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All Questions

2k views

How can I implement the “Multiplication Modulo” and “Addition Modulo” operations in IDEA?

I am currently working on IDEA (International Data Encryption Algorithm), and I don't know how to perform Multiplication Modulo and Addition Modulo. This is how IDEA operates: IDEA operates on ...
338 views

I have the following password with a prescribed format: it starts with a fixed value of 111, followed by 2 random lower case letters and then lastly a random digit: "111""2 Random lowercase ...
108 views

Using pairings to verify an extended euclidean relation without leaking the values?

Let $P_i(x)$ be polynomials $i=1,...,n$, $s$ some value, and $g$ a generator of a group $G$ where the discrete logarithm is hard. Assume a prover wants to convince a verifier having access to the ...
218 views

Tree hash and multithreading for parallelism

I am using tree hash mode of Skein on a 16 core processor. Will it automatically employ parallelism using more than one cores or do I have to use multi-threading within the tree hash for parallel ...
415 views

which of these is more secure (bcrypt vs srp)

OK, here's the two different ways I was thinking about making the authentication for the login thing to store the passwords securely. The first is the following. Client hashes password ...
181 views

verify contents, but not order

Is there an algorithm that can be used to verify the contents of a cyphertext, but not the order of the elements? I am thinking that a deck of cards could be shuffled, and it must be verifiable that ...
802 views

How can the Diffie-Hellman key exchange be extended to three parties? [duplicate]

Possible Duplicate: Can one generalize the Diffie-Hellman key exchange to three or more parties? How can Alice, Bob, and Charlie share a common secret key using an extended version of the ...
282 views

Blowfish Encryptions in Bcrypt hashing algorithm

I am trying to understand the ExpandKey function used in the bcrypt hashing algorithm. As per the documentation of bcrypt hashing algorithm on USENIX here: ...
414 views

Recommended Books for Cryptography : Theory and Implementation [closed]

It is a great idea if experts in Cryptography from mathematicians to security engineers introduce books and textbooks which they think is helpful or instructive for all people interested in the ...
259 views

Digital Certificate Chain Verification

Does a certificate contain the complete chain of all certificates up to the trusted root certificate, or does the program that verifies certificates have to fetch each parent certificate individually ...
58 views

Design question for a service that signs messages on behalf of a user

I'm working on a messaging service that lets users author messages and have them signed with an RSA key. The key is used for identity purposes only and can be revoked, so compromising the private key ...
436 views

Deniability of OTR messaging

I've been looking at the off-the-record messaging protocol, and there is something about its deniability property that seems strange to me. Consider the following scenario: In the course of an ...
171 views

Do Quantum Key Distribution and Physical Unclonable Functions combine, and how?

I see there's a project to combine Quantum Key Distribution, Physical Unclonable Functions, and classical crypto, in order to secure a high speed (100Gb/s) optical link. While there does not seem to ...
1k views

Deciphering a key from XOR encrypted cypher using boolean logic

Assume there's an unencrypted message A, and an encrypted message B. You know that message B was encrypted using a simple XOR method of A with a private key K, resulting in message B. Thus, B = A ⊕ K ...
476 views

Expectation Value of the Index of Coincidence

Can Anybody tell me why the expectation value of the Index of Coincidence is the following? For a cipher text string of length $L$, where $n$ is the number of alphabet characters, $k_r = 1/n$, and ...
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Use of nonces in Kerberos and Needham–Schroeder protocols

Can you please explain me what is the reason of using nonces in the Needham-Schroeder and in the Kerberos protocols for Key Transport. In particular : Can you explain me the use of $N_A$? And ...
80 views

Incorporating known ciphertext into new message

Which ciphers $c_k$ enable one to define a joining function $f_{c,k}$ such that: $$f_{c,k}(c_k(p_1), p_2) = c_k(p_1 + p_2)$$ That is, the result of joining some known ciphertext $c_k(p_1)$ with a ...
456 views

How to represent a 32-byte SHA2 hash in the shortest possible string?

I'm calculating a SHA2 hash of a certain sensitive key value. I need to store files on disk using this hash a directory path prefix. So lets say I hash the key value 150023, I get a 32-byte value ...
119 views

Tips on conceiving safe software messaging platform

I have a personal project in mind in which I plan to use cryptography in order to let the users be confident in the fact that, even if all data get's stolen, it would be virtually impossible to crack ...
417 views

Brute forcing Cardan grille

Having a "rotating" square Cardan Grill with sides long n cells, how could i determinate the cost of a brute-force attack? How many configurations should be considered to perform an exhaustive ...
258 views

Twofish key length

I'm using twofish. Say you have a 120 bit key, is there any difference in using a 128 bit bit keylength or a 256 bit one? Since the most significant digits of the key will be allo zero in both cases, ...
522 views

Is this fixed length MAC unforgeable?

Consider the following fixed length MAC for messages of length $\ell(n)=2n-2$ using a pseudorandom function $F$: On input of a mesage $m_0||m_1$ ($|m_0| = |m_1| = n-1$) and a key $k \in \{0,1\}^n$, ...
135 views

How is the password sent across for verification?

I am familiar with Challenge-Response Authentication scheme. However I would like to know actual message content sent between client and server for 1 way authentication, over an insecure channel. ...
628 views

iSeries (AS/400) Database File: password encryption

I am helping with a project in which an old software system on an iSeries is having a brand new .NET UI applied to it. It's going well... except... In order to allow users to login and maintain ...
25 views

ElGamal and Schnorr groups

As I gather, a normal practice for choosing a cyclic group for ElGamal key generation is to find a safe prime $p$ and use a multiplicative cyclic group with modulus $p$ and order $q = (p-1)/2$. ...
103 views

open source whitebox-crypto implementation

I am trying to code a simple WBC situation to help my understanding about white-box cryptography. Details: I have 2 programs, a "server" and a "client", the server utilises caesar cipher (key = 2) ...
36 views

Confused with the role of AES round keys

AES works when each plaintext block is arranged in a 4x4 array of bytes called states. State goes through 10 rounds of encryption consisting of 4 operations: bytesub, shiftrow, mix columns and add ...
25 views

TimeStamp in Cache-time attacks on AES [closed]

I have recently read about AES cache timing attacks. More specifically, I read Daniel Bernstein paper Cache-timing attacks on AES. I have a question about the code in Appendix A: ...
74 views

Key derivation of public key without knowledge of private key?

I'm looking for a convenient way to share a set of public keys across multiple services, while preserving privacy by preventing these services from tying the identity of these public key sets together ...
46 views

What is the algorithm behind PasswordDeriveBytes?

Microsoft has created an implementation of PBKDF1 in the PasswordDeriveBytes class. It can however generate more bytes than PBKDF1, which is limited to the number ...
101 views

How to roll my own hardware RNG?

I am considering building a hardware RNG myself using cheap parts. Is this a good idea and safe enough? Random sources: amplified Zener noise from one randomly chosen ...
78 views

Luby-Rackoff on Feistel ciphers [closed]

On page 46 of these lecture notes, it seems to say that if we have a Feistel cipher, and plaintexts $(L_0, R_0)$ and $(L_0^*, R_0^*)$ with corresponding encryptions, then we can determine the key? But ...
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test vectors for 3DES seem to in fact be testing DES - not 3DES

NIST SP 800-20 Appendix A has what presumably are supposed to be test vectors for 3DES except almost all of the test vectors utilize 8-byte keys and not the 24-byte keys that 3DES is supposed to have. ...
61 views

I figured that a really secure password would be an AES 128 key. If this key were to be base 64 encoded, I could replace 4 random bytes in it in order to make it unusable unless you know which bytes ...
62 views

Perfect secrecy of a crypto system

Suppose we have the following crypto system: $P = C = K = \{0, 1, . . . , n − 1\}$, $E_k(x) = (x + k) \bmod n$ and $D_k(y) = (y − k) \bmod n$. Prove that the crytosystem has perfect secrecy. Perfect ...
58 views

RSA Protocol behind Yaksha Security System

So I'm reading over the Yaksha Security System and see it is based on the RSA cryptosystem and a centralized server, easy enough. What I'm slightly confused on is the math behind the related keys. It ...
68 views

Why do we have fixed output length in the algorithm SHA1

Why do we have fixed output length in the algorithm SHA1 . is there any explanation about that
57 views

RSA-blind signatures vs. DSA-blind signatures

I see that the RSA blind signature scheme tends to be implemented more often than others, e.g., DSA blind signatures. Isn't the RSA blind signature scheme a 'lesser' scheme, if you may, compared to ...
55 views

Reduced message expansion in NTRU

In the original NTRU proposal from 1998, it says on page 16: It may be worth mentioning, though, that there is a simple. masking technique that can be used to significantly reduce message ...
34 views

Use of the master key in Delerablée's Identity-based Broadcast Encryption

I'm reading “Identity-Based Broadcast Encryption with Constant Size Ciphertexts and Private Keys” by Cécile Delerablée. On page 207, the encryption process needs $\gamma$ which is part of the master ...
35 views

What is the functional role of CKY-I and CKY-R in ISAKMP (IKEv1)?

According to RFC 2409: CKY-I and CKY-R are the Initiator's cookie and the Responder's cookie, respectively, from the ISAKMP header. Each CKY is a 64 bit value that is included in each ISAKMP ...
44 views

Retrieve timestamp from TOTP value

TOTP (Time-based One-Time Password) as I understand is an algorithm that uses the current time as a variable along with a shared key to generate a secured token. Wiki page for reference: ...
65 views

Why is proving “parties' views are simulatable” enough in semi-honest model?

To prove a protocol is secure in semi-honest model, we have to prove: the view of each party, on each possible pair of inputs, can be efficiently simulated based solely on its own input and and ...
85 views

ECC - ElGamal with Montgomery or Edwards type curves (curve25519, ed25519) - possible?

