So welcome to the sixth lesson today. In the last lesson we studied, we learned about learning and memory in the brain. And we studied some of the mechanisms. We focused on some of the mechanisms underlying learning and plasticity. The question, of course, is, what does the brain do with all these changes, with all this plasticity that it utilizes for understanding the world? So today we are trying to understand the term computation, and in particular, computation at the level of single cells of, in particular, dendrites. The functional aspect of learning and plasticity, in terms of using it to compute aspects of the world in order to behave appropriately. So we should focus actually on several aspects. I will start with the general term of what does it mean to compute? When I say computational neuroscience, what do we mean? And then I will discuss more at the single cell level, so I want to focus on the cell as a computing device, as a microchip that computes. In particular, I want to highlight a very important theory, a very influential theory, one of the most successful theory in neuroscience by Wilfred Rall, cable theory for dendrites, which will serve as a basis for understanding neurons as a computational device. And then I will focus on dendritic computation, showing you that dendrites themselves, with their synapses, can implement specific computations. We have several ideas and recently we have several breakthroughs indeed showing that some of the theoretical ideas are really proven using new techniques, new anatomical and physiological techniques. So this is the plan today for the sixth lecture. I hope you enjoy it. Some of it is going to be easy. Some of it is maybe going to be a little bit more difficult because it is mathematically oriented. So let's start with the notion of brain computes. What do we mean by saying that the brain computes? [COUGH] So basically what I'm saying that the brain computes, I want to understand the following. I want to understand how the neuronal ingredients, the synapses, the neurons, their electrical and chemical signals which you already studied. The synaptic potential, the spike. The interacting neural networks that they all construct, many neurons together. Many spikes running in this neuron. Many synaptic potentials running in such networks. What does it mean that you process information, computes? So there is information coming from outside, visual, auditory, other information. And the system eventually utilize this information, encode this information, decode this information, in order to behave. So basically we can think about three problems that are associated with computational or with any computing system, the brain in particular. So, you have to solve a problem. I have to recognize a face. I have to cross a street. I have to play the piano and move my fingers. I have to grasp a cup. All this is computation. I need to compute something in the world. The distance of the cup, the speed of the car, the shape of the face, in order to recognize it and behave appropriately. So I have to solve a particular problem. The question is, what is the problem I need to solve? Then I have to implement some algorithm, some techniques, in order to solve this particular problem. So the issue of algorithm being used by the brain in order to solve this particular problem is another issue. Because there is the problem, there is the algorithm and eventually, of course, there is the implementation of the algorithm. So there is specific, how do our software, lifeware, our neurons, signals, synapses, spikes. You somehow use these ingredients in different brain regions with this ingredients in order to use specific algorithms, in order to solve specific problems. There is the problem to be solved, algorithm to be used and the implementation using this particular system in order to solve this problem. And of course, when I speak about the brain, the brain does many things and it has many regions. Each region has a particular problem to solve. It has a computational role, a particular region. So I can speak about movement, when I move now. I can speak about touch, so when I touch something and I have to recognize things by touching it, Braille reading. I have a visual area here, which is occupied with vision and has to solve particular vision problem. And there is hearing, so when I hear Bach or Beethoven, I have to recognize it, the sequence of it. If I know it I may predict what is coming. So I have to use my hearing system in order to solve a particular problem. Where does the sound come from? Whose sound is it? And so on. So each system, with a given area of the brain, of course, interacting with other areas, it is not isolated, but as an area, have to solve a particular problem. For example, in movement. So during movement, when I cross the street, when I'm reaching to a cup, it requires specific computation. For example, when I cross the street, I need to know that there are no cars coming nearby me, so I need to compute the distance of the car, so I need to compute distance. I need to use my brain, my neurons, my spikes, to compute the distance of the car from me. This is a computation. I also need to compute the speed of the car, the direction of the car. For example, if the car is coming towards me or from me outside. Then I don't need to care. But if it comes towards me, then maybe I need to care. To cross the street or not to cross the street. When I want to hold the cup, I need to compute the distance between me and the cup. Maybe I need to go forward or maybe not. So this is movement. But of course, I'm using vision as well. I need to move following vision. So these are computations. In the visual system there are other things to compute. For example, I show you now a picture. Some pixels come to your eye now and I'm telling you compute. Is there a dog here? So maybe you can see the dog. So here is the dog. This is the left ear of the dog. This is the mouth of the dog. This is the front left leg. This is the body of