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not 10, but 1 question

Today more than ever we ask ourselves: who bribed David Mills?

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Surprise

When he left this site a month ago, I thought it was an impromptu initiative that would end after a few weeks. But ...

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FM09010 (I)

So, let us start we the new lecture: Fourier methods and their applications to neuroscience .

Preliminary disclaimer: there are many many approaches to the topic. I will follow this one. In fact, Osgood's lecture is by far better than what I can hope to do in my life, but he has a slow pace which is not suitable for PhD students at the BCCN.

In the first lecture we explained the basic idea, which is simple: you have a complex periodic function (where complex stays for both "complicated" and "not real") and you want to represent it as weighted sum of simpler (but also not real) periodic functions. For definiteness, let us say that all functions have period 1.

We can choose to use trigonometric functions or complex exponentials . We will choose the complex exponentials for different reasons. To be precise, we want to express any periodic function of period 1 as the weighted (probably infinite) sum of the functions

  
 e_n(t):=e^{2\pi nit} 
  

where n ranges in the integers .
The difficult problem is: how to find the weights for the sum? It goes in the following way. You start from what you are looking for

  
 f(t)=\sum_{n \in \mathbb Z} c_n e^{2\pi nit} 
  

Here, the numbers c_n are the (unknown!) weights of the linear combination that you want to represent the function f. We now try to isolate a single coefficient, say the kth, to know whether is possible to get a formula for a single coefficient depending only on f and not on the other coefficients. So you get

  
 f(t)- \sum_{n\neq k} c_n e^{2\pi nit} = c_ke^{2\pi kit} 
  

You divide by the complex exponential obtaining

  
 f(t)e^{-2\pi kit}- \sum_{(n-k)\neq k} c_n e^{2\pi nit} = c_k 
  

For this you have to use all properties of the complex exponentials. Which is, by the way, only one. And in fact it is the same as for the real exponential: "sum is mapped into multiplication". This is one motivation for using complex exponentials instead of trigonometric functions.

You now have the problem that you have expressed one c_k in terms of the other ones, but you want to have c_k without its companions. Algebra gave us everything she could, so let us try with Analysis. He suggests to integrate between 0 and 1 (which is the period of all functions here) obtaining

  
 \int_0^1 f(t)e^{-2\pi kit} dt- \int_0^1\sum_{(n-k)\neq k} c_n e^{2\pi nit}dt = c_k 
  

The c_k, integrated, gives c_k! And now the magic. Compute the integral of the complex exponentials: it gives 0.
So, you are left with the famous expression

  
 \int_0^1 f(t)e^{-2\pi kit} dt- \int_0^1\sum_{(n-k)\neq k} c_n e^{2\pi nit} dt = c_k =: \\ hat {f} (k) 
 

Where We Have Introduced the symbol \\ hat {f} (k) . We will call this number by the suggestive name of the kth Fourier coefficient of f.

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... will Bersani.

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jewels of mathematics (I)

Today we are speaking part Unbeschränktheit Über die Quantenmechanik der der Operatoren Helmut Wielandt, appeared in the Mathematische Annalen in 1949.

The title, translated into Italian, means "Sull'illimitatezza operators of quantum mechanics." What are we talking about? Simplifying a bit, in quantum mechanics all the variables become operators. And if two sizes A, B are the Fourier transform of the other, then they must be such that

 [A, B] = i \\ hbar 

where we have denoted [A, B] = AB-BA the commutator of two operators.

This relationship is called the canonical commutation relation, more here. Wintner proved in 1947, using a technique developed by Rellich in 1946, that two operators satisfying the commutation relations must be unlimited. This demonstration was, however complicated, and in 1949 gave an elementary proof of Wielandt this fact. How does it work?

Wielandt on the observation that if

 [A, B] = 1 then 

 [A, B ^ {n +1}] = (N +1) B ^ n 

The proof of this fact is a simple algebraic manipulation and with an easy induction.

