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Category Archives: Math

Generative Deep Learning and Bach, a Good Fit?


If you’re like me, you know that there’s never “enough Bach” in one’s life and you can always tap into infinite musical curiosities based on Bach. Using Artificial Intelligence methods such as deep learning to “train” computers for music composition is one of the fascinating recent trends in this area, and applying these automated, statistical methods to Bach chorales is an active topic of research with interesting results. The book by David Foster, “Generative Deep Learning – Teaching Machines to Paint, Write, Compose, and Play“, has a chapter dedicated to using generative deep learning methods such as MuseGAN for music composition, and explains how such “generative” models can be trained on Bach’s real polyphonic compositions to output new musical pieces in the style of Bach.

Below is an original piece created by the Generative Adversarial Deep Learning Network (GAN, in particular the famous MuseGAN network architecture). The MuseGAN deep learning network system was able to create this after training for only 1000 epochs on a moderate laptop for 2 hours (without using GPUs), based on the data set at https://github.com/czhuang/JSB-Chorales-dataset (a set of 229 Bach chorales). In other words, this is definitely not representative of what Deep Learning can achieve as best because such a system can be easily trained for longer on much more powerful systems (see further examples below). The focus of these examples is the fact that you can also start to experiment with deep learning systems that start to model musical aspects without explicit musical teaching, hard-encoded rules in software, etc.

You can click on the image below to visit SoundCloud and listen to MP3 file generated by MuseScore.

Example created by the GAN by randomly applying nornally distributed noise vectors - Click to listen on SoundCloud

Example created by MuseGAN by randomly applying normally distributed noise vectors – Click to listen on SoundCloud

Among the actual Bach chorales in the data set, the “closest” one to the artificially generated example (“close” in the sense of Euclidean distance) can be seen below. Read the rest of this entry »

 
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Posted by on December 17, 2019 in Math, Music, Programlama

 

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The Level of High School Mathematics Education in France 220 Years Ago


Whenever new PISA (Programme for International Student Assessment) results are announced, or some journalist writes a piece on the latest state of French baccalauréat exams, many people take a critical look at educational matters and make comparisons. I think a little example from the dusty pages of the history of mathematics can shed some light at the level of high school education in France back in 1800s, that is, almost 220 years ago. Who knows, it might even give some inspiration to people who want to check their standards.

The example is about the famous German mathematician Gauss: He wrote a remarkable book in 1798, humbly titled as “Disquisitiones Arithmeticae” (“Arithmetical Investigations”). The book was first published in 1801, and only 6 years later it was translated into French and published in 1807 as “Recherches arithmétiques“.

The translator of this important book was Antoine Charles Marcelin Poullet-Delisle, a math teacher at a high school: Lycée d’Orléans. Another French high school teacher, Louis Poinsot, wrote a long review about the translation in a daily newspaper on 21 March 1807, Saturday. Poinsot was a mathematics teacher at Lycée Bonaparte in Paris, just like the French translator of Gauss’s book.

The archives of the daily newspaper where Poinsot published his review of “Recherches arithmétiques” is available online at DigiNole Home » FSU Digital Library » Napoleonic Collections » Le Moniteur universel » Moniteur universel

And you can read the review on the second page of the newspaper: Read the rest of this entry »

 
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Posted by on December 11, 2019 in Math, Tarih

 

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Normality Testing: is it normal?


It is largely because of lack of knowledge of what statistics is that the person untrained in it trusts himself with a tool quite as dangerous as any he may pick out from the whole armamentarium of scientific methodology. –Edwin B. Wilson (1927), quoted in Stephen M. Stigler, The Seven Pillars of Statistical Wisdom.

Imagine you’re responsible for testing some aspects of a complex software product, and one of your colleagues comes up with the following request:

  • Hey, can you write a self-contained function to test the results of software component X, and returns TRUE if the data set generated by X is normally distributed, and FALSE otherwise?

What’s a poor software developer to do?

Well, you cherish the fond memories of your first statistics class that you took more than 20 years ago, and say: “I’ll plot a histogram of the data, and see if it’s normal!”

