📄 Hidden geometric correlations in real multiplex networks
Kaj-Kolja Kleineberg, Marián Boguñá, M. Ángeles Serrano & Fragkiskos Papadopoulos
http://www.nature.com/nphys/journal/v12/n11/full/nphys3812.html
📌 ABSTRACT:
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
Subject terms:
#Applied_physics
#Complex_networks
#Statistics
Kaj-Kolja Kleineberg, Marián Boguñá, M. Ángeles Serrano & Fragkiskos Papadopoulos
http://www.nature.com/nphys/journal/v12/n11/full/nphys3812.html
📌 ABSTRACT:
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
Subject terms:
#Applied_physics
#Complex_networks
#Statistics
Complex Systems Studies
Cantor set (the mathematical equivalent of a croissant).
How does nonlinearity manufacture fractals and chaos? There is one and only one answer: #stretching and #folding. All flows and all #maps that manufacture fractals do it by stretching and folding. Let’s look at a simple example. Think of a pastry chef making a #croissant. She puts down the dough and stretches it with a rolling-pin. Then she puts a layer of butter on it and folds it. She rolls and stretches it again, puts another layer of butter, and folds it again. And so on ad infinitum, or almost. What you get is an object, a delicious croissant, which is a fractal in the direction perpendicular to the table, with a very large (quasi-infinite) number of layers. This is the way all dynamical chaos works!
Forwarded from Sitpor.org سیتپـــــور
🌀 برای اینکه از دنیای فرکتالها سر دربیارید، نگاه کنید به نوشته فرکتالها (برخالها – fractals) در سیتپور:
Sitpor.org
1⃣ «مقدمه و معرفی»:
https://goo.gl/uPkpaa
2⃣ «ویژگیها و تعاریف»:
https://goo.gl/SHRJ03
3⃣ «خمهای فضاپرکن و فرکتالهای تصادفی»:
https://goo.gl/5LE8Ck
4⃣ «مجموعه ژولیا»:
https://goo.gl/3OFlG7
5⃣ «مجموعه مندلبرو»:
https://goo.gl/g14LRc
Sitpor.org
1⃣ «مقدمه و معرفی»:
https://goo.gl/uPkpaa
2⃣ «ویژگیها و تعاریف»:
https://goo.gl/SHRJ03
3⃣ «خمهای فضاپرکن و فرکتالهای تصادفی»:
https://goo.gl/5LE8Ck
4⃣ «مجموعه ژولیا»:
https://goo.gl/3OFlG7
5⃣ «مجموعه مندلبرو»:
https://goo.gl/g14LRc
A Model-Based Approach to Predicting Graduate-Level Performance Using Indicators of Undergraduate-Level Performance👇👇👇
#سلسله_سمینارهای_هفتگی گروه سیستم های پیچیده شهید بهشتی
علاقه مندان می توانند برای ارائه موضوعات خود به ادمین پیام داده یا به صورت حضوری در جلسه مطرح نمایند.
@onmjnl
علاقه مندان می توانند برای ارائه موضوعات خود به ادمین پیام داده یا به صورت حضوری در جلسه مطرح نمایند.
@onmjnl
🔵 Traffic generation model - Wikipedia
https://en.wikipedia.org/wiki/Traffic_generation_model
https://en.wikipedia.org/wiki/Traffic_generation_model
Wikipedia
Traffic generation model
simulated flow of data in a communications network
🎯 Chaos, Complexity, and Entropy
A physics talk for non-physicists
http://www.necsi.edu/projects/baranger/cce.pdf
🌀 The twenty-first century is starting with a huge bang. For the person in the street, the bang is about a technical revolution that may eventually dwarf the industrial revolution of the 18th and 19th centuries, having already produced a drastic change in the rules of economics. For the scientifically minded, one aspect of this bang is the complexity revolution, which is changing the focus of research in all scientific disciplines, for instance human biology and medicine. What role does physics, the oldest and simplest science, have to play in this? Being a theoretical physicist to the core, I want to focus on theoretical physics. Is it going to change also?
🌀 Twentieth-century theoretical physics came out of the relativistic revolution and the quantum mechanical revolution. It was all about simplicity and continuity (in spite of quantum jumps). Its principal tool was calculus. Its final expression was field theory.
🌀 Twenty-first-century theoretical physics is coming out of the chaos revolution. It will be about complexity and its principal tool will be the computer. Its final expression remains to be found. Thermodynamics, as a vital part of theoretical physics, will partake in the transformation.
A physics talk for non-physicists
http://www.necsi.edu/projects/baranger/cce.pdf
🌀 The twenty-first century is starting with a huge bang. For the person in the street, the bang is about a technical revolution that may eventually dwarf the industrial revolution of the 18th and 19th centuries, having already produced a drastic change in the rules of economics. For the scientifically minded, one aspect of this bang is the complexity revolution, which is changing the focus of research in all scientific disciplines, for instance human biology and medicine. What role does physics, the oldest and simplest science, have to play in this? Being a theoretical physicist to the core, I want to focus on theoretical physics. Is it going to change also?
