To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/ArtemKirsanov . You’ll also get 20% off an annual premium subscription
This surely belongs to the top-5 list of youtube videos ever made on the subject, makes you truly accept how a man driven with pure enthusiasm and determination can outperform the entire university departments when it comes to teaching.
Your video on dendritic systems inspired me to study about neuromorphic computing, and then reservoir computing, and as an extension, dive deep into DEs and dynamical systems. It feels weird how the rabbit hole that started me on my journey has caught up to me 😅😅
@@joeystenbeck6697 I'd even go as far to say that it's a sort of dynamical system with attractor points lol. Similar people ofter gravitate towards similar interests
Good point. Just don't analyze it *too* much or you'll accidentally do the observer effect on the whole universe and collapse reality into a single one or zero 😂 I hope we score a point
Learned yesterday about Hopfield networks from ur video. And today John Hopfield & Geoff Hinton wins 2024 physics Nobel prize. Keep making in-depth videos on such topics Artem, they’re very intriguing.
I don't know what exactly you did differently in this video, but it's working. Normally I find the concepts you discuss too hard to follow and then end up clicking off the video. This time I was engaged all the way through. This is great content! Keep it up 🙂
doing brilliant work spreading the beauty of computational neuroscience as always. as a physics major doing comp-neuro research, your videos synthesize topics in math, physics, and biology together very well and are a must watch for any who seek a deeper understanding of electrophysiology and neural networks. perhaps the next hopfield is a member of this lovely community :)
I live on an island with no foxes (or other rabbit predators) and the rabbit numbers becomes overwhelming, but then every few years a rabbit virus wipes out nearly the entire island’s rabbit population. It’s both a relief to us (farmers) and terrifying to see literally thousands of rabbits on the island all drop dead within a few days. So, yeah, other variables in a dynamical system 🤷🏼♀️.
where were you 4 months agoooo 😭😭I really needed this vid for a course in my previous semester. thnx for making and as always excellent quality! I hope nothing but the best happens to you 😄
I just discovered your channel, and it's remarkable! The explanations are so smooth, and the graphics are fantastic. I'd love to learn more about how you create them!
I powered through dif eq in college just to get the job. And now you’re really teaching me to know what I do rather than to just do the math cuz I know the formulas.
Hey very nice video. Just wanted to pinpoint a typo at 10:23 minute. The numerical equation "N(t+dt) = N(t) + kdt" should have been "N(t+dt) = N(t) + kN(t)dt" . Thanks a lot for putting out such videos.
I am currently writing a new ML engine in Haskell, based more on how real neurons work, and you video has been very helpful, describing neurons as dynamical systems! I want to create a simplified numerical model of the differential equations here, because they need to be performant. But I am liking what I see here a lot.
These videos are consistently amazing! Very excited for the next in the series! Getting into the actual math/dynamics of a neuron seems _extremely_ fascinating!
Loved how he simplifies the topic to be suitable for people who have no stomach for math. Is there any book recommended to study differential equations in the same way he did?
I first got turned-on to this stuff when studying the Duffing Oscillator in my Classical Mechanics class. Dynamical Systems put the WOW! back into Physics for me.
An English tip: in English we don't say "our today's video".. Not sure if you're German, but German's "unser heutiges Video" doesn't translate directly into English. You would just say "today's video", or perhaps "our video today".
You should do a video on neurophysiology: I would love to learn why neurons and large interconnected sets of neurons cause certain effects. Like why does a biological neural network cause act x rather than act y? We know that neurons depolarize and hyperpolarize, and are numerous in amount and also amount of synapses, and we know that there are certain structures and regions and pathways in BNNs, but ultimately how/why does act x occur rather than act y? That's a question that I am extremely interested in and really want to determine the answer to.
Классные видео и крутая тема для видео! Подозреваю, что в следующий раз тема видео уйдёт куда-то в бифуркации и это будет крайне интересно Кроме того, было бы занятно почитать, над чем ты работаешь, если есть такая возможность
OMG Literally my phd studies are related to this, where was this video 1 year ago when I needed it :((( . Also! Which software are you using for such beautiful animations?? Love the video!