From this fact, and the reverse triangle inequality operatoriale applied the standard of A and B, yields an estimate of the standard

 B (n +1)  

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Fourier multipliers

Yesterday I finally figured out what they are, or rather, made what is the use of Fourier multipliers . of explaining, we need two assumptions. The first premise:

temporal representation and

spectral representation of a function are equivalent in that they contain the same amount of information.
The second premise in functional analysis of linear operators often consider very simple, called

multiplier, the multiplier, call M, with a given function, say m, is defined as
Mf (x) = m (x ) f (x) These operators are designed for simplicity and because it is possible to illustrate many definitions and many theorems using these operators. For example, the specter of a multiplier (less than technical details) corresponds to the image of the function m. Now, since as we said temporal representation and spectral representation are equivalent, it is permissible to use multiplication operators for a function in frequency domain. That is, if \\ mu
is a function, the multiplier in the frequency domain is
\\ mathcal Mf (\\ omega) = \\ mu (\\ omega) f (\\ omega) Now we can define a Fourier multiplier

 T, which is the temporal representation of a frequency multiplier space, ie 

Tf = \\ mathcal F ^ {-1} \\ mathcal M \\ mathcal F f
said in Italian: we consider the spectral representation of a function f, the multiplied with a function
\\ mu , and that we get the temporal representation. This series of operations defines a Fourier multiplier.

 Cui prodest? What is the benefit of these operators? But of course! What you can control exactly how these operators act on the spectrum! 

Some important examples

: the Laplacian 

, the Hilbert transform
, all

convolution operators, all
differential operators with constant coefficients are Fourier multipliers.

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Diplopazzia

- Did you read that good news? Finally we are friends with Gaddafi!
- But Gaddafi is a dictator. Why should I be your friend?
- What do you care if it's dictator. For oil makes us comfortable. See the end we know that Berlusconi do?
- Mah To me, this thing leaves a bit of oil 'as well. Is not it better to focus on other things, on something cleaner and home?
- Well, the President has thought of that. We will return to nuclear power.
- Well, yes, exactly. Maybe something less dangerous?
- In short, how many claims. Those who are content, enjoy.
- or die. And the sun?
- Too expensive.
- Five nuclear power plants might cost less?
- No, but produce more.
- certainly more than there servant. It will be available in fifteen years. And in the meantime? And the toxic and radioactive waste where you put it?
- will pay other countries to dispose of them there. I know.
- But this will cost us more oil, what kind of investment?
- Look, you all broke up with 'ste questions. Berlusconi is solely and exclusively the interests of the Italians, should know. He always says.
- Yes, yes. But with the Alfano and interceptions what have the Italians?
- ste Enough questions! Discuss with you is useless. If you do not like his method, then change his nationality.
- Well, very nearly.

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I'm with immigrants. Sardo is

I am fascinated by the Northern League. I do not say with irony, I really am, deep down. In front of the league I feel like a child in front of a lion, a biologist who discovers a rare species, as a poet before his muse. Fascinated and afraid.
This morning I went out cycling for a round of flyers (political activism). Around the corner I run into the usual series of election posters that colors the city ahead of elections, "Mayor Tom of all", "Caio for the country", "Vote for Harry," ... and Sitting Bull. No, I do not mean to make a name at random (in that case I would use Mevio). No, it was he, Sitting Bull. Or perhaps it was Geronimo? It matters little, call it Mad Indian and nothing else. Here it is, in the midst of familiar faces - and less - of aspiring mayors, Mad Indian, complete with feathers on its head and that air of pensive, almost sad that the Indian has lost the war. And he has reason to be melancholy: it is confined by time on a billboard in the League, alongside a slogan that wants to be convincing, but the only thing that has convinced me that ignorance has no limits. The slogan reads: "They suffered immigration. Now they live in reserves! Think about it. "
Think? Well I thought about it, and all members of the League say ignorant, cheap, stupid and ignorant again.
I hope that some sympathetic League see this sign (and other similar series is, like the figurine) and is smart enough to shake his head. And you come home to reflect on political persuasion that is embracing. Because this sign is not the gaffes of a single author, it would be too easy to think so. This slogan has been studied theoretically, designed, reviewed and corrected before being printed. It is a symbol of a thought, your thought, dear League. You will graduate, entrepreneur, professor, what you want but embraces a thought dull and limited. Are you proud?

