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# All Questions

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### Validity of authentication scheme?

Here's an authentication scheme I had in mind that combines the simplicity of HTTP Digest Authentication and the security of real crypto primitives. I have in mind the user-level authentication, ie ...
63 views

### AES multiple devices to server communication

I have multiple devices connecting to a server, whose communication needs to be encrypted. At the moment I have an AES library doing the job (possibly inadequately): I am using a database of keys on ...
93 views

### Protocol: Coin Flipping over phone

Protocol: Coin Flipping over telephone Hypothesis: Alice and Bob have agreed: a one to one function $f$ which is easy to compute $f(x)$ from $x$ and while given any value $f(x)$ it is nearly ...
43 views

### Malicious KGC attack in the identity-based authenticated key exchange protocol

There are two users $A$ and $B$ who are in different domain. Let's assume that $A\in KGC_1$ and $B\in KGC_2$. If they want to establish secure session, then they must run an identity-based ...
67 views

119 views

### Is it possible to perform a rudimentary asymmetric key encryption algorithm by hand?

I have at least three, distinct motivations for having a simple way to use asymmetric key encryption by hand or without modern computers. First, I was recently demonstrating to a 12-year-old how ...
135 views

### User-specified PBKDF2 password, salt, and iterations limits

For a decentralized login where a user is left to select the password, salt, and iterations, what minimums for each should be enforced? In other words, because none are ever stored by the ...
283 views

### Elliptic Curve based blind signature implementation

I want to use Elliptic Curve based blind signature scheme for my research. There is no proper implementation of ECC-based blind signatures. Can someone describe to me which things I need to follow ...
151 views

### RSA encryption and signature padding flaw

This is Oxford's computer security exam question: Suppose that Bob has published an RSA encryption key $ke$ (retaining in secret the corresponding decryption key $kd$), and Alice has published a ...
126 views

### Proxy re-encryption mod operations

I managed to implement the proxy re-encryption scheme from http://eprint.iacr.org/2009/189.pdf in Python 2.7, however I am having performance issues. As it is, I can run the algorithm for key sizes up ...
99 views

### How can I make a message into a blocks for NTRU?

I have more bits than the degree of the NTRU polynomial. For example: $x^{11}-1$ message: Hello (I am using ascii, 8 bits for 1 symbol) got: ...
46 views

### Common pitfalls of session key activation?

Assume that initiator $I$ and responder $R$ of a key agreement protocol have agreed on new symmetric session keys $K'_{auth}$ and $K'_{enc}$, e.g. by way of Diffie-Hellman and key derivation, possibly ...
102 views

### Can I decrypt the message having it encrypted with different keys?

I have some encrypted binary data I want to decrypt. I know nothing about it, but I can get it encrypted with as many different (random, unknown) symmetric keys as I want. The keys are long enough to ...
576 views

### HMAC-SHA1 vs HMAC-SHA256 for data storage

Reading the question “HMAC-SHA1 vs HMAC-SHA256”, I figured out that the known attacks on SHA1 don't apply to its HMAC version. So, HMAC-SHA1 is quite strong right now. In a protocol like SSL, if it ...
181 views

### implementing a cryptographic hash with a block cipher [duplicate]

How can a cryptographic hash function be implemented/created using the block cipher? I was wondering if we can use AES in cipher block chaining mode to implement it.
106 views

### Threshold signatures vs. certificate authority+voting verification

Perhaps a silly question, but I am wondering what the advantages are of threshold signatures. Let's consider the following two signature schemes: $(t,n)$-threshold signature with a trusted dealer, ...
428 views

### An example of Knapsack Cryptosystem cracks/attacks? [closed]

I have been studying papers on various ways to crack the knapsack cryptosystem, unfortunately the mathematics in these papers involves lattices and LLL which is over my head. The paper "New Attacks ...
80 views

### Reliability of a single-pass deniable authentication protocol?

I look for one-pass deniable authentication protocol with a short message payload for my project and find a solution: ...
167 views

### Rotation table for 8 round DES

I'm trying to implement DES from scratch using the NIST paper and the Wikipedia article on DES. I got 16 round DES done, but I can't seem to get 8 round DES working. I figure it's because I got the ...
69 views

### Separate TLS Client Write and Server Write Keys in AES-CCM Mode

I am designing a system that uses TLS-like handshaking on a resource-constrained embedded system. I have settled on AES-CCM mode for symmetric session encryption and authentication, allowing ...
45 views

### Delinearization in whitebox techniques

I'm reading through Chow et al.'s paper and Link et al.'s paper. There's a part I don't understand about Delinearization. They convert some steps of AES/DES into a Matrix, then divide the matrix in ...
245 views

### Is Encryption without knowing the input directly possible at all?

I know the question is rather unusual, but let me clarify what I'm searching for: There is one person, lets call her $Alice$. $Alice$ has $n$ plaintexts $t_1..t_n$ and $n$ public keys $pk_1..pk_n$ of ...
176 views

### Defending hybrid encryption schemes against padding oracle attacks

I intend to use a generic integrated/hybrid encryption scheme for transmitting information between a client and a server. Key encapsulation: a 128-bit symmetric key is generated and asymmetrically ...
96 views

### Obfuscating point-like functions

There are standard schemes for obfuscating a point function; I'm wondering if we know how to obfuscate a slight generalization of a point function. I'll elaborate more precisely. Definition 1. A ...
81 views

### Timing attacks against RSA, DH and AES

I have been reading about “Timing Attacks on RSA: Revealing Your Secrets through the Fourth Dimension” by Wing H. Wong. I was wondering if this attack is feasible while signing with RSA and, if yes, ...
183 views

### Sane implementations of Bitcoin cryptography routines w.r.t. side-channel attacks

Bitcoin uses SHA-256, Base58Check, ECDSA (Sep256k1) and RIPEMD-160 as the basis of its encryption (see this article for a short guide on how addresses are created). I would like to create an ...
58 views

### Why the same characteristics cannot be used to recover all FEAL4 keys

I am trying to understand how differential Cryptanalysis works. Here I read how to use differential cryptoanalysis for cracking FEAL4 cipher. The big gotcha with this process is that you cannot ...
86 views

### Is ecryptfs safe after unmounting but before turning off the computer

I've read that one of the vulnerabilites of ecryptfs is leaks to swap memory, and that the solution is to encrypt swap. But even if swap is encrypted, it's still open until I reboot. I've also read in ...
115 views

### encrypted file sharing protocol

I am trying to design a file exchange protocol for learning purposes, inspired by PGP, but fixing some of its shortcomings. Assuming the machine where the creation and decryption of the file happens ...
66 views

### Machine Learning with Encryption [duplicate]

Machine Learning is sometimes associated with cryptography. Many of such cross field studies have been majorly done in use of machine learning for cryptanalysis/decryption. I am interested in knowing ...
163 views

### File Encryption (EFS method)

I'm implementing (for learning purposes) a file encryptor, which uses the following method (from http://en.wikipedia.org/wiki/Encrypting_File_System). I have 3 kind of keys: RSA public/private, AES ...
318 views

### Non-standard signature security definition conforming ed25519 malleability

According to the paper “High-speed high-security signatures”… Malleability. We also see no relevance of "malleability" to the standard definition of signature security. Aside from the example, ...
123 views

### Gallant-Lambert-Vanstone method

I am experimenting with the GLV method but cannot manage to get the right results according to the literature. I managed to find lambda, beta, split $K$ into $k_1$ and $k_2$ etc. for the curve I'm ...
62 views

### How to generate initial vectors during DPA attack on stream cipher in real life?

I was trying to understand the procedure of the DPA attack on Stream cipher (like Mickey-128). I learned that, the attacker need to build hypothetical power consumption matrix with different initial ...
153 views

### Storing password or derived key in keychain?

Currently I am developing an application that stores and reads encrypted data. The data is encrypted with AES and the actual AES key is derived from the users password (and some nonce) with PBKDF2 ...
173 views

### Which gives better deterministic encryption SIV or Plain ECB mode?

Lets say , if we encrypt a plain text message $msg$ with key $key$ in below two ways. Which is the below would give better deterministic encryption and why ? AES-ECB($key$ , $msg$) SIV($key$, NIL , ...
154 views

