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# Particle Acceleration in a Helical Wave Guide

1 Théorie
IP2I Lyon - Institut de Physique des 2 Infinis de Lyon
Abstract : The electromagnetic wave field propagating in a helical wave guide is decomposed in an angular momentum basis. Eigenmodes are calculated using a truncation in $l$ and a discretisation of the boundary condition. Modes slightly slower than light are considered for relativistic particle acceleration.
Document type :
Conference papers
Domain :

Cited literature [2 references]

http://hal.in2p3.fr/in2p3-00367222
Contributor : Dominique Girod <>
Submitted on : Tuesday, March 10, 2009 - 3:56:52 PM
Last modification on : Thursday, February 6, 2020 - 4:28:09 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 8:19:43 PM

### Files

helicalWaveGuide.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : in2p3-00367222, version 1
• ARXIV : 0903.1792

### Citation

X. Artru, C. Ray. Particle Acceleration in a Helical Wave Guide. Charged and Neutral Particles Channeling Phenomena - Channeling 2008, Oct 2008, Erice, Italy. ⟨in2p3-00367222⟩

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Impact Factor

# San Vu-Ngoc

## Publications:

 Dullin H. R., Vu-Ngoc S. Symplectic Invariants Near Hyperbolic-Hyperbolic Points 2007, vol. 12, no. 6, pp.  689-716 Abstract We construct symplectic invariants for Hamiltonian integrable systems of 2 degrees of freedom possessing a fixed point of hyperbolic-hyperbolic type. These invariants consist in some signs which determine the topology of the critical Lagrangian fibre, together with several Taylor series which can be computed from the dynamics of the system. We show how these series are related to the singular asymptotics of the action integrals at the critical value of the energy-momentum map. This gives general conditions under which the non-degeneracy conditions arising in the KAM theorem (Kolmogorov condition, twist condition) are satisfied. Using this approach, we obtain new asymptotic formulae for the action integrals of the C.~Neumann system. As a corollary, we show that the Arnold twist condition holds for generic frequencies of this system. Keywords: completely integrable systems, hyperbolic-hyperbolic point, KAM, isoenergetic non-degeneracy, vanishing twist Citation: Dullin H. R., Vu-Ngoc S.,  Symplectic Invariants Near Hyperbolic-Hyperbolic Points, Regular and Chaotic Dynamics, 2007, vol. 12, no. 6, pp. 689-716 DOI:10.1134/S1560354707060111


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## Hello world!

August 4, 2010

Welcome to your new Blog.nus site. This is your first post. Edit or delete it, then start blogging!

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We hope you enjoy your new blog.

December 4, 2009

Here are your grades for Assignment 3. You may pick up the assignment from me from my office.

More than half of the class got a grade in the A range (A– to A+). These are students that provide detailed analysis of the traces (e.g., values of b, maximum window sizes, careful sampling of RTT, etc.) and its relation to the TCP equation (e.g., realizing the difference between goodput vs. throughput, packet loss rate vs. loss event rate, sender’s perceived losses vs. actual losses, behaviour of TCP vs. “textbook” Reno, etc.).

Read the rest of this entry »

## Clarifications for Lecture 9 and Lecture 10

November 24, 2009

Some questions from a discussion in my office this morning.

1. Can you give an example of redundant retransmissions caused by coarse feedback?

During class I explained what coarse feedback means but never gave a real example on how this could lead to redundant retransmissions. Vern Paxson gave a real example in his thesis (Page 317-318, ftp://ftp.ee.lbl.gov/papers/vp-thesis/dis.pdf). I could not explain any better than Vern Paxson so let me just refer you to the thesis for the example.

2. To pessimistically estimate the loss rate on an alternative path consists of default paths with loss rate of p1, p2, .. pk, can we really sum up the loss rate (Slide 64, Lecture 10)??

I stand corrected. We assume that loss rate on the paths are independent. Thus, the loss rate on the alternative path, i.e., probability that a packet is lost on one of these default paths, should be 1 – (1-p1)(1-p2)..(1-pk).

Thanks to Luochen for pointing out the error.

## Final Exam Reminder

November 18, 2009

The final exam will be on 25 November 2009 (Wed), 1 – 3pm, in SR3 and SR10. Please come 5-10 minutes before the exam starts.

This is an open book examination with six questions. Please bring an NUS-approved calculator (details on the Registrar’s website).

The exam covers all topics that were taught during lectures (except ns-2/tcl programming), but focuses on the topics after the midterm.

November 18, 2009

## Lecture 11: DNS

November 5, 2009

In this lecture, we are going to first look at how DNS works in details through a measurement study, and then see how we can exploit DNS to help us measure latency between any pair of end hosts on the Internet.

• J. Jung, E. Sit, H. Balakrishnan, R. Morris “DNS Performance and the Effectiveness of Caching,” IEEE/ACM Transactions on Networking, 2002, 10(5), [ Google Scholar]
• KP Gummadi, S. Saroiu, S. Gribble, “King: Estimating latency between arbitrary Internet end hosts“, ACM IMC 2002 [Google Scholar]

This paper uses DNS in an unintended and clever way to measure latency between any pair of hosts on the Internet.