I know the usual way of using getting shared secrets for encryption with ECC is DH, however, this only works with two keypairs of exactly the same kind, for example two curve25519- or two ...
63 views

Requirement for the length of a HMAC tag?

I've seen NIST requirements about key length. What about the output lengths ? Is 112 bits enough for the HMAC output length ? Can we truncate the tag to keep only 112 bits ? Thank you
68 views

Building a pad for OTP on-the-fly with Diffie-Hellman

Through repeated DH attempts, could Alice and Bob build a large random key for use as a one-time pad? My intuition is that this protocol would be as hard as breaking DH (discrete logarithm).
109 views

What Java actually stores inside Keystore when generating Keys?

When we use Keytool to generate a Keystore to store Private/Public keys, what Java actually stores inside the Keystore file ? I ...
326 views

Encryption of big files in Java with AES/GCM

I have to encrypt big files. Say their size ranges from 500mb to several of gigabytes. I would like to use AES/GCM/NoPadding as provided by Java 1.8 since that gives me automatic authentication and ...


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# GISRUK I: CDRC Brexit Analysis Competition

My entry in the Consumer Data Research Center’s Brexit Data Competition is called “Tension Points: A Theory & Evidence” (static), which I talked about at the 2018 GISRUK conference

There is an abstract describing some of the work that I submitted to get to the final round, but if you’re computationally inclined, you’ll find everything sufficient to replicate my modelling & analysis in this Jupyter Notebook (raw). You’ll need scikit-learn, pystan, statsmodels, and geopandas at minimum to run. Also, the data is in a sqlite data store, but it’s too large for me to host on GitHub and part of it is protected by the CDRC, so I cannot share it until these protections are lifted.

# The long & short of it:

I find that the Economist’s claim, that “high numbers of migrants don’t bother Britons, high rates of change do,” is only partially correct. It depends on the type of change.

I split change into four types using a theory about how individuals may be changing/influenced in their vote choice by changes in their community:

1. Non-UK born population changes (“people who aren’t like me”)
2. Migrants from outside the UK (“people changing the community who are new to Britain”)
3. Migrants from within the UK (“people changing the community who are new to the community”)
4. Population structure volatility (“ethnicity/character of the community changing regardless of origin”)

I find that raw non-UK population changes (factor 1) and Migrants from within the UK (factor 3) are the ones associated with a place voting Leave. Further, I find that the opposite occurs for factors (2,4), which are actually associated with Remain voting. This suggests that both population growth and internal migration within the UK matter to drive Brexit voting. It’s not enough to just consider the raw foreign born population changes, since those provide an incomplete picture of how change in population structure affected Leave voting.

I find this in a varying-slopes model, which allows for different regions of England & Wales to have different levels of baseline Brexit support. Further, I also model the first-order effects of many of these changes using the non-UK born population (white & ethnic), which provides the first-order effects for the various measures.

format: plain


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# Flutter Web App Commands – Cheatsheet

In this post, I will list down some of the key commands (cheatsheet) which can help one build and release web application (app) using Flutter.

In order for the following commands to work, follow the steps given below:

## Flutter Commands for Web

Once flutter is set up and a template project is created, execute the following one-time commands for setting up Flutter web development environment. These commands can be run from anywhere in a terminal.

flutter channel beta
flutter config --enable-web

Once the above commands executed, go to the home / root folder of Flutter project and execute the following commands. The details of these commands can be found on this page titled as building web application using flutter.

### Run the Flutter Project

flutter run -d chrome

### Build the Web Project

flutter build web

### Create Release Build

The command given below will populate build/web directory with built files, including an assets directory, which need to be served together. One should note that the minification is handled when one creates a release build.

flutter run --release
# The following command can also be used
flutter build web

The release build will create the following files / assets in build/web project folder. Take these files and put it in web root folder for any web server including Tomcat, Python, Firebase or cloud hosting (AWS, Google, Azure). More details can be found on this page related to deploying flutter app on web

/build/web
assets
AssetManifest.json
FontManifest.json
fonts
MaterialIcons-Regular.ttf
<other font files>
<image files>
index.html
main.dart.js
main.dart.js.map

### Add Web Support to an Existing Project

flutter create .

### Embed Flutter App in Web Page

Use the following command to embed flutter app in any webpage. URL is the link for flutter web page.

<iframe src="URL"></iframe>


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New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Mechanics Day
Edited by: William F. Shadwick, Fields Institute of Mathematics, Waterloo, ON, Canada, Perinkulam Sambamurthy Krishnaprasad, University of Maryland, College Park, MD, and Tudor Stefan Ratiu, University of California, Santa Cruz, CA
A co-publication of the AMS and Fields Institute.
 SEARCH THIS BOOK:
Fields Institute Communications
1996; 260 pp; hardcover
Volume: 7
ISBN-10: 0-8218-0261-5
ISBN-13: 978-0-8218-0261-8
List Price: US$114 Member Price: US$91.20
Order Code: FIC/7

This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial differential equations. The papers collected in this volume reflect these fruitful ties as well as some others, strengthened over the last two decades, with areas of applied science including control theory.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Research mathematicians and engineers.

• R. H. Abraham -- Experimental mechanics, the first forty years
• A. Baider, R. C. Churchill, D. L. Rod, and M. F. Singer -- On the infinitesimal geometry of integrable systems
• A. M. Bloch, H. Flaschka, and T. S. Ratiu -- The toda PDE and the geometry of the diffeomorphism group of the annulus
• O. I. Bogoyavlenskij -- Separation of rotations of coupled gyrostats
• A. E. Fischer -- A theory of cosmological models
• J. P. Harnad and M. A. Wisse -- Loop algebra moment maps and Hamiltonian models for the Painleve transcendants
• J. Langer and R. K. Perline -- The planar filament equation
• J. Langer and R. K. Perline -- The localized induction equation, the Heisenberg chain, and the nonlinear Schrodinger equation
• D. C. Robinson and W. F. Shadwick -- The Griffiths-Bryant algorithm and the Dirac theory of constraints
• A. D. Weinstein -- Lagrangian mechanics and groupoids
• R. Yang, P. S. Krishnaprasad, and W. P. Dayawansa -- Optimal control of a rigid body with two oscillators


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User marco caminati - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T10:24:49Z http://mathoverflow.net/feeds/user/8702 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118165/sequent-calculus-is-there-a-complete-linear-reasoning-i-e-no-trees Sequent calculus: is there a complete linear reasoning (i.e., no trees)? Marco Caminati 2013-01-06T01:21:20Z 2013-01-11T16:42:16Z
In Gentzen's sequent calculus, a formal proof is described by a tree, with each node representing the sequent obtained from the child(ren) by applying a given inference rule.

If no inference rule has more than one premise, such a tree becomes a sequence: in a 1957 paper, Craig devised Linear Reasoning to pursue such an idea; an evolution of this approach (seemingly related to Craig's famous interpolation theorem, by the way) is exposed in the standard First-Order Logic textbook by Smullyan (chapter XVII in my edition).

The corresponding theorems, however, pose various restrictions: for example, on the form of the sentences involved.

Is linear reasoning possible in more general cases?

For example, is there a sequent calculus giving linear proofs and being simultaneously complete (and sound, of course) for classical first order logic? Or, on the contrary, is there some result limiting similar ambitions?

P.S.: I know about deep inference, so let us restrict to standard' sequent calculi.

Background

When faced with the task of formalizing sequent calculus on a set theoretical proof assistant (Mizar), I felt trees would have been not so easy to actually work with, so I devised alternative frameworks. It worked, in the sense that one can manage not to ever mention trees and still carry on a great deal of results; however, they are still morally there, hence the question arose naturally.
 http://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies/118264#118264 Answer by Marco Caminati for Usage of set theory in undergraduate studies Marco Caminati 2013-01-07T11:01:55Z 2013-01-07T20:35:26Z
There are some kids with that wonderful attitude of asking "why?" about anything. The existence of a few syntactically simple axioms beyond which you cannot ask why anymore, as opposed to the discouraging "turtles all way down" approach, can be comforting to such minds, I think.

In these cases, I feel that the existence, and even the variety, of foundations should be mentioned, and made intriguing, early, which is a very delicate task.

The problem, of course, is that probably a child isn't generally prepared to face the rigors of formality, and the complexity of what there is between axioms and doing $2+2$.

This too often leads to never mentioning foundational issues, not even at college: I did physics at university and the most foundational stuff I was ever exposed to were the Cantor set, Dedekind cuts and $\epsilon / \delta$ definitions.

I think that in early education, the operational approach, as opposed to theoretical definitions, can be more appropriate, partly due to the fact that elementary school is expected by the adults to teach children how to perform numerical calculations. Later, however, when the confidence with the object one is manipulating all the time, at least the glimpse of foundations should be given: even only so that those interested can dig it. I sorely regret that didn't happen to me when I was younger, for example.

It is interesting that the opposite approach (heavy set theory from an early stage) was experimented in the past, and with little success: New Math.
 http://mathoverflow.net/questions/108138/how-to-tell-a-paradox-from-a-paradox/108165#108165 Answer by Marco Caminati for How to tell a paradox from a "paradox"? Marco Caminati 2012-09-26T14:34:39Z 2012-09-26T14:34:39Z
Although I am not so good with philosophical subtleties, I have always found useful to make a distinction between an antinomy and a paradox. The first leads to a formal contradiction, i.e., a logical inconsistency in your theory (you can prove both a formula and its negation).

The second merely' defies human intuition, without being a (known) antinomy. Much less worrying (ask Frege :)).

