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# CS545 fall 2016

### Site Tools

assignments:assignment2

# Differences

This shows you the differences between two versions of the page.

 assignments:assignment2 [2016/09/06 09:54]asa assignments:assignment2 [2016/09/14 09:38]asa [Assignment 2] Both sides previous revision Previous revision 2016/09/14 09:38 asa [Assignment 2] 2016/09/07 13:22 asa 2016/09/06 09:54 asa 2016/09/06 09:51 asa 2016/09/06 09:40 asa 2016/09/04 10:19 asa [Grading] 2016/09/04 10:16 asa [Submission] 2016/09/04 10:13 asa 2016/09/04 10:12 asa 2016/09/04 09:55 asa 2016/08/30 09:27 asa 2016/08/30 09:22 asa 2016/08/30 09:21 asa 2016/08/30 09:20 asa 2016/08/30 09:19 asa 2016/08/27 11:50 asa 2016/08/27 11:27 asa 2016/08/27 11:24 asa 2016/08/27 11:19 asa 2016/08/27 11:18 asa 2016/08/27 11:17 asa 2016/08/09 10:25 external edit2015/09/28 12:24 asa 2015/09/25 13:52 asa 2015/09/16 16:52 asa 2015/09/16 16:50 asa 2015/09/16 16:47 asa 2015/09/16 16:45 asa Next revision Previous revision 2016/09/14 09:38 asa [Assignment 2] 2016/09/07 13:22 asa 2016/09/06 09:54 asa 2016/09/06 09:51 asa 2016/09/06 09:40 asa 2016/09/04 10:19 asa [Grading] 2016/09/04 10:16 asa [Submission] 2016/09/04 10:13 asa 2016/09/04 10:12 asa 2016/09/04 09:55 asa 2016/08/30 09:27 asa 2016/08/30 09:22 asa 2016/08/30 09:21 asa 2016/08/30 09:20 asa 2016/08/30 09:19 asa 2016/08/27 11:50 asa 2016/08/27 11:27 asa 2016/08/27 11:24 asa 2016/08/27 11:19 asa 2016/08/27 11:18 asa 2016/08/27 11:17 asa 2016/08/09 10:25 external edit2015/09/28 12:24 asa 2015/09/25 13:52 asa 2015/09/16 16:52 asa 2015/09/16 16:50 asa 2015/09/16 16:47 asa 2015/09/16 16:45 asa 2015/09/16 09:47 asa 2015/09/16 09:38 asa 2013/09/20 14:11 asa 2013/09/20 14:04 asa 2013/09/20 13:43 asa 2013/09/20 13:37 asa 2013/09/20 13:13 asa 2013/09/20 12:39 asa 2013/09/20 12:35 asa 2013/09/19 12:57 asa 2013/09/19 12:54 asa created Line 3: Line 3: ====== Assignment 2 ====== ====== Assignment 2 ====== - Due date:  Friday 9/16 at 11:59pm + Due date:  Friday 9/17 at 11:59pm ==== Datasets ==== ==== Datasets ==== Line 61: Line 61: The variable $\eta$ plays the role of the learning rate $\eta$ employed in the perceptron algorithm and $\delta \alpha$ is the proposed magnitude of change in $\alpha_i$.  The variable $\eta$ plays the role of the learning rate $\eta$ employed in the perceptron algorithm and $\delta \alpha$ is the proposed magnitude of change in $\alpha_i$.  We note that the adatron tries to maintain a //sparse// representation in terms of the training examples by keeping many $\alpha_i$ equal to zero.  The adatron converges to a special case of the SVM algorithm that we will learn later in the semester; this algorithm tries to maximize the margin with which each example is classified, which is captured by the variable $\gamma$ in the algorithm (notice that the magnitude of change proposed for each $\alpha_i$ becomes smaller as the margin increases towards 1). We note that the adatron tries to maintain a //sparse// representation in terms of the training examples by keeping many $\alpha_i$ equal to zero.  The adatron converges to a special case of the SVM algorithm that we will learn later in the semester; this algorithm tries to maximize the margin with which each example is classified, which is captured by the variable $\gamma$ in the algorithm (notice that the magnitude of change proposed for each $\alpha_i$ becomes smaller as the margin increases towards 1). + + **Note:** if you observe an overflow issues in running the adatron, add an upper bound on the value of $\alpha_i$. Here's what you need to do: Here's what you need to do:


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# paracol with manyfoot

I try to combine the two mentioned packages, as in the following example:

\documentclass{book}
\usepackage{lipsum}
\usepackage{paracol}
\usepackage{manyfoot}

\newfootnote{A}
\newfootnote{B}
\begin{document}

\footnotelayout{m}
\lipsum[1]

\FootnotetextA{}{\lipsum[2]}\FootnotetextB{}{\lipsum[3]} %comment this line and uncomment the following to see the desired results
%\footnotetext{\lipsum[2]}\footnotetext{\lipsum[3]}

\begin{paracol}{2}
\lipsum[4]
\end{paracol}
\lipsum[5]

\end{document}

as can be clearly seen, the results are not quite satisfactory...

if you use the commented-out line instead of the commented-on line (as described in the comment), you get the way it should look like.

I need paracol, since my real work contains many many areas where 2-3 alternative texts reside by each other. I thought about ledmac/ledpar, but I also need the great twosided options of paracol - to switch between left-right columns according to page parity. also the alternatives do not necessarily share the same paragraph structure - they are not parallel versions but full alternatives (even written in different font size sometimes) that should not depend on each other's contents or organization, while ledpar doc seems to insist on paragraph parallelism.

I need manyfoot, simply because my real work will contain multiple types of footnotes: one level is used as yet another way to specify alternative texts, while the other(s) are real short notes. if any alternative exists that works better with paracol, it would be welcome.

• Welcome to TeX.SX! Perhaps you should provide a screen shot of the output the current state of your code generates? – user31729 Apr 24 '14 at 6:22
• Where is \footnotelayout defined? Your MWE does not compile unfortunately – user31729 Apr 24 '14 at 6:48
• @christian: I use version 1.31 of paracol. there it's defined. – Avner Shapiro Apr 24 '14 at 7:52
• Oh my, I have 1.22 installed :-) I will update immediately. – user31729 Apr 24 '14 at 8:18

You can use the package parcolumns instead of paracol.

The corresponding parcolumns environment seems to be not affected by that strange behavior.

Note that the usage of parcolumns is very similar to paracol, so you shouldn't have any difficulty to switch to it.

Here is your MWE modified with parcolumns:

\documentclass{book}
\usepackage{lipsum}
\usepackage{parcolumns}
\usepackage{manyfoot}

\newfootnote{A}
\newfootnote{B}
\begin{document}

\lipsum[1]

\FootnotetextA{}{\lipsum[2]}\FootnotetextB{}{\lipsum[3]} %comment this line and uncomment the following to see the desired results
%\footnotetext{\lipsum[2]}\footnotetext{\lipsum[3]}

\begin{parcolumns}{2}
\colchunk[1]{\lipsum[4]}
\end{parcolumns}

\lipsum[5]

\end{document}

Output:

• thank you. but does parcolumns support something like the twosided option of paracol? as mentioned, I want the feature that the 1st column is always on the outer side and the last is always on the inner side. again I mean the newest version of paracol (1.31). – Avner Shapiro Apr 24 '14 at 7:56
• @AvnerShapiro I'm not aware of this new feature in paracol, anyway I think the answer is no. – karlkoeller Apr 24 '14 at 8:10
• indeed it seems to lack this option. also I place some non-trivial structs inside my columns (e.g. tables, text with different linestretch, etc) - parcolumns splits the boxes line by line, so these will not look as meant. all in all, I chose paracol because it's the most flexible solution I could determine, but it has the drawback of being too complex and has to handle footnotes on its own, and this is still somewhat problematic. – Avner Shapiro Apr 24 '14 at 10:41

format: plain


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# Double integral over a region with two bounds

Calculate the integral of $$f(x, y)$$ $$=$$ $$3x$$ over the region bounded above by $$y=x(2-x)$$ and below by $$x=y(2-y)$$.

What I tried to do here was first expand the two equations out to get $$y=x^2-x$$ and $$x=y^2-y$$.

I then rearranged the second equation to get $$y=1-\sqrt{1-x}$$.

But when i tried to graph this region, I ran into a problem as the second equation is invalid for values of $$x$$ larger than $$1$$.

But I do feel that the first equation will be the lower bound of the double integral and the second equation will be upper bound of the integral. But because of the above problem, I can not find any intersection points so I am a little confused on how to proceed further.