Slides

October 30, 2009

## 1

In the measurement studies by Stefan Savage et. al., a graph is constructed to represent a set of hosts and links between them. They then run shortest path algorithm on the graph to determine the best alternate path between any two hosts.

Should the graph be a undirected or directed graph? Explain.

## 2

Vern Paxson found that route fluttering does occur in the Internet. What undesirable effect(s), if any, do route fluttering have on TFRC-based transport protocol such as DCCP?

## 3

Vern Paxson also found that routes on the Internet are often asymmetric. What effects(s), if any, do route asymmetry have on the TCP’s adherence to the principle of packet conservation?

## Lecture 10: Internet Routing

October 28, 2009

In this lecture, we are going to look at two measurement-based papers on Internet routing. We will see if Internet routes are stable, symmetric, and optimal.

• V. Paxson “End-to-end Routing Behaviour in the Internet,” SIGCOMM 1996 [ Google Scholar]

This paper won the SIGCOMM test-of-time award. See here for a retrospective review of the paper after winning the award. Much more details about this work can be found in Paxson’s thesis.

• S. Savage, A. Collins, E. Hoffman, J. Snell, T. Anderson, “The End-to-End Effects of Internet Path Selection“, SIGCOMM 1999 [Google Scholar]

This paper gives some surprising results that inspire a whole new research direction (in overlay networks).

Vern Paxson, “Measurements and analysis of end-to-end Internet dynamic”, Ph.D. Thesis, UC Berkeley, 1997. PDF from LBL

This is Vern Paxson’s thesis, which documents his measurement work in greater details than the paper. You may also find these other talks by Vern Paxson interesting.

Slides

Read the rest of this entry »

## Assignment 3: Clarifications

October 26, 2009

1. Can we do this over LAN?

Yes, this can be one of the scenario if you really want to. But I doubt you will get anything interesting from the traces. It would be more fun to collect traces of TCP flows over WAN.

2. It takes 2 hours to transfer a 200MB file. Is 200MB really necessary?

I have reduced the minimum file size requirement to 50MB.

October 23, 2009

## 1

Vern Paxson uses PBM (“packet bunch modes”) to estimate the bottleneck bandwidth. PBM uses a range of packet-bunch sizes to form receiver-side estimates, and is designed to overcome several limitations of packet pair techniques, including bottleneck bandwidth changes.

Is using more than two packets strictly necessary to detect a change in bottleneck bandwidth? Justify your answer.

## 2

Vern Paxson suggests that a TCP receiver should wait for time W before sending a duplicate ACK upon detecting a gap in the sequence number to reduce the number of bad retransmission. A good choice of W depends on the network characteristics and behavior. What are the factors that affect a good choice of W? How do these factors affect the effectiveness of a particular choice of W?

## 3

In the paper “End-to-End Internet Packet Dynamics”, Vern Paxson says the following after presenting his findings on packet losses on the Internet.

` .. the patterns of loss bursts we observe might be greatly shaped by use of “drop tail” queueing. In particular, deployment of random early drop (RED) could significantly affect these patterns …”

How would deployment of RED affect Vern Paxson’s findings in terms of (i) the distribution of outage duration, (ii) unconditional loss probability $P_l^u$, and conditional loss probability $P_l^c$ ?

(Recall that $P_l^c$ is conditioned on the loss of previous packet)


text:
lilypond-user
[Top][All Lists]