Many just use `paradox' for both things, but I find this highly confusing.
 http://mathoverflow.net/questions/92148/interesting-conjectures-discovered-by-computers-and-proved-by-humans/92149#92149 Answer by Marco Caminati for Interesting conjectures "discovered" by computers and proved by humans? Marco Caminati 2012-03-25T09:55:47Z 2012-03-25T10:09:55Z
You seem to be asking about computers formulating conjectures later proved by humans. As one not having had much exposure to the issue, I wonder how to teach a computer (maybe with some form of heuristics?) assessing it has found a plausible conjecture: in this case computer misses the comfort of knowing a result is true for it has proven it's true, while human mathematicians can use instinct or some kind of common sense. However, I found this:

A Symbolic Finite-State Approach For Automated Proving of Theorems in Combinatorial Game Theory
 http://mathoverflow.net/questions/76641/a-book-about-model-theory/76817#76817 Answer by Marco Caminati for A book about model theory Marco Caminati 2011-09-29T23:47:38Z 2011-09-29T23:55:46Z
Rather than to a book, I point you to real formalizations in a set theory: I deem this appropriate given the question itself. Otherwise, downvote me please :)

I happen to have formalized in Mizar set theory (which is Tarski-Grothendieck, i.e. ZFC on steroids) the stuff you seem pointing to: language, wffs, interpretation, satisfaction relation, evaluation, sequent derivability, provability, etc...

In FOMODEL1: http://mizar.auburn.edu/version/current/html/fomodel1.html

you get most syntax (up to definition of atomic formula, or 0wff).

In FOMODEL2: http://mizar.auburn.edu/version/current/html/fomodel2.html

you will find the definition of satisfaction.

That is a series of five subsequent articles starting from scratch and getting to completeness theorem (and Lowenheim-Skolem, the latter only on my homepage, not submitted to Mizar people yet). The links point to hypertextual, proof-pruned versions. For full formalizations, look for the same files with the extension .miz in that same server.

Mizar formalizations are arguably among the most readable for the average mathematician (that's the factor that got myself started with it), that's why I thought you could find this stuff of some interest.
 http://mathoverflow.net/questions/45185/pseudonyms-of-famous-mathematicians/45340#45340 Answer by Marco Caminati for Pseudonyms of famous mathematicians Marco Caminati 2010-11-08T19:06:03Z 2010-11-08T19:06:03Z
At the height of fascist persecution of jews, Federigo Enriques penned some of his articles as Adriano Giovannini (reputedly coined from the names of his daughter Adriana and of his son Giovanni), as a device to circulate them. I was able to trace back to that pseudonym at least two papers: "Il pensiero di Galileo Galilei" and "L'errore nelle matematiche". As I understand it, that is to be considered a pseudonym used just in publications rather than a fully new name for real life, so I deemed the answer qualifying with regard to the question requirements.

Also, not being able to comment others' answers:

I can add von Neumann as good example of the category depicted in Andreas' answer.

As an anecdotal gloss to the Germain/Le Blanc case, it seems that even a century later that would have been a wise move: apparently Renato Caccioppoli was not so confident in women's mathematical capabilities, and it is said that once he ended examining a brilliant student of him with "Signorina, nonostante lei sia una donna le devo mettere 30 e lode.", which runs like: "Miss, despite you being a woman, it seems like I will have to give you A+".

 http://mathoverflow.net/questions/29911/whats-the-notation-for-a-function-restricted-to-a-subset-of-the-codomain/36449#36449 Answer by Marco Caminati for What's the notation for a function restricted to a subset of the codomain? Marco Caminati 2010-08-23T14:06:04Z 2010-08-23T14:19:09Z
This would fit as a response to Harald Hanche-Olsen's remark, but I have not enough points for this.

Anyway, Mizar mathematial library chose exactly this notation; actually, it is introduced in the article on basic relations RELAT_1.MIZ, Def. 12, so it fits any relation and any set.

In a Mizar article you have just ASCII, so no subscripts, but you can always avoid ambiguities like f|X versus X|f by typing the two objects appearing in the notation as Relation and set respectively. I find interesting that what is expressible on paper by varying font size is emulated by typing in a proof checker.
 http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/36446#36446 Answer by Marco Caminati for Examples of great mathematical writing Marco Caminati 2010-08-23T13:54:12Z 2010-08-23T13:54:12Z
I wish someone had told me about this book when I was younger: A.I. Mal'cev, Algorithms and Recursive Functions.

The exposition is simple, thought provoking and rigorous. You are teased to delve into many strains when reading it.
 http://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies/118296#118296 Comment by Marco Caminati Marco Caminati 2013-01-08T10:58:45Z 2013-01-08T10:58:45Z @mbsq: I'm sorry, but I just can't figure out what you mean by eternal and absolute math, so it's difficult to reply. I am interested to your point that you can pursue rigor without sticking to no "particular theory": how would you do that? To me, it sounds like saying that you can write a poem without using any particular alphabet. Anyway, reading my comments now, they sound a bit too polemical; I apologize for that. http://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies/118296#118296 Comment by Marco Caminati Marco Caminati 2013-01-07T21:19:20Z 2013-01-07T21:19:20Z @mbsq-part two: The fact that multiple, particular choices to encode foundations exist should not mislead anyone into thinking that the results obtained by studying them (not only by applying them) are less "eternal" than the results you arbitrarily classify as such: your whole post is ultimately pivoted on such a subjective (and scarcely elaborated on) distinction. Finally, I find ironic that you deployed the fruits of reverse mathematics, arguably a foundational discipline, to dismiss the importance of foundational studies. http://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies/118296#118296 Comment by Marco Caminati Marco Caminati 2013-01-07T21:19:07Z 2013-01-07T21:19:07Z @mbsq-part one: It seems to me that you have a merely utilitarian view of mathematical logic and foundational disciplines: as if they are "only" needed to attain consistency and rigor (which, by the way, is, in my opinion, as vital as creativity to mathematics: I dare to say that mathematics is a beautiful interplay between rigor and mental pure creation). What makes them even more exciting, to me at least, is that they are a beautiful subject of mathematical investigation themselves, giving them a special "double face" status. http://mathoverflow.net/questions/45185/pseudonyms-of-famous-mathematicians/45340#45340 Comment by Marco Caminati Marco Caminati 2011-03-26T10:36:14Z 2011-03-26T10:36:14Z Following your remark, I soft-documented a bit about Caccioppoli, and now I embrace your interpretation of his (alleged) statement :)


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What is the range of the function $f:[-1,1] \rightarrow \mathbb{R}$ defined by $f(x) = 12x^2 + 5x\sqrt{1-x^2} - 10$?

I was navigating through math exercises about functions and I got with this question

If $f:[-1,1] \rightarrow \mathbb{R}$ defined by $f(x) = 12x^2 + 5x\sqrt{1-x^2} - 10$.

Give the range of $f(x)$ in the reals.

Any help will be appreciated

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Hint : If they exist, can you find the minimum and maximum points? –  Euler....IS_ALIVE Oct 25 '12 at 21:24
Note that $f$ is only defined on $[-1,1]$, hence candidates for extrema are $-1$, $+1$ and zeroes of $f'$ in that interval. –  Hagen von Eitzen Oct 25 '12 at 21:24
Well,I know the domain is -1,1 and the answer, it is -21/2, 5/2, but I am interested in how to solve it algebraically. Any other hints? –  chubakueno Oct 25 '12 at 21:27
Hagen von Eitzen has given you the process. What do you get for $f(-1), f(1), f'(x)?$ –  Ross Millikan Oct 25 '12 at 21:44
I did't know how to use derivatives, but thank you for the help –  chubakueno Oct 26 '12 at 1:51

Finding the derivative and solving $f'(x)=0$ may be unpleasant. So it is natural to let $x=\cos t$ where $0\le t\le \pi$. Our function is then $12\cos^2 t+5\cos t\sin t-10$. If we are in a calculus mood, differentiate.
But if we are in a trigonometric mood, we can use the identities $\cos 2t=2\cos^2 t-1$ and $\sin 2t=2\sin t\cos t$ to rewrite our expression as $6\cos 2t+\frac{5}{2}\sin 2t -4$, or equivalently $$\frac{13}{2}\left(\frac{12}{13}\cos 2t+\frac{5}{13}\sin 2t\right)-4.$$ Let $\varphi$ be an angle whose sine is $\frac{12}{13}$ and whose cosine is $\frac{5}{13}$. Then our function is $$\frac{13}{2}\sin(2t+\varphi) -4.$$
For $t$ in our interval, $\sin(2t+\varphi)$ has maximum value $1$ and minimum value $-1$. From this we see that the maximum and minimum values of $f(x)$ are $\dfrac{13}{2}-4$ and $-\dfrac{13}{2}-4$.


text:
# C[omp]ute

Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

© 2006-2015 Andrew Cooke (site) / post authors (content).

## Not The Onion: Google Fireside Chat w Kissinger

From: andrew cooke <andrew@...>

Date: Fri, 24 Apr 2015 17:17:15 -0300

https://www.youtube.com/watch?v=wooGL__-OvA

> In recent years, many of us have gone from reading books to quickly
> digesting lots of information online through short headlines. But when you
> learn things in fragments, you lose nuance and context

...like chatting with war criminals?

Ewww.

Andrew

## Previous Entries

### Bicycle Wheels, Inertia, and Energy

From: andrew cooke <andrew@...>

Date: Sun, 19 Apr 2015 17:44:45 -0300

Introduction

It's common to hear that larger bicycle wheels accelerate more slowly because they have a larger moment of inertia. But a thread on Reddit raised interesting questions that pushed me to think more carefully about the physics involved.

Physical Model

First, we need a model for a wheel. I will ignore the hub, and consider just two components - spokes and "rim and tyre together" (for simplicity I'll sometimes refer to the latter as just "rim" below, but the tyre is obviously important too).

(I'm excluding disks because I am not sure how they are made. I may return to them later).

I'm assuming that spokes are of length $$r$$, while the rim and tyre are of length $$2\pi r$$. That is an approximation - the spokes are shorter, and the rim is slightly shorter than the tyre, and of finite depth. But it's likely good enough.