🌀 Twentieth-century theoretical physics came out of the relativistic revolution and the quantum mechanical revolution. It was all about simplicity and continuity (in spite of quantum jumps). Its principal tool was calculus. Its final expression was field theory.
🌀 Twenty-first-century theoretical physics is coming out of the chaos revolution. It will be about complexity and its principal tool will be the computer. Its final expression remains to be found. Thermodynamics, as a vital part of theoretical physics, will partake in the transformation.
🌀 Neural Networks for Machine Learning
About this course: Learn about artificial neural networks and how they're being used for machine learning, as applied to speech and object recognition, image segmentation, modeling language and human motion, etc. We'll emphasize both the basic algorithms and the practical tricks needed to get them to work well. This course contains the same content presented on Coursera beginning in 2013. It is not a continuation or update of the original course. It has been adapted for the new platform. Please be advised that the course is suited for an intermediate level learner - comfortable with calculus and with experience programming (Python).
https://www.coursera.org/learn/neural-networks?recoOrder=16&utm_medium=email&utm_source=recommendations&utm_campaign=recommendationsEmail%7Erecs_email_2016_11_20_17%3A58
About this course: Learn about artificial neural networks and how they're being used for machine learning, as applied to speech and object recognition, image segmentation, modeling language and human motion, etc. We'll emphasize both the basic algorithms and the practical tricks needed to get them to work well. This course contains the same content presented on Coursera beginning in 2013. It is not a continuation or update of the original course. It has been adapted for the new platform. Please be advised that the course is suited for an intermediate level learner - comfortable with calculus and with experience programming (Python).
https://www.coursera.org/learn/neural-networks?recoOrder=16&utm_medium=email&utm_source=recommendations&utm_campaign=recommendationsEmail%7Erecs_email_2016_11_20_17%3A58
🌀 Introduction to Data Science in Python
About this course: This course will introduce the learner to the basics of the python programming environment, including how to download and install python, expected fundamental python programming techniques, and how to find help with python programming questions. The course will also introduce data manipulation and cleaning techniques using the popular python pandas data science library and introduce the abstraction of the DataFrame as the central data structure for data analysis. The course will end with a statistics primer, showing how various statistical measures can be applied to pandas DataFrames. By the end of the course, students will be able to take tabular data, clean it, manipulate it, and run basic inferential statistical analyses. This course is number 1 in the Applied Data Science with Python specialization and should be taken before any other courses in the specialization.
https://www.coursera.org/learn/python-data-analysis?recoOrder=4&utm_medium=email&utm_source=recommendations&utm_campaign=recommendationsEmail~recs_email_2016_11_20_17%3A58
About this course: This course will introduce the learner to the basics of the python programming environment, including how to download and install python, expected fundamental python programming techniques, and how to find help with python programming questions. The course will also introduce data manipulation and cleaning techniques using the popular python pandas data science library and introduce the abstraction of the DataFrame as the central data structure for data analysis. The course will end with a statistics primer, showing how various statistical measures can be applied to pandas DataFrames. By the end of the course, students will be able to take tabular data, clean it, manipulate it, and run basic inferential statistical analyses. This course is number 1 in the Applied Data Science with Python specialization and should be taken before any other courses in the specialization.
https://www.coursera.org/learn/python-data-analysis?recoOrder=4&utm_medium=email&utm_source=recommendations&utm_campaign=recommendationsEmail~recs_email_2016_11_20_17%3A58
Coursera
Introduction to Data Science in Python | Coursera
Learn Introduction to Data Science in Python from ...
📄 Big data need physical ideas and methods
https://arxiv.org/pdf/1412.6848v1
📌 If a person looks at WHITE paper through BLUE glasses, the paper will become BLUE in the eye of the person. Likewise, in the current study of big data which play the same role as the white paper being looked at, various statistical methods just serve as the blue glasses. That is, results obtained from big data often depend on the statistical methods in use, which may often defy reality. Here I suggest using physical ideas and methods to overcome this problem to the greatest extent. This suggestion is helpful to development and application of big data.
#Data_Analysis , #Statistics and #Probability (physics.data-an)
https://arxiv.org/pdf/1412.6848v1
📌 If a person looks at WHITE paper through BLUE glasses, the paper will become BLUE in the eye of the person. Likewise, in the current study of big data which play the same role as the white paper being looked at, various statistical methods just serve as the blue glasses. That is, results obtained from big data often depend on the statistical methods in use, which may often defy reality. Here I suggest using physical ideas and methods to overcome this problem to the greatest extent. This suggestion is helpful to development and application of big data.
#Data_Analysis , #Statistics and #Probability (physics.data-an)