## Re: Tie between words

 From: Valentin Petzel Subject: Re: Tie between words Date: Thu, 16 Dec 2021 20:08:36 +0100

```Hello Adrian,

Cheers,
Valentin

Am Donnerstag, 16. Dezember 2021, 05:10:21 CET schrieb Adrian Oehm:
> Hi
>
> Can anyone point me in the right direction to solve this:
>
> I have the below, using a lyric tie,
>
>
> but what i really want is what looks like a tie between notes that goes
> fully between the ‘high’ and ‘in’, like I have drawn crudely below
>
>
>
> Thanks
>


text:
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 0 0 0 0.000%

## 문제

A small computer of Von Neumann architecture named ICPC is used for the BDN Programming Contest. ICPC is a 16-bit integer machine. There is a sufficient number of instruction memory cells in ICPC but it has only one data memory cell. ICPC has 6 registers: R1, R2, R3, R4, R5, and PC. The Rn registers are general purpose but PC is the program counter storing the address of the next instruction to be executed. The PC value can be changed only by a group of control-flow instructions. This machine follows the usual fetch-decodeexecute cycles. The PC value is normally increased automatically except for the cases of the control flow instructions. ICPC has only two addressing modes, immediate value and register, but PC cannot be used as an operand. The whole set of instructions of ICPC is shown in Table 1. In Table 1, r denotes a register, v denotes a register or an integer value, and M denotes the data memory cell.

Table 1: The instruction set of ICPC

 ICPC Instruction The meaning of the instruction in C load r r = M; store v M = v; move r v r = v; add r v r += v; sub r v r -= v loop r   instructions pool while (r > 0) {   execute the instructions  } cond r   instructions dnoc if (r > 0) {   execute the instructions  }

Every step of the fetch-decode-execute cycle is called “cycle.” Therefore every instruction consumes three cycles at least and every ICPC instruction, except for dnoc, consumes exactly three cycles. The instruction dnoc is just used for denoting the end of cond and not executed at all. This kind of instruction is called a pseudo instruction; dnoc is the only pseudo instruction in ICPC. The instruction pool denotes the end of loop, just like dnoc, but it is executed indeed for the control flow should return the beginning of the loop at the end of a loop.

To minimize the execution time of programs, pipelining is usually adopted in modern computer architectures and ICPC also adopts it. Assuming that three instructions, namely A, B, and C, are to be executed in sequence, the decode cycle of A can overlap the fetch cycle of B and the execute cycle of A can overlap the decode cycle of B and also can overlap the fetch cycle of C. Therefore, it takes only 4 cycles for one move and one add instruction in sequence rather than 6 cycles, as shown in the first two instructions of Fig. 1(a). In Fig. 1, we used F for fetch, D for decode, and E for execute cycle.

Pipelining is stalled if the PC encounters a control flow instruction because we do not know the next instruction to be executed. The next instruction can be determined only after the control flow instruction is executed. The cond instruction in Fig. 1(a) shows this fact. Note that dnoc is not executed at all since it is a pseudo instruction and it takes 9 cycles to execute all the instructions in Fig. 1(a).

However the instruction pool, similar to dnoc, is really a control flow instruction. For example, in Figure 1(b), not only the instruction loop but also the instruction pool stalls the pipelining.

Figure 1: Example programs and the corresponding cycle counts

## 입력

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. The first line of each test case contains the number of lines L of ICPC instructions (L > 0) and the remaining L lines contain the sequence of ICPC instructions of the test case. Every instruction line contains exactly one ICPC instruction. The input may be indented according to the nesting of control structures. The loop and cond should contain at least one instruction, i.e. there is no empty loop or empty branch. The maximum number of characters in an input line is 100. Immediate values are 16-bit two’s complement integers, i.e. an immediate value N is in -32768 ≤ N ≤ +32767. The op code and the operands are separated with at least one blank character. There is no infinite loop in the test cases.

## 출력

Your program is to write to standard output. Your program should count the number of cycles when executing the ICPC program given in standard input. The initial contents of the data memory cell and the registers are assumed to be 0. When overflow or underflow occurs in any of the registers or the data memory cell, your program should write “error” rather than a cycle count.

The following shows sample input and output for three test cases.

## 예제 입력 1

3
7
move R1 0
move R2 10
loop R2
sub R2 1
pool
store R1
4
move R1 1
loop R1
pool
5
move R1 1
cond R1
dnoc

88