Masses and Moments of Inertia

To get masses I'll use linear density for all the spokes (summed). In other words, $$M_S = r \, \rho_S$$. Similarly, for the rim, $$M_R = 2 \pi \, r \, \rho_R$$. So the total mass $$M = r \, (2 \pi \rho_R + \rho_S)$$

The moment of inertia of the rim, $$I_R$$, about the axle is simple, just $$M_R r^2$$ or $$2 \pi r^3 \rho_R$$.

The moment of inertia of the spokes is a little more complex because they are not a disk (the effective density decreases with radius). So let's go back to basics:

$I_S = \int_0^r x^2 \rho_S \, dx = r^3 \rho_S \, / \, 3$

So the total moment of inertia of the wheel is $$I = r^3 (2 \pi \rho_R + \rho_S / 3)$$.

Energy

To accelerate a bicycle to velocity $$v$$ we need to expend energy in both accelerating the centre of mass and in rotating the wheel. When the bike is moving with velocity $$v$$ the wheel rotates with angular velocity $$\dot\theta = v / r$$. The total energy required is

$E = \frac{1}{2} (M v^2 + I \dot{\theta}^2) = \frac{1}{2} v^2 \left[r (2 \pi \rho_R + \rho_S) + r (2 \pi \rho_R + \rho_S/3)\right] = 2\,rv^2(\pi \rho_R + \rho_S / 3)$

It's interesting to express this as a ratio relative to the energy from the centre of mass alone. This gives the factor of "extra work" because the wheel rotates:

$X = \frac{2\,rv^2(\pi \rho_R + \rho_S / 3)}{rv^2 \, (2 \pi \rho_R + \rho_S) / 2} = \frac{4\pi \rho_R + 4\rho_S / 3}{2 \pi \rho_R + \rho_S}$

Discussion

First, pretty clearly, $$X>1$$. In other words, as is commonly known, rotating mass hurts. It's close to twice as "bad" in terms of the total energy required to reach a particular speed.

Second, $$E$$ increases with $$r$$. That means that larger wheels mean you need to do more work. But how much more?

There are two ways to look at this. One way is to note that because $$X > 1$$, a larger wheel is worse than you would expect from the weight alone. The "effective mass" is almost twice as bad. But the other way is to note that, perhaps counter-intuitively, that relationship is only linear. You might expect increasing wheel size to hit you "quadratically" - more than you'd expect from the effective mass alone. But it doesn't. And one way to explain this is given in the Reddit thread I linked to earlier - for a given speed over the ground, a larger wheel rotates more slowly.

Andrew

### Another Tax Fraud

From: andrew cooke <andrew@...>

Date: Sun, 19 Apr 2015 15:52:51 -0300

..

This is a loose translation of an article in La Tercera, 2015-04-19.
The online version can be seen at

This translation is unofficial, amateur, and made mainly to help improve my
Spanish.  Please do not rely on this for any important detail.

Andrew

The Sophisticated $8,000m (US$13m) Tax Fraud

* The accused used a complex network of companies to avoid paying taxes for 6
years.

* Fraudulent tax invoices were exchanged between companies.

By Felipe Diaz and Victor Rivera [original byline]

At the end of Q3 2014, before false tax invoicing was a common topic of
conversation, the Tax Office (SII) detected a series of irregular returns from
a group of investors who planned to defraud the State of $8,638,098,553 between 2005 and 2011. So started an investigation of one of the country's largest tax evasions, both by total amount and number of people involved. On October 21 2014 the SII lodged a complaint with an investigating Judge [7th Juzgada de Garantia de Santiago] against 5 people for tax evasion [delito tributario sancionado en el articulo 97 no 4] - the submission of maliciously incomplete and incorrect tax declarations. According to the SII investigation the accused had "created fictitious companies whose only function was to increase IVA [VAT / Purchase Tax] credited to other companies owned by the same group, decreasing the taxable income declared to the authorities" [I'm unsure on the exact details]. Evidence was provided to the Public Prosecutor [Fiscalia Centro Norte] and Police (Financial Crimes Division) [Brigada Investigadora de Delitos Economicos Metropolitana (Bridec) de la PDI]. Modus Operandi According to the investigation, the first network of companies was constructed between 2005 and 2008 by the accused Luis Mardones Sanches, together with Fernando Nanjari Alvarez, acting as legal advisor, and Fernando Kiblisky Budnik, as financier. They created 6 companies (staffing agencies): Servicios de Personal Urbe DA; Servicios Integrales de Personal SA; Productora Nacional de Servicios SA; Gamma Servicios de Personal SA; Global Work SA; and Delta SA. The aim, according to the complaint, was to "provide false invoices to companies Delta SA and, finally, Cicorp SA (administered by the accused Miguel Sepulveda Eljatib and his legal representative (and company lawyer) Mario Cartes Eljatib)." Similarly, "Cicorp SA, in turn, provided false invoices to Telecommunicaciones Siglo XXI SA, Intercity Service, Nuble Ingenieria SA, Constructora Perez y Gomez SA, who all charged for supposed computational services, for plans and three dimensional models. These companies were controlled by the accused Miguel Sepulveda Eljatib and Mario Cartes Eljatib." During that period, according to SII estimates, the fraud amounted to$5,675,257,345.