### Known vulnerabilities in (EC-)KCDSA

Does anybody know if there's known vulnerabilities in KCDSA/EC-KCDSA? I have been researching for the past few hours and I haven't found anything. Wikipedia has very limited amount of information and ...
76 views

### For $e(g, d) = c$, can we compute $d$, given others

Given $$e(g, d) = c$$ where, $e$ is bilinear pairing function chosen by the user/attacker, the values of $g$ and $c$ are known $g, d ∈ \mathbb{G}_1$ , $c$ depends upon the $e$ can we somehow ...
137 views

### On the Definition of a PRG and a CSPRG

I've been looking at the definition of a PRG, here. This is a broader notion than a cryptographically secure PRG ("CSPRG"), which is described here. I am realizing that I am very confused by this ...
98 views

### /dev/random only needed for key generation / CPU pattern encryption

Consider the following scenarios: using OpenSSL to encrypt a file with Rijndael-256 using LUKS to encrypt a hard-drive that is used every day Exactly when is entropy from ...
210 views

### One-Time-Pad with key-reuse: Faster way of decrypting?

I know there are already of few questions about this and I'm working with the advices that were given but I still doubt my approach is the fastest, so I'd really appreciate if you helped me find a ...
77 views

### How do you distribute secret shares without knowing who to first distribute them to?

Figure 1 on page 1249 of the “Multiparty Computation Secure Against Continual Memory Leakage” paper shows $m$ committees are elected in step 1 and then later in step 3 are each given a secret share. ...
81 views

### Using HMAC to secure a “widget”

Let's say I have a web "widget" that a customer could include on their website. They would include the widget by adding an iframe that points to a URL on my site. I want to ensure that my widget can ...
340 views

### Hierarchical Encryption

Is there a way to setup a hierarchical encryption using public key encryption? Let's say a higher level user can decrypt messages encrypted by lower level users. Is that possible? I guess it is only ...
65 views

### A confusion about linear span of modified de Bruijn sequence

Recently i'm reading "Cryptographically Strong de Bruijn Sequences with Large Periods" . In the section 2 2.1 Basic Denitions and Properties , property 1 says that ...
106 views

### When do I need to renew keys for Salsa20 or HMAC?

I currently have a system which uses two keys sourced from a single key subjected to HKDF. One key is used in the Salsa20 stream ...
135 views

### Rabin/RSA four possible messages?

Given this encryption method: $$f_{N,e} : Z^{*}_{N} \to QR(N)^{*};\quad f_{N,e}(x) = x ^{2e} \bmod N$$ I need to show that, for any $x_{0} \in Z^{*}_{N}$, there are four elements $x \in Z^{*}_{N}$ ...
I am actually preparing for a cryptography exam, and I found a question asked by the professor in the class, below are the lines that I copied from the slide : Example: Let $Ek$ be the encryption ...
I know a protocol for bit commitment using regular OT (Bob has 1/2 chance of learning the bit Alice transferred to him) which goes like this: COMMITMENT PHASE Alice chooses a bit $b$ For ...


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# Laplace transform to solve a nonhomogeneous equation

1. May 27, 2016

### victor77

Mod note: Moved from a Homework section
can i use the Laplace transform to solve a nonhomogeneous equation if
i have these Initial condition s(x) and s(-x)

Last edited by a moderator: May 27, 2016
2. May 28, 2016

### BvU

Hi,
A first order differential equation only needs one initial condition, so the two you have might contradict each other.
A second order needs two. One per differential. So if you have two for the differentiation wrt x only, you are back to the previous problem. And you still don't have anything for ${d\over dx}({d\over dx})$

3. May 30, 2016

### matematikawan

Looks like you have a boundary value problem not initial value problem. If your DE is a linear constant coefficient, I think you still can solve it with Laplace transform.

4. Jun 12, 2016

### MidgetDwarf

You have to use power series solutions, if the coefficients are non constant. This is just a guess, because you have not posted the DE you have questions on.

format: plain


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# LSA/UL "Tundra" Tire request for advice

### Help Support HomeBuiltAirplanes.com:

#### Victor Bravo

I have a Kolb Firestar that I'm trying to get set up for off-airport fun, "extreme STOL" as they call it now. NOT "real" bush flying, which involves carrying people and/or cargo. Just "dirt bike in the desert" stuff for fun. I want to do all that fun stuff the guys with Super Cubs do in those wild youtube videos, but I don't have $250K to do it. Didn't even have 10% of that money to play with I just put a much taller landing gear on it to get the nose up for better AoA. It will have VG's, and it has a 60HP HKS engine with a ground adjustable propeller. Will be operated as a single seat aircraft, no need to use the laughable "rear seat" that would barely fit my Dachshund. The airplane came with Azusa Tri-Star aluminum wheels 6 inch by 4 inches wide. I just got a set of Tracy O'Brien hydraulic brakes for it. I had planned to put the new Desser Tire light aircraft "tundra" tire on it, which is an 8.00 x 6 tire with an oversize outside diameter of 21 inches. One or two of the guys on the Kolb list mentioned that they had problems with this tire and wheel combination, the tire spinning on the rim, shearing off the valve stem, etc. The subject of "rim screws" or "tire screws" came up. Apparently you drill holes in the wheel, and put in sheet metal screws so that the sharp point goes into the thick part of the tire "bead", which resists the shear loads when the tire tries to rotate on the wheel. Now drilling a hole through an aircraft wheel rim... creating stress risers and crack initiators... then continuing to drill right into your !*#&*% tire... sounds crazy to me. But JEGS sells a kit for this, and other automotive and off-road people appear to be doing this all the time. My instinct as a mechanic tells me that if you did want to run a screw through your aluminum wheel you'd at least want to use a tapped hole and a machine screw instead of just gorilla-twisting a sharp sheet metal screw through it. Does anyone on HBA have experience and wisdom with this? Can I do this with confidence, or do I create a high probability of cracking my wheels? How does this affect changing your tires, or servicing the wheels, bearings, etc? #### Mcmark ##### Well-Known Member Bill, I have done it automotive/racing applications, but never for aircraft. I have broken off one in a wheel slick combo. Might be better off using a short self tapping screw with the "drill" portion just into the tire. I don't think it will take much to keep them in place, if they have enough air in them. That's the "rub" isn't it? Puns, the lowest form of humor! YMMV Mark #### blane.c ##### Well-Known Member HBA Supporter I have a Kolb Firestar that I'm trying to get set up for off-airport fun, "extreme STOL" as they call it now. NOT "real" bush flying, which involves carrying people and/or cargo. Just "dirt bike in the desert" stuff for fun. I want to do all that fun stuff the guys with Super Cubs do in those wild youtube videos, but I don't have$250K to do it. Didn't even have 10% of that money to play with

I just put a much taller landing gear on it to get the nose up for better AoA. It will have VG's, and it has a 60HP HKS engine with a ground adjustable propeller. Will be operated as a single seat aircraft, no need to use the laughable "rear seat" that would barely fit my Dachshund.

The airplane came with Azusa Tri-Star aluminum wheels 6 inch by 4 inches wide. I just got a set of Tracy O'Brien hydraulic brakes for it.

I had planned to put the new Desser Tire light aircraft "tundra" tire on it, which is an 8.00 x 6 tire with an oversize outside diameter of 21 inches. One or two of the guys on the Kolb list mentioned that they had problems with this tire and wheel combination, the tire spinning on the rim, shearing off the valve stem, etc.

The subject of "rim screws" or "tire screws" came up. Apparently you drill holes in the wheel, and put in sheet metal screws so that the sharp point goes into the thick part of the tire "bead", which resists the shear loads when the tire tries to rotate on the wheel.

Now drilling a hole through an aircraft wheel rim... creating stress risers and crack initiators... then continuing to drill right into your !*#&*% tire... sounds crazy to me. But JEGS sells a kit for this, and other automotive and off-road people appear to be doing this all the time.

