model for Unsupervised Anomaly Detection paper. The encoder compresses the data while the reconstructed instances generated by the decoder are used to create additional features based on the reconstruction error between the input and the reconstructions. These features are combined with encodings and fed into a Gaussian Mixture Model (GMM). The AEGMM outlier detector is first trained on a batch of unlabeled, but normal (inlier) data. Unsupervised or semi-supervised training is desirable since labeled data is often scarce. The sample energy of the GMM can then be used to determine whether an instance is an outlier (high sample energy) or not (low sample energy). The algorithm is suitable for tabular and image data.

## Usage¶

### Initialize¶

Parameters:

• threshold: threshold value for the sample energy above which the instance is flagged as an outlier.

• n_gmm: number of components in the GMM.

• encoder_net: tf.keras.Sequential instance containing the encoder network. Example:

encoder_net = tf.keras.Sequential(
[
InputLayer(input_shape=(n_features,)),
Dense(60, activation=tf.nn.tanh),
Dense(30, activation=tf.nn.tanh),
Dense(10, activation=tf.nn.tanh),
Dense(latent_dim, activation=None)
])

• decoder_net: tf.keras.Sequential instance containing the decoder network. Example:

decoder_net = tf.keras.Sequential(
[
InputLayer(input_shape=(latent_dim,)),
Dense(10, activation=tf.nn.tanh),
Dense(30, activation=tf.nn.tanh),
Dense(60, activation=tf.nn.tanh),
Dense(n_features, activation=None)
])

• gmm_density_net: layers for the GMM network wrapped in a tf.keras.Sequential class. Example:

gmm_density_net = tf.keras.Sequential(
[
InputLayer(input_shape=(latent_dim + 2,)),
Dense(10, activation=tf.nn.tanh),
Dense(n_gmm, activation=tf.nn.softmax)
])

• aegmm: instead of using a separate encoder, decoder and GMM density net, the AEGMM can also be passed as a tf.keras.Model.

• recon_features: function to extract features from the reconstructed instance by the decoder. Defaults to a combination of the mean squared reconstruction error and the cosine similarity between the original and reconstructed instances by the AE.

• data_type: can specify data type added to metadata. E.g. ‘tabular’ or ‘image’.

Initialized outlier detector example:

from alibi_detect.od import OutlierAEGMM

od = OutlierAEGMM(
threshold=7.5,
encoder_net=encoder_net,
decoder_net=decoder_net,
gmm_density_net=gmm_density_net,
n_gmm=2
)

### Fit¶

We then need to train the outlier detector. The following parameters can be specified:

• X: training batch as a numpy array of preferably normal data.

• loss_fn: loss function used for training. Defaults to the custom AEGMM loss which is a combination of the mean squared reconstruction error, the sample energy of the GMM and a loss term penalizing small values on the diagonals of the covariance matrices in the GMM to avoid trivial solutions. It is important to balance the loss weights below so no single loss term dominates during the optimization.

• w_energy: weight on sample energy loss term. Defaults to 0.1.

• w_cov_diag: weight on covariance diagonals. Defaults to 0.005.

• optimizer: optimizer used for training. Defaults to Adam with learning rate 1e-4.

• epochs: number of training epochs.

• batch_size: batch size used during training.

• verbose: boolean whether to print training progress.

• log_metric: additional metrics whose progress will be displayed if verbose equals True.

od.fit(
X_train,
epochs=10,
batch_size=1024
)

It is often hard to find a good threshold value. If we have a batch of normal and outlier data and we know approximately the percentage of normal data in the batch, we can infer a suitable threshold:

od.infer_threshold(
X,
threshold_perc=95
)

### Detect¶

We detect outliers by simply calling predict on a batch of instances X to compute the instance level sample energies. We can also return the instance level outlier score by setting return_instance_score to True.

The prediction takes the form of a dictionary with meta and data keys. meta contains the detector’s metadata while data is also a dictionary which contains the actual predictions stored in the following keys:

• is_outlier: boolean whether instances are above the threshold and therefore outlier instances. The array is of shape (batch size,).

• instance_score: contains instance level scores if return_instance_score equals True.

preds = od.predict(
X,
return_instance_score=True
)

## Examples¶

### Tabular¶

Outlier detection on KDD Cup 99


text:
The Annals of Mathematical Statistics

Alternative Efficiencies for Signed Rank Tests

Jerome Klotz

Abstract

Asymptotic efficiency curves for the one sample Wilcoxon and normal scores tests are obtained by comparing the exponential rate of convergence to zero of the type I error $(\alpha)$ while keeping the type II error $(\beta)$ fixed $(0 < \beta < 1)$. A wider than usual view of test performance consistent with small sample results is obtained. The Pitman efficiency value is derived as a special case when the alternative approaches the null hypothesis. Comparisons of the signed rank tests relative to $\bar{x}$ or $t$ for normal location alternatives yield small efficiency values for extreme alternatives. The relative performance of the Wilcoxon is seen to be slightly better than the normal scores for normal alternatives with larger location parameter values despite the local (Pitman) optimality of the normal scores. Similar results hold for two other non-normal alternatives considered.

Article information

Source
Ann. Math. Statist., Volume 36, Number 6 (1965), 1759-1766.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177699804

Digital Object Identifier
doi:10.1214/aoms/1177699804

Mathematical Reviews number (MathSciNet)
MR185760

Zentralblatt MATH identifier
0151.23604

JSTOR


text:
# What to do with questions of the form "Someone or something says ___, are they right?"

"My friend/professor/teacher/parent/solution manual/etc. says ___ are they right?"

What should we do with these types of posts? I feel like it's missing a ton of context. We don't know what the person said and we can't comment really. We're really just left guessing and trying to figure out what another person may or may not have said. Are questions of this type salvageable?