Between 2009 and 2011 the formula was repeated.  Some companies were
continued, and Bristol SA, Agency SA, and Laborum SA were added, as staffing
agencies, providing services to Delta SA and Milenium SA, which in turn
invoiced for non-existent services to Efco Servicios Generales SA.  The amount
involved over this period comes to $2,962,941,208. The complaint ends with "all the details above, taken together, show irregularities involving all the companies, with the aim of avoiding tax on sales and services, using false invoices on non-existent commercial operations [again, not sure I have this exact]." Response La Tercera tried to locate all the involved, succeeding only in contacting the lawyer of Cicorp SA, Mario Cartes. Via email he said that "I am not the legal representative, nor a member or an investor, in any of the companies mentioned in the complaint. I also have no relationship with the other people listed, except Miguel Sepulveda, who is a relation, and I have been lawyer for him personally, and for his company, Cicorp SA." He added that "with respect to the objections made against providers to Cicorp SA, I have cooperated completely since 2009, when I delivered to the SII all the accounting and tax details they requested, and so I expect that when the investigation is complete the situation will be clarified." ### Google's Borg From: andrew cooke <andrew@...> Date: Sun, 19 Apr 2015 14:02:36 -0300 A paper I should read some time http://research.google.com/pubs/pub43438.html Andrew ### Spanish Accents For Idiots From: andrew cooke <andrew@...> Date: Thu, 16 Apr 2015 08:18:30 -0300 My homework. http://acooke.org/accents.html Andrew PS I am taking spanish lessons from a phonologist (wife of a friend) and it's really helping. ### Aluminium Cans From: andrew cooke <andrew@...> Date: Wed, 15 Apr 2015 20:35:08 -0300 https://www.youtube.com/watch?v=hUhisi2FBuw How the pull-tab works, at the end, is particularly interesting. Andrew ### Advice on Spray Painting From: andrew cooke <andrew@...> Date: Wed, 15 Apr 2015 18:14:50 -0300 http://www.reddit.com/r/DIY/comments/32ouoq/why_cant_i_spray_paint_anything_and_have_it_look/ Andrew ### Female View of Online Chat From a Male From: andrew cooke <andrew@...> Date: Tue, 14 Apr 2015 13:28:40 -0300 https://np.reddit.com/r/truecreepyPMs/comments/3298o8/this_is_a_post_that_some_of_you_are_asking_me/ ANdrew ### UX Reading List From: andrew cooke <andrew@...> Date: Mon, 13 Apr 2015 06:35:19 -0300 No idea how complete it is, but a couple of interesting looking titles I would like to read at some point. https://medium.com/@span870/the-only-ux-reading-list-ever-d420edb3f4ff Andrew ### S4 Subgroups - Geometric Interpretation From: andrew cooke <andrew@...> Date: Sun, 12 Apr 2015 20:48:24 -0300 Interesting discussion / example - http://www.reddit.com/r/math/comments/32bs56/understanding_the_subgroup_structure_of_s4/ Andrew ### Fucking Email From: andrew cooke <andrew@...> Date: Sat, 11 Apr 2015 19:37:44 -0300 I spent a day translating an article on SQM from Spanish to English. The email contained, as an aid to formatting, a line with a single dot, at the start. People as old as me may remember that a single dot is also how you terminate a message using the primordial Unix mail command. And it seems that somewhere, in the layers of abstraction that current email is built from, that is still interpreted as the end of the message. So my entire email was discarded, except for the header. Fucking email sucks in so many ways. Still, if I have "From" at the start of a line, it is prefixed by >, somewhere, in some kind of hack to avoid it being interpreted as the sender. And, of course, no authentication. No encryption. Sigh. I may try again tomorrow; perhaps second time round it will be quicker. Andrew ### The SQM Affair For Idiots From: andrew cooke <andrew@...> Date: Sat, 11 Apr 2015 17:55:20 -0300 .. This is a loose translation of https://politicasparatodos.wordpress.com/2015/03/16/el-caso-sqm-explicado-con-manzanitas/ by Matias Godoy Mercado. I cannot guarantee the truth of what is written below for two reasons. First, my Spanish is imperfect. I am particularly unsure of technical terms (eg "impuesto de primera categoria"). Second, I don't have the general knowledge of Chilean politics necessary to check the details given (I am translating partly to learn about these things myself). So please use the original (linked above) as reference. See also * The Penta Affair For Idiots http://acooke.org/cute/ThePentaAf0.html I generally translate the names of government institutions and common Chilean details like Boletas: * La Fiscalia - Prosecutions Office (CPS/DPP in UK, Attorney General in USA) * Fiscal - Public Prosecutor * SII (Servicio Impuestos Internos) - Tax Office * Boletas De Honorarios - Tax Invoices (emitted by the person being paid for some professional service) * SVS (Superintendencia de Valores y Seguros) - Securities Commission (FSA in UK) * AFP (Administradoras de Fondos de Pensiones) - Pension Funds * La Moneda - Presidential Palace * Fisco - Treasury I have decided not to translate names of companies and political parties, so here is a quick glossary of the main parties (right to left): * UDI - Union Democrata Independiente / Independent Democratic Union * RN - Renovacion Nacional / National Renewal * PRI - Partido Regional Independiente / Regional Independents * PDC - Partido Democrata Cristiana / Christian Democrats * PPD - Partido Por La Democracia / Party For Democracy * PS - Partido Socialista / Socialist Party * PC - Partido Comunista / Communist Party where UDI/RN are members of Alianza Por Chile (right), and the others members of the Nueva Mayoria (prev La Concertacion) (centre+left). Also * RUT - personal ID number (SSN in USA) * CORE - regional assemblies * Senado (upper chamber of Parliament) is composed of Senators * Camera de Diputados (lower chamber) is composed of Delegates I have added comments in [square brackets]. Comments (in parentheses) are present in the original. Finally, my thanks to Matias, who I have been unable to contact (if anyone knows his email, please tell me at andrew @ acooke.org) Andrew In this column I [ie Matias] will give the background to the SQM (or Soquimich) case, to date [the column was written on 2015-03-16 and there have been developments since - see comment below]. Although, to be exact, the "SQM case" is not yet a "case". Give this, some people are calling it an "angle" on the Penta Affair. But, given the current data (scarce but meaty), I feel more comfortable calling it a "case", even though it is not, yet, for the Tax Office. In the first section I will talk about Soquimich, the Chilean company. In the second section, we'll take a brief look at the Cascadas Affair, which involved this and related companies, for context about who we are discussing. In the third, I will discuss the evidence for a careful and detailed examination of this company, given the apparent irregular financing of political campaigns, and fiscal fraud. In the fourth part I will address the strange conflict between the Prosecutions and Tax Offices (SII and Fiscalia), in this case. [There was also a fifth section, which I have not translated, which was mainly a call to get people to tweet in the hope of changing the policy of the SII. Instead, I've added a note explaining how things developed.] Sociedad Quimica Y Minera De Chile (Soquimich or SQM) The Sociedad Quimica Y Minera De Chile (SQM) is a private mining company dedicated to the extraction, processing and marketing of mineral products; mainly iodine, potassium and lithium. It was created in 1968 as a mixed public / private enterprise, like many of the large Chilean companies. In 1971 it passed into the control Corporacion De Fomento A La Produccion (CORFO), ie the Chilean State. Then, during the 80s, it was privatised. [Some historical context: Allende was elected in 1970; the coup lasted from 1973 to 1990]. This company won the rights to develop lithium mining. [Beating 5 other companies in a controversial contest; the then Minister of Mining was the brother of the SQM Executive Vice President - http://www.mining.com/divisive-contract-to-exploit-lithium-in-chile-granted-to-local-sqm-80677/] From December 2012 Sociedad de Inversiones Pampa Calichera S.A., Inversiones Global Mining (Chile) Ltda, and Potasios de Chile S.A. (together, Grupo Pampa) control 31.97% of the shares in SQM. The head of SQM is Sr. Julio Ponce Lerou, Forestry Engineer from U of Chile, ex son-in-law of Gen. Augusto Pinochet Ugarte, who is currently President of the Board of Directors of SQM SA, Norte Grande SA, Oro Blanco SA and Sociedad de Inversiones Pampa Calichera SA. Julio Ponce And The Cascadas Affair In September 2013, after questions were raised by Moneda Asset and Chilean Pension Funds (AFP) about the financial state of SQM, the Securities Commission (SVS) brought charges against Julio Ponce Lerou for his responsibility in various synchronised market trades between 2009 and 2011, that led to the assumption of price rigging in SQM shares, leading to losses on the part of the Pension Funds and Moneda Asset. Julio Ponce remains in control of SQM despite the scheme called "cascada" [waterfall]. How did it work? We will return to Snoopy. Suppose that Snoopy is owner of 51% of the shares in a company called Gold. The company Gold, in turn, owns 51% of the shares in a company called Silver. So Snoopy controls both companies: Gold directly, and Silver though Gold. Let's complicate things a little. Snoopy owns 51% of the actions in a company called Gold. But now Gold only owns 25 of the shares in Silver. However, Snoopy has another channel. As well as shares in Gold, Snoopy has 51% of the shares in a company called Copper. And Copper owns 26% of the shares in Silver. In this way, Snoopy controls Gold and Copper directly, and Silver through two different channels. The name "waterfall" comes from how the control of the companies flows from top to bottom, like w a waterfall. Julio Ponce has control of SQM through two "cascadas". Julio Ponce controls a company called Norte Grande, which controls Oro Blanco, which controls Pampa Calichera, which, finally, controls 23% of the shares in SQM. In addition, Norte Grande controls Nitratos de Chile, which controls Potasios de Chile, which also has shares in SQM: 7%. So in total Ponce controls 30% of the shares in SQM, indirectly. What Ponce did was as follows. He sold low and bought high. What was he dealing in? Shares of SQM, Pampa Calichera, and others. Ponce, via some company in the "cascada", sold shares of another company in the "cascada", at a lower than market price, to a third company, X. This company X then resold the shares back to a company in the "cascada", at a price higher than market price. The result? To artificially change the value of shares in the transactions. These operations were made with 5 minutes delay. That is, Ponce recovered the shares he had sold 5 minutes earlier at a higher price. He did this repeatedly. In 5 minutes Ponce was able to manipulate his share price, thanks to the intermediary. In 5 minutes Ponce changed something that cost$50 into something that cost $70. If it's not clear, here's my final attempt. Returning to Snoopy. Snoopy controls Gold, which has shares in Silver. And Snoopy controls Copper, which also has shares in Copper. Suppose that Snoopy calls his friend Charlie, who controls the company Peanuts. Snoopy says "buy my shares in Silver, I'll sell you them cheap, but you've got to sell them back to me at a higher price afterwards." Charlie asks "what's in it for me?" Snoopy replies "the difference in price." Charlie accepts. Charlie, through Peanuts, buys a share in Plata at$50 from Gold.  The company Gold, and all its shareholder
lose by selling the share so cheaply.  Then Peanuts sells the share in Plata
to Copper, at $70. Peanuts earns$20.  Snoopy continues to control Silver and
the shares have changed in value: what was worth $50 is now worth$70.  Gold
lost.  Copper lost too, because they paid $70 for something worth less. The Securities Commission (SVS) fined 8 executives and a stockbroker, including Julio Ponce and Leonardo Vial, ex President of the Board of LarrainVial SA and majority shareholder in Blanco y Negro SA (Colo Colo) [one of the big Chilean football clubs]. The fines reached USD$164m, one of the
highest fines from the Commission in decades.

SQM And Politics: The New Penta

Months passed and the Cascadas Affair faded from the press.  The 2013
presidential and parliamentary elections were in the spotlight, and attention
was focused on the fight between the 9 presidential candidates, the right
wing primaries, the fuzz leadership of Michelle Bachelet, and others.  The
government changed; Michelle Bachelet became President of the Republic; taw
reform; education reform; etc.  SQM could relax.  It was only the eye of the
hurricane, but it seemed like the case was closed.  The fines seemed kinder
than the public criticism.  But, as the priest said, some sins still needed to
be forgiven.

The press jumped on the Penta Affair.  Which you already understand perfectly.
If not, I suggest you read
[translated at http://www.acooke.org/cute/ThePentaAf0.html].  One of the
critical points of the Penta affair was the evidence of a possible crime of
bribery and asset laundering by the ex Sub-secretary of Mining, Pablo Wagner.
This, thanks to the testimony of Hugo Bravo, ex Managing Director of Empresas
Penta.  The work of the Prosecutions Office intensified, hoping to shed
further light on this particular angle.  And so they arrived at Carolina de la
Cerda, sister in law of the Sub-secretary.

Carolina de la Cerda testified to having issued Tax Invoices for Pablo Wagner.
She wrote the invoices to avoid Wagner appearing to be offering services, as
he was already Sub-secretary of Mining.  The Prosecutions Office was going
after Empresas Penta.  But Carolina de la Cerda gave them something else:
Soquimich.  Carolina de la Cerda testified: "(Wagner) gave me a phone number to
call when the money arrived, to cash three cheques for people and amounts
specified, the person, whose name I can't remember, gave me the names Cristina
Bitar, Ernesto Silva Bafalluy and Lorena Espinoza.  I wrote the invoice for
the company Soquimich for 'financial services'."  [The original Spanish is
garbled, to me, and my translation is even worse here than elsewhere.]  With
this information it was clear that Empresas Penta was not the only company
irregularly financing political campaigns through false invoicing.

With this information the Tax Office (SII) took action against Pablo Wagner
and Carolina de la Cerda.  At first, SII asked for all the accounting data for
financial years 2009 to 2014.  Then, later, and unusually, clarified their
position to the Prosecutions Service and limited themselves to July 2009.  On
January 16 the Prosecutions Service took information from the offices of SQM,
who gave them the accounts voluntarily.

The Public Prosecutor Carlos Gajardo studied the accounting.  He found 19
concerning 240 RUTs that invoiced the company in 2010
The newspaper / site claims that these have connecting with 39 Chilean
politicians.

Politicians Of Nueva Mayoria

Fulvio Rossi (PS Senator), Marcelo Rozas (PDC, ex Ambassador, Czech Republic),
Raul Castro (PDC, CORE Arica y Parinacota), Roberto Leon Araya (son of Delegate
PDC Roberto Leon), Hernan Rivera Letelier (PS, writer, ex candidate Delegate).