Amazing video Artem. I did Economics and Applied Maths in University, and I chose Economics. Now I'm coming back to Applied Math, because i want to learn to solve complex problems. Any suggestions for software I can use to create and visualise models with as you did in this video? Thanks
Hey Artem your videos are insanely good. I have question what combination of software did you use for the animations? How did you combine LaTeX with the other animations, I know that you don't use Manim.
Thank you for this video. It makes me excited to learn more about my courses I'm currently taking: Differential equations and numerics. Is it possible to do research in e.g. Computational Neuroscience coming from a purely math background?
Great video overall, but limit cycles are technically defined differently. What you showed is just oscillatory behavior. Limit cycles happen when different phase space paths converge onto a cycle, as opposed to a single point. This isn’t possible in two dimensions, which is maybe why you didn’t show it, but a disclaimer would have been nice.
I think a limit cycle actually is possible in two dimensions. But I think you are right that a truly exactly periodic system would not technically be a limit cycle, since limit cycle implies that other paths tend to converge to it. And the population system is made up of infinitely many "shells" that don't transition between each other. Which maybe you could consider to be infinitely many limit cycles, depending on your definitions?
You're correct that these are indeed no limit cycles, however limit-cycles in 2-dimensional phase space are certainly possible (see, e.g., Van der Pol oscillator)
Feeling kinda proud that I knew all math in the video in my 16, and also reminded that I haven't studied DE for a few month already. Your videos are amazing, i find answers for exact questions that bothered me for a long time. Thank you
The part about limit cycles is wrong: the Lotka-Volterra equations (the differential equations you show) do not contain any limit cycle, as a limit cycle must be an isolated closed-loop trajectory, meaning all neighboring trajectories (in an open neighborhood) either spirals in or out, which is not the case here. As all neighboring trajectories are closed-loop trajectories themselves, this indicates that there is not an infinite number of limit cycles as you suggest (there are no limit cycles).
If the output of a *single* neuron depends on its own state some time ago, does that mean a single neuron has its own "memory"? If so, do we know the mechanism behind this memory?
@@Fracasse-0x13 Imagine if the neuron's output _right now_ depends on its state at an earlier _range_ of time, then there is information stored on what the states are during that range of time so that the neuron can "know" If the neuron's output now only depends on its state _just immediately_ before (infinitesimal slice of time), the concept I mentioned above is unnecessary But if a neuron's output now depends on its state not just immediately before, but also on how its state evolved for the past 100 miliseconds for example, that evolution of states in a finite duration is an information that the neuron "knows" to spit out the right output
@@GeoffryGifari So I get that the sequence of past interactions can leave behind some state information for a short term duration of time since each interaction changes chemical properties such as ion concentration and changes in the synapse etc. But I don't see why that would be described as the neuron "knowing" how to process the next input or smt?
@@Fracasse-0x13 I phrased it as a neuron "knowing its evolution of state going back a finite span of time", to contrast it with simple mechanical motion, like how position and momentum are described in the video. Example: 1. A particle following newton's laws: the position and momentum x(t +dt), v(t+dt) can be *fully* determined from x(t), v(t), using the equation of motion. 2. A dynamical system having "memory": to make it easier, let's discretize time. If there are two trajectories (following the same dynamical law) of the system state S(t) (represented by a number, could be ion concentration or something) for t=0 to t=5 S(t) = 0.4 -> 1.3 -> 2.7 -> 3.3 -> 3.6 -> S(5) S(t) = 8.4 -> 8.3 -> 8.0 -> 5.9 -> 3.6 -> S(5) The value of S(t) at t=5 for the two trajectories *will not be the same* even though the state just before (S(4)=3.6) are equal. The states going back several units of time matter here. Hence, to get S(5) from S(4), the extra information regarding the past several states needs to be stored somewhere (what I referred to as "knowing"). Can you see the contrast between the two examples?
I remember having a lot of problems understanding the concept of phase space due to my professor being terrible explaining it when I took the dynamical systems class. But your explanation was infinitely more clear and perfectly understandable. After seeing some of your videos I can honestly say you're one of the best science youtubers out there.
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/ArtemKirsanov . You’ll also get 20% off an annual premium subscription
I love you man, please keep at it. I cannot stress enough how useful and informative your videos are. You deserve the world for this work.
Thank you! Really appreciate it ❤️
@@ArtemKirsanovYes thanks for sharing but I hope you can respond to my other comment when you can Artem. Thank you much.
