Alright, so as a reminder, so far in the class we discussed the maximum informative nonlinearity for a single neuron, where the solution is to, if the neuron is not noisy then the nonlinearity is the cumulative distribution of the input signal and if it is noisy, then noisy binary neuron, then the optimal solution is to cut the input distribution in half. Then we discussed maximum informative solutions for two neurons and how they coordinate their thresholds. Then last lecture we discussed optimal filtering in a linear multidimensional case and today I will give some additional examples on the optimal filtering in the multivariate case because my sense is that it wasn't, I wasn't sufficiently clear and I will give you additional examples and today the plan is for today is to prepare for analyzing multidimensional case with multiple neurons. So for that we need to understand how to read out information from large neuronal arrays. So I will ask, I will present some background material from the information theory textbook and then you can let me know if it is too familiar but the necessary material includes knowing data processing inequality, mark of chain, chain rule for information, what is the sufficient statistics and then I will derive the sufficient statistics for large neural population and show that it actually exists. There is a simple read out and then we will talk about computing this formula for large neural arrays and then applied to retinal data. So that's a material depending on questions and so on maybe it will be some of the lecture today and on Monday. So to go back to the optimal filtering in the multivariate case I want to begin with a demonstration. So it's a little psychophysical experiment and you will be able to see these effects that I was describing or we will go over it one more time on yourself. So the experiment goes like this. You see these two photographs? Yes. They're identical and there is a blue dot and we are supposed to look at the blue dot but then I will, so right now these images are identical. Then I will show you the images like this so you can keep looking at the blue dot and the two images are either blurred or sharpened so the frequency contents is changed. So let's look for it for maybe 30 seconds and then I will switch to the original two images and you will tell me what you see. So I did this through Zoom. I'm hoping that you, what you were supposed to see that once you are, the two eyes or different parts of the visual space are adapted to different frequency content. When you switch to original images then there is a transient and the image where the statistics was sharper looks blurry and the one that is, was blurry looks sharper and then it normalizes to the baseline. Did everybody see that or do I need to make it bigger? I think so. Yeah. Okay. So I think this, I like this illustration because what I was talking about last lecture pertains to single neurons but because every single neuron does it, you see that it's true. So at the level of the brain. So here is a little bit more background on the experiment that I described last time. So in this case the neurons in the cat are presented either with white noise or with natural scenes. So white noise in the Fourier domain will have a flat spectrum and natural scenes has this, so this is actually the logarithm of the power spectrum, one of our F structures. So it's much more correlated. And okay. And then what, and then if we have natural scenes times the filter pass through nonlinearity then let's see. So this is the data I described last time. So you have stimuli now as a cross section, natural scenes have bigger power than white noise and the neural filters change within a certain range of frequencies here, low frequency, low frequencies. And then after that they go to same nonlinearity, same filtering part. And if you look in the temporal domain, then in the same range of spatial frequencies the changes in the opposite direction. Meaning because the natural scenes are smoother at higher temporal frequencies then there is an extra enhancement at low spatial frequencies but high temporal frequencies and then they match to the same filtering part. So that's the review from last lecture. Any questions on the filtering part? So is it clear what the relation between these plots and the experiments that we did with the two phases is? Yes. So there is also adaptation to other other high order parameters such as facial characteristics and so on. Any questions? Hello. Okay. So I have a question. Is this because it is completely clear or is this because you are completely lost? Which one of the two? Completely clear. Okay. Okay. So can you express your... Give me the starting point. Where can I find you? Yeah. I say I'm a little bit lost but I'm not sure what point. I see. Okay. Well let me try again maybe in a different way here. So this is a different slide. So a review is that we have say a linear system and in a linear system the outputs so if we do you see my slides right with the background. Yes. Okay. So some you know the one of the ideas of the linear filtering with multivariate case is that if you have stimuli that for example is a function of the spatial frequency if they are non equally used for example one frequency is over-represented compared to some other frequencies in the input. So in natural world the low frequency dominate so there is more input at low frequencies than it is at high frequency. So the at the output to maximize information I would like to use all channels at equal power. Yes because they have the same limitations in terms of energy. So the the solution is up to of course at some point the noise will dominate but in the range within which suppose the kind of neural noise is constant then in this range if the input if the stimuli are decreasing then as a function of frequency then because these stimuli are overused then I reduce the selectivity to the stimuli in such a way that after I take a product the output will be equally used. Okay. So this is one statement so in the linear system now if you now you can like with this image was of a girl that was a sharper image was sharpened or not sharpened you can say when it is blurred it looks more like this so you emphasize low spatial frequencies when it is sharpened you downgrade low frequencies and you enhance high frequencies. Is that okay? Any questions about sharpening? So the kind of one of the test so this is an example from my work but then there are many other papers where we compare how neurons respond when you change the input distribution and so to test these ideas so when these stimulus changes how should neurons change their selectivity and the theory will predict for example that they will change in such a way as to keep the product of stimulus power spectrum times the filter power spectrum constant but we can see how exactly that happens because the real neural system may not be able to fully adapt due to various constraints. It can be tuned to natural scenes statistics that are common and unable to change or there could be some possibility for adaptation to local stimulus statistics. Is that okay? I think I need some questions because the probability that everything is clear is approaching zero I think. So I think this was very explicative but probably the other questions Carlos you are okay right now and with the next image you're so you should switch on the microphone is it on yeah yeah I hear well yes yeah so the next image here says there is a series of papers of probing different stages of neural processing with stimuli that gradually approximate the natural world so you can have photographs here or movies and you can have white noise so that is the case where you match the mean for example luminance between white noise and natural scenes and you can match the overall variance but the structure of the power spectrum is different and then there are other experiments which match the power spectrum but the kind of the burstiness that is present in natural scenes is not matched and you ask whether the neurons can adapt to these high order changes like force order changes but in this case it shows that you can probe neurons with stimuli with different power spectrum which is second order statistics and ask how the nonlinearities are changing did I recapture part of the okay so we have a question there we need the microphone what is a in in that in that image so a you mean here yeah so a is the normalization scale so you think about the the pixel size so I need the frequent the spatial frequency times a length scale to give dimensionless oh okay okay thanks yeah so there are many questions one could ask for example I'm not you notice that in natural world here there are all one of our apps or they're decreasing with frequency but the horizontal and vertical components decay slower than signals at orientations at other domains so it shows that for example natural since power spectrum is not isotropic and any guesses for why that would be what do you think what's the physical force that creates dominance towards horizontal and vertical components in nature world yes yes thank you right yes thank you so you know either you know things are either standing up or they're falling down and lying down so even in the you would think that it's easier to see that in the office or in the man made environments you will have a lot of dominance of vertical and horizontal edges but this is from the forest and you still see the the dominance of horizontal and vertical components and in fact some people turn this around and say this is the natural world we know this is the statistics of signals in the natural world then if you look in the brain we are more there are more neurons than code this vertical and horizontal direction then oblique directions and then once this is the perception property of the human perception that we are better at coding horizontal and vertical direction that explains why we go to great lengths to create man made environments where these frequencies dominate okay so in this particular case these white noise in natural movies were presented for about i'm going to say 10 minutes yes 10 minutes so there is a limit to how much the neurons can adapt within these 10 minutes but these are the results that i showed that if you have a stimuli times filter and now with taking into account nonlinearity you have sorry this is going back so in the linear model this is the prediction that stimuli times filter should give you the constant output but now we have a nonlinear model meaning stimulus times filter and then there's some nonlinearity and in this case the thought was is that you have stimulus times filter it should be some function of the filtered stimulus that passes through nonlinearity and it's no longer a constant but it should be the same across different stimulus distribution so when the stimulus distribution changes the filters would change but the filtered stimulus whatever it is which we don't have a theory for what's the optimal filtered stimulus distribution should be constant if we are working in a more general case of a linear nonlinear system any questions about that so we have a question there she cannot hear without the microphone my question is why the filter changes in this case because if the stimulus if we just change the stimulus why the filter change as well so one possibility is that the filter doesn't change and so imagine that the we know that natural scenes have certain statistics let's build a filter that is optimal for that stimulus statistic and the animal then has this these filtering properties and then it doesn't and when the stimulus changes the filter is not capable of changing in that case the if we go back to the linear case if the stimulus changes but the filter doesn't change then the output will no longer be uniform and the information will not be optimal for that stimulus ensemble it will be optimal