My instinct as a mechanic tells me that if you did want to run a screw through your aluminum wheel you'd at least want to use a tapped hole and a machine screw instead of just gorilla-twisting a sharp sheet metal screw through it.

Does anyone on HBA have experience and wisdom with this? Can I do this with confidence, or do I create a high probability of cracking my wheels? How does this affect changing your tires, or servicing the wheels, bearings, etc?
"TUNDRA TIRES" do not use inner tubes. The valve stem is in the sidewall of the tire. The belly of the tire is "rubber-ed" from sidewall to sidewall. This is so it can rotate around the rim without losing air pressure.

#### Victor Bravo

##### Well-Known Member
"TUNDRA TIRES" do not use inner tubes. The valve stem is in the sidewall of the tire. The belly of the tire is "rubber-ed" from sidewall to sidewall. This is so it can rotate around the rim without losing air pressure.
Uhhh, well... yes, uhhh, but upholding the technically correct definition of "Tundra Tire" is not quite important enough to pay 10 times as much as an incorrectly labeled tube type tire of similar diameter

Desser's 21 inch tire is \$110, and the Airstreak is a grand, and I do need two of them but I don't need the TSO.

I did not know that the tire was airtight by itself without even be ing installed on a wheel. Wow!

#### blane.c

##### Well-Known Member
HBA Supporter
I am having trouble choking on the price of them. I remember when I ran them on the cub I was shocked then to (it is starting to come back to me)
We talked about it back then. It is not a big deal how it is done really, and felt you could modify any tire you wanted to do the same thing, just vulcanize in a belly and a valve stem. It helps if you have seen a real one first. The man who originally made them did them in his garage I believe I was told. And having had a pair I believe it. They are big not high tech.

The screws in the sidewall trick works to a limited degree then they just score the tire bead as it rotates and shears off the valve stem.

#### Victor Bravo

##### Well-Known Member
If the screws are really not that good, what do you think I can do to not spin the valve stem off while running low pressure on larger tires?

#### Daleandee

##### Well-Known Member
I had planned to put the new Desser Tire light aircraft "tundra" tire on it, which is an 8.00 x 6 tire with an oversize outside diameter of 21 inches. One or two of the guys on the Kolb list mentioned that they had problems with this tire and wheel combination, the tire spinning on the rim, shearing off the valve stem, etc.
You may be solving a problem you don't have. If it's a concern for "one or two of the guys" it may be their technique rather than the combination itself. Still I get that you want to do all you can to avoid that scenario. Perhaps a bit higher pressure and some bead sealer will do the trick. Some suggest using something like Gorilla Glue but I can't go there as at some point you have to remove them. :ermm:

Dunno if this helps at all ...

Dale
N319WF

#### Victor Bravo

##### Well-Known Member
No, it's hard enough to separate the tire from the wheel without glue. I tried removing the small tire from my Azusa wheel, and I realized I could not do it by hand. Next stop... wooden block and sledgehammer

#### Daleandee

##### Well-Known Member
No, it's hard enough to separate the tire from the wheel without glue. I tried removing the small tire from my Azusa wheel, and I realized I could not do it by hand. Next stop... wooden block and sledgehammer
Yep ... sometimes a "C" clamp will find its way onto the work bench when changing tires ...

Dale
N319WF

#### TFF

##### Well-Known Member
Racing classes, where screws are not allowed, glue the bead. Low pressure, you will either have to glue or screw the bead and still be ready with some way to inflate it if you knock it off like CO2 cartriges or pump and rachet strap. Not umless you got some bead lock rims. Ouch for one piece rims. Valve stem a whole different problem. I would have thought proper Cub tires would give you similar performance at you weight. Those big wheels are not light.

#### pictsidhe

##### Well-Known Member
If I was going to tundra an ultralight, I'd have a look at cheap riding mower tyres, usually tubeless and fairly light for the size. ATV tires are usually heavier. Some off road motorcycles use tyre bolts. These are basically clamps to firmly hold tyre beads to the rim. Sometimes several are used.

#### blane.c

##### Well-Known Member
HBA Supporter
If the screws are really not that good, what do you think I can do to not spin the valve stem off while running low pressure on larger tires?
The Super Cubs operating "light" were going in and out of around 100 feet and weighed around 1200lbs all up (pilot, fuel, fishing equipment, etc.) and the ones working heavy into 300 to 400 feet were 2200lbs or more. When you are trying to stop over a ton in 300 feet and stand on the brakes if the tire slides around the rim a bit, it is like a low tech. computer assisted braking in a sense and worked empirically. A lot of ideas were tried over several decades and so some things were hit on over time that just worked. In order to not slip the tires, you have to have less force acting on them, so the way to make screws in the the rim work is to not try to land as much weight as short.

#### Victor Bravo

##### Well-Known Member
you have to have less force acting on them, so the way to make screws in the the rim work is to not try to land as much weight as short.
Well, that's precisely the law of physics that I'm trying to outfox

Going on a diet would be too... simple... and just too ordinary for a man of my intellect :whistle:

#### blane.c

##### Well-Known Member
HBA Supporter
Well, that's precisely the law of physics that I'm trying to outfox

Going on a diet would be too... simple... and just too ordinary for a man of my intellect :whistle:
There was some experimentation ... with replacing the wheel with a yoke on the axle. The yoke had a minimum of three arms and each arm had a small diameter wheel, when the lead wheel hit something the top wheel rotated into lead. I am not sure if they had brakes or how.

I know people have had success with the screw in the rim thing they went about it scientific. They calculated were to put the holes and they did not use screws they threaded the holes and they used little machine screws/bolts. They may have pre-drilled the tire as well for all the little machine screws I would have, just prep everything and mount the tire after drilling the pilot holes for tapping the threads in the rim and put a stop on the drill bit for how deep you want to go in the bead and go to it, then you can tap the tire bead too. This will work until the tire slips on the wheel once, which may be never depending on how well it is done and what abuse is actually put on it. Some red locktite is a good idea until you have to heat the wheel/tire to 500 degrees to get the screws out, but they probably won't move until then.

#### pictsidhe

##### Well-Known Member
Drilling the bead seems a bad idea to me. Why not rim locks? Well proven to stop tyres spinning on rims, not going to damage the bead. The bad is they can be a royal PITA to get in place.

#### Battson

##### Well-Known Member
Yes, I've done what you describe in the OP with my Goodyear tires and flown hundreds of hours off-airport. It works 100% and it's a fairly common solution to this problem.

Carefully drill the holes right through without damaging the existing threads. Tap them right through, remember proper cutting fluid is your friend with small delicate taps, and don't rush - back out the tap a 1/2 turn often, to break the swarf clear. Remove all sharp edges and burrs afterwards. Measure the bead thickness. Sharpen the necessary screws and check the length is right for your tires / bead thickness, don't go too deep into the bead. Even just 1/4" is deep enough. Assemble and enjoy. You also want to paint some lines on your tires, so you can see if things DO move; trust but verify.

More details and instructional photos here:


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# How rude is “Quatsch!”?

I've seen Quatsch! translated as Bullshit, which I was fine with as I had only heard it used among friends. Today, a university teacher used the Q-word in response to a student's serious suggestion in a somewhat professional setting.

How rude is Quatsch?

• @jae not necessarily. Imagine a student expressing the opinion that you should parse HTML using regular expressions for example. Or something else that is blatantly untrue, or an often-misquoted urban legend. Depending on the tone, "Quatsch" can then be just a very straightforward dismissal - but not necessarily rude. – Pekka 웃 May 24 '11 at 22:16
• I would usually translate "bullshit" to "Schwachsinn". – balpha May 25 '11 at 8:10
• So would Quatsch! be more akin to Crap! or Bullcrap!, perhaps? – Kyralessa Jun 2 '11 at 3:03
• I regurlarly use “Nee, Quatsch!” in front of students, however always because I said something stupid right before (e.g. “33 weniger 24 ist 8... Quatsch! 9!”). I wouldn't do it if I thought it'd be rude. – cgnieder Apr 26 '12 at 18:52
• is more like nonsense than bullshit. – user2614 Mar 6 '13 at 22:11

Quatsch is not vulgar at all and can be used in normal everyday speech to denote "nonsense":

Kinder machen Quatsch. (The children fool around in a harmless and funny way, e.g. making faces.)