Any help would be highly appreciated!

\begin{align} y=x(2-x)&\implies y=2x-x^2\color{red}\ne x^2-x \\ x=y(2-y)&\implies x=2y-y^2\color{red}\ne y^2-y \end{align}
You were correct that the second original equation can be rearranged as $$y=1-\sqrt{1-x}$$, so you can set that equal to the first equation and solve the resulting equation to find the points of intersection of the two graphs.
$$2x-x^2=1-\sqrt{1-x}\implies x=0,1$$
$$\int_0^1\int_{1-\sqrt{1-x}}^{2x-x^2}3x\,dydx$$


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• Test Rank of an Abelian Product of a Free Lie Algebra and a Free Abelian Lie Algebra

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/121/03/0291-0300

• Keywords

Automorphism; free Lie algebras; test elements; test sets; test rank.

• Abstract

Let 𝐹 be a free Lie algebra of rank $n\geq 2$ and 𝐴 be a free abelian Lie algebra of rank $m\geq 2$. We prove that the test rank of the abelian product $F\times A$ is 𝑚. Morever we compute the test rank of the algebra $F/\gamma k(F)'$.

• Author Affiliations

1. Department of Mathematics, Çukurova University, Adana, Turkey

• Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019


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# Real-time Option

The Real-time option provides the capability to execute programs written in the C programming language on the RISC microprocessor of the HF2 Instrument with predictable latency and comes with an extensive programming environment.

This chapter describes:

 RT programming can be used only if the HF2LI-RT / HF2IS-RT option has been purchased and activated. This option is no further available for purchase from Zurich Instruments.
 The LabOne User Interface does not have a tab for configuring and working with the Real-time Option. Please use the ziControl graphical user interface to use the Real-time Option and refer to the ziControl Edition of the HF2 User Manual for more details.
 The Real-time Option programming reference guide is also available as HTML. The HTML documentation is bundled with the Real-time installation zip-file available from the Zurich Instruments download page.

## Installation of the Real-time Development Environment

In this section we describe the installation process of the HF2’s real-time development environment, see Installation on Windows for Windows and Installation on Linux for Linux. The real-time development environment is available from the Zurich Instruments download page.

 The RT development environment does not include a special editor. Please use an editor of your choice, for example: notepad++ or PSPad on Windows, emacs, vim, etc. on Linux.

### Installation on Windows

#### Software Requirements

To use the compilation tools on Windows the RT development environment requires the 32-bit version of Cygwin which provides a Linux-like environment. Cygwin is free and open source software, for more details see the Cygwin website. The only Cygwin package necessary is the make package. Installation of Cygwin is also detailed below.

 Even if your PC is natively 64-bit, the 32-bit version of Cygwin is required to run the compiler tools distributed with the RT development environment.

#### Installation Steps

1. Download the 32-bit version of Cygwin and run the Setup executable.

Figure 1. Cygwin website with install link
2. Go through the installation and, if possible, use default installation settings. There is one mandatory development package that must be installed in addition to the default installation. The package is called make. Select the package at the end of the installation. Select devel, then package make and select it in order to install it (see screenshots below).

Figure 2. Cygwin installation
Figure 3. Cygwin package selection: Choose package make
3. When the Cygwin installation has been finished, download the ziRTK software bundle and unzip it in your Cygwin home folder.

The home folder is located at: [Cygwin installation path]\home

The default path is: C:\cygwin\home

4. Now open the Cygwin shell by clicking either by navigating to the Cygwin start menu entry or by clicking on the Desktop icon.

5. Navigate into the extracted directory. The install script is called "install.sh".

cd ziRTK-Win-[VERSION]

6. Run the install script and go through the guided installation.

bash install.sh

Alternatively, you can also give executable rights to the install script and run it directly.

If possible, use default installation paths.

### Installation on Linux

#### Software Requirements

Officially, only Ubuntu 10.04 LTS is supported, but it should be possible to run the tools on any recent Linux distribution. The program GNU make is required to compile the examples. Since the RT tools were compiled on a 32-bit architecture, you need the package ia32_libs installed on a 64-bit architecture in order to execute 32-bit programs on a 64-bit architecture. On a Debian-based system, both packages can be installed with:

sudo apt-get install ia32_libs make

#### Installation Steps

1. Before you begin with the ziRTK installation make sure that the development package "make" is installed.

sudo apt-get install make

2. Extract the ziRTK bundle in a temporary directory.

tar xzf ziRTK-[build number]-linux.tar.gz

3. Navigate into the extracted directory. The install script is called "install.sh".

cd ziRTK-Linux-[VERSION]

4. Run the install script with root rights and go through the guided installation.

sudo bash install.sh

Alternatively, you can also give executable rights to the install script and run it directly.

If possible, use default installation paths.

### Accessing the Documentation

The developers of Zurich Instruments now happily recommend you to browse remaining examples and reference documentation in HTML format, which duplicates the following section of the user manual. You can find the HTML version of the documentation in

[INSTALLPATH]/ziRTK/doc/html/index.html,

which is typically found at

C:\cygwin\usr\share\zi\ziRTK-XX.XX\doc\html\index.html

on Windows or

/opt/zi/ziRTK/doc/html/index.html

on Linux.


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# Pay what you want! Does it have a serious future in gaming?

This topic is 2300 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Well first let me explain what pay what you want actually means. Essentially a developer puts a game out and asks the perspective player how much money they deserve to give for it. Now this has been done a few times in the music industry (not sure if it was a success there though) but has now moved into the games industry with the most prominent being the Humble Indie Bundle. Now so far as i know it has been a success in that case since there on their 3rd (?) instalment of the promotion. I would almost certainly put down to the quality of the games they use and the fact it's for charity.

What I am asking specifically is if such a system can or should be used in gaming in general, not just in these "special" cases. Why would I ask this? Well I happened across this RPS article which lead to this article by an "indie developer" (I use quotes because he implies he's more of a hobbyist than a full time developer). It's an interesting read although I don't agree with his conclusion, I feel it's more down to the lack of content and niche style of the game that I didn't do better, and some of his working is just down right confusing, for instance he talks about piracy although he seems to made it legally possible to get the game for free.

So back on topic. Do you think such a system has a place in gaming say for indie developers or even larger studios either in its original form or in the form now used by Joost "Oogst" van Dongen?

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I believe this is more of a Business question than a Design question. So that's why I'm moving this.

##### Share on other sites

From what I understood on the piracy issue, the game was available legally for free but people still downloaded it via a non-official route. I imagine what's implied in that statement is the people downloaded the game without even looking at the price.

I think the system has huge potential for indie developers. Both in the individual sense and in the indie bundle sense. I'm less convinced that people would be as generous towards an EA or Activision released game.

It'll be interesting to see what the data says in the future as he is changing it to a $1 minimum pay what you want system. My instinct is to think that selling at$1 or $5 and then soliciting tips on top of that price is going to be less fruitful than truly being pwyw. But it's cool to hear that someone is putting that plan into action rather than it just being theoretical. Setting the minimum payment to$1 might raise the number of paying customers slightly, but the vast majority of $0 customers were probably unable or unwilling to go through the hassle of paying anyway which would only result in them either going the piracy route or not playing the game, I think getting the game onto a service such as steam where a large number of users allready have all the details necessary for a purchase stored would have a far greater impact on revenue even if the price was fixed at$4.99 or even higher. (I found myself buying far more games online since my bank started generated short duration VISA numbers for me with fixed amount of money) (I can basically log onto my bank, generate a new visa number with a $x limit on it and set its expiry date and then use that for the transaction which means that i: 1) Don't have to trust the online store with more than the amount needed for that specific purchase and 2) I don't have to lift my ass to grab my real creditcard), it is however still far more of a hassle than it is to buy a game on steam (Which has my real CC number stored so i just have to click on the game i want), The other thing i think more online stores should do is to support payment via SMS (Most kids have a mobile phone, most don't have a credit or debit card, if you want them to buy your game its probably a good idea to provide a payment method they can actually use, i know it can be quite a hassle to set it up to work in most major countries and the transaction fees can be a bit silly but its probably still worth trying, especially if you're targeting a younger crowd) #### Share this post ##### Link to post ##### Share on other sites 1) What I am asking specifically is if such a system can or should be used in gaming in general, not just in these "special" cases. 2) Do you think such a system has a place in gaming say for indie developers 3) or even larger studios You need to undersand that this is not a new business model. At it's core this is a barter method where the merchant and buyer negotiate a price. In this case it is the extreme where the seller only sets a minimal bound and lets the buyer negotiate with his conscience. In the modern world it is much less frequent. Historically there were always people involved in the transactions. When people dealt with each other face-to-face you could negotiate a cost easily. When ordering from catalogs (including older software catalogs) you could buy through mail order and write a check; attach a note with the check saying "I love you guys, here is a big tip because I think you are worth it. Keep being awesome!" Or you could send in insufficiant funds and a note explaining why that should be enough and asking for the goods at the reduced cost. It wasn't until companies grew into international conglomerates that we saw the current form of standardized pricing, and it wasn't until automated money transactions that the human-to-human appeals and tips (extra money because it is awesome) started to go away.Even that is a negotiated price, but at the opposite end of the spectrum where the seller sets a price and the buyer decides to take it or leave it. 1) The terms "can" and "should" are very subjective. Can they be? Obviously the answer is yes. Should they be? That is a bigger issue of a policy debate that is going to vary based on the specifics. What may be good for one may be bad for another. 2) Yes, this is a better model for hobbyists and small indie studios. It can (through some implementations) give the customer a better chance to look at the software and determine the value to them personally. It was used extensively in the shareware days when people would be able to try the software for a while, and then based on what kind of user they were (corporate user, home user with minimal use, or enthusiast who used it extensively) could pay different amounts. Businesses would be told to pay a higher standard rate. Home users were on the honor system to send what they felt it was worth. For quite a few programs this was a very successful model. 3) No, this is not a good model for large developers, and a very bad model for publishers. You would have a difficult time convincing the major brick-and-mortar retailers (gamestop, walmart, target, toys r us, etc) to keep your game on the shelves when consumers can get a legal copy for$0.01 on the Internet. It would be difficult for many existing contracts through Valve or Amazon or other online distributors. It would seriously complicate issues of billing and bookkeeping. It would require an even more complex audit trail for any business to ensure compliance with tax laws and money laundering laws in every country they do business. It would directly result in many more audits for publishers by their sources; that would drive up costs, although the extra audits would likely be a good thing overall.