This surely belongs to the top-5 list of youtube videos ever made on the subject, makes you truly accept how a man driven with pure enthusiasm and determination can outperform the entire university departments when it comes to teaching.
Your video on dendritic systems inspired me to study about neuromorphic computing, and then reservoir computing, and as an extension, dive deep into DEs and dynamical systems. It feels weird how the rabbit hole that started me on my journey has caught up to me 😅😅
I'd love to see a node graph that shows a bunch of people's paths and see how similar they are. All living things strive for their source I guess haha
@@joeystenbeck6697have a look at my geocog sims, i have one that models people
@@joeystenbeck6697 I'd even go as far to say that it's a sort of dynamical system with attractor points lol. Similar people ofter gravitate towards similar interests
Good point. Just don't analyze it *too* much or you'll accidentally do the observer effect on the whole universe and collapse reality into a single one or zero 😂 I hope we score a point
@@joeystenbeck6697 wait whats this? i dont want to that.. is that why people cant process my stuff.. stops the universe breaking?
Learned yesterday about Hopfield networks from ur video.
And today John Hopfield & Geoff Hinton wins 2024 physics Nobel prize.
Keep making in-depth videos on such topics Artem, they’re very intriguing.
This is the best channel on computational neuroscience ever!
I don't know what exactly you did differently in this video, but it's working. Normally I find the concepts you discuss too hard to follow and then end up clicking off the video. This time I was engaged all the way through. This is great content! Keep it up 🙂
doing brilliant work spreading the beauty of computational neuroscience as always. as a physics major doing comp-neuro research, your videos synthesize topics in math, physics, and biology together very well and are a must watch for any who seek a deeper understanding of electrophysiology and neural networks. perhaps the next hopfield is a member of this lovely community :)
Thank you so much!
Thanks!
The astounding visuals makes the video hundred times more interesting. Love your work.
Great video. You rekindled my interest to restart studying differential equations.
I live on an island with no foxes (or other rabbit predators) and the rabbit numbers becomes overwhelming, but then every few years a rabbit virus wipes out nearly the entire island’s rabbit population. It’s both a relief to us (farmers) and terrifying to see literally thousands of rabbits on the island all drop dead within a few days. So, yeah, other variables in a dynamical system 🤷🏼♀️.
Babe wake up, the new video from Artem Kirsanov has been released.
Thanks babe
cringe
@@carlossegura403r/whooosh
Hey, what's your pfp from?
And schizophrenia within philosophy of the mind
Underrated chanel, love to hear that more is coming up
Looking forward to the next video!
PS. 12:44 minor issue in definitions? x dot is change in population.
Awesome stuff! Would love to see how this can be used to visualize recurrent neural network activity!
@@foreverjoyous u can see how recurrent information loops work in cortical columns in some of my simulations
You're an amazing teacher. This was very insightful, well-structured, and wonderfully presented. Reminds me of 3B1B. Keep it up!
where were you 4 months agoooo 😭😭I really needed this vid for a course in my previous semester. thnx for making and as always excellent quality! I hope nothing but the best happens to you 😄
I just discovered your channel, and it's remarkable! The explanations are so smooth, and the graphics are fantastic. I'd love to learn more about how you create them!
@@neurosciencebeyond i think he has a video explaining his process
I powered through dif eq in college just to get the job. And now you’re really teaching me to know what I do rather than to just do the math cuz I know the formulas.
Brother you have a knack for this. Keep up the good work, love your videos 👍🏻
Thank you for making these videos! You really made difficult concepts easy to understand. Bravo!
Hey very nice video. Just wanted to pinpoint a typo at 10:23 minute. The numerical equation "N(t+dt) = N(t) + kdt" should have been "N(t+dt) = N(t) + kN(t)dt" . Thanks a lot for putting out such videos.
Wow so amazing explanation mind blowing !!!
I am currently writing a new ML engine in Haskell, based more on how real neurons work, and you video has been very helpful, describing neurons as dynamical systems!
I want to create a simplified numerical model of the differential equations here, because they need to be performant. But I am liking what I see here a lot.
These videos are consistently amazing! Very excited for the next in the series! Getting into the actual math/dynamics of a neuron seems _extremely_ fascinating!
Impecable explanation, as expected from Artem. Thanks for another great video
Definitely deserved an immediate subscribe!!