But replying with "Quatsch!" might be perceived as offensive in the same way as "Nonsense!" would be in English - depending on the tone, facial expression and other situational factors.

Edit: If you're in Bavaria or in Austria, you could use the equivalent expression "Schmarrn!".

• +1 for “nonsense”, that’s actually a very good translation! – poke May 24 '11 at 21:06
• I would like to emphasize on the relevance of the tone. Quatsch itself is more or less inoffensive, but using a loud and angry tone can make it quite offensive. That's probably quiet similar to the English nonsense. – Koraktor May 24 '11 at 21:21
• My grandmother used to become angry when I said "Quatsch" to her. The term was/is perceived as much more offensive by older people. – Tomalak May 25 '11 at 11:54
• +1 for Schmarrn :) ! – Sebastian Jun 1 '11 at 11:57
• In British English, I think "rubbish" would be more common than "nonsense"; but with that word too, the offensiveness depends on how you say it. – Nick Dixon Jun 3 '11 at 10:42

Quatsch is not as strong as Bullshit.

In Germany you can use Ach, Quatsch for example if someone tells you some news you can hardly believe, and it won't be offensive at all. You may not want to use it in a very formal context.

• true, a tiny little "ach" before makes it much less offensive. :) – ladybug May 25 '11 at 12:35

Quatsch states that something is nonsense. In your described situation, it is not appropriate to say this to a student but it is not offensive.

It is the informal way to say: "This obviously does not make sense".

Welcome to the university, where (like it or not) students' 'serious suggestions' are often utter bullshit, or rubbish, or what have you, and where professors (like it or not) are tasked with the responsibility not to be polite, but to formulate and express coherent, accurate thought.

Also, no, it doesn't mean 'bullshit.' It is more like saying, 'That's absurd!'

## protected by Wrzlprmft♦Nov 20 '14 at 15:16

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?


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# Computation Workshop Solution Checker

## The Fibonacci Sequence

The sequence $$1, 1, 2, 3, 5, \ldots$$ is called the Fibonacci Sequence. It is the sequence $$f(1)$$, $$f(2)$$, $$f(3)$$, $$f(4)$$, $$\ldots$$ defined by

• $$f(1) = 1$$,
• $$f(2) = 1$$, and
• $$f(n + 2) = f(n + 1) + f(n)$$ for all $$n \ge 1$$.

So for example $$f(12) = 144$$. So the first two digits of $$f(12)$$ are $$14$$ and the last two digits of $$f(12)$$ are $$44$$.

Part A What are the first three digits of $$f(123)$$? What are the first six digits of $$f(123456)$$? What are the last six digits of $$f(123456)$$? What are the first nine digits of $$f(123456789)$$? What are the last nine digits of $$f(123456789)$$?

## Digital Self Powers

The self-power of a number $$x$$ is defined to be $$x^x$$. The digital-self-power of a number is defined to be the sum of the self powers of all of its digits (in base 10). For example, the digital-self-power of $$402$$ is $$4^4 + 0^0 + 2^2 = 256 + 1 + 4 = 261$$.

Part A Find an integer which is one more than its digital-self-power. Find an integer (greater than 1) which equals its digital-self-power Find a positive integer which is one less than its digital-self-power Find the largest integer which is at most one away from its digital-self-power


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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Ivory Billed Woodpecker ##### This topic has expert replies ### GMAT/MBA Expert GMAT Instructor Posts: 2193 Joined: 22 Feb 2010 Location: Vermont and Boston, MA Thanked: 1186 times Followed by:512 members GMAT Score:770 ### Ivory Billed Woodpecker by David@VeritasPrep » Thu Sep 02, 2010 9:04 am "The Ivory-billed Woodpecker has been considered extinct for the past several decades. Recently, researchers claim to have found a pair of Ivory-bills in Arkansas. Their best evidence is video that shows a large woodpecker flying away from the camera. The bird has the characteristic large white patches on the trailing edge of the wings. This is one of the factors that distinguishes Ivory-bills from the closely-related Pileated Woodpecker. However, skeptics of the discovery argue that some abnormal Pileated birds can have extra white on the wing and that the bird in the video is most likely an abnormal Pileated. They conclude that the evidence offered for the existence of a living Ivory-billed woodpecker has been overstated and that the species is probably still extinct." Which of the following, if true, would most strengthen the skeptics' conclusion? A) Before this discovery, the last reported Ivory-billed woodpecker was seen in Louisiana, not in Arkansas. B) In the area where the video was shot, researchers listened for the distinctive "double-tap" drumming sound made exclusively by Ivory-billed woodpeckers, but did not hear the sound. C) The first person to see the reported Ivory-billed woodpecker and the photographer who shot the footage were not scientists. D) Of the five key features used to identify Ivory-billed woodpeckers, only the extra white on the wing was seen and this feature also occurs on abnormal Pileated woodpeckers. E) The bird in the video is clearly seen using the motion of the wing that is characteristic of both the Ivory-billed and the Pileated woodpecker. Source GMAT for Dummies, Wiley, 2006. Here is one of the first Critical Reasoning questions that I wrote back in 2005 while contributing to the "GMAT for Dummies" book. I did not see it posted anywhere yet and that makes it almost as good as new. I think those who are very serious about the GMAT are probably not familiar with this book as it is not nearly as in-depth as the other materials we use... However, there are some questions in there that most people have not seen, so why not try this one? Good luck! Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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by FightWithGMAT » Thu Sep 02, 2010 9:46 am
David@VeritasPrep wrote:"The Ivory-billed Woodpecker has been considered extinct for the past several decades. Recently, researchers claim to have found a pair of Ivory-bills in Arkansas. Their best evidence is video that shows a large woodpecker flying away from the camera. The bird has the characteristic large white patches on the trailing edge of the wings. This is one of the factors that distinguishes Ivory-bills from the closely-related Pileated Woodpecker. However, skeptics of the discovery argue that some abnormal Pileated birds can have extra white on the wing and that the bird in the video is most likely an abnormal Pileated. They conclude that the evidence offered for the existence of a living Ivory-billed woodpecker has been overstated and that the species is probably still extinct."

Which of the following, if true, would most strengthen the skeptics' conclusion?

A) Before this discovery, the last reported Ivory-billed woodpecker was seen in Louisiana, not in Arkansas.

B) In the area where the video was shot, researchers listened for the distinctive "double-tap" drumming sound made exclusively by Ivory-billed woodpeckers, but did not hear the sound.

C) The first person to see the reported Ivory-billed woodpecker and the photographer who shot the footage were not scientists.

D) Of the five key features used to identify Ivory-billed woodpeckers, only the extra white on the wing was seen and this feature also occurs on abnormal Pileated woodpeckers.

E) The bird in the video is clearly seen using the motion of the wing that is characteristic of both the Ivory-billed and the Pileated woodpecker.

Source GMAT for Dummies, Wiley, 2006.

Here is one of the first Critical Reasoning questions that I wrote back in 2005 while contributing to the "GMAT for Dummies" book. I did not see it posted anywhere yet and that makes it almost as good as new. I think those who are very serious about the GMAT are probably not familiar with this book as it is not nearly as in-depth as the other materials we use... However, there are some questions in there that most people have not seen, so why not try this one? Good luck!
I am confused between D and E.

IMO E

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by beatthegmatinsept » Thu Sep 02, 2010 9:57 am
I'd go with D.
Being defeated is often only a temporary condition. Giving up is what makes it permanent.

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by gsinghal » Thu Sep 02, 2010 10:00 am
IMO D

because out of the 5 characteristics only the white wing was seen that can occur on both the species of woodpecker. So, ultimately it states that the bird seen was not the Ivory Woodpecker.

wats d OA??

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by BlindVision » Thu Sep 02, 2010 10:20 am
OA = B
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by David@VeritasPrep » Thu Sep 02, 2010 11:05 am
The OA is D.

The conclusion is that "the evidence offered ....has been overstated" and therefore the "species is probably still extinct."