You can do a little more homework on how it worked in the Shareware world back in its heyday. The major shareware organizations still exist and have extensive libraries and market research that can help explain what works, what doesn't, and why.

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I believe this is more of a Business question than a Design question. So that's why I'm moving this.[/quote]

I sat there for a few minutes before I posted wondering if it would be better suited in another forum. Thought better of it in the end. Silly me .

From what I understood on the piracy issue, the game was available legally for free but people still downloaded it via a non-official route. I imagine what's implied in that statement is the people downloaded the game without even looking at the price.[/quote]

My problem was that if you can get a version of the game for free the word piracy (a somewhat loaded word anyway) seems out of place and frankly wrong. To me piracy implies a person acquired a game for free which they should have paid for. Yes there may be cases of people getting it for free without realising you could pay for it but that feels more like the game went viral (can't think of a better work at the moment) especially considering part of the buzz around the game was the PWYW method so I would bet most people who played if where aware you could pay.

@frob, thanks for all the information I'll be sure to have a look at the Shareware models. I agree that I can't see a big publisher/designer using this sort of method (outside of a charity stunt anyway).

It wasn't so much that I thought it was a something revolutionary or new more that it's somewhat topical given the fact there are two more recent examples of the successful and not so successful use of the business model. Although I'll admit I didn't realise how much such a system has in common with barter methods. Not to sure why seems too obvious now.

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You also have to take into consideration the average economy of the targeted audience of a given product. When you have a huge financial problem(such as here in the US and in the UK), generally people will spend less on products they don't need, especially if given the option to name their price. This presents a problem, as it changes the way people value things. A person might spend \$2 on something because they weren't sure about it, then came to realize that they really liked it, but already allocated funds for it so they may feel nothing as they were given the option to name their price. In some ways "you get what you pay for", but this doesn't necessarily apply to a complete product without some kind of structured payment system, so tread carefully.

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?

Free Version
Moderate

# Simple Harmonic Motion Equation

CLMECH-0EFAE6

The force exerted on a mass, $m$, by an ideal spring, characterized by the spring constant $k$, is described by the equation:

$$F=-k\, x$$

Which of the following is a correct expression of Newton's second law for this force?

A

$m\frac{dx}{dt}+k\,x=0$

B

$\frac{d^2x}{dt^2}+\frac{k}{m}\,x=0$

C

$\frac{d^2x}{dt^2}-\frac{k}{m}\,x=0$

D

$\frac{d^2x}{dt^2}-\frac{m}{k}\,x=0$


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# EIP-2972: Wrapped Legacy Transactions Source

Author Micah Zoltu https://ethereum-magicians.org/t/eip-2972-wrapped-legacy-transactions/4604 Draft Standards Track Core 2020-09-12 155, 2718

## Simple Summary

Two new transaction types for wrapping legacy transactions with and without a chain ID.

## Abstract

Introduces two new EIP-2718 transactions that are signature compatible with legacy transactions and can be automatically upgraded by any client.

• 0x00 || yParity || r || s || 0x65000000 || rlp(nonce, gasPrice, gasLimit, to, value, data)
• 0x01 || yParity || r || s || 0x65000000 || rlp(nonce, gasPrice, gasLimit, to, value, data, chainId, 0, 0)

## Motivation

We would like to eventually deprecate legacy transactions so we no longer have to retain code in the networking and signer layer that deals with them. However, we also want to ensure that signatures for transactions that were generated prior to that deprecation are still valid and funds don’t end up stuck because of an inability to sign a new style transaction. This EIP provides a mechanism for transmitting/including transactions in a way that is EIP-2718 compatible while still being signature compatible with legacy transactions.

## Specification

### Definitions

• || is the byte/byte-array concatenation operator.
• yParity is the parity (0 for even, 1 for odd) of the y value of the curve point for which r is the x value in the secp256k1 signing process.

### Transactions

As of FORK_BLOCK_NUMBER, 0x00 || yParity || r || s || 0x65000000 || rlp(nonce, gasPrice, gasLimit, to, value, data) will be a valid transaction where:

• the RLP encoded transaction portion is signed/processed/handled exactly the same as legacy transactions were signed/processed/handled, with the exception of the final encoding

As of FORK_BLOCK_NUMBER, 0x01 || yParity || r || s || 0x65000000 || rlp(nonce, gasPrice, gasLimit, to, value, data, chainId, 0, 0) will be a valid transaction where:

• the RLP encoded transaction portion is signed/processed/handled exactly the same as legacy transactions were signed/processed/handled, with the exception of the final encoding

### Receipts

As of FORK_BLOCK_NUMBER, 0 || ssz(status, cumulativeGasUsed, logsBloom, logs) will be a valid receipt where:

• the ReceiptPayload will be generated/processed/handled exactly the same as legacy receipts were processed/handled with the exception of its encoding

As of FORK_BLOCK_NUMBER, 1 || ssz(status, cumulativeGasUsed, logsBloom, logs) will be a valid receipt where:

• the ReceiptPayload will be generated/processed/handled exactly the same as legacy receipts were processed/handled with the exception of its encoding

## Rationale

### Signature doesn’t include transaction type as first signature byte

These transaction types are explicitly designed to be signature compatible with legacy transactions, which means we cannot change the data being signed. See Security Considerations section for more details.

### Two transaction types instead of one

With the introduction of typed transactions, we no longer need to do bit packing to avoid changing the shape of the signature. Legacy transactions introduced chain ID in EIP-155 and wanted to avoid changing the transaction array length, so it bitpacked the chainID into the signature’s v value. Since we no longer need to guarantee consistent payload lengths between transaction types, we have opted to have two transaction types with clear fields.

### Signature separate from signed data

When validating a signature, one must first separate out the signed data from the signature and then validate the signature against the signed data. In the case of legacy transactions, this was a bit of a burden since you had to first RLP decode the transaction, then extract out the signature, then RLP encode a subset of the transaction. EIP-155 made this process even worse by requiring the validator to further decode the v signature value to extract the chain ID (if present) and include that in the signed data payload. By having the signed data encoded exactly as it is signed, we make it so one can verify the transaction’s signature without having to do any decoding before hand. By having the signature SSZ encoded up front, we can easily extract the signature without even having to use a decoder.

### TransactionType 0/1 0x65000000 element

0x00 || yParity || r || s || 0x65000000 || rlp(nonce, gasPrice, gasLimit, to, value, data) is the same as ssz(0, yParity, r, s, rlp(nonce, gasPrice, gasLimit, to, value, data)), which may prove convenient for some clients. It costs us 4 extra bytes on the wire (mostly zeros), but the authors deem this a worthwhile trade to be SSZ encodable/decodable.

### SSZ for receipt encoding

There is a weak consensus that RLP is not a particularly encoding scheme for hashed data partially due to its inability to be streamed. SSZ is almost certainly going to be included in Ethereum at some point in the future, so clients likely have access to an SSZ decoder. For this particular case, manual decoding without a full SSZ decoder isn’t too complicated, though it does require doing a bit of “pointer math” since logs is an array of variable length items

## Backwards Compatibility

The new transactions are signature compatible with legacy transactions. Legacy transactions can be decoded and then encoded as type 0 or type 1 transactions. This EIP does not introduce any deprecation process for legacy encoded transactions, though the authors do encourage client developers to upgrade legacy encoded transactions to typed transactions as soon as it is reasonable.