for the first case but not the second so the reason that one should expect some changes in the filter is that when the stimulus statistic changes if you want to maintain efficiency for different environments then the filters have to change so they may not be able to change there can be limits on how fast they can change and at what frequencies they can change but if they are completely rigid then they will not be optimal for different stimulus distributions okay another way of restating yes is that the the optimality is tied to the statistics of signals in the natural world another related point is that if you measure for example this property here power spectrum of natural scenes and then you go to the beach or to the city so this part here 1 over f squared is surprisingly robust to changes in the environment that are salient for us so it will be a small deviation in the exponent it can be 1 over f squared plus minus point 15 depending on the environment so some aspects you can imagine that the neural systems if they adapt if they're designed to process natural scenes with this 1 over f squared structure they will be reasonably optimal under all likely natural scenes distribution because the variation in the 1 over f squared is small so what we are more sensitive is changes in the higher order statistic but this was not tested in this particular experiment so this experiment tests the changes in the 1 over in the second order statistic and and we observed that there is some capacity for change at certain frequencies so in this case so I'm showing you here examples of how the filters change so this was under same neuron under noise and under natural scenes the filter has both different temporal frames showing here at every 30 millisecond resolution and you can see that the filter is similar so it has the same orientation the neuron doesn't change the orientation but there are changes in the spatial kind of a surround structure of the spatial scene so there is some blurring that is going on that is not reflective of the data but of the presentation software but what you're supposed to see is that there is a more broadening in the case of the noise filter and then in the case of the natural scenes filter and that's quantified in this graph that in the case of the natural scenes which is in blue there is less low spatial frequencies and in the case of white noise there is more sensitivity to low spatial frequencies or more broadly so that's any questions I'd like to recapture the the audience thank you yeah sorry just trying to recap a little bit my question my question right now is so there is an input then there is a filtering before the neuron receives the input that's correct or I'm wrong it's almost almost correct so the way we model the neuron and you can so the model of the neuron here is that there is a stimulus and this part is the neuron the neuron includes filtering and nonlinearity now it's not it's important to realize the limitations of this model because for if we're talking about the neuron in the visual cortex this filtering and nonlinearity is happening at many many stages so this is an effective filter and an effective nonlinearity after many stages in other words imagine the nonlinearity wasn't here then initial neurons in the retina would filter signals with small pixels then also in the retina they would then take averaging over bigger regions and then they will align averaging such a way as to obtain selectivity for an edge and this will be the final filter that summarizes all of the processing from the photoreceptor to that part of the brain like primary visual cortex but in reality there is this filtering and nonlinearity happening at many stages and we summarize it as one effective filter and one effective nonlinearity in principle the other generalization of this model include multiple filters and a nonlinearity that depends on all of the filters that you would be able to estimate now please continue with your question yeah thank you thank you and the spike will be represented in we seeing the picture or what will be the spike and the spike is represents the response of one neuron and so now the many neurons collectively will result in you seeing the picture okay thank you yes so we will talk a little bit you know more about the multi-neuronal case later but for now it's a single single neuron okay any any more questions here my my question is in computer science when they processing the the image they will use many different kinds of filter like Gaussian filter, medium filter so my question it is for our human being for the new neuron what kind of filter we have so in this case and the let me see how to answer this question I will I will I will find a slide that I think will answer the question well so the issue that we are we are estimating each filter for each neuron independently and so maybe I yeah I don't think I will be able to so I will answer without slides and the idea is that you um so for each neuron the filter is different and they're estimated by presenting thousands maybe maybe I do have a slide yeah like that so you present many many thousands of stimuli and you observe which stimuli elicited the spike and which did not and after building on this correlation between stimuli and the responses you find the effective filter for that neuron and different neurons will have a different filter to in the linear model we are just using a linear stimulus response function and we you can average stimuli that elicited a spike and that will produce an estimate for that filter okay so maybe that I think that's the best slide I have right now so Tanya are those what are called Gabor filters ambition yes so this is another slide that can help with understanding this is from a Hubel visual paper in they won a Nobel Prize for finding this orientation selectivity in the visual cortex so if you know a little bit of review of the say visual system and so so this is the macaque brain flattened and if you go to this visual cortex which is in the back of the brain so this is a schematic view of the primate brain so in the back of the head under the skull here you have primary visual cortex and here neurons are selected for edges so that's the discovery by Hubel in the visual and they show that if you take an edge and you it's almost horizontal there is no response if it is you increase the angle towards vertical for that neuron there is more spikes and so for that neuron the optimal filter will be similar to the one that I showed will be a Gabor that is oriented at 45 degrees so the filter is so in their case they discovered this as you may have heard accidentally accidentally because prior to this people were studying the eye that is missing here and they were showing dots of light and they were continuing with the dots of light in the visual cortex and they were not getting a strong response until the slide itself had an edge to it so it was sliding back and forth and one neuron responded very strongly so they found that these neurons in the visual cortex were driven by bars and edges which can be modeled as Gabor's and subsequent but the method that I've been describing to you about this correlation it is useful because it doesn't rely on the serendipitous discovery I put on natural sins in front of the animal I record responses if I record responses in the retina as a result of processing statistical averaging I'll get filters which look like little dots I applied the same algorithm to neural responses in the visual cortex and I will get these Gabor filters and then it gets more complicated but my group and others are working on estimating what are the relevant features across different stages of visual processing so after v1 there is a secondary visual area v2 then v4 is the main one and then goes to the this part of the brain under near ears this is inferior temporal so closer here and here you can have neurons that respond to hands so the neurons you see present an image of a hand or a method the response goes down there are face selective neurons but that particular neuron is not selective for a face on it for a hand and the miracle here is that you rotate the hand and the selectivity comes back so the big question both in machine learning research and in neuroscience how to create selectivity for these complex objects that are invariant towards various positions and orientations and to answer the question that was posed which filter we are using in principle one should be able to correlate natural scenes with responses in different brain areas and recover the relevant filters but in practice this is only possible for the first few stages of processing because of these nonlinearities because we are attempting to summarize many many nonlinear stages as one filtering and one nonlinearity I had a question yeah have this result ever been implemented as convoluted as a convoluted convolutional neural network yes so it's true so they so now one can fit convolutional neural networks to neural data and using this convolutional neural network one can recapitulate the selectivity that you see here but there are two in my opinion there are two open challenges open problems that remain one is that we have a brain we don't fully understand how the signals are wired and what are the computations that take you from edges to hands in the brain because and then you have a convolutional neural network that reproduces this result but we still do not understand what are the computations so we have recreated the machine but we have just as many difficulties looking inside the kind of simulated machine as inside the real machine so that's one question because if you know technically speaking if I going to encode a hand so I need at least you know say 10 edges for all five fingers but then it's across different positions across different orientations so there is a massive convergence of signals from v1 to even area v4 and what are the rules that guide that convergence that is not clear even though we can reproduce it in a convolutional neural network so that's one problem the second problem is that the result that we get with this convolutional neural network is less robust to perturbations compared to what we have in the brain so some of you may have heard of adversarial attacks and adversarial neural networks uh how many people have heard about those should be a few right two three people yeah so the adversarial attacks I think you know worry people a lot because you can take an image and perturb it a little bit and the machine will think that this is now something else so it has a lot of concerns for us relying on artificial vision you can think about in the case of self-driving cars or assisting a camera that assisted driver you have a stop sign you interfered with the image a little bit and now instead of stop sign it says you know drive 40 miles an hour or for security purposes I can impersonate somebody if I know how to manipulate the input so this happens much less in the brain through a variety of non-linear error corrective checks that we don't fully understand um okay I think there's maybe there's another question or I think not now okay so thank you for your question yeah thank you and um so um so um yeah so these are the summary of uh sorry where is my so this is the where are the gabor so the gabor selectivity would be an example of select the reason it's shown here because this is for the visual cortex and would approximate selectivity of neurons in the primary visual cortex so do we do do we think like we covered this part um and um what um here what is presented and we can move forward with data processing inequalities and looking at multiple neurons yes or what do you think I think so you agree okay so what we discussed so far was the optimal filtering for one neuron but um this kind of for one neuron as a member of the population we say well this is what how each neuron should change and now we