Beautiful. This is incredible! Thanks a lot. Solve a lot of things in my mind!
An Artem Kirsanov a day keeps the brain rot away
Loved how he simplifies the topic to be suitable for people who have no stomach for math.
Is there any book recommended to study differential equations in the same way he did?
Very nice and clear presentaion.
Beautifully simple yet perfectly explained
Thanks for the class, professor Kirsanov. You have didactics!
What’s great video!! Differential equations is the most interesting thing to understand and you do an amazing job!!
This is truly amazing! I think you can make almost everyone love mathematics and neuroscience through your videos:))
I first got turned-on to this stuff when studying the Duffing Oscillator in my Classical Mechanics class. Dynamical Systems put the WOW! back into Physics for me.
im a simple man: i see an Artem Kirsanov video and i click...s/o you the goat man!
An English tip: in English we don't say "our today's video".. Not sure if you're German, but German's "unser heutiges Video" doesn't translate directly into English. You would just say "today's video", or perhaps "our video today".
I’m sharing your channel to everyone I know… Come on guys we need Artem’s channel to grow!
Your channel is of such a high quality, I hope to be able to convey my ideas with such skill one day.
Your graphs are so pretty! What visualization tool are you using for your phase portraits?
Thanks! Just vanilla matplotlib quiver + a little After Effects magic for glow effects 😅
Artem > College. (I got my piece of paper, but school is so outdated).
Great quality educational video. 👍
Thank you so much ❤😊
You should do a video on neurophysiology: I would love to learn why neurons and large interconnected sets of neurons cause certain effects. Like why does a biological neural network cause act x rather than act y? We know that neurons depolarize and hyperpolarize, and are numerous in amount and also amount of synapses, and we know that there are certain structures and regions and pathways in BNNs, but ultimately how/why does act x occur rather than act y? That's a question that I am extremely interested in and really want to determine the answer to.
Классные видео и крутая тема для видео!
Подозреваю, что в следующий раз тема видео уйдёт куда-то в бифуркации и это будет крайне интересно
Кроме того, было бы занятно почитать, над чем ты работаешь, если есть такая возможность
Артём, у тебя великолепный канал 👏 все лучше и лучше!
Рад снова тебя увидеть
OMG Literally my phd studies are related to this, where was this video 1 year ago when I needed it :((( .
Also! Which software are you using for such beautiful animations??
Love the video!
Excellent video!!!
This is so intuitive youre hella creative
Thanks for making this!
great work Artem ! keep going :)
Extremely good Video
I would love some Future Videos about more biological Applications
Amazing video Artem. I did Economics and Applied Maths in University, and I chose Economics. Now I'm coming back to Applied Math, because i want to learn to solve complex problems.
Any suggestions for software I can use to create and visualise models with as you did in this video?
Thanks
MATLAB
Looking forward to the next video!
Brilliant, thank you! NY finest!
Hey Artem your videos are insanely good.
I have question what combination of software did you use for the animations?
How did you combine LaTeX with the other animations, I know that you don't use Manim.
Wow! 😲 Never knew about limit cycles
very good explanation
Hi! Awesome Video. What do you use for your videos? I really admire the quality
Thank you! Mostly After Effects + Python (matplotlib for mathematical animations)
Love this idea for a series! Do you think you'll work up to population dynamics and RNNs?
Thank you for this video. It makes me excited to learn more about my courses I'm currently taking: Differential equations and numerics.
Is it possible to do research in e.g. Computational Neuroscience coming from a purely math background?
Great video overall, but limit cycles are technically defined differently. What you showed is just oscillatory behavior. Limit cycles happen when different phase space paths converge onto a cycle, as opposed to a single point. This isn’t possible in two dimensions, which is maybe why you didn’t show it, but a disclaimer would have been nice.
I think a limit cycle actually is possible in two dimensions. But I think you are right that a truly exactly periodic system would not technically be a limit cycle, since limit cycle implies that other paths tend to converge to it. And the population system is made up of infinitely many "shells" that don't transition between each other. Which maybe you could consider to be infinitely many limit cycles, depending on your definitions?
You're correct that these are indeed no limit cycles, however limit-cycles in 2-dimensional phase space are certainly possible (see, e.g., Van der Pol oscillator)
Thank you, this is quite interesting, as always
Feeling kinda proud that I knew all math in the video in my 16, and also reminded that I haven't studied DE for a few month already.