The signature compatibility means that a client may see the same transaction encoded both ways. In such a case the client can choose which to retain, but it is encouraged to retain the typed transaction rather than the legacy encoded transaction. Since the two transactions would share a nonce, only one will ever be valid in a chain at a time.

TBD

TBD

## Security Considerations

While EIP-2718 strongly recommends including the transaction type as the first byte of the signed data, we cannot accomplish that in this case because we need to remain signature compatible with legacy transactions. Luckily, EIP-2718 also excludes transaction types 0xc0 to 0xfe from valid transaction types, and the first byte of the signature in this case is in that range so we can be sure this will not conflict with any future transaction types.

A signature for these transaction types does collide with legacy transactions, but the transactions will be processed the same so it doesn’t matter if the transaction ends up included as a legacy transaction or a typed transaction.

Copyright and related rights waived via CC0.


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Linear representation theory of projective general linear group of degree two over a finite field

Contents

This article gives specific information, namely, linear representation theory, about a family of groups, namely: projective general linear group of degree two.
View linear representation theory of group families | View other specific information about projective general linear group of degree two

This article describes the linear representation theory of the projective general linear group of degree two over a finite field. The order (size) of the field is $q$, and the characteristic prime is $p$. $q$ is a power of $p$. The group is denoted $PGL(2,q)$ or $PGL_2(q)$.

See also the linear representation theory for: special linear group, projective special linear group, and general linear group.

Summary

Item Value
degrees of irreducible representations over a splitting field Case $q$ odd: 1 (2 times), $q - 1$ ($(q - 1)/2$ times), $q$ (2 times), $q + 1$ ($(q - 3)/2$ times)
Case $q$ even: 1 (1 time), $q - 1$ ($q/2$ times), $q$ (1 time), $q + 1$ ($(q - 2)/2$ times)
number of irreducible representations Case $q$ odd: $q + 2$, case $q$ even: $q + 1$
See number of irreducible representations equals number of conjugacy classes, element structure of projective general linear group of degree two over a finite field#Conjugacy class structure
quasirandom degree (minimum degree of nontrivial ireducible representation) 1
maximum degree of irreducible representation $q + 1$
lcm of degrees of irreducible representations Case $q$ odd: $q(q + 1)(q - 1)/2 = (q^3 - q)/2$; Case $q$ even: $q(q+1)(q-1) = q^3 - q$
sum of squares of degrees of irreducible representations $q(q + 1)(q - 1) = q^3 - q$, equal to the group order; see sum of squares of degrees of irreducible representations equals group order

Particular cases

$q$ (field size) $p$ (underlying prime, field characteristic) Case for $q$ Group $PGL(2,q)$ Order of the group ($= q^3 - q$) Degrees of irreducible representations (ascending order) Number of irreducible representations ($= q + 1$ if $q$ even, $q + 2$ if $q$ odd) Linear representation theory page
2 2 even symmetric group:S3 6 1,1,2 3 linear representation theory of symmetric group:S3
3 3 odd symmetric group:S4 24 1,1,2,3,3 5 linear representation theory of symmetric group:S4
4 2 even alternating group:A5 60 1,3,3,4,5 5 linear representation theory of alternating group:A5
5 5 odd symmetric group:S5 120 1,1,4,4,5,5,6 7 linear representation theory of symmetric group:S5
7 7 odd projective general linear group:PGL(2,7) 336 1,1,6,6,6,7,7,8,8 9 linear representation theory of projective general linear group:PGL(2,7)
8 2 even projective special linear group:PSL(2,8) 504 1,7,7,7,7,8,9,9,9 9 linear representation theory of projective special linear group:PSL(2,8)
9 3 odd projective general linear group:PGL(2,9) 720 1,1,8,8,8,8,9,9,10,10,10 11 linear representation theory of projective general linear group:PGL(2,9)

Irreducible representations

Case $p \ne 2$, $q$ odd

Description of collection of representations Parameter for describing each representation How the representation is described Degree of each representation Number of representations Sum of squares of degrees
Trivial -- $x \mapsto 1$ 1 1 1
Sign representation -- Kernel is projective special linear group of degree two, image is $\{ \pm 1 \}$ 1 1 1
Unclear a nontrivial homomorphism $\varphi:\mathbb{F}_{q^2}^\ast \to \mathbb{C}^\ast$, with the property that $\varphi(x)^{q + 1} = 1$ for all $x$, and $\varphi$ takes values other than $\pm 1$. Identify $\varphi$ and $\varphi^q$. unclear $q - 1$ $(q - 1)/2$ $(q - 1)^3/2 = (q^3 - 3q^2 + 3q - 1)/2$
Nontrivial component of permutation representation of $PGL_2$ on the projective line over $\mathbb{F}_q$ -- -- $q$ 1 $q^2$
Tensor product of sign representation and nontrivial component of permutation representation on projective line -- -- $q$ 1 $q^2$
Induced from one-dimensional representation of Borel subgroup $\alpha$ homomorphism $\mathbb{F}_q^\ast \to \mathbb{C}^\ast$, with $\alpha$ taking values other than $\pm 1$, up to inverses. Induced from the following representation of the image of the Borel subgroup: $\begin{pmatrix} a & b \\ 0 & d \\\end{pmatrix} \mapsto \alpha(a)\alpha(d)^{-1}$ $q + 1$ $(q - 3)/2$ $(q + 1)^2(q - 3)/2 = (q^3 - q^2 -5q - 3)/2$
Total NA NA NA $q + 2$ $q^3 - q$


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# II.1.6

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• a) Show exactness on stalks (this is II.1.2); show $F_p/F'_p \cong (F/F')_p$. This can be done by a universal property argument since you know what the universal property of $(F/F')_p$ is.
• b) use a) to show $0\to \mbox{im}\alpha \to F \to F/\mbox{im}\alpha \to 0$ is exact and use the 5-lemma with the original exact sequence to get the desired result.


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In this tutorial you will learn how to control many different tasks at the same time and how to execute high priority tasks interrupting all other tasks.

Equall timing for on and off state.

Non-equall timing for on and off state.

Eeee... How to blink more than one LED?!

Now you will make a step closer to the heart of the problem. Controlling one thing doesn't sound complicated. Tnings became intersting when you have to control two different objects at the same time, both working with different timing.

Extend previous circuit and add one more LED (green).

You can start with a toy problem: control two leds with the same timing of HIGH and LOW state:

or in short:

The code for this is simple:

Even if you have non-equall timing for on and off state, the problem is trivial because there is no need for real "concurrency" as both leds changes their state at the same time:

The problem becomes apparent, when timings for different object are different:

Second from the above cases are feasible:

The same but with shifted timing for green LED:

The disadvantage of this solution is that every delay affects both leds and it may be difficult to control them independently. It may happend that changing timing of one led will force you to change code drastically. In more complex dependencies it may be difficult to find "cycle" -- repetable pattern you can harcode:

Now you will see better approach allowing you to control independently (almost) as many objects as you want.

You will use very short delay to avoid blocking and count how many will happen. If you reach a given number of calls, you will take an action.

To make things simpler, start with equall timing for on and off state with only one led:

Now you can extend the previous case to non-equall timing for on and off state:

Because counterRedOff and counterRedOn are increased inclusively (either counterRedOff or counterRedOn) you can use one counter as it is showned bellow:

Finally you can adopt this approach to non-equall timing for on and off state of two leds.

Problems with this improvement:

Lack of control over code "outside" delay -- it may take as much time as it want and delay will have no idea how much time elapsed between two subsequent calls. It means that you have to "collect" 100 delay(10)s regardles of the time passed between every two delay(10)s. In consequence 100*delay(10) is not equall to delay(1000). It wouldn't be less but it may be (much) more.

The problem with previous solution is that sometimes 90*delay(10)+T would be equall to delay(1000) or next time 98*delay(10)+T would be equall to delay(1000), where T is an extra (non-constant, unpredictable) time microcontroller needs to complete some task(s) between every two delay(10)s

That's why thing you are looking for is rather a variable counter increment, something of the following form:

Non-blocking equall timing for on and off state.

In most cases this is implemented as below:

In the above solution you still count something (number of milliseconds from starting/reseting your microcontroller) but this process of counting depends on time. In most cases instead of counter you will use different names -- below you have the same code as above but with different names for variables:

Adopting this approach to non-blocking non-equall timing for on and off state is quite easy:

Non-blocking non-equall timing for on and off state of two different LEDs.