would like to think about how to put these spikes um towards perception how to read out information from large neuronal array so in this case we have to do um um some some mathematical background so we I need to know about um data processing inequality and um other other features because we would like ideally we have stimuli that will be eliciting responses across a number of neurons it can be thousand millions of neurons and one of the open questions is how to read out information from this many neurons and I will show it to you hopefully um on the next lecture if not today is that there is a simple formula actually that um you can read out information from arbitrary large neural populations and the reason for because ultimately the algorithm can't be too complicated otherwise how it will be implemented with um neural software hardware but for now the data processing inequality how many people know about it two three four five six seven I mean I think uh most of them should know it but uh maybe it's useful to recall it yes so it's a very useful theorem a very useful check on um um on various results um you know to make sure that sometimes when you review papers or read papers or even do your own research you want to avoid making a statement that you did some processing on the data and as a result of the processing the information increased so the theorem is that if a set of um if a random variable x causes y and y causes z then there is the information between x and y has to be bigger that information between x and z meaning that because I did some additional processing to get from y to z then information can only decrease or it can stay constant so for the future applications that we will need x will be the stimulus y will be the neural response and z will be our measurement of the neural response so we would like ideally we'll have to have such a measurement as to um capture all the information that provided by the neural response because we will know that that's the best we can do we cannot create more information than is captured in the neuronal response so um to prove this theorem we um we need some other facts such as the chain rule for information so um the chain rule for information if I have mutual information between x and joint variables y and z so that is equal to information between x and z and information between x and y conditional on z any questions about that it's okay it's okay so this is information between x and y conditional on z but y and z are kind of equivalent things so we also can write it as information between x and y and information between x and z conditional on y but um so actually what I think I'm missing here is that x and y and z form the so-called Markov chain which means that y fully determines z and x fully determines y so in this case the x and z are conditional independent given y and so this last term is equal to zero and so we get that information between x and y is information between x and z plus this extra term because information is a non non-negative quantity we will get that information between x and y is bigger than information between x and z yeah so that's our data processing inequality any questions it's okay they show this in my course it was a while back but they were traumatized enough to remember I guess okay all right so if so if z is a function of y then I can only decrease or keep it equal so maybe we can skip the second law of thermodynamics um but the entropy of the isolated system does not decrease and we can model the system as a mark of chain and the transitions are being is that also was covered in in in the past course so I mean it's not absolutely necessary for us we can um but this also kind of the transition between states between x and y so knowledge of the present state should be sufficient to determine the future state independent of the past and you know that we can make various statements using this such as the relative entropy between states has to decrease with n and the relative entropy of a current state and the stationary state to which the system is converging also has to decrease with n and entropy increases if the stationary the overall entropy is increases if the stationary distribution is uniform okay so any questions about um about this okay no no no hands no it's okay I don't see questions all right so the next question is about sufficient statistic oh we have a question in the chat no um can you clarify your question um mu is the distribution of um um the the stationary distribution towards which the system is evolving and menu is the current um the current distribution of states so then very important quantity is a sufficient statistic and um um so we said that I for example think about the neural response I have set of stimuli I have neural responses and I would like to take some function of neural responses and I know that the information will that I can capture from neural responses using this function will be less than what is provided in the full neural response but there is a limiting case or ideal case of the so-called sufficient statistic where I will take not full neural response but some reduced function of it and still capture all the information that is contained in the neural responses so that's our goal is to find sufficient statistics for neural responses so a few examples about um about this so if we have a set of observations x1, x2, and xn um and these observations are drawn with the probability distribution that has a that is characterized by the parameter theta um and so theta can be a particular stimulus then the sufficient statistics is um for example it can be mean or any or some other function of this set of observations so it's in some cases this sufficient statistic is the one that forms a mark of chain so it's the statistics that is fully captures information that is available between the sequence and the parameters of the distribution um so was it also covered um can we skip over sufficient statistics or review it um more fully how many people know about statistic yes games you don't know so the information between the parameter of the distribution and x the set of observation has to be greater than information between theta and some statistic and it is sufficient when this information is um equal so that's our goal is to find such summary that will capture the information about the parameters of the distribution so um some examples so if we have independent and identically distributed sequence of quintosses with unknown bias then what will be a sufficient statistic that question yes for example hi um probability of zero no statistics is a function of the body the mean of zero yes yes so i mean that's what we would like to know is the probability of zero is theta is a parameter and we would like to kind of estimate it by um taking a function of the sequence observations yeah you can do that yes okay thank you so um so number of ones or a number of zeros is a sufficient statistics other examples sequences with the same mean um and n are equally likely so um that's i guess that's the proof but we all know we all know so we now have a statistics where the theta times the sum of these values which is number of ones and then the sequence itself forms a mark of change so that's one example so then a Gaussian distribution we know what that would be right with the mean theta and variance one so variance is given you need to find theta so that will be the sufficient statistics will be what so um here the variables are not between zero and one right all the other yeah so it's a Gaussian distribution okay what is sufficient statistics for a Gaussian for the mean of a Gaussian come on hello okay yes the mean okay very good yeah good all right so we don't need that um so i think if we figured it out so um the sufficient statistics for a uniform we have a question in why we consider thank you for your questions variance one because then i will need another i will not be able to get away with one variable if i don't tell you what the variance is then you have to also estimate it so your sufficient statistics will have two parts one will be the mean and the other one you have to estimate the variance um and uh what is important for um so let's see so now um like for a uniform distribution then it will be maximum and minimum but um um it's okay so we don't need maybe minimal sufficient statistics if it is a function of every other sufficient statistics but uh what is interesting is um what we need to pay attention to are the exponential um the the fact the the Gaussian is important because it's an example of an exponential family of the distributions and that's actually will be important for the neural case so before we get there we will we can discuss the the so-called factorization theorem so that may also have been covered in the class and this is out of covering thomas so if um um did people know about it or should i skip it um so basically if you have a random sample from as before of the probability distribution f of theta and theta we don't know and we need to form a function of x1 and xn to determine this um so we need a statistics that will be sufficient if the probability distribution factorizes so um f theta as a sequence of x will be some function of x plus another function that depends on theta and on the sufficient statistics so it's a kind of a coupling term between the parameter of the distribution and the sufficient statistic and everything else that depends on the particular instantiation is a separate function so if that happens then our this will be a derivation of these we will know that this function t is a sufficient statistic so we will use it to derive a sufficient statistic for um for neural for neural responses um maybe do we need to go through the proof um we can go or we can skip it it's uh the audience call i think uh we also did this in in class so what okay all right so we can skip it and go back to neurons so um the key assumption is that we are going to model responses of an individual neuron as the logistic function of the stimulus um by this i mean that the probability that the neuron produces a spike um which is rn equals to 1 is equal to 1 over 1 plus and then there is an exponential of some function of the stimulus and um so um the what's important is that once I have this sigmoidal tuning what we will derive now is that um it is possible to uh form it in the exponential form and derive a sufficient statistic for the neural responses for arbitrary large population okay so that's our goal so our stimuli are vectors they can be the dimensional vectors and the neurons um to begin with are conditionally independent meaning that the probability of um responses from two neurons uh multiply given the stimulus so there are no noise correlations and then we will add noise correlations but for now it's a product it is still a complicated problem because the neural responses are not independent because they are filtering um there are couples through filters any any questions about this equation so in the first equation uh I think this is the probability that rn is equal to 1 right yes so because the right hand side does not depend on other n no yes right that's correct I lost that somehow yeah so this is um should be probability of rn equals to 1 uh is a function of s and then um similar to what we discussed in the past rn equals to 0 will be 1 over 1 plus e to the plus 2 f of s uh the the object and um now our goal is to show that uh this p of r given s can be rewritten in this form uh exponential sum over n the various um spiking and not spiking from individual neuron times this function for now specific for neuron n minus some function of the stimulus once we rewrite this in this form our sufficient statistic will be um will be this will be this term okay and um so now um maybe uh it's useful to write some things on the board um and we will consider the case where this f of s is a linear function