• Well, you can always ignore the "my friend says" part, and discuss the ways in which whatever follows might, or might not, be right. Sep 26 '15 at 5:52
• They aren't really salvageable. Without more details, and without the other side of the story, we can't really comment on who is wrong and who is right. Sep 26 '15 at 7:56
• It is salvageable only when the questioner is responsive. So comment and ask for clarification. Depends on how bad the question is, one can downvote and/or vote for close before or after the questioner response.... Sep 26 '15 at 11:11
• Often knowing more about the incorrect argument is not necessary to give a correct argument. ff the question was instead about debugging the incorrect argument then it might be the case that more context is needed. Sep 26 '15 at 13:24

I am not sure there is any need for special rules for this type of questions, if I understand the type of question you have in mind correctly.

My sister says there is no fraction whose square is $2$ but the calculator on my phone says $1.41421356237$ is the solution which is just $141421356237/100000000000$. Thus I do not believe her but she insist she is right. Who is right my sister or my phone?

I would not see any problem with this question (besides it surely being a duplicate). There is a clear question that can be answered; the story even provides the context.

I would even consider the following as about alright.

My brother says there is no number whose square is $2$ but the calculator on my phone says $1.41421356237$ thus I do not believe him. Who is right my brother or my phone?

That question is somewhat problematic as it is more unclear what the brother meant (or said exactly) when number is invoked. But I still feel one can answer this, explaining that there is no fraction but etc.

Now, if we were to get:

My uncle said square roots do not exist. But I do not believe him. Am I right?

Then, we start to get into unclear territory as there are several things the uncle might have meant or even said (and been correct) or might have misunderstood. But it may still be feasible to answer this, though personally I rather would not attempt it. Yet one might ask the questioner for their background and then give them some response on roots.

Of course, there will also be questions of this form that are too unclear or otherwise unsuitable. Yet, as a rule I do not see any particular problem with this type of question. Indeed, on the contrary, such a questioner usually will be at least invested in their question.

To put this differently, while we sometimes may not know and have reasonable doubts as to what the quoted source actually said, it is not always crucial for us to know this to give an answer. Only we should strive to be clear and precise as to what we answer and use some common sense to correct for likely imprecisions, yet again being precise regarding what one does:

The [literal statement] is wrong [because] but [whoever] may actual have said/meant [something very similar], which is true.

• The literal statement is wrong because, but whoever may actually have said or meant something very similar which is true. <-- Words to live by.
– Asaf Karagila Mod
Sep 26 '15 at 13:57
• The uncle meant that there aren't trees with square roots. Oct 5 '15 at 0:56


text:
# Viz - Key Frame (Target Value)

Key frames are images that defined the states of an animation.

The images created between this key image are created with a process called inbetween or tweening.

Keyframes are specific frames in the animation that have specific target values.


text:
# Tangents to a parabola from a point

Problem
The angle between the tangent lines from the point $A(0,-1)$ to parabola defined as $y=x^2-ax+3$ is $135^{\circ}$. Then what could be the value of $a$?

My attempt
First I found that if $tan(\alpha)$ is $m$, i.e. slope of the first line, then $tan(\alpha +135^{\circ})$ must be $\frac{m-1}{m+1}$ since $tan(\alpha +\beta)=\frac{tan(\alpha)+tan(\beta)}{1-tan(\alpha)tan(\beta)}$. Say, the first line is tangent to the parabola at $x_1$, then the slope will be $2x_1-a$ (taking the derivative at $x_1$). Continuing with the similar variable naming, slope of the second tangent line will be $2x_2-a$.

Other facts:
$m=\frac{y_1-(-1)}{x_1-0}$ where $y_1=x_1^2-ax_1+3$ and $y_2=x_2^2-ax_2+3$
I proceed from here with $\frac{m-1}{m+1}=\frac{y_1-x_1+1}{y_1+x_1+1}=\frac{y_2-(-1)}{x_2}$. Then putting the formulas for $y_1$ and $y_2$ gives me another equality in terms of $x_1$ and $x_2$.

Using all these, I can't seem to extract $a$ and canceling other terms or relating above equations to slope found from derivative.

How to solve this problem, what should be done?

HINT...A line passing through $(0,-1)$ with gradient $m$ is $$y=mx-1$$

If you solve this simultaneously with the curve $y=x^2-ax+3$ the resulting quadratic in $x$ must have double roots, and therefore zero discriminant, and this will give you two possible values of $m$ in terms of $a$.

You can then use the angle between the lines formula $$\tan\theta=\left|\frac{m_1-m_2}{1+m_1m_2}\right|$$ to find the four possible values of $a$

• I found $x^2-(m+a)x+4=0$ then $(m+a)^2=16$ since the discriminant is zero. Similarly, for the other line we have $x^2-(\frac{m-1}{m+1}+a)x+4=0)$ then equating both discriminants gave me $(m-1)/(m+1)+a=m+a$ or $(1-m)/(m+1)+a=m+a$. First one cannot happen because it gives a complex value for $m$. Using second one I got $m^2+2m-1=0$ and the roots are $-1-\sqrt{2}$ and $-1+\sqrt{2}$. Using $(m+a)^2=16$ gives me 4 different $a$ values, specifically, $-3+\sqrt{2}$, $-3-\sqrt{2}$, $5+\sqrt{2}$ and $5-\sqrt{2}$. Is it correct? – Motun Apr 10 '16 at 11:19
• @Motun see my edited answer. – David Quinn Apr 10 '16 at 12:38
• $tan(135^{\circ})=-1$, how can this be equal to absolute value of something? – Motun Apr 10 '16 at 12:46
• Set the expression without the modulus sign equal to $\pm1$ since the angle between the tangents can be regarded as either 135 or 45 – David Quinn Apr 10 '16 at 12:49

$$\dfrac{dy}{dx}=2x-a$$

So, the gradient$(m)$ at $(t,t^2-at+3)$ will be $2t-a\iff2t=m+a$

So, the equation of tangent at $(t,t^2-at+3)$ will be $$\dfrac{y-t^2-at+3}{x-t}=2t-a$$