Interrupts

Problem description

Add button to the previous circuit:

Upload to microcontrole the followng code to switch on and off red LED:

To simulate time-consuming task add delay(10000):

As you can see, now it's almost impossible to switch LED. If you are lucky, you can do this only in short time-slots between delay(10000)s.

Interrupt

Interrupt, as it name states, interrupt the current work of microcontroller such that some other work can be done. What is important, it does not stop or break other activity but only interrupts it. After completion, microcontroller return back to interrupted job.

To understand this consider the following simple story:

Suppose you are sitting at home, chatting with someone (current work). Suddenly the telephone rings (interrupt occure). You stop chatting, and pick up the telephone to speak to the caller (the interrupt service routine is called). When you have finished your telephonic conversation, you go back to chatting with the person before the telephone rang (return back to interrupted job).

Here are some important features about interrupts:

• Interrupts can come from various sources:
• Hardware external source Microcontroller uses a hardware interrupt that is triggered by a state change on one of the digital pins.
• Hardware internal source Microcontroller uses a hardware interrupt that is triggered by a state change on one of the internal component -- very often timer or counter.
• Software source A software interrupt is requested by the processor itself upon executing particular instructions or when certain conditions are met. It may be intentionally caused by executing a special instruction which, by design, invokes an interrupt when executed. Such instructions function similarly to subroutine calls and are used for a variety of purposes, such as requesting operating system services and interacting with device drivers (e.g., to read or write storage media). Software interrupts may also be triggered by program execution errors or by the virtual memory system.
• Every software interrupt signal is associated with a particular interrupt handler.
• Microcontroller has dedicated pins to work with interrupts:
• ISR (Interrupt Service Routine) is a common name for routine called when interrupt occures.
• You define the routine and specify conditions related to interrupt occurence: the rising edge, falling edge, change state etc.
• Generally, an ISR should be as short and fast as possible.
• You can mask an interrupt. Masking means disabling interrupt making it to be deferred or ignored by the processor. When the interrupt is disabled, the associated interrupt signal may be ignored by the processor, or it may remain pending. Signals which are affected by the mask are called maskable interrupts. Some interrupt signals are not affected by the interrupt mask and therefore cannot be disabled; these are called non-maskable interrupts (NMIs). These indicate high-priority events which cannot be ignored under any circumstances, such as the timeout signal from a watchdog timer.

A watchdog timer (sometimes called a computer operating properly or COP timer, or simply a watchdog) is an electronic or software timer that is used to detect and recover from computer malfunctions. Watchdog timers are widely used in computers to facilitate automatic correction of temporary hardware faults, and to prevent errant or malevolent software from disrupting system operation.

During normal operation, the computer regularly restarts the watchdog timer to prevent it from elapsing, or "timing out". If, due to a hardware fault or program error, the computer fails to restart the watchdog, the timer will elapse and generate a timeout signal. The timeout signal is used to initiate corrective actions. The corrective actions typically include placing the computer and associated hardware in a safe state and invoking a computer reboot.

Delay in ISR

The code presented in previous section works in Tinkercad simulator but there is a question wether it is as it should be and you are allowed to use delay inside ISR or not. Why you may have some doubts? Well, it may happend that clock is controled by interupt so when you are inside ISR to handle interrupt, clock interrupt may be blocked. If this is a case, delay may not be able to detect time passing and you will block forever you code inside ISR. Or maybe this statement is false, and everything works as expected?

Unfortunatelly an Internet with tones of blogs, vlogs and any other -logs doesn't help as you can find contradictory descriptions:

• From ARDUINO PROGRAMMING GUIDE SERIES Can You Use Delay() Inside Interrupt Service Routine?
A question I often receive is about the contents of the ISR:
"Can I include arbitrary code?"
"Can I include slow functions like delay() or even Serial.print()?"
Although this is possible, you should not.

Conclusion: yes, you can.

• From Arduino delay inside of an Interrupt
The first problem is that delay() is a busy loop monitoring millis(). The value that millis() returns will not change inside an ISR as interrupts are turned off inside an ISR; this is why ISRs must be as short and fast as possible, or they will interfere with other interupts.

So if you call delay() within an ISR your poor AVR is now deadlocked! It is waiting for something to happen that can now never happen.

A second problem is that if your ISR takes too long, you can miss other interrupts; millis() and micros() can miss ticks and become inaccurate!

Conclusion: no, you can't.

Hmm... Now you can test it on your own on real device. In my case everything was working as expected.

Anyway, using delay everytime blocks your microcontroller. You may say: Only for twenty milliseconds! Only? Let's test what microcontroller can do for you in this time. First prepare "testing environment":

Now you can replace the line

with

and run your code. In my case the following output was printed:

As you can see, in 10 milliseconds time slot my microcontroller was able to repeat for loop 5779 times!

When you replace the line

with

and run your code you will get differnt result:

Notice that only because you change type for i from int to unsigned long my code slowed down from 5779 to 4371 iterations.

Now paste the line:

just after previously pasted:

If I run this code, I got the following results:

2938 is much lower than 5779 but it is still a lot of power to do many interesting tasks.

As you can see, it makes sense to implement ISR without delay inside (regardless of whether you can or cannot use delay inside ISR). Below I present my code:

With this code again you should be able to switch the state of your LED anytime you want but you don't use blocking delay.

By the way, as now you know interrupts, you can test switch bouncing described in tutorial Pull resistors. Upload the following code to your microcontroller:

If you press the batton again and again you will notice some gaps as in my case:

The gaps are caused by sipkes which apear in unstable membrane time when you press the button. When you press the button, you increase iRising by 1 and from time to time this variable is also increase by HIGH states of spikes.


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Home / Tin tức, sự kiện / dimension of velocity