Answer choice D goes to directly to the evidence (as gsinghal said in a prior post). The only solid evidence in favor of the ivory-billed is presence of the large white wing patches and answer choice D makes this evidence much less decisive by indicating that the large patches can be on pileated as well.

Choice B is deceptive because hearing the sound would make very good evidence, but not hearing the sound does not undermine the visual evidence like choice D does.
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Save $100 off any live Veritas Prep GMAT Course Legendary Member Posts: 1119 Joined: 07 May 2010 Thanked: 29 times Followed by:3 members by diebeatsthegmat » Thu Sep 02, 2010 11:16 pm David@VeritasPrep wrote:The OA is D. The conclusion is that "the evidence offered ....has been overstated" and therefore the "species is probably still extinct." Answer choice D goes to directly to the evidence (as gsinghal said in a prior post). The only solid evidence in favor of the ivory-billed is presence of the large white wing patches and answer choice D makes this evidence much less decisive by indicating that the large patches can be on pileated as well. Choice B is deceptive because hearing the sound would make very good evidence, but not hearing the sound does not undermine the visual evidence like choice D does. David, i always like your CR, but do you think its a bit long for a real test CR? if the real CR in test are as long as the CR you posted, i am a bit worried ### GMAT/MBA Expert GMAT Instructor Posts: 2193 Joined: 22 Feb 2010 Location: Vermont and Boston, MA Thanked: 1186 times Followed by:512 members GMAT Score:770 by David@VeritasPrep » Fri Sep 03, 2010 2:55 am It is on the long side to be sure. If they were all this long you might have some concerns but you can handle one or two that are this length. I also think that this one makes up for the length by being fairly understandable. For comparison, question 82 (of 82) in the 1st edition of the OG verbal review (page 142) is more than 30 words longer than "ivory-billed woodpecker" and the answer choices are much longer as well. Do you have that book? Should I post that question? I do not see that it has ever been posted on BTG, although it is an OG question? It is a tough one.... Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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by deeyah » Fri Sep 03, 2010 10:18 am
David, could you please post the other CR question you are referring to?

Thanks
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by David@VeritasPrep » Fri Sep 03, 2010 12:17 pm
I just posted the bold faced OG question!

David
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Save $100 off any live Veritas Prep GMAT Course Senior | Next Rank: 100 Posts Posts: 89 Joined: 03 Sep 2009 Thanked: 14 times Followed by:1 members GMAT Score:770 by prepgmat09 » Fri Sep 03, 2010 1:12 pm Hi David, Could you please explain why E is wrong? Thanks. ### GMAT/MBA Expert GMAT Instructor Posts: 2193 Joined: 22 Feb 2010 Location: Vermont and Boston, MA Thanked: 1186 times Followed by:512 members GMAT Score:770 by David@VeritasPrep » Fri Sep 03, 2010 2:28 pm Answer choice E does indeed mention something that is true of both woodpeckers and is not unique to ivory billed woodpeckers - this could weaken under the right circumstances. However, in this problem the case in favor of the ivory-billed was not relying on the wing motion of the woodpecker, but on the large patch of white on the wing. Answer choice D directly undermines that main evidence of the large white patches on the wing so this is the correct answer. Hope that helps! Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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by prepgmat09 » Fri Sep 03, 2010 2:50 pm
David@VeritasPrep wrote:Answer choice E does indeed mention something that is true of both woodpeckers and is not unique to ivory billed woodpeckers - this could weaken under the right circumstances.

However, in this problem the case in favor of the ivory-billed was not relying on the wing motion of the woodpecker, but on the large patch of white on the wing. Answer choice D directly undermines that main evidence of the large white patches on the wing so this is the correct answer.

Hope that helps!

But choice D partially just mentions what is already given in the argument. The argument already says "some abnormal Pileated birds can have extra white on the wing". Choice E provides us a new evidence that supports skeptics point of view that there are reasons to believe that the bird is in fact a Pileated woodpecker. Shouldn't E be a better choice in this case?

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by David@VeritasPrep » Fri Sep 03, 2010 3:19 pm
Thank you for pointing that out. You are absolutely correct. This should have been edited so that the stimulus did not say that about the wing patches, then D would be new information!!

This has been in print for several years -- we should have had you edit!

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by samarpan_bschool » Sat Sep 04, 2010 10:34 pm
David@VeritasPrep wrote:Thank you for pointing that out. You are absolutely correct. This should have been edited so that the stimulus did not say that about the wing patches, then D would be new information!!

This has been in print for several years -- we should have had you edit!

David
Hi Dave,

I am somehow not convinced with D. Option D clearly states that 'white patches' can appear on both ivorey billed and abnormal pileated. So there is a possibility that the evidence could still point to ivory bill, in which case Option D will weaken skeptics argument. !!

Option B on the other hand says that 'ivory bill' failed on the other evidence too - (i.e.) peculiar sound. Also please note that the evidence offered in the passage is 'video' and the characteristics large white patch is one of the observations.

Can you explain? Thanks


text:
# Anyone here ever programmed an FPGA?

#### ratstar

Aug 20, 2018
485
I've been doing GPU's for ages now, and I need to move onto something more mature.
I'm wondering if FPGA's will make my robots run better than my GPU ones.

What I need (even tho its slightly metaphorical) is to simply run something like frogger as many times as I can at once, I need to hit a collected (including parallel) frame rate of about 1 million fps or higher would be better. Because I need to sample a small model this many times to search in it.

Will FPGA's be able to do this?

#### Nanren888

Nov 8, 2015
623
VHDL? It's sort of a different way of thinking.
Parallelism is up to you. If you want massively parallel, you have to pay for realestate.
.
Can't picture how frogger fits into it. FPGA's like GPUS are good at simple & pipelined.Sort of depends on which tool you choose.
With people selling FPGA add-on boards to go with devkits & such, I'd guess there are a lot of introductions out there now.
.
One thing about FPGA tools, is some, especiialy for linux are free & the included simulator lets you get the experience without any money down.
Also finishing the design in the simulator first, lets you see what size you need to buy to get he space & speed you want.
.
Never quite sure where you are going: Thought of mining bitcoins?

#### Bluejets

Oct 5, 2014
5,856
Never quite sure where you are going:

Quite a few with the same thoughts I think.

#### ratstar

Aug 20, 2018
485

VHDL? It's sort of a different way of thinking.
One thing about FPGA tools, is some, especiialy for linux are free & the included simulator lets you get the experience without any money down.
Also finishing the design in the simulator first, lets you see what size you need to buy to get he space & speed you want.
.Never quite sure where you are going: Thought of mining bitcoins?

If you would be so kind could you point me to a freeware FPGA IDE for windows?
I've wrote a few virtual machines before myself, so I know what its like, but something that works for real I havent done yet.

.Never quite sure where you are going: Thought of mining bitcoins?
If I can run alot of chess games in parallel, the computer ends up being able to play it by itself. I'm doing something along those lines, and the GPU performance doesn't cut it anymore, I need something more powerful.
The smaller I can make the individual "core" the more I can have running simultaneously, that could get my core count higher.

#### ratstar

Aug 20, 2018
485
Hello,

Have a look at this package:
https://www.staticfreesoft.com/

Bertus

That looks quite intimidating, is there something easier like a unit to buy thats already assembled and then u just write the code for it? (similar to purchasing a gpu for example.)

Moderator
Nov 17, 2011
12,610

#### ratstar

Aug 20, 2018
485
So, what makes one fpga worth picking over another, theres alot to choose from there.

I want->
* lots of space to put program logic
* I only want very little ram or state space.
* I require only a small amount of input and output to and from the FPGA.
* Id like a fast HZ.

Is there anything that fits those specifications. (But I don't know what I'm doing yet at all.)

Moderator
Nov 8, 2019
2,632

#### ratstar

Aug 20, 2018
485
Maybe I'm making a mistake, when would an FPGA be desirable over a GPU? cost effectiveness wise, I just don't even know how to begin... because I could just keep going with GPUs and already know the performance I'm going to get, but with FPGA's is it about the same for cost? Because then there would be no point in shifting over.