It needs to pass through $(0,-1)\implies$ $$\dfrac{-1-t^2-at+3}{0-t}=2t-a\iff t^2-2at+2=0$$

Replacing $2t$ with $m+a$ $$m^2-2am+8-3a^2=0$$ which is a Quadratic equation in $m$

So, $m_1+m_2=2a, m_1m_2=8-3a^2$

$(m_1-m_2)^2=(m_1+m_2)^2-4m_1m_2=16a^2-32$

So, we need $16a^2-32\ge0\iff a^2\ge2$

WLOG $m_1>m_2\implies m_1-m_2=+\sqrt{16a^2-32}$

$$-1=\tan135^\circ=\dfrac{m_1-m_2}{1+m_1m_2}=\dfrac{\sqrt{16a^2-32}}{9-3a^2}$$

Clearly, $9-3a^2<0\iff a^2>3$

Square both sides and solve for $a^2$


text:
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text:
Science Forums Biology Forum Molecular Biology Forum Physics Chemistry Forum A version of QED without ultraviolet divergences

 Physics Forum Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

# A version of QED without ultraviolet divergences

## A version of QED without ultraviolet divergences - Physics Forum

### A version of QED without ultraviolet divergences - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

#31
08-07-2004, 07:00 AM
 Bill Hobba Guest Posts: n/a
A version of QED without ultraviolet divergences

"Eugene" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
an
you
for
great

Eugene you admit you do not understand Weinberg's discussion of how Wilson's
view resolves the issue of infinites yet claim you know for sure that 'QFT
swept infinities under the rug'. This I do not follow at all. Surely you
should reserve you opinion until you understand Wilson's approach. The
prediction of QFT is if we have a certain very high cutoff (but not
infinite) for energies much less than that cutoff then our theories look
like they are renomalisable. This view even predicts the scale it starts to
be a problem; it is way beyond our current technology and is before we
believe other theories such as the electroweak theory dominate. This means
the infinites of renormalization are simply a byproduct of the energies we
work at and not necessarily and indication of anything fundamental.

Bill

Without finite Hamiltonian

#32
08-07-2004, 09:54 AM
 Eugene Guest Posts: n/a
A version of QED without ultraviolet divergences

Bill Hobba wrote:

There are many things which I do not understand, I am ready to admit
that. If you do not want to speak my language, I have no
other choice but to learn yours. I spent some time
reading "The floating cutoff" chapter again, and I think I got it.
It does not change my view of renormalization. As Weinberg said there:
"At bottom, the difference between the conventional and the Wilson
approach is one of mathematical convenience rather than of physical
interpretation" Let me explain why, using QED as an example.

Conventional arroach: If we use normal QED Hamiltonian with finite
masses m and charges e, and take all integrals to infinity (cutoff
L=inf), we obtain, as is well known, infinite S-matrix. I will write it
as S(m,e,inf) = inf. For finite cutoff L, the S-matrix S(m,e,L) is,
of course finite, but it has nothing to do with reality. For example,
the Lorentz invariance is violated. The solution of this problem
(renormalization) is to use INFINITE masses M and charges E in the
Hamiltonian. Then, the S-matrix S(M,E, inf) = S(inf, inf, inf) is
finite, Lorentz-invariant and perfectly agrees with experiment. How
do we calculate S(inf, inf, inf)? We identify physical finite mass m
with the pole of the electron propagator, and physical finite charge e
with the coefficient in front of the electron-electron scattering
amplitude at low energies. These two numbers are, of course expressed
by divergent integral as L -> inf, but the same infinite integrals
are present in the expressions for all other elements of the the
S-matrix. So, each time we see
such an infinite integral in the expression for the S-matrix, we
do not calculate it, but simply substitute with the finite number m
or e. This is equivalent to using infinite Hamiltonian, i.e., with
infinite parameters M and E.

Wilson's approach: We assume that the bare masses and charges in the
Hamiltonian are cutoff-dependent m(L) and e(L). In agreement with
the conventional approach, in the limit L -> inf these functions
must tend to infinity m(L) -> M = inf e(L) -> E = inf. The trick of the
approach is to select functions m(L) and e(L), so that at finite
L the S-matrix S(m(L), e(L), L) is close to the accurate value
S(M,E, inf). It can be shown, that indeed, for low energy processes
(momenta much lower that the cutoff L) such a fitting can be done.
Such a theory with finite cutoff is rather ugly: as Weinberg says
"the resulting effective field theory will contain all Lorentz-
and gauge-invariant interactions". Moreover, "the cutoff generally
destroys manifest gauge invariance, and either manifest Lorentz
invariance or unitarity". This theory with finite cutoff has only
two good properties: everything is finite, and low-energy scattering
is described in a good approximation. You can obtain perfectly
accurate S-matrix, just as in the conventional approach, if you
take the limit L->inf, but then again, the parameters in the Hamiltonian
become infinite m(inf) = M = inf and e(inf) = E = inf.