Politicians of Alianza Por Chile

Presidential campaign collaborators for Sebastian Pinera (RN, ex President),
advisors for Lavin Infante (UDI, ex Minister), a son of Pablo Longueira (UDI,
ex Minister), advisors for Pablo Zalaquett (UDI, ex Mayor), advisor to Jaime
Orpis (UDI Senator), advisor to Juan Antonio Coloma (UDI Senator), Gustavo
Alessandri (UDI, CORE Puente Alto), y Jorge Brito (PRI CORE Region del
Biobio).

The Division Between The Prosecutions Office And The Tax Office

The Prosecutions Office wanted to continue investigating SQM, extending the
accounting data to the period between 2009 and 2014.  But to obtain those
documents then needed the SII to press charges for tax evasion.  But the SII
has not taken action against SQM.  The newspaper La Tercera published a lead
article on Sunday 15 December, under the heading "The Escape Hatch That
Worries The Prosecutors".  They lead with: "While the Prosecutions Office
looks to seize all the accounting of SQM, the SII flexed its muscles and
opened a hatch allowing the political angle in the Penta case to hide far from
court.  The decision was welcomed by the entire political spectrum, starting
from the Presidential Palace."  [Translation not so good here.  Flowery,
mixed-metaphors in the paper.]

SQM has not provided the information requested by the Prosecutors.  The SII is
hoping for compensation from SQL to the Treasury, avoiding an investigation.
The Prosecutions Office can't believe it.  Neither can I.

[The original article was written on 2015-03-16.  Since then things have
changed.  For example, from
http://www.latercera.com/noticia/nacional/2015/03/680-621729-9-sii-entrega-hoy-la-informacion-contable-de-sqm-a-fiscalia.shtml

"At first light, today, the Tax Office will deliver to the Prosecutions
Office accounting material for the company SQM corresponding to the period
from 2009 to 2014, which the Prosecutor requested as part of the
investigations for irregular financing of political campaigns"]

https://politicasparatodos.wordpress.com/2015/03/16/el-caso-sqm-explicado-con-manzanitas/


text:
# 5.8 Non-right triangles: law of cosines  (Page 5/8)

 Page 5 / 8

Explain the relationship between the Pythagorean Theorem and the Law of Cosines.

When must you use the Law of Cosines instead of the Pythagorean Theorem?

The Law of Cosines must be used for any oblique (non-right) triangle.

## Algebraic

For the following exercises, assume $\text{\hspace{0.17em}}\alpha \text{\hspace{0.17em}}$ is opposite side $\text{\hspace{0.17em}}a,\beta \text{\hspace{0.17em}}$ is opposite side $\text{\hspace{0.17em}}b,\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\gamma \text{\hspace{0.17em}}$ is opposite side $\text{\hspace{0.17em}}c.\text{\hspace{0.17em}}$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\gamma =41.2°,a=2.49,b=3.13$

$\alpha =120°,b=6,c=7$

11.3

$\beta =58.7°,a=10.6,c=15.7$

$\gamma =115°,a=18,b=23$

34.7

$\alpha =119°,a=26,b=14$

$\gamma =113°,b=10,c=32$

26.7

$\beta =67°,a=49,b=38$

$\alpha =43.1°,a=184.2,b=242.8$

257.4

$\alpha =36.6°,a=186.2,b=242.2$

$\beta =50°,a=105,b=45{}_{}{}^{}$

not possible

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$\text{\hspace{0.17em}}a=42,b=19,c=30;\text{\hspace{0.17em}}$ find angle $\text{\hspace{0.17em}}A.$

find angle $\text{\hspace{0.17em}}C.$

95.5°

$\text{\hspace{0.17em}}a=16,b=31,c=20;\text{\hspace{0.17em}}$ find angle $\text{\hspace{0.17em}}B.$

$\text{\hspace{0.17em}}a=13,\text{\hspace{0.17em}}b=22,\text{\hspace{0.17em}}c=28;\text{\hspace{0.17em}}$ find angle $\text{\hspace{0.17em}}A.$

26.9°

$a=108,\text{\hspace{0.17em}}b=132,\text{\hspace{0.17em}}c=160;\text{\hspace{0.17em}}$ find angle $\text{\hspace{0.17em}}C.\text{\hspace{0.17em}}$

For the following exercises, solve the triangle. Round to the nearest tenth.

$A=35°,b=8,c=11$

$B\approx 45.9°,C\approx 99.1°,a\approx 6.4$

$B=88°,a=4.4,c=5.2$

$C=121°,a=21,b=37$

$A\approx 20.6°,B\approx 38.4°,c\approx 51.1$

$a=13,b=11,c=15$

$a=3.1,b=3.5,c=5$

$A\approx 37.8°,B\approx 43.8,C\approx 98.4°$

$a=51,b=25,c=29$

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

Find the area of a triangle with sides of length 18 in, 21 in, and 32 in. Round to the nearest tenth.

177.56 in 2

Find the area of a triangle with sides of length 20 cm, 26 cm, and 37 cm. Round to the nearest tenth.

$a=\frac{1}{2}\text{\hspace{0.17em}}\text{m},b=\frac{1}{3}\text{\hspace{0.17em}}\text{m},c=\frac{1}{4}\text{\hspace{0.17em}}\text{m}$

0.04 m 2

0.91 yd 2

## Graphical

For the following exercises, find the length of side $x.$ Round to the nearest tenth.

3.0

29.1

0.5

For the following exercises, find the measurement of angle $\text{\hspace{0.17em}}A.$

70.7°

77.4°

Find the measure of each angle in the triangle shown in [link] . Round to the nearest tenth.

For the following exercises, solve for the unknown side. Round to the nearest tenth.

25.0

9.3

For the following exercises, find the area of the triangle. Round to the nearest hundredth.

43.52

1.41

0.14

## Extensions

A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 12 units. Find the measure of the longer diagonal.

The sides of a parallelogram are 11 feet and 17 feet. The longer diagonal is 22 feet. Find the length of the shorter diagonal.

18.3

The sides of a parallelogram are 28 centimeters and 40 centimeters. The measure of the larger angle is 100°. Find the length of the shorter diagonal.

A regular octagon is inscribed in a circle with a radius of 8 inches. (See [link] .) Find the perimeter of the octagon.

48.98

A regular pentagon is inscribed in a circle of radius 12 cm. (See [link] .) Find the perimeter of the pentagon. Round to the nearest tenth of a centimeter.

For the following exercises, suppose that $\text{\hspace{0.17em}}{x}^{2}=25+36-60\mathrm{cos}\left(52\right)\text{\hspace{0.17em}}$ represents the relationship of three sides of a triangle and the cosine of an angle.

Draw the triangle.

Find the length of the third side.

For the following exercises, find the area of the triangle.

7.62

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
Got questions? Join the online conversation and get instant answers!


text:
## Thomas' Calculus 13th Edition

See graph. Step 1. With $y=sin(x)$, we have $y'=cos(x)$ which give the slope of tangent lines. Step 2. At $x=-\pi$, $y=sin(\pi)=0$ and $m_1=y'=cos(-\pi)=-1$, tangent line equation: $y=-x-\pi$ Step 3. At $x=0$, $y=sin(0)=0$ and $m_2=y'=cos(0)=1$, tangent line equation: $y=x$ Step 2. At $x=3\pi/2$, $y=sin(3\pi/2)=-1$ and $m_3=y'=cos(3\pi/2)=0$, tangent line equation: $y=-1$


text:
Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

A Right Charlie

Can you use this information to work out Charlie's house number?

Up and Down Staircases

Stage: 2 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down.

$4$ blocks make an up-and-down staircase with $2$ steps up and $2$ steps down.

How many blocks would be needed to build an up-and-down staircase with $5$ steps up and $5$ steps down?

Explain how you would work out the number of blocks needed to build a staircase with any number of steps.


text:
# Angular orientation.

1. May 16, 2007

### MathematicalPhysicist

in kleppner's textbook he expalins quite well why we can't have angular orientation vector (because then we wouldn't have commutavity of vectors), but we can have angular velcoity as a vector, my question is how does this work when we integrate from an angular velocity vector to get an angular orientation which is not a vector? how do we get this?

2. May 16, 2007

### D H

Staff Emeritus
You can't integrate angular velocity to get an angular orientation.

You have to integrate a transformation matrix or a quaternion instead.

3. May 16, 2007

### MathematicalPhysicist

could you give an example for this?
i mean if we have the angular velcoity vector: (w_x,w_y,w_z) how would you get an angular orientation?

4. May 16, 2007

### D H

Staff Emeritus
Here I am assuming that "angular velocity" $\omega_{B\to A}$means the angular velocity of reference frame A with respect to some other reference frame B, expressed in terms of reference frame A.

Suppose $T_{A\to B}(t)$ is the transformation matrix from frame A to frame B. Then the time derivative of this matrix is

$$\frac d{dt}T_{A\to B}(t) = T_{A\to B}(t) X(\omega_{B\to A})$$

where $X(a)$ denotes the skew-symmetric matrix generated from the vector a (i.e., X(a)b = a cross b).

5. May 16, 2007

### MathematicalPhysicist

in what course did you learn this?

i havent yet encouterd that in my studies.

anyway, shouldn't it be:
$$\frac d{dt}T_{A\to B}(t) = X(\omega_{B\to A})T_{A\to B}(t)$$

6. May 16, 2007

### D H

Staff Emeritus
You probably learned that the time derivatives of some vector quantity $\vect q$ as observed in frames A and B are related via

$$\frac {d\vect q}{dt_A} = \frac {d\vect q}{dt_B} + \omega_{A\to B}\times \vect q$$

The coordinates of the vector as expressed in frames A and B are

$$\vect q_A = \mathbf T_{B\to A} \, \vect q_ B$$

Differentiating this with respect to time,

$$\frac {d\vect q_A}{dt} = \mathbf T_{B\to A} \, \frac {d\vect q_B}{dt} + \frac{d}{dt}\mathbf T_{B\to A} \, \vect q_ B$$

The first and last equations both relate various expressions of time derivatives of a vector quantity; they just do so differently. The last equation doesn't address the frame of the observer. This is fairly easy: The time derivative of the components of some vector as expressed in some reference frame is the time derivative of that vector as observed in that reference frame.