um or maybe we it should be tried to rewrite um I will have a derivation in the linear case and then we will um you can try it yourself for the uh general case the same um form so um let's see how to do it so that's um um maybe I will ask for some help on with the blackboard um let's see so um maybe um so how to write it so the way to write it is um let's write um p of rn is um um okay do you think I can let's see can we see the blackboard yeah r and s and this is one flash into the f and of s right yes let's see yes so that I should write um the p of r even s is given s is the product of this thing over n of e to the rn time f n of s e to the sum over n rn f n of s divided by this product over n of one plus e to the f n of s so and this part here is independent of r now this part is what is called uh this uh one can say partition function or um a n of s okay so this uh a n of s is equal to the logarithm of uh this is sum over n logarithm one plus e to the f of s okay okay yes thank you so the critical part is that our sufficient statistic is sum over n rn rn of n uh isn't there a factor two missing p of r n given s so it is um no I think because we wrote it as um um because there is a difference between if you multiply by the e to the f of s both my equation then um yeah I think there is a factor two I mean there is only a factor two difference yeah in in the exponent okay so otherwise it's okay um I was thinking that there isn't but um so like in the second equation here on the left board I think we have to write e instead of one we write e to the minus um no the denominator is e to the a n of s okay um yeah it is just this yeah I I see okay so maybe it's two two is okay um um as a cosine yeah so if um yeah so you see I have two cos two cos so it's two exponentials e to the plus e to the minus or it is uh e to the plus times one plus e to the minus two okay so ah maybe your r n is not zero one but it's plus one minus one and that that is possible so if r n is plus minus one then this thing is is e to the minus f n of s plus e to the f of s so which means that uh yeah so then your first question is okay and uh and then this is uh e to the uh minus f n of s and like this also and so this is two cosine of uh f n of s actually then you call a n of s this this thing right which is your equation uh yeah okay thank you okay so now um if you have a linear fun if f n of s is a linear function w dot s then our sufficient statistic is um um so then instead of f n of s we write s times w m uh and omega does not depend on n okay no it does w so w I guess I'm trying maybe it's omega or maybe it's um this this function here um okay so then this is uh let's call this uh uh so e to the sum over n r n times omega times s minus alpha n minus this a n of s and so and then you can write this as s times e to the s times t of r minus some a of s and then uh your t of r of uh r is equal to the well sum over n if this omega depends on n it's a sum over n of uh omega n times r n right yes very good and uh and then uh uh yes and this a of s is okay yes so now let's take this into a very nice box because I think it's a very important result we just derived an equation for how to read out neural responses without information loss by taking a linear combination of neural responses okay for arbitrary large populations and I'll show you the the miracles of this equations so um kind of very very important so um I'll switch to powerpoint and we will talk about applications of this equation and the history of it how um you know it was guessed and okay and then um so very important equation so some background um how it was discovered and not discovered so before this equation was discovered uh people talk about population factors it's um for those who work in neuroscience many of you might have heard about this um how many people have heard about um population factors population vectors was heard about I think no one has heard about okay no but okay good so then we are not redundant so there was an experiment by tergeopolis in college in 1986 and um they were a steady movement and it was in a in a monkey and monkey was making movements in different directions up down and so on and here is an example of the neural activity and um so 10 trials 10 movements in this direction are shown here with spikes from one neuron so in this case you can see if you look at this neuron um if the movement is down um to the bottom um then uh it produces more spikes so this also goes back to this earlier question what is the filter for the neuron so they would say oh for this neuron the preferred feature is the movement down to the right and so we will assign to that neuron that vector uh w n and then they said oh but actually um what we notice is that if we take these vectors w and in their case they were normalized to length one just the direction and multiply by whether the neuron produces spike or not then um so imagine that this neuron um has a preferred movement in this direction and if it produces a spike then it's likely the movement was in that direction if another neuron has a preferred direction um diagonally to the top and it did not produce a spike then its preferred direction will be downgraded so the construction is you have many neurons for each neuron you find it its preferred direction of motion the preferred stimulus and that's that and then you democratically weigh their responses zero or one or one and minus one with their preferred features and then because each neuron has a preferred vector the sum across the population is also a vector so they're called population vectors and um it is a vector so if you have 1000 neurons but if the motion of the hand is described by a three-dimensional vector the population vector is a three-dimensional vector and so this population vector uh captures the actual movement that the animal made uh quite accurately so um so in the georgiopolis example this is um um an example of a democratic redoubt from a population each neuron has its preferred direction and it votes up and down on a given stimulus and it says the stimulus matches my preferred direction or it doesn't and we average across neurons and we get the final movement so that's the widely used activity construction and you see it's kind of similar to what we have on the board but the difference with the georgiopolis equation is that they normalize the vector to have unit lengths and that caused some um necessitated a series of papers that we will be discussing um maybe today how much time no maybe next time um but basically it's a population redoubt and um um um we will discuss how this population redoubt differs from the information preserving sufficient statistics that we derived on the board next time but you see that they are structurally very similar okay any questions any questions yeah i have a question uh is uh are these neurons uh linked to the action of movement or to the perception of movement i mean if the monkey is moved or if the monkey is still and the cage is moved uh do they trigger too um so in this particular brain area this is uh monkey movement um and then there are other brain areas that are you know would be triggered by when the cage is moving or where the visual stimulus is moving but um the advantage of this information theory derivation is that we have a general description um you know for various kinds of responses and as you can see i'm writing here that it is um widely used to decode place cells in the hippocampus modern neurons as is here eye movements visual neurons sensory neurons so it's a general um general equation um and then in in a specific context you say well what is the space was in which my uh these receptive fields or preferred directions live to to to make it applicable um you know what will be the space in which this population vector moves the interpretation of rhythm thank you okay so i think maybe that's a good place to stop and then we will continue with um um with interpretation of this equation i think it's very important and how it can be used for reading out neural activity okay thank you so i have a question so so looks like uh the there is a key assumption here that uh uh um neurons are independent and uh so that the response is independent which i think uh it's another important principle no in neuroscience of efficient coding is this true yes so um so the equation that we derived assume that it is independent but actually you can generalize to foreshadow some of the discussion on monday is that you can add some correlations between neurons as long as these correlations are not uh stimulus dependent they will not affect the form of the sufficient statistic and therefore um the slide is here um let's see here the equation so if i can write the total probability distribution of responses given a stimulus in this form which we had before plus some correlations between neurons uh so the jj but if the jj are not dependent on the stimulus it will not affect the form of the optimal readout so we can use this equation in some cases with um neurons not being independent okay okay any question and uh if not uh should we stop here uh tanya yes and then uh we continue on monday and uh very good so thank you very much tanya and uh have a nice weekend nice weekend to you all and uh we reconvene uh on monday at nine a.m okay thank you recording stopped


The T2 Tile project is building an indefinitely scalable computational stack. Follow our progress here on T Tuesday Updates. Our time story is this week, an update on the science pundit last week. I got quoted in this, you know, the scientist thing about this work by Mike Eleven and Josh Bongard and their students that was, you know, marvelous proof of concept where they were using actual cells and putting them in configurations that have been developed by genetic algorithms for soft robots on supercomputer. Well this is still blowing up bigger and bigger to the point where this weekend Josh Bongard was on CNN. Scientists create first living self-healing robots. There you have it. It really does make me think a little bit that, well also in combination with Rod Brooks, who was probably known most for inventing the Roomba robot vacuum cleaner, but, you know, as an MIT roboticist for decades and also an A-Life and an AI guy and it's kind of a friend. We meet at conferences and so forth who recently, I guess, December posted a tweet that got a fair bit of attention within Twitterverse suggesting that the next revolution of artificial intelligence, AI, may be artificial life. That if you follow what happened back in the 1980s, most of the important things about modern deep learning AI or at least the foundational things were developed back then, you know, I was there. But we had the computers that we were so slow that and there wasn't giant data sets and I've said this before so Rodney is saying it as well, but now he's making the point that you could get things happening using artificial life techniques, genetic algorithms, he's kind of muddling some things together that could be pulled apart, that similarly they were lacking, you know, computational power and that's coming on now and so forth. So the next step is to take artificial life techniques, evolution and so forth and use them to apply to AI kind of tasks and, you know, that may be kind of what's happening or what's starting to come down the pipe. So it may be a good time for the T2 Tile project with explicitly using AI life techniques for robust first computing to be starting to come together, what we can hope. All right, mostly what I want to talk about today is this new software design that I've worked on for the last couple of weeks for doing artificial chemistry, for doing chemical bonds in the T2 Tile removal feast machine.  