You may say that Wilson's approach solves the problem with the infinite
Hamiltonian and the lack of description of time evolution, which I keep
stressing in each of my postings. Indeed,
in this approach, at finite cutoff L, we do have a Hamiltonian with
finite parameters m(L) and e(L), which we may try to use to calculate
the time evolution. However, this Hamiltonian has serious drawbacks:

1. it is approximate (works only for energies below the cutoff)
2. It has an infinite number of interactions in each perturbation order
3. It is not relativistically invariant (in the sense that there is
no interacting boost operator such that Poincare group commutators are
satisfied, otherwise the S-matrix would be Lorentz invariant, which
is not true).
4. It contains interactions (trilinear and others) which create
particles out of vacuum, and additional particles out of one-particle
states. This leads to the funny and unphysical picture of vacuum as
a "boiling soup" and "dressing" of particles by virtual "coats".

My approach is better: I construct the Hamiltonian which
1. Yields exactly the accurate S-matrix of the renormalized QED
for all energies (of course, at very high energies we need to take
into account the possibility of creation of pairs of heavy particles
not included in the theory. But the same problem is characteristic
for the Wilson's approach)
2. Is finite. The parameters m and e entering my Hamiltonian are
exactly measured mass and charge of the electron.
3. Satisfies exactly the condition of relativistic invariance
(there is an interacting boost operator such that all Poincare
commutators are correct).
4. Vacuum and one-particle states are exactly eigenstates of this
operator, so there is no spontaneous creation of virtual particles
from the vacuum and around single particles. Interaction acts when
there are two or more particles.
5. The interaction terms in this Hamiltonian have direct physical
interpretation: In the 2nd perturbation order I already obtained
usual Coulomb potential plus relativistic corrections: spin-orbit,
contact, spi-spin, etc. The method is proven to work at all perturbation
orders. I am sure that in the 4th order I'll obtain the Uehling
potential and the correct value for the Lamb's shift. What is different
from the S-matrix approach, which can give only the energy of the
Lamb's shift, is that I can also obtain the radiative corrections to the
wave function.

At very high cutoff, the Wilson's Hamiltonian will have very large mass and
charge parameters, and all other ugliness described above. Though,
the S-matrix will look pretty good, I agree.

Eugene.

#33
08-08-2004, 12:21 AM
 Bill Hobba Guest Posts: n/a
A version of QED without ultraviolet divergences

"Eugene" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
Wilson's
'QFT
you

Welcome to the club. I am still trying to get around the idea of the landau
pole and quite a few other things.

I learnt QFT about 4 or 5 years ago now and the effective field theory
approach is what I learnt. In fact what prodded me to investigate the
technicalities was John Baez's review article:
[Only registered users see links. ]. What got me was the
conclusion:

'Wilson's analysis takes just the opposite point of view, that any quantum
field theory is defined fundamentally with a distance cutoff D that has some
physical significance. In statistical mechanical applications, this distance
scale is the atomic spacing. In quantum electrodynamics and other quantum
field theories appropriate to elementary particle physics, the cutoff would
have to be associated with some fundamental graininess of space-time,
perhaps the result of quantum fluctuations in gravity. We discuss some
speculations on the nature of this cutoff in the Epilogue. But whatever this
scale is, it lies far beyond the reach of present-day experiments. Wilson's
arguments show that this this circumstance *explains* the renormalizability
of quantum electrodynamics and other quantum field theories of particle
interactions. Whatever the Lagrangian of quantum electrodynamics was at the
fundamental scale, as long as its couplings are sufficiently weak, it must
be described at the energies of our experiments by a renormalizable
effective Lagrangian.'

The renormalization and it infinites is really nothing to worry about at
all - it fact it would be surprising if you theories were not
renormaliseable and had the problems of the infinities.

Yes.

Yes - but note m(L) and e(L) are written as mr + delta m and the same for
but that does not really change anything) where mr is the renormalized mass
which is the observed quantity - not m(L). The idea is as L goes to
infinity the renormalized mass can be made arbitrarily close to some fixed
value for L << L0 whew L0 is some very high cutoff. And in fact the theory
that describes the physics in the region of L0 does not even have to be the
same theory - for QED to be renormalisable L simply must be much less than
L0. In fact we know in that region the elctroweak theory operates anyway.

Yes

You bet - but we are looking at questions of principle here.

The point being the infinity is avoided.

Well it really only works for energies a long way below the cutoff.

and

The point though is this - for energies much less than the cutoff the theory
looks renomlaisable, and has all these infinites even though the real one
may not. That is the key point. We recognize that QED is not findamamental
and so the infinites we 'sweep' under the rug are not fundamental either -
they are simply a result of it being a low energy approximation to another
better theory. That is the basis of the effective field theory approach.

Bill

means
we

#34
08-08-2004, 12:39 AM
 Eugene Stefanovich Guest Posts: n/a
A version of QED without ultraviolet divergences

Bill Hobba wrote:

I am afraid you are mixing here the notions of renormalization and
renormalizability. Renormalizability means that renormalization
(subtraction of infinite integrals, or adding infinite counterterms
to the Hamiltonian in my language) can be performed by modifying
(setting to infinity) a finite number of parameters in the Hamiltonian.
In the case of QED these are mass and charge of the electron.
In non-renormalizable theory you need to modify infinite number of
parameters. QED and standard model are renormalizable, but you
still need to perform the subtraction of divergences there.

OK, we may disgree whether infinites create a problem or not. My
bottomline is this: I have a consistent Hamiltonian which allows
to calculate the time evolution of interacting charged particles.
I claim that existing theory cannot do that. If you think otherwise,
I would appreciate references with the explicit form of the
Hamiltonian, at least in low orders of the perturbation theory.

Eugene.

#35
08-08-2004, 05:18 AM
 FrediFizzx Guest Posts: n/a
A version of QED without ultraviolet divergences

"Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
|
|
| Bill Hobba wrote:
|
| >
| > The renormalization and it infinites is really nothing to worry about at
| > all - it fact it would be surprising if you theories were not
| > renormaliseable and had the problems of the infinities.
|
| I am afraid you are mixing here the notions of renormalization and
| renormalizability. Renormalizability means that renormalization
| (subtraction of infinite integrals, or adding infinite counterterms
| to the Hamiltonian in my language) can be performed by modifying
| (setting to infinity) a finite number of parameters in the Hamiltonian.
| In the case of QED these are mass and charge of the electron.

