hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
🎂PsPM is turning 15, and we are celebrating with a new release: Version 7.0.0. Streamlined user experience, improved robustness, and better maintainability. All teaching material on our website is updated too: https://t.co/ziOtvjmNhd
#PsPM#psychophysiologicalmodelling
📢 JOB ALERT: We are looking to hire a postdoc or PhD researcher interested in working on naturalistic #neuroimaging with an wearable MEG. Come join our team! One more week to apply for our MEG researcher position. Applications are due on January 15. 🗓️
https://t.co/rkCclSkcb4
We get a lot of advice about getting a good night's sleep. You know, circadian rhythm, a solid 7-9 hours etc., but it is not so easy when your mathematical mind is ticking.
Sleep and other stories from Roger Penrose.
PS: Yes, he does the puzzle. Stay tuned.
First person in the family to become an academic:
Cons:
- No money
- No investments
- Questionable career prospects
- Wearing a backpack
Pros:
- more peer-reviewed articles than siblings
Published #otd in 1986: a seminal 4-page paper on backpropagation from Geoff Hinton that helped reignite the field of neural networks.
https://t.co/GEfsq5e9Mq
Swiss radio SRF asked Dominik Bach to give a neuroscientific perspective on Donald Trump's initial response to the recent attack on his life. Listen to/read the interview here (in German):
This looks like a robot dog dancing to disco lights, but it's actually a very cool visualization of the neural network that controls the bot!
Blue -> green -> red corresponds to stronger neural activation.
The NN is a multilayer perceptron that maps proprioception (e.g. position, orientation, and acceleration of each body part) to motor control. It can be learned by reinforcement learning in physics simulations.
I have trained a gazillion control NNs before, but never did I see it presented this way. Recently, PyTorch also open-sourced a tool that lets you step in matrix & attention computations immersively. Most people are intuitive learners - we should spend more efforts on visualization!
Created by @brandon_xyzw with NVIDIA Isaac Gym, three.js, and custom shaders.