So I always use the phrase turn in, you know, turn in script I never said submit but of course you had to turn it in. Anyway, that's coming up March 1st, that's only five weeks away now and there's a lot of science that has to be done. So this is probably going to be about the last major event talking about the stuff that's going into that but what I want to talk about today is mostly about the software engineering of it because we've made some progress and it's also involved some changes to Oolong 5 which is still hanging around, gaining striking new functionality when it was supposed to be in future freeze quite some time ago. All right, so, right, so here it is. Multiple inheritance plus class reflection gives us clean artificial chemistry.  Now in programming languages, in object-oriented programming languages, this goes way back and, you know, there's all kinds of people who can fight back and forth about whether inheritance is a good thing or a bad thing. It's the idea that, you know, you can say, I'm describing all this behavior but in addition, I want to take all of that behavior as well and I'm going to refine it. So whatever a mammal is, is, you know, I am a human so by default I do everything that a mammal does and I can add stuff and tweak stuff specific to humans. Mammal in turn inherits from animal, it does everything that animal does and so forth. That's inheritance and, you know, there's questions like I said about whether how good an idea it is but it also reflects the notion that you can be expressing your abilities to other classes, to other objects. You say, well I am a human then other classes can interact with the me object assuming that the things that go with being human are something that I can respond to. And to me there seems to be a deep connection between that idea of a public base, a base class that says, you know, whatever it is I can respond in this way and a chemical bond that in biology, you know, we have these incredibly complicated molecules that have these, you know, expose a bond over here and a bond over there and this bond is in certain shape so it does this and this bond in certain shape does that and so forth. But the idea is, is that anything that has the certain shape or the matching shape for that can interact with that molecule via that bond and, you know, do whatever it's going to do. And so, but it's critical that you be able to have multiple bonds. So in languages like Java you are called single inheritance languages where you can only have one base class, one super class. Now they've gradually made it more and more powerful so that you can do a lot of other stuff without it and we did the same path. Ulam up through Ulam 4 was a single inheritance language or Ulam 3 but now in Ulam 5 we have multiple inheritance. So the idea would be to say I inherit from, you know, next pointer bond. I inherit from previous pointer bond and you can bond me together, my next with somebody else's previous and we can make chains or trees or whatever by expressing bonds that we can do. So we need to have multiple inheritance in order to have multiple possible bonds and that's where it was a few weeks ago, a month or so ago, when I first started looking at this. Now on the general topic of artificial chemistry the idea of focusing on bonds has been something that goes way back and I wanted to just show a minute. This is 2011, it's almost a decade old. There's more stuff trying to get big things to move in the movable feast. We've got these two meshes that have privileged end on the right and red that are the red guys specifically try to move to the right whenever they can. The light blue guys that are going nowhere just diffuse and these dark blue guys that are trucking pretty good here. So what I wanted to point out here is that it's not just a collection of colored circles like we see in the movable feast machine all the time. It's got these lines in between them and the lines that represent chemical bonds and some of them are longer some of them are shorter. Each of these has a potential for four bonds so that it makes kind of a mesh and you know this was this was coded oh man I don't even know it was probably in C++ it was probably before the Java code and all this stuff was custom done and in the first version of the so we're currently on what's called the P3 atom using the movable feast it's 96 bits and it has all these various properties and the P1 atom which I don't even think this was it this was before the P1 atom was formalized but one of the major papers about the stuff that we've done was all about the P1 atom and explicitly had room for these bits represent these kind of bonds and those bits represent those kind of bonds and and there's a little count of how many bonds are supposed to be and it allowed you to write things that had these kind of you know connections between them that would stretch and shrink but try to stay attached fairly easily but also it took up a tremendous amount of the atom as being hard-coded with this one particular style for atoms I'm sorry for bonds and there was really no place else to go with it so we went to the P3 atom we threw away the bonds entirely now you just have this raw empty apartment of you know 71 bits that you can do whatever you want with and you can implement you know sort of bond-like structures by saying you know this this group of bits indicates the site where the opposite guy is and the opposite guy has group bits points back at me and so forth and we've done that several times but what we're doing now is saying can we build up some slightly more you know formal structures more software library stuff that will allow us to get some of the flavor of this without having it fundamentally burned into the movable feast machine and therefore unchangeable and everybody's stuck with it and that's what we have now so okay the without going through the details of it because I'm eating up way too much time and I want to do a demo the idea is we have a base class called Cubond that describes what bonds are supposed to be able to do they're supposed to check their consistency they're supposed to be able to say could you move here and here's how we're going to do it please update and can I bond with you please make a bond and so forth the problem with all this is you see these all all all is that we need to be able to not have just one bond because we're going to use multiple inheritance and have a preview bond and an x bond a head bond tail bond whatever it may be and that means we can't decide can we move to a given place by just asking one bond we have to ask all of the bonds so where we were last october when i was first trying to lay out this structure is the we had these base classes but in order to use them as you got more and more complicated structures you had to write more and more let's say bondo yeah so head bondo all right so here it is check consistency could move to all the things you have to do for that and so forth now the the head guy just has one bond going backwards the mid guy where's the mid mid guy this is the mid guy so when he checks consistency he has to in turn call call these to from and to from and to and so forth and and even went to i went to a thing that had four bonds and now so now that the the amount of sort of overhead code that you had to write so to be a monomer you know q monomer with two bonds and so forth uh uh here's your rationalize your move your swap your bond with and then here's the other one and and the classes were just getting completely filled up with this boiler plate to dish out to the bonds and the bonds that we had i didn't like that it really meant the code was not pretty and not pretty code matters because this is what forms our mental models as programmers and if we're just completely in the swamp of taking care of this low level uh sort of you know maintenance of of bonds over and over and over again it's going to be terrible and that's where it was but instead what has happened now uh is we have invented invented we have implemented class reflection a simple form of class reflection in ulam for ulam 5 now what that means is is normally in an object-oriented language you declare things like class square class triangle class circle class shape whatever it is and you make relationships among them and that and those defined types which are fairly rigid and the compiler for language understands them and can do things with them and it makes as many decisions about what it can do at compile time when you're turning the code into something runnable not when the code is actually running a class reflection system allows at runtime one class to ask another object like what class are you what are your base classes what do you inherit from and deal with that not by pre-compiled saying oh you are a cuban but having some other way of doing it so now we have a class utils that's appearing in standard lib and we have the idea of a class id and you can take a reference to anything you can take an atom and say what is the class id that is currently in here and you can do different stuff based on it and so we're using that in the cuban class now so that and now we have iterators you can say please go through this loop at runtime showing each base class of a given object and we can make decisions about what to do that and what that has allowed us to do is take all of that consistency checking the consistency checking the can we swap can we move can we make a bond and so forth and instead of having to rewrite that over and over and over again we can do it using reflection so we're saying okay how do we update for a swap for something that's some kind of cuban it may have multiple bonds multiple ones we don't know but we know it inherits from cuban so it has at least one bond well what we're going to do is we're going to iterate through all of the base classes it's got with the class base iterator that we just got and take all of the the base classes that are a subclass of cuban and we'll ask them one by one and there's a new structure so q qb cuban square brackets ci where the square brackets ci allows you to say here's a class index saying i want to call a specific base class method that is associated with this class id so we can go through it using this new syntax and saying check this base check this base check this base and it's lovely so when we saw before that the polymer classes say um we're all full of and now this is it this is yeah this is it um so polymer takes the the base class which tells us how to do an event for these particular polymers but now there's very very little code in it there's how to make a choose to hook up if you can between your monitor and set colors and that's it that's the whole code all of the check consistency can i swap do the swap has all been lifted out by using class reflections so let's you know oh geez we're already out of time but let's try this real quick um uh oh and now we're compiling so it's going to take forever well this one's going to run a little long it's also going to be late because it's working all last night monday night into tuesday morning getting this stuff working because there's another cool thing in it that we'll see in just a second uh so this we may be going 20 minutes today i'm sorry uh especially because compilation takes so much longer when we're all recording uh screen grabbing and so forth um geez this thing for everyone we're also optimizing uh there we go all right so let's get rid of this all right so we'll put down a seed we give it a seed we give the seed an event it springs out into a head tail check it out bonds are getting drawn how could that be uh uh the the code to write do this graphics is all very specific to mfms the simulator i mean it's going to be on the tiles as well but it's not something that ulam previously any way of doing so does that mean that we have now uh you know gone back to hard coding bonds in the underlying engine no in addition to doing this class reflection system and supporting multiple inheritance now in ulam five we're exposing a graphics interface that allows atoms to draw stuff