I think if it were possible to isolate a "bare" electron, you would find
that the mass and charge are zero. As strange as that may seem. Mass and
charge are emergent from the electron's interaction with the quantum vacuum.

| In non-renormalizable theory you need to modify infinite number of
| parameters. QED and standard model are renormalizable, but you
| still need to perform the subtraction of divergences there.

It seems so simple. You just need to get rid of divergences that shouldn't
be there in the first place. I don't see any problem as Bill mentions
below.

| > The point though is this - for energies much less than the cutoff the
theory
| > looks renomlaisable, and has all these infinites even though the real
one
| > may not. That is the key point. We recognize that QED is not
findamamental
| > and so the infinites we 'sweep' under the rug are not fundamental
either -
| > they are simply a result of it being a low energy approximation to
another
| > better theory. That is the basis of the effective field theory
approach.
| >
|
| OK, we may disgree whether infinites create a problem or not. My
| bottomline is this: I have a consistent Hamiltonian which allows
| to calculate the time evolution of interacting charged particles.
| I claim that existing theory cannot do that. If you think otherwise,
| I would appreciate references with the explicit form of the
| Hamiltonian, at least in low orders of the perturbation theory.

What does this mean "to calculate the time evolution of"? Why do we need to
know that? Particles go in and particles come out and we have effective
theory that can describe the initial and final states. Do we really need to
know exactly what is happening "during" the interaction? IMHO, space-time
is funny and wierd at the quantum level anywise.

FrediFizzx

#36
08-08-2004, 06:57 AM
 Eugene Stefanovich Guest Posts: n/a
A version of QED without ultraviolet divergences

FrediFizzx wrote:

I would like to see a consistent theory based on this assumption.
In my approach, electron has experimentally measured charge and mass
from the beginning. These parameters are present in the Hamiltonian
and do not change due to renormalization or "interaction with the
quantum vacuum". Actually, there is no interaction unless there are two
or more particles, which is kind of obvious: in order to interact
there should be at least two partners.

The problem is that the charge and mass calculated from the theory are
not the same as the charge and mass put there in the beginning. If this
is your ideal of consistency, then fine. I think, we can do better.

You would probably agree that we can observe time evolution of charged
particles in the macroscopic world: particles move along some
trajectories, or if you like more quantum mechanics, the wave functions
evolve in time. QFT does not provide this kind of description.
So, QFT is completely useless in the macroscopic low-energy limit.
It can predict only asymptotic limits of time evolution.
My suggestion is very simple: we just need to
modify the Hamiltonian of the theory, so that old predictions (S-matrix)
are still valid, and new predictions (time evolution) are now possible.
What's wrong with this idea?

Eugene.

#37
08-08-2004, 05:20 PM
 FrediFizzx Guest Posts: n/a
A version of QED without ultraviolet divergences

"Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| FrediFizzx wrote:
| > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | Bill Hobba wrote:
| > |
| > | >
| > | > The renormalization and it infinites is really nothing to worry
| > | > all - it fact it would be surprising if you theories were not
| > | > renormaliseable and had the problems of the infinities.
| > |
| > | I am afraid you are mixing here the notions of renormalization and
| > | renormalizability. Renormalizability means that renormalization
| > | (subtraction of infinite integrals, or adding infinite counterterms
| > | to the Hamiltonian in my language) can be performed by modifying
| > | (setting to infinity) a finite number of parameters in the
Hamiltonian.
| > | In the case of QED these are mass and charge of the electron.
| >
| > I think if it were possible to isolate a "bare" electron, you would find
| > that the mass and charge are zero. As strange as that may seem. Mass
and
| > charge are emergent from the electron's interaction with the quantum
vacuum.
|
| I would like to see a consistent theory based on this assumption.
| In my approach, electron has experimentally measured charge and mass
| from the beginning. These parameters are present in the Hamiltonian
| and do not change due to renormalization or "interaction with the
| quantum vacuum". Actually, there is no interaction unless there are two
| or more particles, which is kind of obvious: in order to interact
| there should be at least two partners.

I don't think you will find many particle physicists that don't think the
charge of an electron is screened by a cloud of virtual particles. They do
think that and are pretty sure about it (see Topaz experiment). This is a
simple example of an electron *interacting* with the quantum vacuum. And
produces a running coupling "constant". Funny that it is called a constant
because it isn't really constant at all. Actually this is a very big clue
to what is really going on. An electron (or all charged fermions) observed
from a distance is really a product of a "bare" point-like entity and the
quantum vacuum. Virtual e+e- pairs are dominate but there will be some
other pairs also including hadronic pairs to a small extent. All charged
fermions are a mix of all other fermions when you include the quantum vacuum
and you *have* to include quantum vacuum becuase it is impossible to remove
it. So you can see right away that the situation is complex even for a
lonely electron. Do you really think you can get a proper time evolution of
the wavefunction of the electron *during* an interaction with another
charged fermion through this complexity? Feynman was right; it has to be
simplified. The interaction "space" is really a blob and all we care about
are initial states and final states. But it is not wrong for us to
eventually want to know exactly what happens in the "blob". I think we just
don't know what all the quantum vacuum objects are yet is what is preventing
us from figuring out the exact complexity.

