✨ https://machinelearningmastery.com/standard-multivariate-multi-step-multi-site-time-series-forecasting-problem/

💲 The #economy includes two flows—wages for work that people use to buy goods and services, and investing that leads to returns. Understanding how these two loops should be balanced can lead to sustained economic growth for all.

http://necsi.edu/research/economics/econuniversal?platform=hootsuite

☸ https://www.quantamagazine.org/simpler-math-tames-the-complexity-of-microbe-networks-20180119/

🕸 شکل‌گیری شبکه‌های کارآمد
http://www.psi.ir/news2_fa.asp?id=2374

مدلی جدید نشان می‌دهد که برای توضیح نحوه تشکیل شبکه‌های عروقی سلسله مراتبی و بهینه‌سازی‌شده، دانستن رشد بافت‌ها حیاتی است، و این درست همانند آن چیزی است که در گیاهان و حیوانات دیده می‌شود.

http://www.psi.ir/upload/news/1396/tavakolidust/961016Images_PhysRevLett_117.png

💡 https://aeon.co/essays/how-a-polymath-transformed-our-understanding-of-information

🔅 Networks and graph theory are beautifully introduced in this package of articles, a great starting point for anyone curious about this exciting part of math and science:
https://plus.maths.org/content/graphs-and-networks

🔖 Random Multi-Hopper Model. Super-Fast Random Walks on Graphs

Ernesto Estrada, Jean-Charles Delvenne, Naomichi Hatano, José L. Mateos, Ralf Metzler, Alejandro P. Riascos, Michael T. Schaub

🔗 arxiv.org/pdf/1612.08631.pdf

📌 ABSTRACT
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multi-hopper's hitting times between any two nodes in the graph converge to their minimum possible value, given by the hitting times of a normal random walker on a complete graph. Stated differently, for small parameter values the multi-hopper explores a general graph as fast as possible when compared to a random walker on a full graph. Using computational experiments we show that compared to the normal random walker, the multi-hopper indeed explores graphs with clusters or skewed degree distributions more efficiently for a large parameter range. We provide further computational evidence of the speed-up attained by the random multi-hopper model with respect to the normal random walker by studying deterministic, random and real-world networks.

🔅 https://www.johndcook.com/blog/2017/01/04/cover-time-of-a-graph-cliques-chains-and-lollipops/

💻 Fundamentals of Machine Learning is NOW OPEN! Take this excellent tutorial here:

www.complexityexplorer.org/courses/81-fundamentals-of-machine-learning,

and read an interview with the instructors here:

https://www.complexityexplorer.org/news/85-what-s-so-special-about-fundamentals-of-machine-learning

🎞 https://youtu.be/-6INDaLcuJY

🎞 https://www.aparat.com/v/5YC87
https://youtu.be/MOdlp1d0PNA

💻 Great profile about MIT math professor Philippe Rigollet. We have three courses of his on OCW:

Mathematics of Machine Learning:
https://ocw.mit.edu/courses/mathematics/18-657-mathematics-of-machine-learning-fall-2015/

High-Dimensional Statistics:
https://ocw.mit.edu/courses/mathematics/18-s997-high-dimensional-statistics-spring-2015/

Statistics for Applications:
https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/

💡 Complexity is not just a measure of how intricate, or sophisticated, something is. It defines the topology of information flow and of the processes which make Nature work!

🔗 https://resiliencepost.com/2018/01/16/on-the-extraordinary-importance-of-complexity/amp

#Complexity #Entropy #Energy #DNA #Nature

🔖 Markov Brains: A Technical Introduction

Arend Hintze, Jeffrey A. Edlund, Randal S. Olson, David B. Knoester, Jory Schossau, Larissa Albantakis, Ali Tehrani-Saleh, Peter Kvam, Leigh Sheneman, Heather Goldsby, Clifford Bohm, Christoph Adami

🔗 arxiv.org/pdf/1709.05601.pdf

📌 ABSTRACT
Markov Brains are a class of evolvable artificial neural networks (ANN). They differ from conventional ANNs in many aspects, but the key difference is that instead of a layered architecture, with each node performing the same function, Markov Brains are networks built from individual computational components. These computational components interact with each other, receive inputs from sensors, and control motor outputs. The function of the computational components, their connections to each other, as well as connections to sensors and motors are all subject to evolutionary optimization. Here we describe in detail how a Markov Brain works, what techniques can be used to study them, and how they can be evolved.

🌀 https://softbites.org/2018/01/24/how-swimming-bacteria-spin-fluid/amp/

Using Self-Organizing Maps to solve the Traveling Salesman Problem https://t.co/2KkTgcGDaY & https://t.co/5frWZeK056 https://t.co/nmYIrTBGsq

Why Complexity is Different
https://mystudentvoices.com/why-complexity-is-different-ecd498e0eccb

❄️ Nice article about extreme difficulty most people have understanding p-values. Even worse: confidence intervals. And most statisticians don't even compute p-values very accurately except for the simplest models.
https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/amp/