the dog. So here maybe some of you may be able now to see the dog. This is what is called the figure-ground separation. So one of the fundamental aspects of visual computation is to segment, to segregate, to bind certain dots that may be associated with some memory that you have. Remember, last time I showed you cows, I showed you trees, and you segregate, you bind all these aspects to call it a tree, to recognize it as a tree. To recognize this as a dog. This is a computation that the visual system, or any robot that needs to recognize objects in the world, needs compute. So you use your cells. You use your spikes. You use your synapses. You use the anatomy of this particular network that is involved now with this particular computation. And of course, you use memory in order to recognize a goat or a cow or a tree. This is vision. And you can see that the brain computes. It has particular algorithms to recognize faces or horses or cows. In this particular very, very classical example, I can show you that the fact that you scan using your visual system, but of course, your eyes are moving, so it's movement as well, in order to scan a face. So here is a face. You are now looking this face, and I'm telling you now that we can now record your eye movement during scanning the face, and your eyes are doing something like this. So these black dots now highlight where your eye tend to stop more, to focus on. So your eyes now are stopping a lot on the eye of the image you're looking at. This is why this area is dark. There is also here, so you are also focusing on the other eye. And you move between the eyes. You can see this. You stop a lot on the mouth. A little bit on the ear. So you can see that it's not random scanning and it's not systematic point by point. You don't scan the whole pixels here. But you have some kind of algorithm that the brain developed in order to scan a figure, a face in this case, and eventually come to a recognition. You know that this is a girl. You know that she's laughing. All these things are very important for you, and so you need to compute what is the mood of this image? What is the age of this image? Do you know this image or not? And you can see that your brain mechanisms dictate, so to speak, the way that you scan algorithmically. Don't scan everything. This point, for example, is not important for you so you don't stand there. Your eyes are not fixating there. These point are not very important. But the mouth are very important for recognition. So eventually comes the recognition. You know that you don't know this girl, probably. You know that this is a young girl, that you like her, and all these other aspects that are a result of appropriate computation. You did not make a mistake and thought that this is a house. You know that it's a face, and you know that this is particular face. So this is a computation that the brain is performing using particular algorithms and the question is how these mechanisms of algorithms being implemented by the neurons, by the spikes, by the mechanisms. And of course, some examples of things that do not exist in the world. I don't know if you can see it, but this is supposed to be a square. It comes up. Although there is no square here, there are only these four Pac-Mans. Orient it in appropriate way and suddenly you see an illusion. An illusion means that it is not there, so there is no line here. Or if you look here, you may be able to see a circle, a full circle. But the circle is not there. It is something that the brain, so to speak, invents. It computes something, just because it is connecting things using the experience of the brain from the past. Using some other local mechanisms within the brain, it eventually tells the brain that there is a square there. And you can not avoid the square, so there are some algorithms that are being implemented automatically, and the solution of this computation is that there is a square. The solution of your computation looking at these lines is that there is a circle there. So this is a result of a particular structure of your networks, of a particular utilizing your spikes and your synapses, to eventually come to a computational solution that there is a circle, that there is a square here. Another computation that is very important for us is, as I mentioned already before, motion. So the visual system is very, very sensitive to motion, to changes, physical change, or for example, a spot in the world. So you see there is a motion here. This spot, so to speak, starts here and moves in this direction. Motion. So this another important aspect of the brain, to compute motion. Do I move now or not? Is the car coming towards me or away from me? Motion is a very, very fundamental, absolutely fundamental aspect of the nervous system, any nervous system of any animal, to compute the motion, direction, speed, and so on. An so this particular thing we shall discuss a lot, the capability of nerve cells and networks to compute using the mechanisms of this, the network involved, the spikes involved, to compute this. So this is basically what it means that the brain computes. It has a mission. It has a problem to solve. It implements some algorithm using specific ingredients, synapses, dendrites, spikes and so forth. This is what I mean when I'm saying the brain computes. And in each module, auditory, somatosensory, vision, motion it is using the relevant network or networks in order to eventually, hopefully, come to a correct computation, using the input and then behaving appropriately. Hopefully crossing the road, moving my hand to the cup appropriately. Otherwise, we will be in a big problem. If we're crossing the wrong time, it may be be fatal. If you don't reach the food, we may remain hungry or thirsty. So computation is the most fundamental thing that any behaving machine has to do when it walks, when it moves, when it behaves in the world. And the question is how does this particular network, this particular computational system, implement computation?