Last edited:

#### Nanren888

Nov 8, 2015
623
If you have a budget: AWS? - instantiate any size machine that you need.

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,610
Do you realize the difference between an FPGA and a GPU?
A GPU is a special purpose processor but nevertheless a processor. Typically with lots of processing units (shaders) it can be programmed in a dedicated programming language (shader language).
An FPGA is not programmed to execute code as a processor. An FPGY is a collection of hardware units (cells) that are programmed to perform a specific task an also the connections between the cells are programmable. That means an FPGA is essentially a piece of fixed hardware once it is programmed (of course the programming can be changed and thus the hardware represented by the FPGA - but usually not on the fly, a reset is required to load a new configuration.
Having the FPGA represent a piece of dedicated hardware with lots of parallel operation performed simultaneously is what makes it so fast compared to a program running on a processor.

I want->
* lots of space to put program logic
* I only want very little ram or state space.
* I require only a small amount of input and output to and from the FPGA.
* Id like a fast HZ.
You won't get that. Generally the more computing cells there are within an FPGA, the more I/O pins the chip has. I know of no chip with high number of cells but small number of IOs.

I just don't even know how to begin... because I could just keep going with GPUs and already know the performance I'm going to get,
Possibly the quickest way at the time being. It will take some time to understand FPGAs, the different options you have with them and write efficient code. But if you don't start, you will not reap the benefits from FPGAs. Imho using a starter kit is the best option to get you going. FPGAs will (maybe with exceptions) generally come in hobbyist-unfriendly cases (BGA) and sometimes require sophisticated power supplies (multiple voltages, power sequencing etc.), all of which is dealt with when you buy a starter kit.

How come you want to look into FPGAs? These are MOSFET based. From your previous posts I got the impression that you are no fan of these. Why not use your super secret, super high speed DIY computer you've been hinting at in previous threads?

#### ratstar

Aug 20, 2018
485
Do you realize the difference between an FPGA and a GPU?
How come you want to look into FPGAs? These are MOSFET based. From your previous posts I got the impression that you are no fan of these. Why not use your super secret, super high speed DIY computer you've been hinting at in previous threads?

Cause I'm impatient, and I need things sooner. I dont mind transistors as long as I didnt need to fabricate them myself, I had a real banger of an idea just not long ago tho, with spark gap based transistors. (You set up the arc with hivoltage low amp over the gap, and then it continue's to arc with lower voltage high amp.)

Making my own computer from scratch definitely seems like the real cost saver... But I'm judging things way too early, Ive got heaps to discover yet about fpgas...

You won't get that. Generally the more computing cells there are within an FPGA, the more I/O pins the chip has. I know of no chip with high number of cells but small number of IOs.

Thats a bit of a shame, Because if u reduce the ram and state and I/O, it should reduce the overall machine, If I plugged that into the FPGA id be wasting 75% of whats there because it's not designed for it.

#### ratstar

Aug 20, 2018
485
I was watchin Felix's magic FPGA tutorials. and it actually looks to me like they are better than GPUs by a mile... just need to wait a bit... I feel a bit bad that I wasted my whole life with GPUS right now... *face palm*

It looks to me i can get a $100 FPGA do better than a GTX3080ti for$2000.

wth.

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Aug 20, 2018
485

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,610
355k CLB's
Be careful. Study in detail what a CLB is. This differs from manufacturer to manufacturer and between FPGA families. A CLB is definitely way less than a shader unit in a GPU. I don't know what you are comparing but this comparison definitely would be nonsensical. Have a look at e.g. this discussion.
Before you dismiss GPUs, you need to get a grasp on what an FPGA is and what it can do - and what not.

#### ratstar

Aug 20, 2018
485
Ok, I'm ready to start simulating, but I dont know what simulator to get.
Id like it to be VERILOG. but I dont know what program to get, Bertus can u help me plz?

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text:
# Surface Science Cluster

FlexPES HR ARPES instrument, which was produce by SPECS Surface Nano Analysis GmbH, is devoted to the high angular- and energy-resolution electronic structure studies of different objects which must be in the monocrystalline or polycrystalline form. (Powder and wet samples are generally not possible; some special samples can be discussed case-by-case.) This instrument was installed in our group in January 2021 and is in full operation since October 2021. We also provide access to this instrument to different users under conditions which are placed below.

This XPS/ARPES instrument consists of two chambers, preparation and analysis, and load-lock for sample loading. Main components are:

• Energy analyzer: SPECS PHOIBOS 150 with 2D-CMOS detector
• Monochromatized UV source: UVS 300 with TMM 304
• Sample handling in the analysis chamber: Motorized 5-axis manipulator Ganymed with temperature range 7 K – 300 K
• Monochromatic x-ray source: FOCUS 500/600 with two lines (Al K$\alpha$, 1486.6eV and Ag L$\alpha$, 2984.3 eV)
• Ion source for sample preparation: IQE 11/35, ion energy range 0 eV – 3000 eV
• Sample morphology characterization: ErLEED 100 with ErLEED 1000-A power supply
• Sample handling in the preparation chamber: Motorized 4-axis manipulator with temperature range 100 K – 1200 K
• Sample heating in the preparation chamber: high temperature heating stage with temperatures up to 2300 K
• Thin films preparation: a series of e-beam evaporators (commercial EBE-1 and home-made)

The access to this instrument inside Shanghai University and for external users is provided only under the full control performed by members of the group lead by Prof. Yuriy Dedkov and Prof. Elena Voloshina.


text:
# mask: Positional conservation and gap filtering.¶

Citations

 [alignment:mask:Lan91] DJ Lane. 16s/23s rrna sequencing. In E Stackebrandt and M Goodfellow, editors, Nucleic Acid Techniques in Bacterial Systematics, pages 115–175. John Wiley and Sons, New York, 1991.

#### Docstring:

Usage: qiime alignment mask [OPTIONS]

Mask (i.e., filter) unconserved and highly gapped columns from an
alignment. Default min_conservation was chosen to reproduce the mask
presented in Lane (1991).

Options:
--i-alignment ARTIFACT PATH FeatureData[AlignedSequence]
The alignment to be masked.  [required]
--p-max-gap-frequency FLOAT     The maximum relative frequency of gap
characters in a column for the column to be
retained. This relative frequency must be a
number between 0.0 and 1.0 (inclusive),
where 0.0 retains only those columns without
gap characters, and 1.0 retains all columns
regardless of gap character frequency.
[default: 1.0]
--p-min-conservation FLOAT      The minimum relative frequency of at least
one non-gap character in a column for that
column to be retained. This relative
frequency must be a number between 0.0 and
1.0 (inclusive). For example, if a value of
0.4 is provided, a column will only be
retained if it contains at least one
character that is present in at least 40% of
the sequences.  [default: 0.4]
The masked alignment.  [required if not
passing --output-dir]
--output-dir DIRECTORY          Output unspecified results to a directory
--cmd-config FILE               Use config file for command options
--verbose                       Display verbose output to stdout and/or
stderr during execution of this action.
[default: False]
--quiet                         Silence output if execution is successful
(silence is golden).  [default: False]
--citations                     Show citations and exit.
--help                          Show this message and exit.

#### Import:

from qiime2.plugins.alignment.methods import mask

#### Docstring:

Positional conservation and gap filtering.

Mask (i.e., filter) unconserved and highly gapped columns from an
alignment. Default min_conservation was chosen to reproduce the mask
presented in Lane (1991).

Parameters
----------
alignment : FeatureData[AlignedSequence]
max_gap_frequency : Float % Range(0, 1, inclusive_end=True), optional
The maximum relative frequency of gap characters in a column for the
column to be retained. This relative frequency must be a number between
0.0 and 1.0 (inclusive), where 0.0 retains only those columns without
gap characters, and 1.0 retains all columns regardless of gap character
frequency.
min_conservation : Float % Range(0, 1, inclusive_end=True), optional
The minimum relative frequency of at least one non-gap character in a
column for that column to be retained. This relative frequency must be
a number between 0.0 and 1.0 (inclusive). For example, if a value of
0.4 is provided, a column will only be retained if it contains at least
one character that is present in at least 40% of the sequences.