But of course, in less than a second you realize that manual visual inspection of a plot will not make an automated test, not at all! So as a brilliant software developer with math background, you say, “easy, I’ll just grab my secret weapon, that is, Python and its SciPy library to smash through this little statistical challenge!” You’re happy that you can stand on the shoulders of the giants, and use a well-documented, simple function such as scipy.stats.normaltest.
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Posted by on September 11, 2019 in Math, Programlama, python, Science

 

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What was the state of AI in Europe almost 70 years ago?


When it comes to the history of Artificial Intelligence (AI), even a simple Internet search will tell you that the defining event was “The Dartmouth Summer Research Project on Artificial Intelligence“, a summer workshop in 1956, held in Dartmouth College, United States. What is less known is the fact that, 5 years before Dartmouth, USA, there was a conference in Europe, back in 1951. The conference in Paris was “Les machines à calculer et la pensée humaine” (Calculating machines and human thinking). This can be easily considered the earliest major conference on Artificial Intelligence. Supported by the Rockefeller foundation, its participant list included the intellectual giants of the field, such as Warren Sturgis McCulloch, Norbert Wiener, Maurice Vincent Wilkes, and others.

The organizer of the conference, Louis Couffignal, was also mathematician and cybernetics pioneer, who had already published a book titled “Les machines à calculer. Leurs principes. Leur évolution.” in 1933 (Calculating machines. Their principles. Their evolution.) Another highlight from the conference was El Ajedrecista (The Chess Player), designed by Spanish civil engineer and mathematician Leonardo Torres y Quevedo. There was also a presentation based on practical experiences with the Z4 computer, designed by Konrad Zuse, and operated in ETH Zurich. The presenter was none other than Eduard Stiefel, inventor of the conjugate gradient method, among other things.

The field of AI has come a long way since 1951, and it is safe to say it’s going to penetrate into more aspects of our lives and technologies. It’s also safe to say that like many technological and scientific endeavors, progress in AI is the result of many bright minds in many different countries, and generally USA and UK are regarded as the places that contributed a lot. But it’s also important to recognize the lesser known facts such as this Paris conference in 1951, and realize the strong tradition in Europe: not only the academic, research and development track, but also the strong industrial and business tracks. Historical artifacts in languages other than English necessarily mean less recognition, but they should be a reason to cherish the diversity and variety. I believe all of these aspects combined should guide Europe in its quest for advancing the state of the art in AI, both in terms of software, hardware, and combined systems.

This article is heavily based on and inspired by the following article by Herbert Bruderer, a retired lecturer in didactics of computer science at ETH Zürich: “The Birthplace of Artificial Intelligence?

 
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Posted by on July 11, 2019 in Math, Programlama, Science

 

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How Students Should be Taught Mathematics


After completing the online ‘How to Learn Math‘ class give by Prof. Boaler from Stanford University, I wanted to note down many valuable references, resources and 1-page summary provided, so that I can use them in the future. (You can read another blog entry related to this: Impressions after completing the ‘How to Learn Math’ class.)

"Please submit a word that, in your opinion, describes the most important aspect of a student's ideal relationship with mathematics."

“Please submit a word that, in your opinion, describes the most important aspect of a student’s ideal relationship with mathematics.”

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Posted by on September 1, 2013 in CogSci, Math, psychology

 

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One does not simply mess with Fibonacci (especially in Belgium)


I have nothing against combining art and mathematics. After all, Leonardo da Vinci still stands as a major example who successfully did this, right? But if you are going to do it, well, at least do it correctly: I have recently read that an artist who created a sculpture to depict first few numbers from the famous Fibonacci sequence actually did not:

One does not simply mess with Fibonacci

One does not simply mess with Fibonacci


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Posted by on March 10, 2013 in komik, Math

 

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Between the Folds: An Ode to Origami (or the unlimited imagination of humanity)


I watched “Between the Folds” yesterday evening and I don’t have words or expressions beautiful and creative enough to describe and praise this masterpiece.

This beautifully prepared movie presents enough evidence that the art and science of origami is on its glorious way to be on par with other grand intellectual achievements of humanity such as music and mathematics. In less than an hour, the movie presents you with the jaw dropping examples of the progress of origami within hundred years. There are many lessons to be learned but I leave it to you to discover them by yourself.

 
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Posted by on March 3, 2013 in Cinema, Math, Science

 

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