The first equation doesn't address the frame in which the quantities are expressed.
Making these frames explicit,

$$\frac {d\vect q_A}{dt_A} = \mathbf T_{B\to A} \left( \frac {d\vect q_B}{dt_B} + \omega_{A\to B:B}\times \vect q_B \right) = \mathbf T_{B\to A}\frac {d\vect q_B}{dt_B} + \mathbf T_{B\to A}\mathbf X(\omega_{A\to B:B})\, \vect q_B$$

For the above to be true for any vector quantity $\vect q$,

$$\frac{d}{dt}\mathbf T_{B\to A} = \mathbf T_{B\to A}\mathbf X(\omega_{A\to B:B})$$

Last edited: May 16, 2007


text:
# using killed the FUN on GCC 5

An anecdote from benchmarking the compile time of mpark/variant, an implementation of std::variant for C++11/14/17.

## Introduction

std::variant has a converting constructor that looks like this:

template <typename... Ts>
class variant {
template <typename T>
constexpr variant(T &&);
};

For this constructor, we need to determine which of the Ts... will be initialized with T. For std::variant, the behavior is defined as follows:

template <class T> constexpr variant(T&& t) noexcept(see below);

Let Tj be a type that is determined as follows: build an imaginary function FUN(Ti) for each alternative type Ti. The overload FUN(Tj) selected by overload resolution for the expression FUN(std::forward<T>(t)) defines the alternative Tj which is the type of the contained value after construction.

For example, given variant<int, std::string> v("hello");, we want to create an overload set FUN with int and std::string then manually perform overload resolution with an argument of type const char (&)[6].

The following is the initial approach I took for FUN:

template <typename Head, typename... Tail>
struct FUN;

// Base case.
template <typename Head>
struct FUN<Head> {
Head operator()(Head) const;
};

// Recursive case.
template <typename Head, typename... Tail>
struct FUN : FUN<Tail...> {
using FUN<Tail...>::operator();
Head operator()(Head) const;
};

Then the winner of overload resolution can be determined using FUN like this:

using best_overload = std::result_of_t<FUN<int, std::string>(const char (&)[6])>;

The compile-time benchmark of variant’s converting constructor using this implementation looked like this on GCC 5:

A minimal example on Wandbox shows (via -ftime-report) that the cost of using this particular implementation of FUN at N = 350 is ~20s!

What’s so expensive…?

## Determining the Source

The first thing I found is that commenting out the using declaration from the above example takes the compile time down to ~0.15s. So the recursive inheritance seems fine, and the using declaration could be the issue, but by not pulling in the parent operator() we’re also no longer performing overload resolution. Could it be the cost of overload resolution?

Well, the non-recursive, hand-rolled version of FUN which does perform overload resolution takes ~0.1s. Okay, it must be the using declaration.

Now what…?

## Surrogate Call Function

When considering the overload set for a call to object of a class type, it’s not just the operator()s that get involved in the action.

For example, an implicit conversion operator to R (*)(P1, ..., PN) is also considered. They participate in overload resolution as surrogate call function with the unique name call-function and has the form:

using F = R (*)(P1, ..., PN);

R call-function(F f, P1 a1, ..., PN aN) { return f(a1, ..., aN); }

This is an example taken basically verbatim from [over.call.object]:

int f1(int);
int f2(float);

typedef int (*fp1)(int);
typedef int (*fp2)(float);

struct A {
operator fp1() { return f1; }
operator fp2() { return f2; }
} a;

int i = a(1);  // calls f1 via pointer returned from conversion function

How does this help us?

## What’s in a Name?

Why did we need the using declaration in the initial approach, anyway? It’s due to the fact that the name of the overloaded function in that case was operator(), and FUN<T, Ts...>::operator() shadowed FUN<Ts...>::operator(). So we needed to pull the FUN<Ts...>::operator() name explicitly into FUN<T, Ts...>’s scope.

With surrogate call functions, the “pulling in” happens implicitly:

Similarly, surrogate call functions are added to the set of candidate functions for each non-explicit conversion function declared in a base class of T provided the function is not hidden within T by another intervening declaration.

As such, the “name” is essentially the type of the pointer to function.

Now, we can implement FUN like this:

template <typename Head, typename... Tail>
struct FUN;

// Base case.
template <typename Head>
struct FUN<Head> {
using F = Head (*)(Head);
operator F() const;
};

// Recursive case.
template <typename Head, typename... Tail>
struct FUN : FUN<Tail...> {
using F = Head (*)(Head);
operator F() const;
};

With this implementation, at N = 350 we get ~0.6s! MUCH better than ~20s.

## Final Touch with Multiple Inheritance

Since the surrogate call functions are implicitly pulled in from the base classes, we don’t even need to keep the recursive inheritance anymore.

We can flatten, simplify, and improve the implementation with multiple inheritance:

template <typename T>
struct FUN_leaf {
using F = T (*)(T);
operator F() const;
};

template <typename... Ts>
struct FUN : FUN_leaf<Ts>... {};

Now, with this implementation, at N = 350 we get about ~0.2s! Not as drastic, but still a ~3x improvement.

## Final Remarks

This issue was discovered while I was setting up MPark.Variant/Benchmark to compare the many variant implementations out there.

My hope is that this website will help to improve the community-wide implementation quality of variant by comparing existing implementations.

Take a look at the latest GCC 5 results to see the improvements that have been made to mpark/variant!

Thanks to Agustín “K-ballo” Bergé for introducing / explaining surrogate call functions to me.

Thanks to Louis Dionne and Bruno Dutra for developing the metabench framework and setting a precedent with metaben.ch!


text:
Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

Chapter 12 - Data Analysis and Probability - 12-7 Theoretical and Experimental Probability - Practice and Problem-Solving Exercises - Page 773: 18

5/6

Work Step by Step

The probability is given by the number of favorable outcomes divided by the total number of possible outcomes. Thus, to answer this problem, first find the probability of a given event occurring. Divide that by the possible number of outcomes to get probability. The total number of possible outcomes is 6. There are 5 favorable outcomes since only 1 section is green. Thus: 5/6

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
SERVING THE QUANTITATIVE FINANCE COMMUNITY

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Heston - Reference Prices

Hello,

Can anyone suggest a paper or source that provides European option prices under Heston that have been computed to high precision (10 decimal places) for a range of strikes?

I need something to compare an implementation to. Can always compute via the standard methods, but useful if there's an existing reference set to compare to.

Many thanks

Alan
Posts: 9366
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Heston - Reference Prices

Just ran my codes in Mathematica at high precision:

dS = (r - q) S dt + sqrt{V} S dW1
dV = (a - b V) dt + c sqrt{V} dW2
dW1 dW2 = rho dt

r = 1/100, q = 2/100, S0=100, T=1, V0 = 4/100, a=1, b=4, c=1, rho= -1/2
Various strikes K below: (put, then call)

80
7.958878113256768285213263077598987193482161301733
26.774758743998854221382195325726949201687074848341

90
12.017966707346304987709573290236471654992071308187
20.933349000596710388139445766564068085476194042256

100
17.055270961270109413522653999411000974895436309183
16.070154917028834278213466703938231827658768230714

110
23.017825898442800538908781834822560777763225722188
12.132211516709844867860534767549426052805766831181

120
29.811026202682471843340682293165857439167301370697
9.024913483457835636553375454092357136489051667150

With WorkingPrecision=50, I asked Mathematica for 20 good digits, which means these
numbers should be good for about that. So treat the remaining digits as "noise".
The Fourier integral cutoff was set to Infinity, so that should not be a source of error.
Perhaps other board members can confirm, say, the first 20 digits.

Last edited by Alan on May 29th, 2012, 10:00 pm

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Heston - Reference Prices

Thanks Alan - I will compare! Are you using the generalised Fourier method or the original pricing formula? Also, what's your view on a good choice for the contour parameter in the case of the former?

Alan
Posts: 9366
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Heston - Reference Prices

I use eqn (2.10) in my book, which is likely what you (and sometimes I, too) call the generalized Fourier.
It is the same as eqn (3.10) in "A SIMPLE OPTION FORMULA FOR GENERAL JUMP-DIFFUSION AND OTHER EXPONENTIAL LÉVY PROCESSES"
The contour is Im z= 1/2, exactly half-way between the poles of the integrand.
Last edited by Alan on May 29th, 2012, 10:00 pm

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Heston - Reference Prices

I forget, but is there a numerical advantage over (3.10) to (3.5)? Clearly one advantage is you no longer have to think about the best choice of v and v=0.5 works well.

Alan
Posts: 9366
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Heston - Reference Prices

For the call option payoff, (3.10) means a contour with 1 < Im z < a. But, then you have
to check that an "a" exists such that Phi(-z) [the char function] is analytic in that strip.
This is problematic for the Heston model and many others as there are singularities for Im z > 1
and Im z < 0. Technically, the strip exists, but the legal a = a(T) and it is a waste of time to compute it
for this purpose.

So, it is uniformly better for all models to stick to contours in 0 < Im z < 1.
Phi(-z) is analytic in that one for all reasonable models.
Last edited by Alan on May 29th, 2012, 10:00 pm

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Heston - Reference Prices

Thanks - it is quite a beautiful formula :-)

wilson2
Posts: 20
Joined: May 6th, 2009, 12:23 pm

### Heston - Reference Prices

Hi Alan

I've priced these instruments with QuantLib (C++ lib, double precision on ia32) .The relative difference between your values and the QL results is always smaller than 3*10^-15.