well at the moment all they can draw as lines but it's easy to extend it to be able to do rectangles and circles and what's not and so forth uh so in fact where oops uh there it is uh we have a bond renderer and it works great and it's already the case uh oh well let's um get our polymers as well m2 m4 so the the green guys and the blue guys can interface with each other and so on um and at the moment see unlike the head and tail bondo which you have a c that springs out fully bonded these guys polymerize they just look around themselves and they find stuff that are they are suitable with by matching bond same tag opposite ends you know one one true one false they match up and it oh yeah and this is going really slowly why is this going really slowly because right because we're defaulting to enabling logging there we go so in fact the very first time i started playing with this well so you get the idea i'm pretty excited about this i'm going to be using this to try to do artificial chemistry to get some basic mappings between the chemistry and the software engineering to try to get you know to head in the direction of getting useful stuff done systems engineering in the movable feast machine in the t2 tiles using bonds which has been easily a decade journey away and then finally back again so that's where we are this week it's pretty cool now you know in this case we can also you know if we come in right now and you know erase some of these guys like you know the rest of itself all cleans up we we cause inconsistencies at the moment the default behavior if an inconsistency is found the guy just erases himself and that causes anything he's connected to to be inconsistent and so forth so as a result the thing all cleans itself up it doesn't have to be that way and that's the kind of part of the behavior that we want to be writing all right i gotta stop um so yeah and and so i was gonna say but we've already kind of talked about it that as soon as i got it implemented i started seeing stuff like this this m2 guy thought he was connected to this m4 but the m4 didn't think he was connected back because in fact the rendering system for bonds actually only renders from each side it renders half the bond and then the other one renders the other half so inconsistencies turned out to be really easy to see so i started playing around with this and and i you know delivered an event to this guy deliberately and he moved down here and stole the event back and now this guy looked like he was inconsistent and it's like you know what was that you know so it was some kind of bug it was clearly some kind of bug and i played around with it some more and it was so totally obvious rendering the bonds visually made it so obvious i'd been looking at these numbers you know bond site this bond site that never seen this problem before and this went all the way back to the stuff from october uh it became completely obvious it was also completely obvious that it would the the m2 guy when he was stealing the thing back it wasn't like he was just randomly grabbing a guy it was like he still thought he was connected to him which makes sense because he had his half a bond uh and the thing that should have caused this guy to blow up because he was inconsistent wasn't causing him to blow up and that pretty quickly led me to the check consistency all rule and and it was wrong and this is now the fixed one and and with it fixed everything is good all right uh so artificial chemistry is what it's about we're going behind the wall of science so i'm going to start talking instead about uh the sequencing intertile events so i'm going to be splitting my time between getting the intertile events going because we really need that and working on the artificial chemistry i'm sorry this went so long the next update will be out in a week uh thanks for being here you know i i always say thanks for being here and you know for the folks who do check them out week by week thank you really very much but you know if you're here from the future you know whether it's a week later a month later or who knows 10 years later you know thanks for taking a look and how did we do how did 2020 come out for a life in the movable feast in the t2 tile project i'm really curious to know we'll see you next week


What's up everybody? I'm the Mangus. You are awesome. And today I'm going to take you through the card system for overprime I tried to stream this earlier didn't quite work out for me But what I'm going to do is I'm going to show you how you acquire card points and how the card system works How many slots you have why you have those three empty card slots along with six card slots down there at your bottom Right and then we'll go through each and every card to find out what they do and help give you a leg up On the 18th when the game becomes available to everyone in order to get the game You're going to have to go to their discord I'll have that linked in the video description below as well as a pinned comment in case you're watching on your phone So let's let's get into it So the way you get card points is you get gold if you see the gold Gauge to the left of my health and meter bar that will fill up as you get hit Well if you get last hits on minions It'll fill up more if you're just near a minion that dies It'll fill up a little bit, but as it fills up completely. That's when you earn another card point Another thing I wanted to highlight the minion health bars are a little bit offset So like you would normally aim directly below that you wouldn't hit the minion So you have to their offset. Oh, it's like shooting a fish. Well, they're offset a little bit to the right I missed that last hit because I was tacking And they do highlight a little bit red. So there is kind of a bit of a execution mechanic here There I got that one Get another one and you can see that that gold bar filling up to the left and Bam we got a we got two card points now. Well, actually we got five because I didn't spend any But I'm gonna go get I'm gonna get a few more card points here And they'll head back to the shop and show you how that works so we're back at our card shop you hit left control to open it up and As you can see you got the three active slots the three passive slots What that means is if you put a health potion put a health potion a health potion in the passive slot You're not gonna be able to use it So we'll close out the menu here and you see that the health potion is in my card slots But it's not in an active card slot So I wouldn't be able to use that health potion Luckily for you if you do make that mistake Everything sells back for the exact amount that you that you purchased it for so There we go sell item and I'm back to 11 card points, which is kind of nice It makes it to where You can buy early game cards and you won't be penalized for it at all which that might be good That might be bad it that remains to be seen So if we come in here and we get you know a mixture of items, so I say I want a health potion I'll put that in an active slot. I want a mana potion. I'll put that in an active slot I want a ward I'll put that in an active slot and then I come down here and I want like a this guardians ring That's passive.  Well, you can sell stuff back Come on. Let me sell so I'll sell that and I've got eight points So that I got nine so that and we can get our whoops our wizards bag and that's gonna give us more Ability damage, so that's how the item system works in Overprime so let's go ahead. We're going to take a long slow very boring look at all these items so that you can plan your attack Come the 18th Okay, so here we have all of the cards now. This is going to be a boring look We're gonna take a look at every single one of these cards and and what they do what their passives are and if they have Actives I do warn you some of the descriptions are in Korean, so I have no idea what the card does Kind of a fun thing. They named a lot of some of the cards after various Paragon YouTube or Twitch streamers not really YouTube streamers. They didn't name after any youtubers just all twitch streamers What they did everybody needs to get off twitches dick, man All right, so century Ward Just place the ward that you can see invisible units, but has a smaller view range than the vision Ward so that caused one Card point there and then the vision Ward is you know the exact exact opposite gives you a larger area of vision But it can't detect invisible units, so this would be good if you're not facing a calari This would be good if you are facing a calari Then we have leather boots move speed increased by 3% I don't like any kind of boots in games. However, if you're going to do them I like doing them like this. This is definitely an item that you would drop eventually because it doesn't give you any other sort of Statistics, so you would get these leather boots for early game laning phase after that you would end up dropping the boots a Detection magic book makes you a detector so you could find nearby hidden enemy Units for a short duration.  It's not going to work. It's immediately going to be cancelled Magic shards just gives max health and max mana Lumberjack acts as a passive item and gives you one damage says passive effect of felling deals 20% more damage on minions Won't work for heroes. However, it then says damage 25% So I don't know if it's 20 or 25 and it only works for melee heroes So don't be thinking you just pick this up on an ADC Health potion. We already kind of discussed Vision ward we discussed Health ring. This is kind of like the old health ring from Paragon just max health 40 and gives you a three HP five healing per second. So kind of nice Especially for off laners, maybe even mid laners Guardians ring max health 20 defense 8% and that defense is against basic abilities Skill defense. I think there's what the magic defense is what they call it for ability armor Shovel this is a passive just gives you four damage Beginner shield max health 100 defense of 5% three cost card Guardians necklace magic defense 10% and four cost card Earth Ruby That's a max health 200 and that's a five cost card Vitality enhancement stone max mana 120 max health 120 five cost card Elder staff mana regen point four per second max mana 90 skill damage 5% that is a five cost card claw hammer attack speed 10% five cost card Mana stone mana regen point six max mana 150 five cost card shield of shui passive item damage six critical 4% critical damage 2.5% and that is a six cost card Blood token you get four damage and 2% lifesteal six cost card Spiny stick max health 70 damage 5 and that is a six cost card Indomitable helm max health 50 defense 5% healing 4 per second. So that's a health regen card six cost card Karna's great sword damage 12 8 cost card Wizards bag skill cast range 100 so you get a larger range or longer range on your skill abilities such as like Gideon's rock would go further Phase untamed growth you could throw that out further kind of cool kind of nice max mana 130 mana regen point six per second magic damage penetration 5% skill damage 5% Seems like a pretty strong one 10 cost card Asura This is a cast type instant activation active item Damage six attack speed 5% the active effect movement speed increases for a certain period of time Duration is 3.5 seconds bonus move speed 30% that is a 10 cost card Gale stone passive item attack speed 20% and you can only purchase two of them and it is a 10 cost card Gravity staff it is a cast type hero choice cast range 1000 max health 60 active effect gravity pushes selected enemy to the direction where they are looking at So I guess you could force somebody into a position They don't want to be like maybe if they're just outside your tower range and there's no minions under the tower You can push them under your tower. I don't know. We'll have to see how this one works really. That's a 10 cost card Oasis is an active item max health 220 