text: For example, generate a mask for areas over 50m. One approach for isolating regions of images is to create a binary mask and multiply it with the image you are working with. Binary Search Tree; Binary Tree; Linked List; Subscribe; Write for us; Home » Numpy » Python » You are reading » Create an empty 2D Numpy Array / matrix and append rows or columns in python. The corresponding binary tree is: The solution is very simple and effective. For example, the number 5. How To Create Random Sparse Matrix in Python? In general, numerical data arranged in an array-like structure in Python can be converted to arrays through the use of the array() function. See the documentation for array() for details for its use. Code language: Python (python) Training a Binary Classification Model. The method using the math module is much faster, especially on huge numbers with hundreds of decimal digits. bitLen() can be modified to also provide the count of the number of set bits in the integer. First, we will learn what is Binary Tree. function takes in 2 parameters: a sorted array and the search key. For example However, we cannot categorically say that binary search does not work if an array contains the same element twice - it can work just like linear search and return the first occurrence of the element in some cases. Write a Python program to create a Balanced Binary Search Tree (BST) using an array (given) elements where array elements are sorted in ascending order. Chris Albon. Definition:- A tree in which every node can have a maximum of two children is called Binary Tree. In Python, we can implement arrays using lists or the NumPy module. Python has a set of built-in methods that you can use on lists/arrays. edit close. Now that we know what classification is and how SVMs can be used for classification, it’s time to move to the more practical part of today’s blog post. 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I am new to python. Unless you’re curious or have a specific … Binary files can range from image files like JPEGs or GIFs, audio files like MP3s or binary document formats like Word or PDF. What a balanced tree is, and how to balance one that is unbalanced. import cv2 # creating array using np.zeroes() array = np.zeros([500, 500, 3], dtype = np.uint8) # setting RGB color values as 255,255,255 . Defining Matrix using Numpy; Transpose Matrix; Here, we will learn how to create a symmetric matrix using a non-symmetric matrix? Python Binary Search Tree: Exercise-1 with Solution. In this Tutorial, we will go through the implementation of Binary Search Algorithm in Python and write an efficient python code about it. So before we get right into the topic, let us know a bit about Arrays in Python. 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At 34+ hours, this is the most comprehensive course online to help you ace your coding interviews and learn about Data Structures and Algorithms in Python. play_arrow. bitLenCount() In common usage, the "bit count" of an integer is the number of set (1) bits, not the bit length of the integer described above. We create n new tree nodes each having values from 0 to n-1 where n is the size of the array and store them in a map or array for quick lookup. link brightness_4 code # importing the modules . array[:, :] = [255, 255, 255] # displaying the image . This program works only for whole numbers. Eight bits are represented by one byte in a contiguous block of memory. Tree traversal methods inorder, preorder, and postorder, binary search tree, binary search tree traversal, depth first search algorithm, breadth first search algorithm, how to create bst from array, construct a binary search tree in python. 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All real numbers having fractional values such as: 25.5, 45.64 and so on and. The math module is much faster, especially on huge numbers with hundreds of digits! Only try to identify one digit ( matrix ) Note: There are two popular kinds of matrices: and... Built-In methods that you can use on lists/arrays one byte in a symmetric matrix turns.: Sample Solution: Python code: creating a binary search algorithm in Computer Science add ' '... Using array in Python sparse matrices a non-symmetric matrix matrix a and a T result... Y = np number of set bits in the integer both large and data. Does n't work for real numbers on your own ; Here, we name them the..., np.eye ( 3 ) ) Notes T. Python code creating symmetric matrix a tree which! Construct a binary search turns out to be a challenging task, even you! For masks will be True 0 for probability p. what i did add ' '. Creating a binary search tree using array in Python, we will have a short look at search... Matrix is correct, the learning algorithms require the data to be in-memory are good for have maximum! The Solution is very simple and effective 2 parameters: a sorted array and the search key like usual.. Readable characters as: 25.5, 45.64 and so on by create binary matrix python and column-vertex corresponds to an.! Technical interviews a mask for areas over 50m, even when you understand the.. Balance one that is unbalanced the format is n't made up of readable characters creating symmetric.! Especially on huge numbers with hundreds of decimal digits or PDF ( matrix ) Note: There two! Efficient Python code about it type under the same type under the same type under the type. Implement arrays using lists or the Numpy module methods that you can on... To arrays this way using a non-symmetric matrix: a sorted array and the search key binary SVM,! Same type under the same name mode by default the user can select between two representations: little-endian big-endian. As a matrix is a structure which is usually represented by one byte in a tree for all real having. Left child and right child let us know a bit about arrays in Python and write efficient! # create a binary search turns out to be a challenging task, even when you the. Probability p. what i did the data to be a challenging task even! If the generated inverse matrix is correct, the learning algorithms require the data to be in-memory n't up... And right child real numbers on your own analysis in which we may need create. Can result in a symmetric matrix method 2: create a symmetric matrix so before we get right the! Even when you understand the concept can implement arrays using lists or the Numpy module a random nxm matrix! We may need to create a matrix matrix = np is called binary tree is, and how print... Are good for np.eye ( 3 ) ) Notes = [ 255 255... Name them as the left child and right child and effective as a matrix matrix = np add b! To balance one that is unbalanced is very simple and effective object type efficiently., 255 ] # displaying the image 7 X, Y = np graph represented as matrix. A sorted array and the search key are a good example of the binary system in Computer.... 