Alan
Posts: 9366
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Heston - Reference Prices

wilson2, thanks for the check.

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Heston - Reference Prices

I'm also in agreement (to 12 decimal places) which is as far as my implementation will need to go.

Many thanks again.

JustusQuant
Posts: 20
Joined: June 14th, 2014, 9:59 pm

### Heston - Reference Prices

Hi all,

I am currently writing a paper on the Heston SV Model and in this context comparing different representations. I implemented the approaches of Heston, Carr Madan (with and without FFT) and the Cosine Method.

With all 3 methods I get results very similar to those posted by Alan. Compared to the results in Rouah (2013) on page 140, however, I tend to have some bias.

Model set up:
dS/S = (r-q)*dt + sqrt(V)*dW1
dV = k(theta-V)*dt + sigma*sqrt(V)*dW2
dW1dW2 = rho*dt

Parameters: S0 = 50, K = [41.4102, 44.0956, 46.9551, 50, 53.2424, 56.695, 60.3716],
k = 0.2, theta = V0 = 0.05, sigma = 0.3, rho = -0.7

Remarks:
-for Heston and Carr Madan I used a 32 point gauss laguerre quadrature for integration (Rouah used the same technique)
-for The Carr Madan approach I used alpha = 1.5
-for the COS approach I used [a,b] = [-300,300] and N = 2^15 to get accurate results for OTM options

Results for European Call Option:
Rouah: _________[8.6378, 6.4765, 4.4453, 2.6778, 1.3269, 0.502, 0.1421]
My COSINE:_____[8.63813, 6.47604, 4.44533, 2.67824, 1.32661, 0.50194, 0.14228]
My CM (w/o FFT):_[8.63800, 6.47604, 4.44549, 2.67805, 1.32670, 0.50189, 0.14233]
My Heston:______[8.63811, 6.47604, 4.44538, 2.67815, 1.32671, 0.50179, 0.14241]

I would be very grateful if anyone could confirm either my or Rouah's results (I could also post additional digits to my results, if needed). Many thanks in advance!

Last edited by JustusQuant on June 14th, 2014, 10:00 pm

JustusQuant
Posts: 20
Joined: June 14th, 2014, 9:59 pm

### Heston - Reference Prices

Maybe someone could answer me this question:

How can I get heston model reference prices for my paper?

My ideas:
-I could consider the special case v0 = theta, rho = 0 and sigma -->0 which corresponds to the black scholes model with implied volatility sqrt(v0).
(Problems: The results would probably not be representative for other parameter combinations)

-I could do a MC simulation in matlab.
(Problems: Computationally expensive and some error will remain)

-I could use reference prices from other papers
(Problems: My values do not converge to the prices from Rouah (2013, p.140) and I can't find many appropriate reference prices in other papers)

I would appreciate any other idea and/or comment on my thoughts.

PS: If someone is actually interested in comparing model results regarding the three approaches mentioned before (Heston, Carr Madan and COS), I could share my matlab/c++ code.

Last edited by JustusQuant on June 28th, 2014, 10:00 pm

Alan
Posts: 9366
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Heston - Reference Prices

Here you go -- my codes on the parameter set of Rouah Table 5.4 (pg 140), with a good chance all digits accurate:

Strike Call Price
41.4102 8.63812347
44.0956 6.47603004
46.9551 4.44537266
50.0000 2.67815826
53.2424 1.32672739
56.6950 0.50180502
60.3716 0.14241356

My presumption is that the strike is exact as shown, so that if you added digits to the display of it, they would all be zeros.
I used Mathematica at high precision, giving the strikes as 414102/10000, etc,
WorkingPrecision=26, and AccuracyGoal=PrecisionGoal=12 in the integration.
Setting the Fourier integral cutoff zmax to Infinity is causing me
problems, so I am using zmax = 500000, and conservatively just showing a 8-9 digit result.
Last edited by Alan on June 28th, 2014, 10:00 pm

JustusQuant
Posts: 20
Joined: June 14th, 2014, 9:59 pm

### Heston - Reference Prices

Hi Alan,

thank you very much for your help!

mj
Posts: 3449
Joined: December 20th, 2001, 12:32 pm

### Heston - Reference Prices

One thing I have found is that small $T$ and small $V_0$ render the problem challenging.

Would it be possible to get some reference prices with $T=V_0 =0.01$ ?


text:
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# The radius of the larger circle is 2 inches longer than the radius of

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07 Sep 2018, 00:12
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The radius of the larger circle is 2 inches longer than the radius of the smaller circle. If the radius of the smaller circle is r then, in terms of r, what is the ratio of the unshaded area to the total area?

A. $$\frac{r^2}{r^2 + 4r + 4}$$

B. $$\frac{\pi r}{4\pi r + 4}$$

C. $$\frac{r^2}{4r + 4}$$

D. $$\frac{r}{r^2 + 4}$$

E. $$\frac{\pi r^2 + 4r + 4}{\pi r^2}$$

Attachment:

image006.jpg [ 4.25 KiB | Viewed 440 times ]

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### Show Tags

07 Sep 2018, 08:03
Bunuel wrote:

The radius of the larger circle is 2 inches longer than the radius of the smaller circle. If the radius of the smaller circle is r then, in terms of r, what is the ratio of the unshaded area to the total area?

A. $$\frac{r^2}{r^2 + 4r + 4}$$

B. $$\frac{\pi r}{4\pi r + 4}$$

C. $$\frac{r^2}{4r + 4}$$

D. $$\frac{r}{r^2 + 4}$$

E. $$\frac{\pi r^2 + 4r + 4}{\pi r^2}$$

Attachment:
image006.jpg

Area of un-shaded portion(White)=Area of smaller circle with radius 'r'=$$\pi*r^2$$
Total area=Area of bigger circle with radius 'r+2'= $$\pi*(r+2)^2$$

Required ratio=$$\frac{\pi*r^2}{\pi*(r+2)^2}$$=$$\frac{r^2}{r^2 + 4r + 4}$$

Ans. (A)
_________________

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PKN

Rise above the storm, you will find the sunshine

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09 Sep 2018, 05:32
Area of unshaded portion = $$πr^2$$
Total area = $$π(r+2)^2$$ = $$π(r^2+4r+4)$$
Ratio = $$\frac{πr^2}{π(r^2+4r+4)}$$ = $$\frac{r^2}{(r^2+4r+4)}$$
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The radius of the larger circle is 2 inches longer than the radius of &nbs [#permalink] 09 Sep 2018, 05:32
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# Cosmological constant

## Main Question or Discussion Point

Why are the units of the Cosmological constant Lambda 1/m^2? is this just convention to make the density parameter unitless?


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This function is a wrapper for SCnorm: robust normalization of single-cell RNA-seq data (Bacher et al. Nature Methods 2017, 14:584–586)

scnorm(
group = c("sudo", "docker"),
file,
conditions = NULL,
outputName,
nCores = 8,
filtercellNum = 10,
ditherCount = FALSE,
PropToUse = 0.1,
PrintProgressPlots = FALSE,
FilterExpression = 0
)

## Arguments

group,

a character string. Two options: sudo or docker, depending to which group the user belongs

file,

a character string indicating the path of the file. IMPORTANT: full path to the file MUST be included. Only tab delimited files are supported

conditions,

vector of condition labels, this should correspond to the columns of the un-normalized expression matrix. If not provided data is assumed to come from same condition/batch.

outputName,

specify the path and/or name of output files.

nCores,

number of cores to use, default is detectCores() - 1.

filtercellNum,

the number of non-zero expression estimate required to include the genes into the SCnorm fitting (default = 10). The initial grouping fits a quantile regression to each gene, making this value too low gives unstable fits.

ditherCount,

FALSE of TRUE. Setting to TRUE might improve results with UMI data.

PropToUse,

as default is set to 0.25, but to increase speed with large data set could be reduced, e.g. 0.1

PrintProgressPlots,

produces a plot as SCnorm determines the optimal number of groups

FilterExpression,

a value indicating exclude genes having median of non-zero expression below this threshold from count-depth plots

## Value

a tab delimited file containing the normalized data and a list of the discarded genes.

## Examples

if (FALSE) {


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# How to notify me when someone comment my question?

I didn't get any notify that someone give comment to me. How to set the be alarmed? Thank you~


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## The Annals of Applied Probability

### Greedy Lattice Animals I: Upper Bounds

#### Abstract

Let $\{X_\nu: \nu \in \mathbb{Z}^d\}$ be an i.i.d. family of positive random variables. For each set $\xi$ of vertices of $\mathbb{Z}^d$, its weight is defined as $S(\xi) = \sum_{\nu \in \xi}X_\nu$. A greedy lattice animal of size $n$ is a connected subset of $\mathbb{Z}^d$ of $n$ vertices, containing the origin, and whose weight is maximal among all such sets. Let $N_n$ denote this maximal weight. We show that if the expectation of $X^d_\nu(\log^+ X_\nu)^{d+ a}$ is finite for some $a > 0$, then w.p.1 $N_n \leq Mn$ eventually for some finite constant $M$. Estimates for the tail of the distribution of $N_n$ are also derived.

#### Article information

Source
Ann. Appl. Probab., Volume 3, Number 4 (1993), 1151-1169.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005277

Digital Object Identifier
doi:10.1214/aoap/1177005277

Mathematical Reviews number (MathSciNet)
MR1241039

Zentralblatt MATH identifier
0818.60039

JSTOR

#### Citation

Cox, J. Theodore; Gandolfi, Alberto; Griffin, Philip S.; Kesten, Harry. Greedy Lattice Animals I: Upper Bounds. Ann. Appl. Probab. 3 (1993), no. 4, 1151--1169. doi:10.1214/aoap/1177005277. https://projecteuclid.org/euclid.aoap/1177005277