RB,
not be proud of the League.

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Soriga: review. New drug discoveries

Foreword.

The first thing I thought when I was asked to review a book for RCS was considered a mercenary. If I wanted to get other books to review, I should write a positive review in any case, that the book I liked or not. And the temptation in this sense, I admit, has been strong. I've also tried, and is proof of the file "Soriga.odt Review" I still hold that in the documents.
I started writing this positive review when I was still half the book and I was convinced that much of what I wrote. Last night I finished reading it. I had to change review.

Flavio Soriga, Love in London and other

places I do not like love stories. He loves you, she loves him but is an impossible love because she is married to the Other, which is a repressed homosexual and drug his wife at night, wearing his clothes and goes to dance while you sleep. Eventually he meets the other in a nightclub and falls in love instead of taking a punch: in that dress reminds her too much love.
No, no, no. It is not that stuff for me.
Love in London and other places is, think a bit ', a collection of love stories. Which, in theory, would exclude a priori from my well-stocked library. But it is also an attempt at prose poetry (poetry or prose, you name it), it must be considered from a stylistic point of view, I think, even more than content. The only thing that prompted me to proceed in reading, in fact, is the attempt to make the text a musical score. Successful attempt here, failed.
The collection has eight stories, long and short. Four alone are worth the price of the book, but only if you find it at half price. Others add little or nothing. Had I been the editor, I would have waited another story as good and I published a collection of only one hundred pages instead of one hundred and fifty, in smaller format and more affordable price. But fortunately and unfortunately, not a publisher. Apart
April, the best stories are the most short and can not be otherwise: Soriga uses a rhapsodic style difficult to handle without making forcing. The short form, and in this sense, it makes things easier. For this you will appreciate the fact that you are holding a novel. Are you tired story, jump to the next and if you need advice, ask the bones on the shorter ones, then go to the first story, the only long worthwhile read.
you read the first story (April ) you will notice a difference: Sardinian Soriga is. But quietly, the syntax is not Sardinian annoying or ridiculous ending, even the little that is heard and just like garlic in a good pasta with clams, is used to flavor a plate otherwise poor.

After all, there are collections of short stories perfect. You will always find stories that will please you, others will jump after the first few lines, it hardly matters. What matters is that, sooner or later you'll come across a story that will give you something. A tale of twenty, perhaps, ten to two hundred pages, but a story by itself, as is often said in reviews, worth the price of the book. In this sense, Soriga no exception. Far from being a perfect collection, you will always find something good.

I draw the conclusions. I do not recommend buying this book Soriga with eyes closed. Get it at the library, read a few stories and then decide whether it is worth buy it. Buy a book just to try to read it makes no sense, so there are libraries. It makes more sense to buy a book you've read and I liked it, knowing that one day you read it, highlight the most beautiful phrases, lending it to a friend or why not add a dedication on the title and give it to someone you care.

Love in London and other places Flavio Soriga is published by Bompiani. You can find it in the bookstore at 15 €, or in the library.

ps I've decided that the copy I was sent for review will end on the shelf innovations in the library where I work, available for anyone to read (and disagree).
pps One day I'll take this review and will move up a dedicated blog. For now, I greet you from here.

