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Wolfram Summer School

June 18–July 7, 2017
Bentley University, Waltham, MA
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This project aims at developing a useful optical character recognition by means of a neural network. It is planned that the network will be able to understand every glyph in the world—that is, when a glyph is given as input, the net should give the correct character as output. For that, a set containing all glyphs should be provided so that we can apply many image transformations, like those in images, to train the net with a very comprehensive training set.

Multicolumn[Column[{#,ArrayPlot[Partition[IntegerDigits[#,2,4],2],ImageSize->64]}]&/@Range[0,15],{2,Automatic},Appearance->"Horizontal"]

We consider 2-dimensional block cellular automata (BCA) with intention to meet simple physical requirements such as reversibility and space isotropy. Along with general study of the whole class of 2x2-neighborhood BCA, several rule subspaces that meet physical criteria are studied. It is also interesting to examine the possibility of the energy conservation expressed in terms of local rules. The energy function is set by the Ising model. Interpretation of domain, oscillating, particle and other patterns in terms of physical phenomena were studied. Some statements about impossibility of energy conservation laws expressed by 2D 2x2 BCA local rules were proved and verified experimentally with filtration methods.

I identified four kinds of symmetric fractal trees in 3D that are determined by the type of expressions found in their boundary equations; these are trees with number of branches b=4n-1, b=4n, b=4n+1 and b=4n+2 where n takes the integer values from 1 to ∞. Several animations were produced when one walks around the critical boundaries of the parameter space, showing interesting dynamics and topological critical changes for certain angles.

My project consisted of a set of functions that can extract a plot dataset when provided the vector representation of the plot. I have been able to successfully identify axes, ticks, labels and data points for my self-generated plots. In this situation the error is negligible and depends mainly on a geometric object with nonzero area used to identify the points in the set.

The aim of this project is to identify the manifolds corresponding to networks that are generated by simple substitution rules from Stephen Wolfram's physics project. At first glance, some of the networks resemble a cell complex of a known surface. The idea is to provide techniques to substantiate this impression and figure out the geometric structure that might underlie the purely combinatorially given network.

We propose to explore a number of analytical galaxy rotation curves to create a template library of cellular automata galaxies. A quantitative measure of galaxy morphology needs to be ascertained to compare observations (perhaps at multiple wavelengths) to the CA galaxies. Polar basis functions consisting of Chebyshev rational functions TLn(r) and Fourier series (Jimenez-Teja & Benitez 2011) can be applied to both the archival survey imaging as well as the simulations. The basis coefficients for observations and models can be used as a figure of merit or metric for comparison, matching CA simulation galaxies to sets of cataloged images via the parameterized effective radius.

We have devised a simple way to introduce temporary perturbations in trinet computations and have visualized their effects by the revisit indicator, which turns out to be especially useful for this purpose. This technique can indeed be used also for exploring behaviors starting from random initial conditions.

In Their Words

Nestor Diaz

“The Wolfram Summer School was one of my greatest life experiences; I gained new tools that help me to do my research in a better way, and meeting people from many cultures around the world is something unique.”

Brian Mayer

“A life-changing experience that anyone who wants to learn the latest subjects in science and get in touch with great people should try.”

Anshul Jain

“The best three weeks of my life! From discussions about AI to art, it really was a great learning experience.”

Sa'di Altamimi

“It's like infinite knowledge compressed into a three-week program—hard working, no tiredness, only excitement!”

Milad Abou Dakka

“This Summer School went far beyond my expectations in terms of benefit to my research, smart and friendly staff, networking opportunities and an intellectually stimulating atmosphere.”

Mayla Boguslav

“I enjoyed the experience and learned a lot from other students, instructors and my mentor. The idea of looking through a defined space, searching for the interesting cases is fascinating and will change how I research, because you never know what you will find.”

Raúl Cázares

“The Wolfram Science Summer School is an amazing multi-disciplinary and multicultural experience. It changes your mind, the way you usually work, gives you more points of view and helps you for your career.”

Emmanuel Salawu

“The best thing that happened to me in July 2013 was attending the Wolfram Science Summer School! Its memories will linger, and the knowledge gathered will forever be handy. I can't predict the future, but I am confident of this.”

Ruaridh O'Donnell

“It doesn't matter that much if you don't have a clear idea for a project, what you do in the end doesn't really matter, it seems like it would be fun doing any project.”

Weili Luo

“It is a truly interdisciplinary and intercultural experience that I will never forget…

The NKS Summer School enabled me to learn many aspects of NKS and Mathematica and to be able to produce meaningful results in a very short time.”

Francisca Aladejana

“With the little I have seen, the world of learning should be getting ready for NKS take-over!”

Dag Sørebø

“The NKS Summer School is an intellectual tour de force, with highly competent instructors and fellow students.”

Sean Lynch

“It's a learning experience for anyone interested in being a part of an exciting new frontier. I got the sense of being one of a large group of people working to build the groundwork for this new science.”

Daniel de Souza Carvalho

“If you want to see life, the universe and everything else from a computing point of view, NKS Summer School is the right place to start!”

Allen Taylor

“The primary value of the NKS Summer School to me was in making it clear what NKS is all about. It is about applying a new mode of thinking to the solution of scientific problems. This has enabled me to look at my research in new ways and has given me new pathways toward solutions to problems.”

Emmanuel Garcés Medina

“It's a great environment for students of everywhere with a lot of conversations about nature, computations, complexity and new ideas arising in these current times.”

Matthew Frank

“All in all, quite an achievement.”

Advice for Future Attendees…

Pedro P.B. de Oliveira

“Learn as much Mathematica as possible beforehand. Try to find a project topic before the school and prepare for it by reading related background material, with emphasis on the relevant parts of the NKS book. In order to help this, browse the booklet of Open NKS Problems.”

Samuel Buteau

“Keep an open mind. Try to identify the most important directions to explore, and if stuck, break tasks down and run through all the subtasks starting with the easiest one.”

Thomas Zheng

“Get ready for some serious intellectual stimulation!”

Martin Schneider

“Learn Mathematica.
Read the book.
Have fun!”

Chris Cooley

“Read the A New Kind of Science book. Prepare to meet people from many diverse backgrounds (this truly is one of the Summer School’s greatest strengths—everyone is from everywhere, and there are a variety of ages and education levels to be seen). Come up with a preliminary project idea. Practice the Wolfram Language with the provided problem sets.”

Pedro P.B. de Oliveira

“Attend the Conference, which will set the scene for your new train-of-thought process and throughout the conference you will get to know a bunch of interesting individuals. Think about what your project will be on; formulate a question and think about how you will be able to solve that.”

Luca Zammataro

“The only way to understand a complex system is to reDr. Brian R. Kentcreate it on your computer. NKS methods are the best.”

Evangelos Georgiadis

“Internalize the key points of NKS!”