Returns
-------
The masked alignment.


text:
# Integrate $\sin^4(x)$

Consider the integral $$\int \sin^4(x)dx$$ Now I could separate the $$\sin^4(x)$$ into two $$\sin^2(x)$$ terms and the use power reducing formula

$$\int \sin^2(x)\sin^2(x)dx$$ $$\int \frac{1-\cos(2x)}{2}*\frac{1-\cos(2x)}{2}dx$$ $$\int \frac{(1-\cos(2x))^2}{4} dx$$ $$\int\frac{1}{4}-\frac{2\cos(2x)}{4}+\frac{\cos^2(x)}{4}dx$$ $$\frac{1}{4} \int1-8\cos(2x)+\cos^2(2x)dx$$

Now would it be good to rewrite that $$\cos^2(2x)$$ as $$1-\sin^2(2x)$$ and then integrate or should I also separate the terms into their own integrands?

The answer I am looking for which is $$\frac{3}{8}x -\frac{1}{4}\sin(2x)+\frac{1}{32}\sin(4x)+C$$.

• Are you sure about parts? The usual way would be to use the double angle formula for $\cos x$ to write $\sin^2(x)=\frac {1-\cos(2x)}2$. – lulu Oct 14 '19 at 19:04
• I mean, I don’t see why you can’t split it into sin(x) and $sin^3 (x)$ and continue using IBP “all the way down”, and then simplify. – Adam Rubinson Oct 14 '19 at 19:17
• @lulu I have updated the question following a different path. – Eric Brown Oct 14 '19 at 19:38
• Ok, well, you can compute $\int \cos^2(x)\,dx$ the same way, by using the double angle formula for $\cos (x)$. – lulu Oct 14 '19 at 19:42

First of all, I think you mistyped the last line of your integral, changing a 2 for an 8. Besides, you can use the linearity of the integral to write $$\int(1-2\cos(2x)+\cos^{2}(2x))dx = \int 1 dx - 2\int \cos(2x)dx+\int \cos^{2}(2x)dx.$$ Now, note that $$\cos^{2}(2x) + \sin^{2}(2x) = 1$$ and $$\cos^{2}(2x)-\sin^{2}(2x) = \cos(4x)$$ so that $$\cos^{2}(2x) = \frac{1+\cos(4x)}{2}.$$ Thus, we have $$\int \cos^{2}(2x) = \int \frac{1+\cos(4x)}{2}dx = \frac{1}{2}x + \frac{\sin(4x)}{8}+C$$. Now, the previous integrals are given by $$\int 1 dx -2\int \cos(2x) = x -2\frac{\sin(2x)}{2}+C = x - \sin(2x) +C.$$
Finally, your integral is $$\frac{1}{4}[x-\sin(2x)+\frac{1}{2}x+\frac{\sin(4x)}{8}]+C = \frac{3}{8}x-\frac{1}{4}\sin(2x)+\frac{\sin(4x)}{32} + C$$
Surely your $$8$$ should be a $$2$$ (not to mention each $$\cos^2x$$ should be $$\cos^22x$$), giving$$\frac14\int(1-2\cos 2x+\cos^22x)dx=\frac18\int(3-4\cos 2x+\cos 4x)dx=\frac{1}{32}(12x-8\sin 2x+\sin 4x)+C.$$


text:
Computer Science and Application
Vol. 08  No. 11 ( 2018 ), Article ID: 27449 , 10 pages
10.12677/CSA.2018.811183

An Algorithm for Choosing Optimal Rank in Tensor Approximation of Multi-Resolution Volume Rendering

Xiaoyan Nie1*, Cai Lu2

1Department of Electronic Engineering, Chengdu College of University of Electronic Science and Technology of China, Chengdu Sichuan

2School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu Sichuan

Received: Oct. 20th, 2018; accepted: Nov. 1st, 2018; published: Nov. 8th, 2018

ABSTRACT

Multi-resolution volume rendering is an effective method to solve the problem of massive data volume rendering. The comentropy based multi-resolution volume rendering has an obvious limitation when handling data of geophysical field which have a low SNR and complex microstructure characteristics. Tensor approximation can extract the characteristic bases of the data, and gain the data approximation with microstructure characteristics by means of the linear combination of the characteristic bases. We made a research about how to choose the rank in tensor approximation multi-resolution volume rendering. Low rank gained a high compression ratio, but low PSNR. High rank gained an ideal rendering effect, but low compression ratio. In this paper, we presented a method that could find the best rank adaptively for every block. Based on high rank decomposition, we did binary search to find the optimal rank which will exactly meet the error threshold. Meanwhile, data were separated into blocks, different blocks have different ranks. Experimental results show that our method has a higher compression ratio and similar render result in comparison with high rank decomposition and our method has a significant better rendering result and a slightly lower compression ratio.

Keywords:Volume Rendering, Massive Data, Multi-Resolution, Rank Truncation, Tensor Approximation

1电子科技大学成都学院电子工程系，四川 成都

2电子科技大学信息与通信工程学院，四川 成都

1. 引言

Ljung P等 [2] 提出了基于统一划分的多分辨率体绘制技术。在统一划分中，每个分块各自独立地确定自己的分辨率，分块与分块之间互不影响。Ljung等 [3] 提出了基于CIELUV (CIE 1976 (L*, u*, v*) color space)空间的误差准则。并且在分块细节水平选择时，引入了传递函数的信息，以此来优化绘制效果。梁荣华等 [4] 提出了基于信息熵的分块细节水平选择方法，并能够自适应的优化用户设定的阈值，以提高绘制效果。

Boada I [5] 等首先提出了基于八叉树的多分辨率数据表示。用一颗八叉树来表示整个三维数据体。每一个节点代表一个分块。将空间中8个相邻的分块重采样成一个相同大小的分块，即构成了这8个分块的父分块。父分块对应八叉树中，这个8个分块所对应节点的父节点。因此，每个分块的点数相同，但其所代表的空间中的实际大小不同。通过对八叉树的遍历，能够很容易地实现对每个分块的随机访问。八叉树多分辨率的很多研究集中在，如何在硬件的限制下确定每一个节点的误差。砖块与视点的距离，感兴趣的区域和块内部数据的同质性以及近似后的误差 [6] [7] [8] 通常被用来确定一个分块的细节水平。Guthe和Straber [9] 提出了一种对失真误差的保守估计方法。他们将误差定义为最大的RGB误差和最大的不透明度误差的和。Ljung [10] 用简化的1维直方图去近似每个分块和它原始分块的均方误差。

2. 高阶张量近似原理

$A\approx B{×}_{1}{U}^{\left(1\right)}{×}_{2}{U}^{\left(2\right)}{×}_{3}\cdots {×}_{n}{U}^{\left(n\right)}$ (1)

Figure 1. Tucker model tensor decomposition

3. 秩截断技术分析

Figure 2. Rank truncation

$\text{MSE}=\frac{{\sum }_{n=0}^{N}{\left({a}_{n}-{b}_{n}\right)}^{2}}{N}$ (2)

$\text{PSNR}=10×{\mathrm{log}}_{10}\frac{{K}^{2}}{\text{MSE}}$ (3)

Table 1. PSNR and compression ratio

4. 最佳秩选取算法

Figure 3. Binary search for optimal rank

$e=\frac{{‖A-\stackrel{˜}{A}‖}_{F}}{{‖A‖}_{F}}$ (4)

${‖B‖}_{F}=\sqrt{{\sum }_{i=1}^{M}{\sum }_{j=1}^{N}{b}_{ij}^{2}}$ (5)

5. 仿真分析

Table 2. Blocks distribution under different threshold by rank

(a) Te = Tp = 0.1; (b) Te = Tp = 0.2; (c) Te = Tp = 0.3; (d) Te = Tp = 0.4

Figure 4. Optimal rank rendering result under different threshold

Table 3. Comparison between optimal rank and unified rank

(a)Te = Tp = 0.25，最佳秩；(b)统一秩(16, 16, 16)分解；(c)统一秩(8, 8, 8)分解；(d)统一秩(4, 4, 4)分解

Figure 5. Comparison between optimal rank and unified rank

6. 结束语

An Algorithm for Choosing Optimal Rank in Tensor Approximation of Multi-Resolution Volume Rendering[J]. 计算机科学与应用, 2018, 08(11): 1665-1674. https://doi.org/10.12677/CSA.2018.811183

1. 1. Balsa Rodríguez, M., Gobbetti, E., Iglesias Guitián, J.A., et al. (2014) State-of-the-Art in Compressed GPU-Based Direct Volume Rendering. Computer Graphics Forum, 33, 77-100. https://doi.org/10.1111/cgf.12280

2. 2. Hadwiger, M., Ljung, P., Salama, C.R., et al. (2009) Advanced Illumination Techniques for GPU-Based Volume Raycasting. Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, New York, 12-53.