For some good analogs of how mass and charge can be emergent from the
quantum vacuum, see Volovik's "The Universe in a Helium Droplet". It is
possible to model the quantum vacuum as if it has bound charge with cells
equal to Q_vac = +,- sqrt(hbar*c). I have been working on this for over a
year now and it gets more consistent as time passes. This means the quantum
vacuum consists of coupled oscillators. Figuring out the exact geometry of
coupling is mind boggling but hopefullly not intractable. It takes quite a
different way of thinking about interactions as gauge bosons require a
different interpretation from the Standard Model.

| > | In non-renormalizable theory you need to modify infinite number of
| > | parameters. QED and standard model are renormalizable, but you
| > | still need to perform the subtraction of divergences there.
| >
| > It seems so simple. You just need to get rid of divergences that
shouldn't
| > be there in the first place. I don't see any problem as Bill mentions
| > below.
|
| The problem is that the charge and mass calculated from the theory are
| not the same as the charge and mass put there in the beginning. If this
| is your ideal of consistency, then fine. I think, we can do better.

True. And you are right; we can do better if we have the correct picture.

| > | > The point though is this - for energies much less than the cutoff
the
| > theory
| > | > looks renomlaisable, and has all these infinites even though the
real
| > one
| > | > may not. That is the key point. We recognize that QED is not
| > findamamental
| > | > and so the infinites we 'sweep' under the rug are not fundamental
| > either -
| > | > they are simply a result of it being a low energy approximation to
| > another
| > | > better theory. That is the basis of the effective field theory
| > approach.
| > | >
| > |
| > | OK, we may disgree whether infinites create a problem or not. My
| > | bottomline is this: I have a consistent Hamiltonian which allows
| > | to calculate the time evolution of interacting charged particles.
| > | I claim that existing theory cannot do that. If you think otherwise,
| > | I would appreciate references with the explicit form of the
| > | Hamiltonian, at least in low orders of the perturbation theory.
| >
| > What does this mean "to calculate the time evolution of"? Why do we
need to
| > know that? Particles go in and particles come out and we have effective
| > theory that can describe the initial and final states. Do we really
need to
| > know exactly what is happening "during" the interaction? IMHO,
space-time
| > is funny and wierd at the quantum level anywise.
|
| You would probably agree that we can observe time evolution of charged
| particles in the macroscopic world: particles move along some
| trajectories, or if you like more quantum mechanics, the wave functions
| evolve in time. QFT does not provide this kind of description.
| So, QFT is completely useless in the macroscopic low-energy limit.
| It can predict only asymptotic limits of time evolution.
| My suggestion is very simple: we just need to
| modify the Hamiltonian of the theory, so that old predictions (S-matrix)
| are still valid, and new predictions (time evolution) are now possible.
| What's wrong with this idea?

There is nothing basically wrong with that idea. I am not sure it is really
needed unless it can give us more fundamental insight as to what is really
going on. Can it?

FrediFizzx

#38
08-09-2004, 02:22 AM
 Eugene Guest Posts: n/a
A version of QED without ultraviolet divergences

FrediFizzx wrote:

I am pretty sure that 99.99% of particle physicists believe that
electron is screened by a cloud of virtual particles, and that vacuum
is a "boiling soup" of virtual pairs, and that interaction occurs when
"real" particles "throw virtual particles" to each other. My point is
nobody have seen these virtual particles in experiment. All these
virtual particles, "soups" and "clouds" are just artefacts of
incorrectly written Hamiltonian. I suggested a way how all this nonsense
can be eliminated from the theory, and, still, all observable
predictions can be preserved (S-matrix) and new predictions
(time evolution) can be added. Could you please give me a reference to
the "Topaz experiment", I'll try to explain it without invoking the
concept of virtual particles.

Of course, it is impossible to predict the time evolution of the wave
function in the complex picture with virtual particles. That's my
whle point. Of course, Feynman was right, and it has to be simplified.
That's what I did: I simplified the theory without losing a bit of
its predictive power, and even added to its predictive power.

You cannot figure out what's inside the "blob" because you are using
wrong QED Hamiltonian. I can predict exactly what's inside the "blob".
Note also that in the macroscopic low-energy limit the "blob" becomes
very big: centimeters, meters, etc. in size. So, the interacting
time evolution becomes directly observable. QED cannot predict this time
evolution, as you already pointed out. In order to make such
prediction you need to abandon QED and switch to the classical
Maxwell's theory with point particles and electromagnetic
potentials. My theory works in the full range of energies.

It would be nice to see how somebody can derive electron mass and charge
from something more fundamental. So far, I haven't seen that.
In my approach, vacuum is just a state without particles. Electron
is a single particle with mass and charge taken directly from
experiment. There is no interaction between single electron and the
vacuum. Interaction is present when there are two or more particles.

It gives a lot of new insight.
First, now you can directly calculate the
time evolution of the wave function during interaction.
Second, you can now forget about the mind boggling picture with
virtual particles and work with real particles and potentials
between them, just as in ordinary quantum mechanics.
Third, I predict that the potentials acting between particles
(Coulomb, magnetic, spin-orbit etc.) are instantaneous. This can be
verified by experiment.
Fourth, the theory predicts small (but fundamentally important)
deviations from Einstein's predictions, for example, in the case of
the decay of fast moving particles.
Finally, this approach demonstrates that Lorentz transformations
are not exact and universal, and that Minkowski space-time is an
approximation.

Eugene.