# dimension of velocity

The straight line in the graph can be algebraically represented as follows: Volume refers to the amount of data, variety refers to the number of types of data and velocity refers to the speed of data processing. Also, the values of some important physical constants and their symbols used to represent them are already written in my previous article about the different charts used in the measurement.. vijayprakashver vijayprakashver 18.08.2014 Physics Secondary School DIMENSION OF VELOCITY 2 See answers kvnmurty kvnmurty Velocity = change in displacement / time duration Length and time are fundamental dimensions. . Sounds astounding but it’s true. We witness constant motion whenever an object slides over a horizontal, low friction surface (when a puck slides over a hockey rink.). The dimension of velocity is L/T. So by multiplying equation (1) and equation (2) we will get the dimension of angular velocity: Angular velocity = Angular displacement × [Time]-1. Therefore dimension of angular velocity = [M0 L0 T0] × [M0 L0 T1]-1 = [M0 L0 T-1] Therefore we can write the dimension of angular velocity as [M0 L0 T-1]. . (b) We require both magnitude and direction to define velocity. Motion in one dimension. The Velocity-time graph is used for explaining the constant acceleration of an object. 2 See answers Therefore, Potential Energy is dimensionally represented as [M0 L0 T-1]. (3). Answered What are dimensions of velocity? Velocity and acceleration both increase when the ball is thrown in the air. An object's position during a 10 second time interval is shown by the graph below: a.) The general of a particle moving with velocity $$\underset{v}{\rightarrow} = k(y\hat{i}+x\hat{j})$$ is given as y2 = x2 + constant. According to the 3Vs model, the challenges of big data management result from the expansion of all three properties, rather than just the volume alone -- the sheer amount of data to be managed. (c) Instantaneous velocity is the velocity at any given moment of time, whereas average velocity is the total displacement divided by total time. 2012 Nov 14;14(1):77. doi: 10.1186/1532-429X-14-77. This combination of units has been given the name Newton (N) in honorof Sir Isaac. The SI unit of velocity is m/s (m⋅s−1). Motion in One Dimension 21 39. This average velocity can then be used to calculate the distance you traveled during your acceleration period, which was 10 seconds long. Instantaneous velocity is the velocity of a body at any given time. (1), The dimensional formula of velocity = [M0 L1 T-1] . Well, the difference between speed and velocity is that speed gives us an idea of how fast an object is moving whereas velocity not only tells us its speed but also tells us the direction the body is moving in. We say that dimension of velocity are zero in mass 1 in length and 1 in time. . Your email address will not be published. This physics video tutorial explains the concept of acceleration and velocity used in one-dimensional motion situations. Speed and velocity can be a little confusing for most of us. Jewel goes to school in her dad’s car every morning. . An instant in time is different from the time taken or the time interval. ... Analyzing two-dimensional projectile motion is done by breaking it into two motions: along the horizontal and vertical axes. Definition of velocity Up: No Title Previous: Dimensional analysis. . Find an answer to your question what are dimensions of velocity? A dimensional formula is always closed in a square bracket. dimension of velocity 75ruk5ii -Physics - TopperLearning.com Thanks , It is soo amazing and fascinating to learn from byjus I really enjoys it and it is tooo much helpful for me in understanding the concepts clearly, Your email address will not be published. (3) On substituting equation (2) and (3) in equation (1) we get, Velocity Gradient = velocity × [distance]-1. (2) And, the dimensional formula of distance = [M 0 L 1 T 0] . The dimensional formula of velocity = [M 0 L 1 T-1] . 1. Vector quantities cannot be added algebraically because they have directions along with magnitude. Its velocity in the original one dimension has reduced. The meaning of velocity of an object can be defined as the rate of change of the object’s position with respect to a frame of reference and time. A non-dimensional velocity for a wall-bounded flow can be defined in the following way: Where is the local velocity and is the friction velocity at the closest wall.. is called the dimensionless velocity and is commonly used in boundary layer theory and in defining the law of the wall. Speed has dimensions of distance/time or [ LT-1 ]. . Kinematics analyzes the positions and motions of objects as a function of time, without regard to the causes of motion. 1. Log in. Speed is a prime indicator of the rapidity of the object. Therefore, 15 mins = 1560 = 0.25 hours. The motion with constant velocity is the simplest form of motion. . . $$x=x_0+vt$$ Join now. Its velocity is now distributed over two dimensions and therefore it’s taking longer for the car to cover the same distance. (d) A changing velocity indicates acceleration. The distance is simply the average velocity multiplied by the time interval, so 45 m. It is therefore useful to use the symbol $$t$$ for an instant in time (for example during the fourth second) and the symbol $$\Delta t$$ for the time taken (for example during the first $$\text{5}$$ seconds of the motion). Average velocity is the total displacement by total time and is given by v = △x△t where ∆x is the total displacement of the body and ∆t is the time. Normal values of aortic dimensions, distensibility, and pulse wave velocity in children and young adults: a cross-sectional study J Cardiovasc Magn Reson . But if their direction of motion is in the opposite direction, then it is difficult to determine the fastest. It is a vector quantity, which means we need both magnitude (speed) and direction to define velocity. Velocity is the prime indicator of the position as well as the rapidity of the object. For example, if your initial velocity was 3 m/s and your object acceleration is 4 m/s, your final velocity is 7 m/s (3 + 4 = 7). Sir Isaac Newton's Second Law of motion states that. Three-dimensional P-velocity structure in the region of the M s= 6.9 Irpinia, Italy, normal faulting earthquake Direction is commonly dimensionless, as in an angle. So, now how would she know her velocity? It involves the relationships between the quantities displacement (d), velocity (v), acceleration (a), and time (t). Well, the average velocity of Jewel’s car could be found by: For convenience, we have considered the car to move in a straight line, and we will convert all the units of time to hours. The dimensions of speed is distance/time e.g; m/s. the magnitude of a force = mass * acceleration. When two objects A and B are moving with different velocities, then the velocity of one object A with respect to another object B is called relative velocity of object A with respect to B. Key Terms. Or, V = [M 0 L 1 T-1] × [M 0 L 1 T 0]-1 = [M 0 L 0 T-1] Therefore, Potential Energy is dimensionally represented as [M 0 L 0 T-1]. Required fields are marked *. To understand the concept of instantaneous velocity and average velocity, let’s take this example. . . This givesthe units clue: mass * acceleration. . The SI unit of it is meter per second (ms-1) if there is a change in magnitude or the direction in the velocity of a body the body is said to be accelerating. We say that dimension of velocity are, zero in mass, 1 in length and -1 in time. queeno01 01.05.2020 Physics Secondary School +50 pts. What are dimensions of Planck's constant. It is helpful in experimental work because it provides a guide to factors that significantly affect the studied phenomena. $$x=x_0+vt$$ In the equation, x 0 is the displacement at time t, v is the constant velocity of the body $$v=\frac{dx}{dt}$$. Add the quantity obtained from Step 1 and Step 2 to obtain the final velocity. And directions cannot be added algebraically. In this chapter, we'll introduce the concepts of velocity and acceleration and apply them to simple situations. The dimensions of velocity are the same as those of speed (speed is the magnitude of velocity which is vectorbquantity i.e. The ability to affect one's own velocity in three dimensions. it has the same position, displacement and velocity as A. In a similar way, all objects in the real world are moving in a four dimensional spacetime, at a constant velocity as that of light. Kinematics in One Dimension. On substituting equation (2) and (3) in equation (1) we get, Velocity Gradient = velocity × [distance]-1, Or, V = [M0 L1 T-1] × [M0 L1 T0]-1 = [M0 L0 T-1]. For example, if the object weighs 30 kg and has a force of 15 N applied to it, then the acceleration would be 4 m/s. Determine the object's total distance traveled and displacement. Velocity = length travelled per unit of time = (L)/(T) In other words, in the equation of motion of a particle traveling at a uniform velocity(V) for a time (T), the distance travelled would be L = VT. During the experiment, the relationship between the position, velocity and acceleration of an object, moving in one dimension, along a straight line is investigated. . Instantaneous speed is defined as the speed of an object at a specific moment of time. In the equation V = d/t, V is the velocity, d is the distance and t is the time. (2), And, the dimensional formula of distance = [M0 L1 T0] . 3.1k SHARES. Velocity defines the direction of the movement of the body or the object. What is VelocityInitial and Final VelocityVelocity UnitsSpeed and VelocityExample of VelocityDifference between Speed and Velocity. It might sound complicated but velocity is basically speeding in a specific direction. In the equation, x0 is the displacement at time t, v is the constant velocity of the body $$v=\frac{dx}{dt}$$. Where L represents length and T represents time. Table 1: Dimensional formula of physical quantities. b.) The detailed comparison in the tabular format is given below. Kinematics in one dimension physics practice problems distance velocity and acceleration equations duration. The dimensional formula of velocity gradient is given by, Velocity Gradient = velocity × [distance]-1 . 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Negative, and, the dimensional formula motion situations above graph is used for the... It ’ s taking longer for the car to cover the same direction on object! A graph of displacement versus time graph for a body moving with constant velocity is m/s ( m⋅s−1 ) the. Us in which direction the object what is VelocityInitial and final VelocityVelocity UnitsSpeed VelocityExample! Distance traveled and displacement be used to calculate the distance covered by an object travels when gravity first force... Speed has dimensions of speed is the velocity of a force = mass * acceleration our slope =... Little confusing for most of us velocity of a force = mass * acceleration two dimensions and therefore ’... Velocity versus time for a body moving with constant velocity homework study ext can be positive negative. Of how quickly something is moving constant acceleration of an object at a moment... Velocity can be positive or negative, and, the concept of velocity and and... A ball period, which means we need both magnitude and direction space... Time interval 's total distance traveled and displacement body at any given time those! Moving faster, now how would she know her velocity of speed is distance/time e.g ; m/s or slow object. Direction in space ) a body at any given time acceleration and apply them to simple situations the of. Analyzes the positions and motions of objects as a function of displacement time. Tell the fastest of the body or the time taken in the opposite direction, then is. Your question what are dimensions of speed ( speed ) and direction define... Tells us in which direction the object velocity can be positive or negative, is... Negative, dimension of velocity, the dimensional formula is always closed in a specific direction this tells us which. Mass, length, and, the dimensional formula of velocity gradient is rate of change velocity... To understand the concept of instantaneous velocity during your acceleration period, which was 10 seconds long of.! Graph is a prime indicator of the two or more objects is moving VelocityInitial! It can be zero M0 L1 T0 ] speed ( speed is a vector quantity, of. Force = mass * acceleration it provides a guide to factors that significantly affect studied! Jewel goes to school in her dad ’ s car every morning the studied phenomena we require both and! M0 L0 T-1 ] at a specific direction ( 2 ), the concept of instantaneous is. And vertical axes dimensional analysis dimensionally represented as [ M0 L0 T-1 ] the answers you need now! 2 ), the concept of instantaneous velocity and average velocity can be defined as the distance by... And dimensions of velocity are the same direction on the same position, displacement and used., speed of an object travels when gravity first applies force on the object moves algebraically because they have along! Moving in the equation V = d/t, V is the time TopperLearning.com. Add the quantity obtained from Step 1 and Step 2 to obtain final. Terms velocity and acceleration and velocity as a. of us velocity which is vectorbquantity.. Object at a specific moment of time, without regard to the causes of.... 'S total distance traveled and displacement SI unit of velocity you have a velocity, in. If their direction of the movement of the body or the object in time... During your acceleration period, which was 10 seconds long mass 1 length... An instant in time be defined as the displacement covered having the identical dimensional formula  5 metres per east! Two motions: along the horizontal and vertical axes motions of objects a! In a square bracket is done by breaking it into two motions: along the horizontal and vertical axes in! Understand the concept of velocity are given in the same road 's total distance traveled whereas velocity the. ( 1 ):77. doi: 10.1186/1532-429X-14-77 you also tack a direction onto,! With magnitude projectile motion is in the same road graph is a of... Graph of displacement versus time graph for a body moving with constant velocity dimension of velocity quantitative!, then it is helpful, which we shall be discussing in this article two dimensions and therefore ’... And apply them to simple situations magnitude ( speed ) and direction to define velocity and t is distance... We 'll introduce the concepts of dimension of velocity of our slope statement-1: velocity gradient = velocity × [ ]. Displacement of the two or more objects is moving - TopperLearning.com kinematics in one dimension a quantity. Force on the same as those of speed is defined as the distance and t is the simplest of. Of our slope m/s ( m⋅s−1 ) they have directions along dimension of velocity.! Are given in the table below the concept of acceleration and velocity as a function distance... 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# Quick note - bugs from mistaking points for vectors.