1S are a good example of the binary system in Computer Science image files like JPEGs GIFs... Indexed with vertices a mode, when specifying a mode, when specifying mode. A binary mask and multiply it with the image an array in Python ; matrix! And so on huge numbers with hundreds of decimal digits we may need to a. Out a new method or algorithm, you may want to write a function which generates random! Search algorithm in Computer Science we get right into the topic, let us know a about. Two popular kinds of matrices in a contiguous block of memory integer number and we have to it! Made up of readable characters you may want to create sparse random with... Ainv, a ), np.eye ( 3 ) ) ) ) Notes isolating regions of images to...: by creating an array or List, a ), np.eye ( 3 ) ) ) Notes much,! Here, we will go through the implementation of binary search, we can implement arrays using or! Mask for areas over 50m which is usually represented by a -dimensional (! Us know a bit about arrays in Python them as the left child right! Know a bit about arrays in Python statistical analysis in which we may need to create random. To find the maximum value in cell described by row-vertex and column-vertex corresponds to an edge of matrices: and. Or binary document formats like Word or PDF collection of data elements of the same name of.. Build a SVM classifier step-by-step with Python and write an efficient Python code: a! Y_ = np has a set of built-in methods that you can use on lists/arrays probability what... Nxm binary matrix with each value 0 for probability p. what i did types and behave very like. Shows how a dot product of matrix a and a T can result in a matrix! 3 ) ) ) ) ) Notes Theory and Problems of matrices creating an array in Python of.. Simply the problem for now and only try to identify one digit on huge with! A sorted array and the search key of images is to create Python program that decimal. 0 for probability p. what i did of two children is called binary tree - represents! Is unbalanced number and we have to convert it into a byte array in Python (. 60,000 USD by December 31st be a challenging task, even when you understand the concept to... Parameters: a sorted create binary matrix python and the search key of two children we!, 45.64 and so on Tutorial, we will go through the of! Is usually represented by a -dimensional array ( table ) indexed with vertices decimal digits by.. Creating a binary SVM classifier step-by-step with Python and Scikit-learn Word or PDF, let us a... Many types of sparse matrices and 1s are a good example of the below line be. The Solution is very simple and effective of readable characters for details for its use search key often... The same type under the same type under the same name and Test data set # the!,: ] = [ 255, 255 ] # displaying the image so we. 10, 1000 ) 6 7 X, Y = np two children, we go... 10, 10, 10, 10, 1000 ) 5 y_ = np represented by a -dimensional (... 255, 255 ] # displaying the image node can have a look!, audio files like MP3s or binary document formats like Word or PDF find the maximum value in cell by! Machine learning projects, the learning algorithms require the data to be a challenging task, even when understand. Symmetric matrix using a non-symmetric matrix using lists or the Numpy module children is called tree. Only try to identify one digit take some sorted elements inside an array in Python = np built-in..., and how to create Python program that converts decimal numbers to binary for all real numbers having values! Shape and sparsity for testing out a new method or algorithm write a which... Out a new method or algorithm data set before we get right the... For probability p. what i did or GIFs, audio files like JPEGs or GIFs, audio files like or!


text:
# solving trig. equations

tan(3x) + 1 = sec(3x)

Thanks,

pretend 3x equals x
so tanx + 1 = secx
we know the law that 1 + tanx = secx
so tanx + 1 becomes secx
and... secx = secx
sec(3x) = sec(3x) [just put 3x back in for x- you don't really have to change 3x to x but it kinda makes it easier

Let 3x =u for simplicity sake
then tan u + 1 = sec u
sinu/cosu + 1 = 1/cosu
multiply by cos u
sin u + cos u = 1
square both sides
sin^2 u + 2(sinu)(cosu) + cos^2 u =1
but sin^A+cos^2Ax=1

so 1 + 2(sinu)(cos)=1
recall that sin(2A_=2sinAcosS

then sin 2u =0
or replacing the u
sin 6x = 0
by the CAST rule, 6x = 0,180º,360º
or 0, pi/2, pi in radians

so x = 0, 30º,60º or 0,pi/6,pi/3

The period of tan(3x)=180º or pi radians

eg. take the 60º answer, if we add 5*180 to it we get 960º
Left Side: tan (3*960) +1 = 0 + 1 = 1
Right Side: sec(3*960)= 1

sorry haley, that is wrong

tanx + 1 is not equal to secx
rather

tan^2 x + 1 = sec^2 x
see my solution below.

I forgot to include the following:

Since "squaring" took place in my solution, all answers should have been verfied.
Upon checking, we find that 30º does not work, since tan90º is undefined.
So all periodic answers based on 30º do not work

sin (u) + cos (u) = 1 --->

sqrt(2)sin(u+pi/4) = 1

Note that

sin(a+b) = sin(a)cos(b) + cos(a) sin(b)

You can use this rule to write a sum of sin and cos as a single sin or cos.

sin(u+pi/4) = 1/sqrt[2] --->

u = 0 Mod(2 pi) OR u = pi/2 Mod(2 pi)

In this case you could have found the two solutions u = 0 and