The Next Straw Hat 2010

(il) logic

It calls PSD502 and it is probably the greatest discovery in pharmaceutical history. A spray that promises to solve one of the greatest evils that humanity has ever suffered: premature ejaculation.
Its operation was, however, the subject of great confusion. Contrary to what has been said in the press, the spray should not be sprayed male organ, but taken orally as a normal perfume for breath. Will be the woman to spray the man with the PSD502 beginning of the relationship, making sure he does not notice. The male will fall into a cataleptic state and will remain there for approximately one hour. The woman will enable the state to take advantage of rigor catalepticus man calmly and reach orgasm, take a shower, get dressed, go out shopping with her sister, come back, undress and start a second sexual relationship, which the man is obviously the first.
The drug appears to work without excessive side effects. The only side effects are found in humans, a numbness genital organ and a slight time zone syndrome. Some cases have also brought a rash of bank account due to uncontrolled use of credit cards. The woman appears to be normal euphoria continued and uncontrollable weight gain of clothes and a decrease in the level of stress. It was also shown that excessive use can lead women to drug addiction.


Two fleshy Flesh News:
- By week released the highly anticipated new blog (or a new section inparallel?) Will talk about books and movies.

- Tomorrow I graduate.

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Pubblicità Progresso

Did you know that there is an incredible system for watching movies and reading books, magazines and newspapers in a free and completely legal? Yes, you read right, free and without breaking the law! Incredible, I know. It is a system that has circulated for some 'time now, but many still do not know. Years ago, when it became public, was a huge success, was a revolutionary thing that marked an era, at least since the birth of the Internet. With this device you can watch for free the entire filmography of David Lynch or Truffaut, for example, listen to that album of rare Pink Floyd you can not find in any store, or read the latest book by Camilleri, comfortably in an armchair and all the calm you desire. All this for free, and no one will give you a thief!
Want to know how you call this system? He has a long name and perhaps difficult to remember, maybe segnatevelo somewhere: it is called Public Library.
Try it, then I'll know.

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Reo Long live! Euthanasia

Scientists confirm this: we will live up to 110 years.
A few hours after the news, shares of Tena Lady had already increased by 27%, 45% of those of Viagra. Producers of dentures cheer. In Parliament you start talking about raising the retirement age, what voices will say indiscreet to eighty. In Bologna, a few young people have left pull out your hair in public at the thought of another forty years of Berlusconi.

The news, in short, has not gone unnoticed. For me, I just get to have white hair without going crazy. If I have to lean on a cane to walk, never mind: Dr. House has made it fashionable. The rack is not that bad, especially for someone who easily forget to brush your teeth. Before going to sleep the stick in a glass of water and Hurry, and you can feel comfortable throughout the night.
What worries me, however, is Berlusconi. In 2042 will have thick hair in a ponytail and facial skin smoother than ever .* The Knights will likely candidate for Galactic Emperor and his smiling face OGN night, introduced by a Editorial Emilio Fede, will be screened in their sleep in all living things ...
They want us to live to 110 years. I hope you do not mind, gentlemen scientists, if I stop first.


* Eminent historians of literature will show that Berlusconi appeared in sleep to Scott Fitzgerald and the inspiration for the character of Benjamin Button.

Do I Have A Broken Blood Vessel In Mouth

a blog? Like hell! Praise

M the wonder of resistance Of this blog. E 'for more than three months since the public something and still have the same six players before. But you do, you are, re-read the same post in a continuous loop? Is there any step that does not understand or is there went into stand-by the optic nerve?

However, after I had almost decided for euthanasia inparallel (it is very fashionable in recent times), I consulted the most eminent personalities of the literary world and on their advice and after careful reflection, I chose to resist and keep alive my creation. The emotional force of that decision was that without even realizing it I got up shooting with clenched fists, tight lips, eyebrows, fingernails dirty and aching and I shouted 'No! Inparallel not die! At the cost of writing at night, at the cost of publishing a post every three months will not give my faithful readers! Never! '* So
here I am, if only to reassure you six-nothing: you can continue to fuck up inparallel . I take this opportunity to postpone all other next month, when hopefully I will have more time to devote to my highly intellectual activities of bloggers.





* The most observant will wonder how I managed myself to cry with her lips tightened. As in other cases, I take refuge behind the abuse and now lisa poetic license, a friend of the illiterate, even more than poets.