A couple of the more time-consuming/confusing bugs to track down have been from mistakenly passing an absolute position (point) instead of a relative position (vector) to functions that use these for drawing or intersection or similar.

These are a little difficult to track down because by default I'm drawing pretty close to the origin, so the relative positions are often very similar to the absolute ones. As a result, the bugs would appear inconsistently. I was attempting to fix these a little while after writing them, and so didn't have all the intentions behind each passed parameter cached in my brain. When stepping through the debugger, the points being passed didn't raise any red flags and so I didn't pay much attention to them. I thought the source of the problem was elsewhere.

Once I had fixed the first bug after an embarrassingly long time, the second time a similar bug came up went much quicker. Awareness is your best defence!

'Best'? Ok, probably not, but it's definitely helpful. There are also a few other potential solutions:

1. Differentiating at runtime
2. This involves adding more data to your vector/point structure that indicates which it is at any point during execution. You can look up the details if you're interested, but suffice it to say that I didn't feel like this bug warranted the memory cost. I believe the normal way to do this for 2D would amount to structs 50% larger.

3. Language-level types
4. Probably viable - if a little cumbersome - in C++, where types are differentiated basically if they have different names. (Un)fortunately, I'm working in C, not C++ where types are differentiated by structural similarity. i.e. because both types would look something like the following, they would both be allowed as parameters anyway.
 1 2 3 4 typedef struct { f32 X; f32 Y; } point/vector;
EDIT: This is wrong. The similarity rule only applies to primitive types, not structs. See comments below.

5. Be smarter and better at debugging
6. Would probably be effective, unfortunately I can only really work with what I have.

7. Hungarian notation (screams, babies crying, dramatic hellish music plays...)
8. I happened to read Joel Spolsky's article 'Making Wrong Code Look Wrong' at around the time I had this issue. This probably won't be popular, but this is the route I have taken. Absolute positions/points are now prefixed with 'po', and I have currently left other vectors unprefixed.

So... just a quick reminder to try and reconsider what assumptions you're making when debugging is unproductive. Stay safe out there!
Dumitru Frunza,
I'm working in C, not C++ where types are differentiated by structural similarity.

I seem to recall that in C, struct types are differentiated by name:
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 #include "dummy.h" struct point { float X; float Y; }; struct vector { float X; float Y; }; void foo(struct point* pt); struct vector v; foo(&v); // --> does not compile
Andrew Reece,
Just tried it out, you're right! It looks like it's just for primitive types - I must have just assumed it was the same for structs...

I might reconsider doing this, but I'm not sure if I want to account for all transformations between points and vectors throughout all my functions, and it's sometimes useful to be able to use either... hmm, I'll have a think.
A very quick and dirty fix would be to move everything away from 0,0 in absolutes position.

That way the absolute positions are around say 1000, 1000 and the relative position are around 0,0 as normal.


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# Can I give continuous rank probability score (CRPS) to Diebold-Mariano (DM) test?

I would like to use DM test for probabilistic forecasting case. My initial thinking was to give CRPS of two forecasting methods instead of raw forecast errors, where CRPS is calculated using prediction interval constructed under parametric assumption (Gaussian).

Let's say I have 100 observations (y) and 100 point forecasts from method-1 (f1) and 100 point forecasts from method-2 (f2). Hence, I have CRPS of 100 points from both method-1 and method-2, instead of raw errors of 100 points (y-f1 and y-f2). In this setting, it seems DM test is working fine when I use CRPS, because I got meaningful results, but I could not find any article backing using CRPS or any other error metric (absolute error, square error, ...) instead of raw errors. If my understanding is correct, there are some papers using CRPS instead of raw errors, but these papers mostly appear in arxiv (probably not published in peer-reviewed journal yet). I also found an R package called SpecsVerification. The function ScoreDiff seems doing the same as the definition of the function is: Calculate the difference (mean score of the reference forecast) minus (mean score of the forecast). Uncertainty is assessed by the Diebold-Mariano test for equality of predictive accuracy.

Simply, my question is that can I use CRPS instead of raw errors in DM test? Or is there any alternatives to DM test that allows using CRPS?


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# Apps Like Dave : The cash that is best Advance Apps For Advance Money

Apps Like Dave : The cash that is best Advance Apps For Advance Money

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## Earnin

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## Interface CapacitatedSpanningTreeAlgorithm<V,E>

• Type Parameters:
V - the graph vertex type
E - the graph edge type
All Known Implementing Classes:
AbstractCapacitatedMinimumSpanningTree, AhujaOrlinSharmaCapacitatedMinimumSpanningTree, EsauWilliamsCapacitatedMinimumSpanningTree

public interface CapacitatedSpanningTreeAlgorithm<V,E>
An algorithm which computes a capacitated (minimum) spanning tree of a given connected graph with a designated root vertex. The input is a connected undirected graph G = (V, E) with a designated root r \in V, a capacity constraint K \in \mathbb{N}, a demand function d: V \rightarrow \mathbb{N} and a capacity function c: E \rightarrow \mathbb{N}. A Capacitated Minimum Spanning Tree (CMST) is a rooted minimal cost spanning tree that satisfies the capacity constraint on all trees that are connected to the designated root. That is, the sum of the demands of all vertices is smaller or equal than K. These trees build up a partition on the vertex set of the graph. The problem is NP-hard.


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# FIDSAM

Fluorescence Intensity Decay Shape Microscopy (FIDSAM) is a fluorescence microscopy technique, which utilizes the time evolution of fluorescence emission after a pulsed excitation to analyse the decay statistics of an excited chromophore. The main application of FIDSAM is the discrimination of unspecific autofluorescent background signal from the target signal of a dedicated chromophore.

## Principle

The FIDSAM method analyses the number of different molecules contributing to a measured fluorescence signal. Assuming a pure fluorescent dye solution in an isotropic surrounding, the individual emitters are indistinguishable. Accordingly, they obey the same fluorescence emission statistics and the time evolution of the fluorescence emission after a pulsed excitation can be described by a monoexponential decay function according to:

$F(t) = A e^{-t/\tau}$

with $A$ = the initial fluorescence intensity after the excitation and $\tau$ = the decay constant (fluorescence lifetime).

In contrast, autofluorescent background consists of a multitude of individual emitters, which obey individual emission statistics. Accordingly, the time evolution samples a summation of numerous individual decay statistics an can be written as:

$F(t) = \sum(A_1e^{-t/\tau_1})$.

The FIDSAM technique bases on a time correlated single photon counting (TCSPC) measurement and analyses the degree of deviation of a recorded fluorescence decay from a monoexponential behavior. This is achieved by fitting the recorded fluorescence intensity decay by a monoexponential decay function convoluted with the instrument response function. In a next step, the error value of the fitting procedure, $\chi^2$, is extracted an its inverse value is multiplied with the original intensity value. This way, fluorescence signal, which originates from autofluorescence background and therefore exhibits increased error-values, is divided by a relatively large number, whereas fluorescence signal from target molecules exhibits small error-values around unity is divided by a small number and remains largely unaffected.

## FIDSAM Imaging

Typically, the FIDSAM technique is applied to a microscopy imaging. Whereas the measurement protocol equals fluorescence lifetime imaging microscopy (FLIM), the read-out parameter is different. In FLIM, the characteristic decay constant is derived, while FIDSAM analyses the shape of the fluorescence intensity decay via the error value. Due to this, FIDSAM is intrinsically not dependent on fluctuations of the fluorescence lifetime, which often occur due to the individual chemical surround of a chromophore, but on analysis of the isotropy of the contributing emitters in a given sample volume.


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# Browse Dissertations and Theses - Linguistics by Title

• (1979)

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• (1969)

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• (2002)
Briefly, the results of the acoustic studies conducted show that there is a difference between the two dialects in their phonological properties: as mentioned, the Belgrade dialect has a pitch-accent and vowel length ...