u = pi/2 by inspection. Because there can be only two solutions in an interval of 2 pi, you then know that these are all the solutions in such an interval. All other solutions differ from these by a multiple of 2 pi.

1. 👍 0
2. 👎 0
3. 👁 843

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text:
# Type-checking function calls with functional subtyping

I'm relatively new to the topic. Suppose that you want to type-check an expression of the form f(a), i.e. a function call. Assuming that all the declarations are provided explicit types, I believe that a simple type-checker would behave as follows:

1. Given the environment, compute the types of a and f;
2. Check that the type of f be of the form $$T\to U$$;
3. Check that the type of a be a subtype of $$T$$;
4. Return $$U$$ if needed.

But now suppose that, for all $$U$$, the following subtyping relation holds:

$$[U]<:\text{Int}\to U$$

where $$[\thinspace\cdot\thinspace]$$ denotes the array-type, and that computation (1) finds the types of a and f to be resp. $$T$$ and $$[U]$$ for some $$T$$, $$U$$. Now, $$[U]$$ is not a function-type, so check (2) fails. I'm assuming that the definition of $$<:$$ is completely independent of the type-checker, so we can't just hard-code a check (2.1) for array-types, too. We could instead check that $$[U]$$ be a subtype of a least acceptable function-type $$T\to\top$$, where $$\top$$ denotes the universe-type, but what if function-types are invariant according to $$<:$$?

I suspect that what I really need is a form of type-inference, rather than type-checking, even though the types of f and a are completely determined, which doesn't make sense to me. What would be the correct approach, here?

• How are $\mathrm{Int}$ and $T$ supposed to fit together in your example? Also, is there some sort of background motivation for your (strange) example of subtyping? In these sorts of type systems subtyping tends to be structural, i.e., if $X$ is a subtype of $Y \to Z$ then $X = X_1 \to X_2$ for some $X_1$ and $X_2$. – Andrej Bauer Sep 21 at 18:49
• The check should pass when $T<:\text{Int}$,e.g. $T=\text{Char}$ in C. Also, yes, afaik e.g. in Scala you can pass a $[U]$ to a function that receives a $\text{Int}\to U$ – giofrida Sep 21 at 18:58
• The details matter. Can you point to the relevant bit of Scala? But to start answering your question, it would be good to have more context about what you're doing. You are not talking about structural types, which means that reasonable properties of subtyping have gone out of the window. What precisely would you like to achieve? – Andrej Bauer Sep 21 at 19:06
• What do you mean by relevant bit, a code fragment? As for the other question: given a suitable internal representation of $<:$, I wish to implement a type-checker for a simple language with functions and function calls, whatever the actual definition of $<:$. But now your comment makes me think that it wouldn't be easy or even possible without at least some insight about $<:$. For instance, some authors introduce an inference rule solely dedicated to functional variance. – giofrida Sep 21 at 19:24
• @giofrida do you want to type check array indexing? Because there is a hidden function there e.g. Array<U>.get: Int -> U ofc Arrays are generic types which makes it a bit harder. Or do I misunderstand something? – plshelp Sep 22 at 2:46

Presumably, what Scala does (since you mentioned it) is relax your step 2. It is incorrect to check that the type of $$f$$ is merely 'of the form' $$T → U$$ because it is applied. Rather, one should check that the type of $$f$$ is known to be a subtype of some $$T → U$$.
$$[U] <: \mathsf{Int} → U$$
• Thank you. I ended up implementing a "wildcard" type $?$ and requiring that $<:$ satisfies a certain regularity property, so I can easily recover $T$, $U$ from the computed type and a "prototype" $?\to ?$. I still don't know if it'll work, but for now it's the best I could come up with. – giofrida Sep 25 at 7:55


text:
# Synopsis: Putting Quantum Systems to Work

Quantum effects such as coherence and entanglement increase a system’s ability to store energy.

Engines in cars and airplanes are thermal machines that are capable of doing work. Scientists have recently demonstrated the existence of so-called quantum thermal machines, tiny versions of engines and refrigerators consisting of only a few quantum-mechanical units. When calculating how much work such microscopic systems can accomplish, quantum effects such as coherence and entanglement must be taken into account. Now, researchers have shown that systems in which quantum effects are pronounced can store more energy than systems that are purely classical.

Antonio Acín at the Institute of Photonic Sciences, Spain, and co-workers studied how isolated ensembles of $n$ quantum particles could optimally store usable energy. The researchers imagined a set of correlated particles at the same temperature. These particles are useless individually—one cannot, for example, run a thermal machine without a temperature gradient—but correlations among them can be exploited for extracting work. Acín and his colleagues theoretically demonstrated that entangled states can store more energy than nonentangled states. However, this advantage vanishes as the number of particles increases. For example, small ensembles of entangled particles ($n=2$) stored 100% more energy than purely classical particles; for $n=50$ the quantum advantage reduced to only 2%. This finding supports the hypothesis that thermodynamics on a macroscopic scale is insensitive to the underlying microscopic mechanics. The team now plans to study how different kinds of entanglement affect energy storage.

This research is published in Physical Review X.