3. 3. Ljung, P., Lundstrom, C., Ynnerman, A., et al. (2004) Tansfer Func-tion Based Adaptive Decompression for Volume Rendering of Large Medical Data Sets. Proceedings of the IEEE Symposium on Vol-ume Visualization and Graphics, Los Alamitos, 25-32.

4. 4. 梁荣华, 薛剑锋, 马祥音. 自适应分块细节水平的多分辨率体绘制方法[J]. 计算机辅助设计与图形学学报, 2012, 24(3): 314-322.

5. 5. Boada, I., Navazo, I. and Scopigno, R. (2001) Multi-Resolution Volume Visualization with a Texture-Based Octree. The Visual Computer, 17, 185-197. https://doi.org/10.1007/PL00013406

6. 6. LaMar, E., Hamann, B. and Joy, K.I. (1999) Multiresolution Techniques for Interactive Texture-Based Volume Visualization. Proceedings of the IEEE Visualization, San Francisco, 24-29 October 1999, 355-362. https://doi.org/10.1109/VISUAL.1999.809908

7. 7. Plate, J., Tirtasana, M., Carmona, R., et al. (2002) A Hierarchical Approach for Interactive Roaming through Very Large Volumes. Proceedings of the EUROGRAPHICS/IEEE TCVG Symposium on Visualization, Switzerland, 53-60.

8. 8. Wang, C.L., Gao, J.Z. and Shen, H.-W. (2004) Parallel Multiresolution Volume Rendering of Large Data Sets with Error-Guided Load Balancing. Proceedings of the EURO-GRAPHICS Symposium on Parallel Graphics & Visualization, Switzerland, 23-30.

9. 9. Guthe, S. and Staßer, W. (2004) Advanced Techniques for High-Quality Multi-Resolution Volume Render-ing. Computers & Graphics, 28, 51-58. https://doi.org/10.1016/j.cag.2003.10.018

10. 10. Ljung, P., Lundstrom, C., Ynnerman, A., et al. (2004) Transfer Function Based Adaptive Decompression for Volume Rendering of Large Medical Data Sets. Proceedings of the IEEE Symposium on Volume Visualization and Graphics, Austin, TX, 12 October 2004, 25-32. https://doi.org/10.1109/SVVG.2004.14

11. 11. Kolda, T.G. and Bader, B.W. (2009) Tensor Decompositions and Applications. SIAM Review, 51, 455-500. https://doi.org/10.1137/07070111X

12. 12. Wu, Q., Xia, T., Chen, C., et al. (2008) Hierarchical Tensor Approximation of Multidi-mensional Visual Data. IEEE Transaction on Visualization and Computer Graphics, 14, 186-199. https://doi.org/10.1109/TVCG.2007.70406

13. 13. Suter, S.K., Makhynia, M. and Pajarola, R. (2013) Tamresh-Tensor Approxima-tion Multiresolution Hierarchy for Interactive Volume Visualization. Computer Graphics Forum, 32, 151-160.

14. 14. Ballester-Ripoll, R., Suter, S.K. and Pajarola, R. (2015) Analysis of Tensor Approximation for Compression-Domain Volume Visualization. Computers & Graphics, 47, 34-47. https://doi.org/10.1016/j.cag.2014.10.002

15. 15. Balsa Rodríguez, M., Gobbetti, E., Iglesias Guitián, J.A., et al. (2014) State-of-the-Art in Compressed GPU-Based Direct Volume Rendering. Computer Graphics Forum, 33, 77-100. https://doi.org/10.1111/cgf.12280

16. 16. Piccand, S., Noumeir, R. and Paquette, E. (2008) Region of Interest and Multiresolution for Volume Rendering. IEEE Transactions on Information Technology in Biomedicine, 12, 561-568. https://doi.org/10.1109/TITB.2007.907986

17. 17. Lorensen, W.E. and Cline, H.E. (1987) Marching Cubes: A High-Resolution 3D Surface Construction Algorithm. Computer Graphics, 21, 163-169. https://doi.org/10.1145/37402.37422

18. 18. Grgic, S., Grgic, M. and Mrak, M. (2004) Reliability of Objective Picture Quality Measures. Journal of Electrical Engineering, 55, 3-10.

NOTES

*通讯作者。


text:
Calculus (3rd Edition)

$v'_{esc} = -1.41$ x $10^7r^{-3/2}\ m/s$
$v_{esc} = (2.82$ x $10^7)r^{-1/2}$ To find the rate of change, we need to find the derivative, which can be done using the power rule: $v'_{esc} = (2.82$ x $10^7)(-\frac{1}{2})r^{-3/2}$ $v'_{esc} = -1.41$ x $10^7r^{-3/2}\ m/s$


text:
# Importance sampling a cosine distribution

Let's take a look at this blog article - https://schuttejoe.github.io/post/ggximportancesamplingpart1/ and image presented as a result of implementing it:

Inside above link, you can see description for this image saying

In order to have something to compare to on the left I generated an image by importance sampling a cosine distribution and on the right I generated an image using the technique described above. [...]

Based on the fact that image on the right was derived based on GGX pdf, how was image on the left generated? I assume we have our standard equation but what does it mean that it's generated with importance sampling a cosine distribution? $$f(w_i,w_o) = \frac{F(w_i, w_m) ~ G_2(w_i,wo_,w_m) D(w_m)}{4 ~ |w_i \cdot w_g| ~ |w_o \cdot w_g|} * PDF[?]$$

So what the author is saying is the image on the left was sampled with $$\omega_o$$ (or maybe $$\omega_m$$, I'm not sure) drawn from a cosine hemisphere distribution, just as an example of a distribution that does not match the BRDF very well. Then they calculate the samples as $$f(\omega_i, \omega_o) / p_{\cos}(\omega_o)$$ where $$p_{\cos}$$ is the pdf for the cosine distribution. This is just to show you that it gives the "correct" result, but with a ton of variance. (Although it looks like there are some black areas on the left image that suggest it's not really converging to the correct answer...but let's assume that's a bug.)
Then the image on the right is sampled with (presumably) $$\omega_m$$ drawn from a distribution matching the $$D(\omega_m)$$ term from the BRDF. Then when you calculate the BRDF you can leave out the $$D$$ factor since it's canceled by the $$D$$ factor in the pdf. (The pdf probably still has some normalization and some conversion of probability from $$\omega_m$$ to $$\omega_o$$, so you still have to divide by those factors.)
• The pdf for the cosine distribution is $\cos(\theta)/\pi$. Oct 2 '20 at 17:10
• So throughput for cosine distribution will be: $$\frac{NoL * ggx}{pdf} = NoL * ggx ~\frac{\pi}{cos(\theta)} = NoL * ggx ~\frac{\pi}{NoL} = ggx ~ * ~ \pi$$ ? I'm not planning to use it due to more efficient methods, but I'm interested if my understanding is correct. Oct 5 '20 at 8:38
• @DirectX_Programmer Yep that looks right. The fact that it cancels out the $N \cdot L$ is exactly why the cosine distribution is used for diffuse light. Oct 5 '20 at 23:56


text:
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part

1. 克雷千禧年七个问题，每个价值100万美金。

2. 关于他的介绍维基百科

3. 欧拉图书奖是为那些传播数学的图书颁奖