Your videos are amazing, i find answers for exact questions that bothered me for a long time. Thank you
🤣I am even prouder I knew them all when I was 13
your videos are amazing thank you for the content
Благодарю Артём. Мне очень понравилось твоё объяснение дифференциальных уравнений и как они помогают понимать мир вокруг нас.
Спасибо! ❤
THANK YOU BRO
LOVE THESE VIDEOS 💯🤩🤩
The part about limit cycles is wrong: the Lotka-Volterra equations (the differential equations you show) do not contain any limit cycle, as a limit cycle must be an isolated closed-loop trajectory, meaning all neighboring trajectories (in an open neighborhood) either spirals in or out, which is not the case here. As all neighboring trajectories are closed-loop trajectories themselves, this indicates that there is not an infinite number of limit cycles as you suggest (there are no limit cycles).
Велиуолепный контент бро, как всегда. Топ-1
Spasibo za video 😉
very informative, please keep doing this💞💕💓💗❣💯❤💯💯💯💯💯💯💯
Another great video :)
Thanks!
How many months of subscriptions so I can appear on your sponsor list page?
Where can I learn it more ? Like a formal online course or something .
Keep these gems coming! Can't wait to watch your next videos!
underrated channel
I think the difference equation is a better formulation of dynamical systems than the differential equation and is more intuitive
If the output of a *single* neuron depends on its own state some time ago, does that mean a single neuron has its own "memory"? If so, do we know the mechanism behind this memory?
How does previous state translate to memory?
@@Fracasse-0x13 Imagine if the neuron's output _right now_ depends on its state at an earlier _range_ of time, then there is information stored on what the states are during that range of time so that the neuron can "know"
If the neuron's output now only depends on its state _just immediately_ before (infinitesimal slice of time), the concept I mentioned above is unnecessary
But if a neuron's output now depends on its state not just immediately before, but also on how its state evolved for the past 100 miliseconds for example, that evolution of states in a finite duration is an information that the neuron "knows" to spit out the right output
@@GeoffryGifari So I get that the sequence of past interactions can leave behind some state information for a short term duration of time since each interaction changes chemical properties such as ion concentration and changes in the synapse etc. But I don't see why that would be described as the neuron "knowing" how to process the next input or smt?
@@Fracasse-0x13 I phrased it as a neuron "knowing its evolution of state going back a finite span of time", to contrast it with simple mechanical motion, like how position and momentum are described in the video.
Example:
1. A particle following newton's laws: the position and momentum x(t +dt), v(t+dt) can be *fully* determined from x(t), v(t), using the equation of motion.
2. A dynamical system having "memory": to make it easier, let's discretize time. If there are two trajectories (following the same dynamical law) of the system state S(t) (represented by a number, could be ion concentration or something) for t=0 to t=5
S(t) = 0.4 -> 1.3 -> 2.7 -> 3.3 -> 3.6 -> S(5)
S(t) = 8.4 -> 8.3 -> 8.0 -> 5.9 -> 3.6 -> S(5)
The value of S(t) at t=5 for the two trajectories *will not be the same* even though the state just before (S(4)=3.6) are equal. The states going back several units of time matter here. Hence, to get S(5) from S(4), the extra information regarding the past several states needs to be stored somewhere (what I referred to as "knowing").
Can you see the contrast between the two examples?
beautiful video
Ever seen the character "Milo" from the movie "Atlantis: The Lost Empire"?
I remember having a lot of problems understanding the concept of phase space due to my professor being terrible explaining it when I took the dynamical systems class. But your explanation was infinitely more clear and perfectly understandable. After seeing some of your videos I can honestly say you're one of the best science youtubers out there.
do you use manim for the animation and captions please?
Masterpiece
excellent!!
i love this channel
Really Nice
Your Fan From Bangladesh 🇧🇩
@ 13:00, you incorrectly labeled the derivatives of populations as populations
So a derivative is like a moving gradient measure?
The thumbnail was enough for me to click
Your videos are very precise and content rich
good video
And since everything changes all the time, DE are the language of being :-)
Sounds very physics-y
Top notch. Amateur here. Understood.
awesome
How does computational neuroscience differ from mathematical neuroscience?