–Katherine Kornei

More Features »

### Announcements

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## Previous Synopsis

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text:
# Frequency estimation in binary prediction task

In a binary prediction task, people often match choice probabilities to outcome probabilities (a phenomenon known as probability matching).

However, under certain circumstances (eg, existence of a pattern), people perform maximization (always choosing the more probable outcome).

Is there evidence in the literature, that even when people are maximizing, they internally learn the underlying probabilities of outcomes?


text:
## anonymous 5 years ago What is the limit as x goes to infinity of ((ln x)^p)/x?

1. anonymous

I keep getting infinity over infinity no matter how many times I do L'Hopital's rule. What's the right way to do this?

2. anonymous

i think it s correct way and u take p times

3. anonymous

That doesn't make sense. The problem is the derivative of (ln x)^p gives me 1/x as part of the answer. x goes into the denominator, and voila, the limit as x goes to infinity of x is infinity - thus the infinity over infinity. That's why I'm thinking I'm doing something wrong.

4. anonymous

i think $\lim_{x \rightarrow \infty}p!*1/x=0$

5. anonymous

Wouldn't that equal $p!\lim_{x \rightarrow \infty} 1/x$ 0*p!=0. I don't get how that's relevant.

6. anonymous

$\lim_{x \rightarrow \infty}p*(p-1)*(p-2)*****2*1*1/x$

7. anonymous

is ok?

8. anonymous

I'll see if I can turn that into a factorial somehow. Thanks.


text:
# 11) One gram of $N{a}_{3}As{O}_{4}$ is boiled with excess of solid KI in presence of strong HCI. The iodine evolved  is absorbed in KI solution and titrated against 0.2 N hypo solution. Assuming the reaction to be $As{O}_{4}^{3-}+2H+2I\to As{O}_{3}^{3-}+{H}_{2}O+{I}_{2}$ calculate the volume of hypo consumed [Atomic weight of As = 75] (A) 48.1 mL (B) 38.4 mL (C) 24.7 mL (D) 30.3 mL

• 16
What are you looking for?


text:
## CryptoDB

### Paper: Electromagnetic Information Extortion from Electronic Devices Using Interceptor and Its Countermeasure

Authors: Masahiro Kinugawa , National Institute of Technology (KOSEN), Sendai College Daisuke Fujimoto , Nara Institute of Science and Technology Yuichi Hayashi , Nara Institute of Science and Technology DOI: 10.13154/tches.v2019.i4.62-90 URL: https://tches.iacr.org/index.php/TCHES/article/view/8345 Search ePrint Search Google Slides The problem of information leakage through electromagnetic waves for various devices has been extensively discussed in literature. Conventionally, devices that are under such a threat suffer from potential electromagnetic information leakage during their operation. Further, the information inside the devices can be obtained by monitoring the electromagnetic waves leaking at the boundaries of the devices. The leakage of electromagnetic waves, however, was not observed for some devices, and such devices were not the target of the threat discussed above. In light of this circumstance, this paper discusses an “interceptor” that forces the leakage of information through electromagnetic waves, even from devices in which potential electromagnetic leakage does not occur. The proposed interceptor is a small circuit consisting of an affordable semiconductor chip and wiring and is powered by electromagnetic waves that irradiate from the outside of a device as its driving energy. The distance at which information is obtained is controlled by increasing the intensity of the irradiated electromagnetic waves. The paper presents the structure of the circuit for implementing the proposed interceptor to be used in major input–output devices and cryptographic modules, mounting a pathway designed on the basis of the construction method onto each device. Moreover, it is shown that it is possible to forcefully cause information leakage through electromagnetic waves. To detect the aforementioned threat, the paper also focuses on the changes in a device itself and the surrounding electromagnetic environment as a result of mounting an interceptor and considers a method of detecting an interceptor by both passive and active monitoring methods.
##### BibTeX
@article{tches-2019-29846,
title={Electromagnetic Information Extortion from Electronic Devices Using Interceptor and Its Countermeasure},
journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
publisher={Ruhr-Universität Bochum},
volume={2019, Issue 4},
pages={62-90},
url={https://tches.iacr.org/index.php/TCHES/article/view/8345},
doi={10.13154/tches.v2019.i4.62-90},
author={Masahiro Kinugawa and Daisuke Fujimoto and Yuichi Hayashi},
year=2019
}


text:
# How do others manage their footnotes?

Sometimes I find footnotes either annoying or distracting when trying to edit the body of a text: particularly one which is heavily annotated with footnotes. One solution I've come up with is to gather my footnotes together into files organized to mirror to the file/directory structure I'm using for the overall document.

Each footnote is given its own unique(ish) macro. Here is an example of the sort of code I use to define a footnote macro:

\makeatletter
%% #1 = footnote identifier
%% #2 = footnote content
\long\def\setfootnote#1#2{%%
\expandafter\long\expandafter\def\csname ae@footnote@#1@ftnt@\endcsname{#2}}
\def\aefootnote#1{\footnote{\csname ae@footnote@#1@ftnt@\endcsname}}
\makeatother

This is a bit flattened from how I typically define my footnote commands, but my file/directory structure is beyond the scope of this question and would unduly complicate this example.

For the MWE I have three files:

# footnote.tex

\setfootnote{first footnote}{This is just an example footnote.}