healing 4 per second max mana 120 and has an on-use effect heals nearby teammates for 250 and this is a 10 cost card protection of Marty Riviera movement speed 5% Max health 200 max mana 100 mana regen point six per second the active effect Select yourself or one of your allies to provide movement speed and shield for a certain period of time Duration three seconds bonus shield 300 bonus move speed 30 percent. This is an 11 cost card pancakes is An active item damage 16 lifesteal 4% active effect rabies Place ward that provides small area vision, but detects invisible units So you get a sentry ward off of this Duration six seconds bonus move speed 10 percent bonus attack 40 percent defense reduce 40 percent I don't get that It places a ward that provides small area vision, but the text invisible units And then it tells us it does it has a duration of six seconds and does all this other stuff So I think the tooltip is wrong here I think that rabies Does not place a ward. I think it probably gives you the bonus move speed bonus attack speed and reduces enemy armor and That is a max purchase is one that is an 11 cost item Seal of madness max mana 230 max health 250 mana regen 1.7 per second that is a 12 cost card Wizard's book mana regen 2 per second max mana 250 skill damage 5% 12 cost card Spirit armor magic defense 15% healing 6 per second max health 270 12 cost card pistol of the Buddha Active effect magic explosion chooses target and emits powerful laser beam and hit enemy Yeah, some of these some of these aren't translated. Well damage 210 basically. It's just You just point a pistol at somebody and shoot them. I guess that is a 13 cost card Kingslayer damage 16 max health 70 passive effect attack range grants bonus attack range for range to heroes only additional attack range 100 units That always confuses me when they just put like a 100 there like I don't even I don't what does that mean? What does that mean purchase restrictions is one that is a 14 cost card and Effects for range heroes only that you can't just put that on Chimer to make him his axes hit longer ways away Flashing doll cat is the active item teleport yourself a maximum of 1800 range. So it's just a blank It's just a blank. I seem to have a passive effect But don't know what that is because it's in Korean and that is a 14 cost card Battle hammer. This is a passive damage 15 healing five per second splash damage 30 max health 70 attack speed 10% passive effects is does cleave damage when hit enemy splash damage rate 20% So this is just deals extra AoE damage and it's only for melee heroes. So What was that thunder cleaver? Was that the card in Paragon? That's what it kind of is And is a 14 cost card The Borey Laurel wreath This is an active item damage five attack speed 10% active effect burning soul chooses target and make them silenced for five seconds Also makes them take more damage Duration 2.5 seconds defense debuff 30% so it's a gag order and that is a 15 cost card Fortified amulet max health 200 damage 10 attack speed 5% 15 cost card CMS harp is an active Max health 300 healing 2 per second skill cooldown reduce 10% Increase the movement speed of friendly units within a certain radius Duration 4.5 seconds bonus movement speed 40% Sages wand this is an active item max health 150 mana regen one per second Max mana 240 skill damage 5% active effect paralysis Select enemy hero and slow them in huge rate. So slow them down a lot duration three seconds movement speed slow 60% this is a 17 cost card Chaos staff another active item max health 100 moves speed 3% mana regen point six seconds max mana 90 Skill damage 5% have no idea what that if active effect is but it is a 17 cost card Dreads sword Damage 15 movement speed 3.5% max health 140 attack speed 10% Manor regen point four per second max mana 90 skill damage 5% this is a 17 cost card Phasma's beads max health 180 defense 4% is a passive item The passive effect is when taking more than a certain amount of damage at once if the phasma is Charged it completely blocks the attack stun silence, etc. Are not blocked Damage defense minimum damage 130. So basically if you take a hundred more than 130 damage at once It will block the ability as long as it's not a stun or a silence or like a slow or something I think that's what that means Little little confused on that one 18 cost card Poison sword damage 17 the physical damage pin 5% This is a passive item and the passive effect is corruption reduces target defense for seven seconds when you hit the enemy Defense reduce 15% so that's gonna be pretty good poison sword does not stack However, the duration will be reset when stacked Poison sword does not stack However, the duration will be reset when stacked I think that just means when it whenever the duration falls off if you hit them again It'll apply the stack once more that is an 18 cost card Commander's shield max health to 20. This is a passive item. I'm sorry maximum health to 20 defense 10% magic defense 7% healing six per second passive passive effect is defense each time you take damage There's a chance to block a certain amount of damage defense rate is 20% damage reduce is 30 So you have a 20% chance of reducing the damage by 30. I think that's what that means And it's an 18 cost card Sword of the dead passive item physical damage pin 5% critical 5% damage 17 Attack speed 10% passive effect. I don't know and it is a 18 cost card Reflection shield active item instant activation stat bonus max health 250 defense 5% damage 5 passive effect damage reflection when you are attacked with your reflective shield Activated all damages were reflected the damage still suffers So duration 3 damage 50% so it's basically Thorne Yomi 20 cost card Soul sword active item damage 10 active effect shadow walk your body becomes transparent and becomes very difficult to see When utilizing a skill or if attacked during this state you are released from stealth It is a 15 second duration passive effect cut off when you Intake damage you may not utilize the shadow sword for 10 seconds. So if you take damage, you can't just Peace out and blink into the shadow shadow plane So this just gives you stealth just gives you stealth on activation as long as you're not in combat So 20 cost card Svetlana zebra passive item stat bonus defense 25% max health 200 skill cooldown reduce So that's a CDR item 10% Use effect as it said passive item, but it says use effect passive effect. Okay.  This is an active item max health 400 healing 6 per second defense 13% The use effect is avatar for a short duration gives immunity for every magic damage and unusual condition. So it's immunity to Abilities and any sort of slows roots or stuns So there you go 22 cost card Magic guards armor max health 400 max mana 200 Defense 5% magic defense 25% and it's got 15% CDR. That is a 22 cost card Angels boots, this is an active item movement speed 7% max health 50 When used assigns one of the allies on the map to teleport to the location if an ally dies They will move to where they are. So it kind of gives you murals reversal of fortune I guess that's why they call it angels boots. That is a 22 cost card Nazgul reactor magic damage penetration 10% skill cooldown reduced CDR 5% Manor regen 1.6 per second max mana 370 skill damage 10% skill cast ranged 100 So this is another one that increases your your cast range for your skills and you can purchase two of them One of that stacks one of you just keep extending your Your your skill range so where you're just straight up artillery firing stuff over into the enemy 23 cost card Victory flag passive item defense 15% magic defense 15% max health 100 max mana 300 Use effect victory flag reduces the movement speed of nearby enemies by 10% 23 cost card dragon droppings passive item max health 620 healing 14 per second damage 10 attack speed 5% and You can only buy two of them 23 cost card Masamune Masamune whatever move speed 3.5% damage 27 attack speed 20% and that is a 23 cost card Mutiny damage 18 max health 70 passive effect mutiny when you basic attack target gives bonus damage based on max health gap giving 100 maximum damage 5% max bonus damage 150 so just However much health they have is however much more damage you're going to deal 24 cost card cherry temper passive item damage 23 crit 14% critical damage 8% You only get two of them and it is a 26 cost card Bloodstone max health 450 mana regen 3.1 per second revive time 35 seconds max mana 380 You can only buy one and you cannot sell it it costs 27 points And it seems that it decreases the amount of time that That it takes for you to revive after you die, which is really nice. I'll do that's that's super powerful If you're losing especially frozen hands passive item defense 20% max health 600 healing 3 per second and Use effect passive frost bite reduces that use effect and then it says passive This is really frost bite reduces the attack speed of nearby enemies by 15% So I guess you have to use it in order to whenever somebody attacks you for them to be Have their attack speed slowed be useful tank item 27 points Ruler is a passive item damage 15 mana regen point six per second skill damage 10% max mana 210 attack speed 10% max health 190 you can only get one of them and it costs 30 points Time backing bracelet active effect refresh cooldowns and reset cooldowns for all items and skills Except the ultimate the cooldown of the time back bracelet is not reset And you can only buy one of them once you buy it. You cannot sell it back. This is This is something I've seen in a lot of other MOBAs just straight resets all of your cooldowns so you could hit somebody with a bramble patch on Fay and an untamed growth and Harvest nettles in the face Hit this and then do her caught her ultimate combo throw down the ultimate do all that shit once again So you could really pump out a lot of damage or a lot of shielding with this time backing bracelet 30 cost Seems like a deal You my cartel Skill CDR 20% max health 250 max mana 40 damage 10 attack speed 10% defense 15% you can only buy one of them and they cost 30 points Mechanical converting stone skill cooldown as well CDR 20% mana regen 2.6 per second max mana 400 skill damage 5% Active effect it says passive item, but the active effect stills enemy health when you give magic damage So that is passive.  I don't know why you would buy two of them And I will probably that 45% attack speed and it costs 33 points Vampire cloak This is an active item lifesteal 6% damage 14 max health 200 attack speed 5% Grants massive lifesteal bonus for a short time that duration is 2.5 seconds lifesteal bonus is a hundred and twenty percent You only buy one of them and they cost 33 points Strafe is an active item the damage is 34 attack speed 30% magic defense 15% Active effective strafe removes all crowd control effects on you and increases movement speed for a certain period of time Seems very powerful duration two seconds bonus movement speed 30% that is a 34 cost card last one miss a monath Passive items skill bonus skill damage 25% magic damage penetration 10% mana regen 0.4 Set per second max mana 90 you can only buy two of them and they cost 34 points So that's it guys. I hope that wasn't too confusing I'm gonna go in game now and and go ahead and test some of these cards out and see how they actually work and see What happens as far as what the description says and especially the ones where the description is in Korean I'm gonna try and figure out what they do But for now I'm gonna go ahead and put this out to you guys so that you can start planning which cards you want to build for which hero and Trying to do some some fun and crazy stuff on the 18th But for now, this is the man who's signing off you guys have a good one man goos Did he say lieutenant Balika? It's not Bellica. It's Balika What that's like a that's like the substitute teacher on a key and pill Where's talking about talking to Blake? Hey, but lucky. But lucky.