#39
08-09-2004, 03:17 AM
 FrediFizzx Guest Posts: n/a
A version of QED without ultraviolet divergences

"Eugene" <[Only registered users see links. ]> wrote:
| FrediFizzx wrote:
| > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | FrediFizzx wrote:
| > | > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | > | Bill Hobba wrote:
| > | > |
| > | > | >
| > | > | > The renormalization and it infinites is really nothing to worry
| > | > | > all - it fact it would be surprising if you theories were not
| > | > | > renormaliseable and had the problems of the infinities.
| > | > |
| > | > | I am afraid you are mixing here the notions of renormalization and
| > | > | renormalizability. Renormalizability means that renormalization
| > | > | (subtraction of infinite integrals, or adding infinite
counterterms
| > | > | to the Hamiltonian in my language) can be performed by modifying
| > | > | (setting to infinity) a finite number of parameters in the
| > Hamiltonian.
| > | > | In the case of QED these are mass and charge of the electron.
| > | >
| > | > I think if it were possible to isolate a "bare" electron, you would
find
| > | > that the mass and charge are zero. As strange as that may seem.
Mass
| > and
| > | > charge are emergent from the electron's interaction with the quantum
| > vacuum.
| > |
| > | I would like to see a consistent theory based on this assumption.
| > | In my approach, electron has experimentally measured charge and mass
| > | from the beginning. These parameters are present in the Hamiltonian
| > | and do not change due to renormalization or "interaction with the
| > | quantum vacuum". Actually, there is no interaction unless there are
two
| > | or more particles, which is kind of obvious: in order to interact
| > | there should be at least two partners.
| >
| > I don't think you will find many particle physicists that don't think
the
| > charge of an electron is screened by a cloud of virtual particles. They
do
| > think that and are pretty sure about it (see Topaz experiment).
|
| I am pretty sure that 99.99% of particle physicists believe that
| electron is screened by a cloud of virtual particles, and that vacuum
| is a "boiling soup" of virtual pairs, and that interaction occurs when
| "real" particles "throw virtual particles" to each other. My point is
| nobody have seen these virtual particles in experiment. All these
| virtual particles, "soups" and "clouds" are just artefacts of
| incorrectly written Hamiltonian. I suggested a way how all this nonsense
| can be eliminated from the theory, and, still, all observable
| predictions can be preserved (S-matrix) and new predictions
| (time evolution) can be added. Could you please give me a reference to
| the "Topaz experiment", I'll try to explain it without invoking the
| concept of virtual particles.

[Only registered users see links. ]

There is a postscript article that you can download at the bottom of the
page. I hardly think they are artifacts since real particles are seen to
get a momentum "kick" from invisible vacuum virtual particles in actual
experiments. So you are wrong about that.

| > This is a
| > simple example of an electron *interacting* with the quantum vacuum.
And
| > produces a running coupling "constant". Funny that it is called a
constant
| > because it isn't really constant at all. Actually this is a very big
clue
| > to what is really going on. An electron (or all charged fermions)
observed
| > from a distance is really a product of a "bare" point-like entity and
the
| > quantum vacuum. Virtual e+e- pairs are dominate but there will be some
| > other pairs also including hadronic pairs to a small extent. All
charged
| > fermions are a mix of all other fermions when you include the quantum
vacuum
| > and you *have* to include quantum vacuum becuase it is impossible to
remove
| > it. So you can see right away that the situation is complex even for a
| > lonely electron. Do you really think you can get a proper time
evolution of
| > the wavefunction of the electron *during* an interaction with another
| > charged fermion through this complexity? Feynman was right; it has to
be
| > simplified.
|
| Of course, it is impossible to predict the time evolution of the wave
| function in the complex picture with virtual particles. That's my
| whle point. Of course, Feynman was right, and it has to be simplified.
| That's what I did: I simplified the theory without losing a bit of
| its predictive power, and even added to its predictive power.

What does it predict that is "additional"?

| > The interaction "space" is really a blob and all we care about
| > are initial states and final states. But it is not wrong for us to
| > eventually want to know exactly what happens in the "blob". I think we
just
| > don't know what all the quantum vacuum objects are yet is what is
preventing
| > us from figuring out the exact complexity.
|
| You cannot figure out what's inside the "blob" because you are using
| wrong QED Hamiltonian. I can predict exactly what's inside the "blob".
| Note also that in the macroscopic low-energy limit the "blob" becomes
| very big: centimeters, meters, etc. in size. So, the interacting
| time evolution becomes directly observable. QED cannot predict this time
| evolution, as you already pointed out. In order to make such
| prediction you need to abandon QED and switch to the classical
| Maxwell's theory with point particles and electromagnetic
| potentials. My theory works in the full range of energies.

I am interested in this. Show me a simple example.

| > For some good analogs of how mass and charge can be emergent from the
| > quantum vacuum, see Volovik's "The Universe in a Helium Droplet". It is
| > possible to model the quantum vacuum as if it has bound charge with
cells
| > equal to Q_vac = +,- sqrt(hbar*c). I have been working on this for over
a
| > year now and it gets more consistent as time passes. This means the
quantum
| > vacuum consists of coupled oscillators. Figuring out the exact geometry
of
| > coupling is mind boggling but hopefullly not intractable. It takes
quite a
| > different way of thinking about interactions as gauge bosons require a
| > different interpretation from the Standard Model.
|
| It would be nice to see how somebody can derive electron mass and charge
| from something more fundamental. So far, I haven't seen that.
| In my approach, vacuum is just a state without particles. Electron
| is a single particle with mass and charge taken directly from
| experiment. There is no interaction between single electron and the
| vacuum. Interaction is present when there are two or more particles.