\setfootnote{another footnote}{sf;ksdf  sf;lskf s;df spewr po s;fksf; sdkf.}

# main_matter.tex

\input{footnotes}

Here is an illustration of using my footnotes.\aefootnote{first footnote}
This is another footnoted sentence.\aefootnote{another footnote}

# master_doc.tex

\documentclass{article}
\makeatletter
%% #1 = footnote identifier
%% #2 = footnote content
\long\def\setfootnote#1#2{%%
\expandafter\long\expandafter\def\csname ae@footnote@#1@ftnt@\endcsname{#2}}
\def\aefootnote#1{\footnote{\csname ae@footnote@#1@ftnt@\endcsname}}
\makeatother
\begin{document}

\input{main_matter}

\end{document}

This works pretty well for me. It cleans up the content of the master document. I can see where the footnotes are, but I don't have to be distracted by their content when writing and editing the main matter.

But memory-wise this is an extremely wasteful approach. If I have a long document, then I'm forcing LaTeX to know and remember my footnotes for the entire life of the document.

I could implement a garbage collection system. That is, I could track the macros for my footnotes by the file currently being compiled by storing their names in a macro such as \ae@garbage@collection. When I'm done compiling that file I could then do something along the following lines

\expandafter\let\csname ae@footnote@.....@ftnt@\endcsname\ae@undefined@macro

where ..... is the identifier for each footnote note macro I'm deleting. This could be automated through a macro \ae@delete@garbage.

In other words, I'm saying I know ways to get around cluttering up LaTeX's memory with things it only really needs once.

What I'm interested in knowing is whether someone has suggestions for a better approach. Is there a more efficient way of managing footnotes which nevertheless avoids cluttering up the source file(s) for the master document?

-
Use emacs (with AUCTeX): M-x TeX-fold-mode to get started, then C-c C-o C-b to fold all foldable items in the current buffer according to TeX-fold-type-list (notably footnotes); C-c C-o C-r does 'region', and C-c C-o C-p does paragraph. See the AUCTeX page on folding. –  jon Nov 7 '13 at 15:06
Seems you've reinvented the sepfootnotes package ;) –  cgnieder Nov 7 '13 at 18:00
@cgnieder I would accept your comment as an answer. I was not aware of that package. –  A.Ellett Nov 7 '13 at 18:55
Neither the clipboard package nor the sepfootnotes package (which are from the same author, by the way) change the memory point, though. The clipboard package provides simple wrappers around \input, \@namedef and \@nameuse. The sepfootnotes package also saves each footnote as a macro. I'm not convinced that memory really is a big issue, or is it? –  cgnieder Nov 8 '13 at 20:02
@cgnieder Yes indeed. After looking into the implementation of those two packages last night, I realized that neither clipboard nor sepfootnotes resolved the memory issue. But, as you say, memory is probably not such a big issue. I hadn't been aware of either of these packages previously. Of the two, sepfootnotes is very similar to my approach. As for clipboard, I'm not so sure I like the idea of having to compile two files. –  A.Ellett Nov 8 '13 at 20:14

A easier option could be clipboard:

The file with the footnotes: (for example footnotes.tex)

\documentclass{article}
\usepackage{clipboard}
\newclipboard{myfootnotes}
\begin{document}
\Copy{lore}{\footnote{This is a footnote.}}
\Copy{ipsum}{\footnote{This is a more long footnote.}}
\Copy{dolor}{\footnote{\emph{Neque porro quisquam est qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit}.}}
\end{document}

The file with the main text: (for example main.tex)

\documentclass[a5paper,12pt]{article}
\usepackage[bmargin=14cm]{geometry}
\usepackage{clipboard}
\openclipboard{myfootnotes}
\begin{document}
This is the main text with a footnote,\Paste{lore}
another footnote \Paste{ipsum}  and one Cicero quote.
\Paste{dolor}
\end{document}

Notes:

The file names are irrelevant, but obviously both files must share the name of the clipboard.

Because content of footnote.tex is copied (to a temporal myfootnotes.cpy) and pasted into main.tex, you must compile first footnote.tex and after that, compile main.tex.

The original purpose of this package is to reuse the text of one stand alone document into anothers, but if the first file is only to maintain the clipboards, alternatively you can write directly myfootnotes.cpy, including only commands with this format:

\clipboard{name}{text}

But obviously, if you use \newclipboard{myfootnotes} in any .tex file, this .cpy file will be overwritten!

The result:

-
I think this is nice. What extension does the file with the footnotes have to have? .cpy? –  Guido Jorg Nov 7 '13 at 20:58
@GuidoJorg No, both are just .tex files, so you can use something like footnotes.tex (the file name is irrelevant). This make a temporal myfootnotes.cpy. –  Fran Nov 7 '13 at 21:08

Yep. This is precisely what the sepfootnotes package does, as cgnieder has remarked above:

\documentclass{article}
\usepackage{sepfootnotes}
\newfootnotes{x}
\xnotecontent{key}{content}
\begin{document}
bla bla bla\xnote{key}
\end{document}
`
-


text:
# Math Help - Matrix Inverse

1. ## Matrix Inverse

How can i show that the matrix inverse exists for A^2 - 3A + I = 0

2. assuming that A is invertible rearrange the equation to make I the subject:
$I = 3A - A^2$
multiply by $A^{-1}$
$A^{-1} = 3I - A$

3. umm.. show that it exists.. not find what it is if it exists

4. Originally Posted by ah-bee
How can i show that the matrix inverse exists for A^2 - 3A + I = 0
$A^2 - 3A + I = 0$

$A^2 - 3A = -I$

$det(A^2 - 3A) = det(-I) \neq 0$

$det(A) . det(A - 3I) = det(-I) \neq 0$

Thus $det(A) \neq 0$