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PDF (7MB)
• (1983)
This dissertation documents John Wilkins' contributions to the science of language analysis. I analyze his Essay towards a Real Character and a Philosophical Language (1668) concentrating on his lexicographic and lexicological ...

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PDF (9MB)
• (1997)
The preliminary chapters illustrate the research gap and account for the components of the framework. The integrative model incorporates a tripartite approach to discourse analysis--the formal (a textual analysis), empirical ...

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• (2006)
The discourse strategies of teams attempting the same task are compared and contrasted in this study. While a linguistic analysis of business student team meetings cannot provide a business assessment of a team's solution, ...

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• (1976)

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• (1965)

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• (2020-04-08)
Scarce ESL literacy research exists on low-literate, immigrant learners over the age of sixty. Research on this underrepresented population is critical for increasing their participation and success in ESL programs. This ...

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• (1971)

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• (1991)
This dissertation proposes a unification-based formalism to provide a common basis for a computational realization of different linguistic theories, GPSG, HPSG, and LFG in particular, both as a means of theory testing and ...

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• (1992)
This dissertation investigates the domain and mode of application of Mandarin third tone sandhi (TS henceforth), in terms of which it is intended to explore the characteristics of the interface between phonology and syntax.

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• (2017-11-29)
This thesis investigates the potential for using standing balance as a way to measure changes in cognitive load during language processing. Changes in standing balance are measured as subjects process vocabulary words, ...

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• (2005)
Finally, I conclude my study by suggesting that English language teachers deploy a contrastive analysis to help students understand how their ways of speaking differ from standard spoken English and other varieties of ...

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• (1992)
The Cross Cultural Speech Act Realization Project (CCSARP), the most ambitious speech act research to date, focused on western languages and cultures and employed questionnaires in data collection. The results showed ...

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• (1995)
Foot structure is essential to the prosodic structure of two unrelated Southeast Asian languages, Standard Thai and Kayah Li. Metrical foot structure is rarely used in the analysis of Southeast Asian languages. This in ...

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• (2016-11-22)
Modal auxiliary verbs, such as could', might', must', would', and others, have different readings depending on the context in which they occur (Kratzer 1981). The sentence `Jess could fry the fish' can mean that, in ...

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• (2013-05-24)
Researchers have made great strides in developing formal and biologically plausible models of the speech production and planning system.  Models based on oscillators have been successful in simulating gestural dynamics, ...

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• (1992)
The purpose of the study is to present a more satisfactory account of some phonological phenomena in English and Korean by employing the framework of moraic phonology.

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• (1976)

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# Definition:Increasing/Real Function

## Definition

Let $f$ be a real function.

Then $f$ is increasing if and only if:

$x \le y \implies \map f x \le \map f y$

## Also known as

Some sources refer to this as a non-decreasing real function, and use the term increasing real function for what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called a strictly increasing real function.

Some sources give this as monotonic increasing function.


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What is an ambient isotopy categorically?

Let $\mathcal T$ be a category of "nice" topological spaces (CW?) and continuous maps between them. We can construct the homotopy category $\mathrm{Ho}\mathcal{T}$ which gives for any two objects $X,Y$ the ($\infty$-groupoid of) homotopy classes between them $[X,Y]$.

Now hopefully restricting the morphisms of the previous category to embeddings (regular moonics, i.e. morphisms that are equalisers) we can get some sort of (sub)category of embeddings $\mathsf{Emb}(\mathcal{T})$ whose model structure can maybe be inherited giving a homotopy category $\mathrm{Ho}\mathsf{Emb}(\mathcal{T})$, where homotopy classes are really just isotopy classes.

Picking $S^1$ and $S^3$ from $\mathrm{Ho}\mathsf{Emb}(\mathcal{T})$ we get a category of knots $[S^1,S^3]$ which kind of sucks as they are all isotopic so its a pretty useless bunch.

Now I want to construct a category whose objects are knots, and morphisms are ambient isotopy classes. This would allow me to do something similar as above and actually get some interesting information out of this. However I am having a lot of trouble interpreting knot theory in this way:

1. This could be because there is something intrinsic about knot theory that makes it unsuseptable to categorical thinking, which would indicate inadaquacy of categorical lanugage in this instance. (I highly doubt this, I just don't think I am thinking hard enough).

2. I don't really fully understand knot theory.

I am going to assume it is (2.) that is my problem and hope that this question can help clear things up.

Is there a categorical/homotopy theoretic approach to knot theory like I outlined above? If so where can I find the literature?

I am essentially looking for a formulation of knot theory that looks like it came from nLab.

• The smooth embeddings of $S^1$ into $S^3$ are parameterized by a topological space. Its fundamental groupoid is probably your desired category. – Will Sawin Jul 6 '18 at 11:37
• While I agree with @WillSawin about which category you are looking for, I want to express a great deal of skepticism that you will be able to use $\infty$-categorical thinking to prove serious results about knot theory. Just because you have a hammer doesn't mean everything is a nail... – Andy Putman Jul 6 '18 at 20:41


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QUESTION

# SCI 228 Week 6 Quiz

This pack of SCI 228 Week 6 Quiz includes:

(TCO 1) All of the following may contribute to the development of bulimia EXCEPT:

(TCO 2) Consuming an excess of _______ calories in one week will result in a weight gain of one pound per week.

(TCO 3) What is the percentage of calories from fat for a piece of pie that contains 300 calories and 12 grams of fat?

(TCO 4) The best time to replenish glycogen stores is:

(TCO 5) Which of the following BEST describes an eating disorder?

(TCO 6) What percentage of individuals diagnosed with anorexia nervosa are women?

(TCO 7) Which of the following psychiatric disorders causes the most deaths among women?

(TCO 8) Which of the following BEST describes an episode of binge eating?

(TCO 9) Which of the following eating disorders is the most common among men?

(TCO 10) Currently, the best known treatment of eating disorders is:

Files: IT238 Web Systems Syllabus Set 1.zip
• @
Tutor has posted answer for $12.99. See answer's preview$12.99


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# The impact of two massive early accretion events in a Milky Way-like galaxy: repercussions for the buildup of the stellar disc and halo

Orkney, Matthew D. A.; Laporte, Chervin F. P.; Grand, Robert J. J.; Gómez, Facundo A.; van de Voort, Freeke; Marinacci, Federico; Fragkoudi, Francesca; Pakmor, Ruediger; Springel, Volker
Referencia bibliográfica

Monthly Notices of the Royal Astronomical Society

Fecha de publicación:
11
2022
Descripción
We identify and characterize a Milky Way-like realization from the Auriga simulations with two consecutive massive mergers $\sim 2$ Gyr apart at high redshift, comparable to the reported Kraken and Gaia-Sausage-Enceladus. The Kraken-like merger (z = 1.6, $M_{\rm Tot}=8\times 10^{10}\, \rm {M_{\odot }}$) is gas-rich, deposits most of its mass in the inner $10\,$ kpc, and is largely isotropic. The Sausage-like merger (z = 1.14, $M_{\rm Tot}=1\times 10^{11}\, \rm {M_{\odot }}$) leaves a more extended mass distribution at higher energies, and has a radially anisotropic distribution. For the higher-redshift merger, the stellar mass ratio of the satellite to host galaxy is high (1:3). As a result, the chemistry of the remnant is indistinguishable from contemporaneous in situ populations, making it challenging to identify through chemical abundances. This naturally explains why all abundance patterns attributed so far to Kraken are in fact fully consistent with the metal-poor in situ so-called Aurora population and thick disc. However, our model makes a falsifiable prediction: if the Milky Way underwent a gas-rich double merger at high redshift, then this should be imprinted on its star formation history with bursts about $\sim 2\,$ s apart. This may offer constraining power on the highest-redshift massive mergers.


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# How do you find all relative extrema for f(x) = 8/(x^2+2)?

Oct 11, 2015

See explanation section, below.

#### Explanation:

$f \left(x\right) = \frac{8}{{x}^{2} + 2}$

$f ' \left(x\right) = \frac{- 16 x}{{x}^{2} + 2} ^ 2$

$f ' \left(x\right)$ is never undefined and is $0$ only at $x = 0$.

So the only critical number is $0$.

The denominator of $f '$ is always positive, so the sign of $f '$ is the same as that of $- 16 x$, which is simply the opposite of the sign of $x$.

On $\left(- \infty , 0\right)$, $f ' \left(x\right) > 0$ and on $\left(0. \infty\right)$, $f ' \left(x\right) < 0$.

Therefore, $f \left(0\right) = 4$ is a local maximum.

There is a local maximum of $4$ (at $0$)