Here is a semi-classical heuristic for electron mass in CGS units.

m_e = (sqrt(hbar*c)e/w_C^2*sqrt(alpha))(2pi/lambda_C)^3

With w = angular frequency, lambda_C = electron compton wavelength and alpha
= fine structure constant. So this tells use that electron mass is an
interaction between vacuum charge and electronic charge divided by frequency
squared per a volume of space. We figure that sqrt(alpha) is a geometric
factor and goes with the volume of space. The above expression reduces to
the familiar electron compton wavelength expression which is known to be
true experimentally.

m_e = 2pi*hbar/lambda_C*c

Now electronic charge is a much tougher one because you have to know the
exact geometrical configuration of the quantum vacuum. But the simple
heuristic is e = sqrt(alpha*hbar*c). The square root of alpha is simply the
ratio between electronic charge and vacuum charge. I believe that alpha is
a geometric factor involving volumes of space.

| > | > | In non-renormalizable theory you need to modify infinite number of
| > | > | parameters. QED and standard model are renormalizable, but you
| > | > | still need to perform the subtraction of divergences there.
| > | >
| > | > It seems so simple. You just need to get rid of divergences that
| > shouldn't
| > | > be there in the first place. I don't see any problem as Bill
mentions
| > | > below.
| > |
| > | The problem is that the charge and mass calculated from the theory are
| > | not the same as the charge and mass put there in the beginning
..Ifthis
| > | is your ideal of consistency, then fine. I think, we can do better.
| >
| > True. And you are right; we can do better if we have the correct
picture.
| >
| > | > | > The point though is this - for energies much less than the
cutoff
| > the
| > | > theory
| > | > | > looks renomlaisable, and has all these infinites even though the
| > real
| > | > one
| > | > | > may not. That is the key point. We recognize that QED is not
| > | > findamamental
| > | > | > and so the infinites we 'sweep' under the rug are not
fundamental
| > | > either -
| > | > | > they are simply a result of it being a low energy approximation
to
| > | > another
| > | > | > better theory. That is the basis of the effective field theory
| > | > approach.
| > | > | >
| > | > |
| > | > | OK, we may disgree whether infinites create a problem or not. My
| > | > | bottomline is this: I have a consistent Hamiltonian which allows
| > | > | to calculate the time evolution of interacting charged particles.
| > | > | I claim that existing theory cannot do that. If you think
otherwise,
| > | > | I would appreciate references with the explicit form of the
| > | > | Hamiltonian, at least in low orders of the perturbation theory.
| > | >
| > | > What does this mean "to calculate the time evolution of"? Why do we
| > need to
| > | > know that? Particles go in and particles come out and we have
effective
| > | > theory that can describe the initial and final states. Do we really
| > need to
| > | > know exactly what is happening "during" the interaction? IMHO,
| > space-time
| > | > is funny and wierd at the quantum level anywise.
| > |
| > | You would probably agree that we can observe time evolution of charged
| > | particles in the macroscopic world: particles move along some
| > | trajectories, or if you like more quantum mechanics, the wave
functions
| > | evolve in time. QFT does not provide this kind of description.
| > | So, QFT is completely useless in the macroscopic low-energy limit.
| > | It can predict only asymptotic limits of time evolution.
| > | My suggestion is very simple: we just need to
| > | modify the Hamiltonian of the theory, so that old predictions
(S-matrix)
| > | are still valid, and new predictions (time evolution) are now
possible.
| > | What's wrong with this idea?
| >
| > There is nothing basically wrong with that idea. I am not sure it is
really
| > needed unless it can give us more fundamental insight as to what is
really
| > going on. Can it?
| >
| > FrediFizzx
| >
|
| It gives a lot of new insight.
| First, now you can directly calculate the
| time evolution of the wave function during interaction.
| Second, you can now forget about the mind boggling picture with
| virtual particles and work with real particles and potentials
| between them, just as in ordinary quantum mechanics.
| Third, I predict that the potentials acting between particles
| (Coulomb, magnetic, spin-orbit etc.) are instantaneous. This can be
| verified by experiment.
| Fourth, the theory predicts small (but fundamentally important)
| deviations from Einstein's predictions, for example, in the case of
| the decay of fast moving particles.
| Finally, this approach demonstrates that Lorentz transformations
| are not exact and universal, and that Minkowski space-time is an
| approximation.

Hmmm... So what is the interpretation of gauge bosons in your idea?

FrediFizzx

#40
08-09-2004, 06:28 AM
 Bilge Guest Posts: n/a
A version of QED without ultraviolet divergences

Eugene:

Consider the decay of the \pi-: \pi- --> \mu-\nubar. Now consider
one of the three diagrams for the weak vector current in a nuclear
beta decay:
e- \nubar
| /
|/
. . The neutron emits a virtual \pi-, the \pi-
\pi- . . \pi_0 decays into a virtual \pi_0, a real e- and
. . a real anti-neutrino.
N ->-+--P-->-+-->

In this instance we have two propagating particles produced by the
weak decay of a vitual pion. If one is to take seriously the idea that
those are virtual pions in the beta decay diagram, then there is an
implied experimental consequence for the decay of the \pi-, namely
the following decay has to exist,

\pi- -> \pi_0 + \e- + \nubar

and in fact, that decay mode was predicted on that basis. The
branching ration is on the order of 10^-8, so this particular
decay was not one of the decays which had been previously
observed (this occured in the 1950's). You also might look up
fierz interference'', for another example.

I don't really see the objection to virtual particles. Have you ever
observed a dipole moment? How about an angular momentum? Is it physical
non-sense to write out a multipole expansion for a charge or mass
distribution and associate particular phenomena with particular terms in
the distribution? Is a quadrupole operator an artifact or does that mean
something? For some reason, lots of people (not just you) seem to have no
problem at all collecting terms in an equation in a specific way and give
them the physical significance of being responsible for particular
phenomena, yet those same people find it odd to do the same thing where
virtual particles are concerned.

[...]

The relation between the quark charges and lepton charges can be
derived and while the precise value for the lepton and quark masses
are not derivable, the fact that the masses are non-zero _is_ derivable.
The uncertainty regarding the neutrino masses being zero was due to
the fact that the neutrinos have no charge and therefore could have
been massless.

What holds the electron charge together?

 Tags divergences , qed , ultraviolet , version

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