So my mom's computer died a couple days ago, and while we're waiting for the next one, she's been using my laptop, and my laptop has Linux on it, and she didn't really care for that, so I had to install Windows on it. I tried to install Windows 11, and the laptop's too old for it, so we ended up having to put Windows 10 on it, which was its own adventure, but it made me realize something. When I install Linux, after I'm done installing it, I feel like I've accomplished something. And it also makes me feel like I'm beginning a journey into putting something together that is my own, and is something that I'll enjoy using. When I install Windows, it just feels like a chore. Now, most of this is my own personal feelings, and it has really nothing to do with Windows. It's just more that when I install Windows, I don't look forward to what comes next. When I install Linux, I look forward to every single thing you have to do after you've installed it to get it set up. With Windows, I have no joy in installing it. I think that's really the biggest difference. It's not the biggest difference, but it's one of those differences that kind of highlight how separate Windows and Linux actually are. So that's it for this time. I'll see you tomorrow.


And then we can ask ourselves, with the next lick or the next bite, is this better than worse than or the same as the previous one? And I think of that as we can map out that pleasure plateau. Because as we start to eat the ice cream, it's, oh, it's really good. It's still really good. It's real still really good. And then it's, it's like, well, it's not as good as the last one.  What's up, everybody? And welcome to the show today. We drop great content each and every week. And we want to make sure that you guys get notified. And in order to do that, you're going to have to smash that subscribe button and hit that notification bell. And if you've gotten a lot of value out of this, make sure you give us a like and share our videos with your friends. And is there a time to pay attention that is crucial? So for example, there's an ice cream shop here in LA, Jenny's ice cream.  And of course, you know, they have eight different flavors that taste amazing. So I get this one, oh, that sounds good. This one sounds good. And all of a sudden, I have three scoops of ice cream, right? I went in hoping to have one. And I'm eating the ice cream and it tastes amazing. And then as the day goes on, those three scoops now are really hitting me the next morning, I'm sluggish. I don't feel myself. So where is that attention component key? Because in the moment, I'm enjoying Jenny's. I'm so happy I'm here. And then it just like tails off until I don't want to get out of bed the next day. Yeah. So you're highlighting two really important pieces. One is that we learn through, you know, reward based learning is based on feedback. We've got to see so the closer that feedback can be to the behavior, the easier it is for us to be able to see, oh, there's the result, you know, positive prediction or negative prediction. That was good. Do it again. Or that wasn't so good. You know, don't do that again. So if you can link back the sluggishness the next day to the ice cream, the previous day, it gets much easier to remember, oh, wait a minute. Last time I had three scoops, that wasn't so good. And so I think of this as, you know, I kind of use the analogy in the book of gears, you know, your first gear gets you moving, that's mapping out these habit loops. The second gear is like asking, what am I getting from this that changes the reward value. And then the third gear is finding the bigger, better offer, you know, like what's better than this. So let's use the three scoops of ice cream as an example here. So with three scoops of ice cream, you know, you get eight, eight tastes and you're like, okay, I'll have those three or those five or those, you know, whatever, let's use three, because that's a, that's a very common thing. Now you tell me, AJ, when you have, when you're eating a bite of ice cream, are you paying attention to how good that is? Or is your mind already thinking about the next lick or the next bite? Oh, I'm thinking about that second flavor that's starting to melt. Totally, totally. So our Brian, this process is set up to help us anticipate the future because that's what drives us to do things. So from a survival standpoint, you know, we, we get the reward of something and then that dopamine fires firing shifts from receiving the reward to anticipating it. So that dopamine starts firing that says, do it again, do it again. That's where craving comes from. So here feedback can also help us tremendously in the moment. And by this, I think of this as like the pleasure plateau. So we can be asking ourselves instead of anticipating that next bite or the next lick, we can ask ourselves, well, first we can just pay attention to the food that's actually in our mouth. So we can actually enjoy the ice cream that we bought because it tasted good, you know, the irony is we're not paying, we're not enjoying it. So we can savor it. And then we can ask ourselves with the next lick or the next bite is, is this better than worse than or the same as the previous one? And I think of that as we can map out that pleasure plateau because as we start to eat the ice cream, it's, oh, it's really good. It's still really good. It's still really good. And then it's like, well, it's not as good as the last one.  So I have my patients or even folks in our, in our E right now program ask themselves how little is enough? How much can you enjoy and then stop before over indulging? Why? Because it's better when you don't overindulge. It tastes you get all the pleasure and then you stop before you go off the cliff. And you're also getting the immediate reward right then that says, Hey, it's better not to overindulge. And so it's even easier to learn that as compared to having to make that connection from the next morning, where it's like, Oh, what, what was it that I did yesterday? Was it the ice cream? Was it the soda? Was it the three pieces of pizza? You know, it's like, then we have to try to separate those pieces out. We drop great content each and every week. And we want to make sure that you guys get notified. And in order to do that, you're going to have to smash that subscribe button and hit that notification bell. And if you've gotten a lot of value out of this, make sure you give us a like and share our videos with your friends. I love all of that. There was a saying that I heard about five years ago that started making me looking at my daily habits and then evaluating what I was getting in return for that investment in that habit. And the saying was the answer to consciousness is more consciousness. So that allowed me to peer into things more so that's the, what you were talking about in this, the second gear that I'm realizing this now. So why is this now? And the second, what that anecdote led me to was the question, what am I getting out of each and one of these? So now that I've recognized that there was a habit that I do, what is the reward? And then understanding that I can put in my own reward. So for instance, I grew up in a family where you ate everything all the time and there was no food left on your plate and all these things. And as you grow older and you were living more of a world of abundance, eating everything became just how I ate and eating to the point of can't eat anymore was a habit that for a lot of people in that position will develop. And the reward of wearing certain clothes was a much better feeling for me than the feeling of being satisfied in that moment or eating to I can't eat anymore. And so that was very easy. And then once I saw it in that manner, I started looking at all of my habits. So it was like, well, quitting Netflix and binging on shows was easy because there was nothing in return. It was another letdown. What was the gain that I had something in common with other people who watched The Lion King and now we can discuss it? That's not a reward. That's fabulous. And maybe the first time watching The Lion King is good because, you know, the music's good, the animation's good, whatever. I think I was referring to Tiger King. Oh, okay. Yeah, even the first time's not good on that one. Exactly. Yeah, you've nailed it. That's what second gear, that second step is all about. What am I getting from this? Our brains know, our bodies know. And what that does, I think of that is it opens up the space for us to find that BBO, that bigger, better offer. And that could be as simple as not getting three scoops of ice cream. It could be as simple as not eating everything on our plate and saving leftovers for later. It could be as simple as watching one episode of a show if it's a good show. And then not trying to binge on the whole series just because they've left us with a cliffhanger. Well, something else that is important to me that I was realizing is if you're able to forego those habits and replace them with things that enhance life that make you more happier, that allow you to thrive, then the feeling that you get from making those choices and how you feel on a daily basis because now your day is filled up with things that have a higher return than the bad habits that you are living through. Once you reach that, there's no going back because you realize how well life can be, how exciting, how transformative, how exciting to wake up every day when your day is filled with habits that enhance every moment. Totally. That's the bigger, better offer. So if we don't eat three scoops of ice cream, the next morning we wake up feeling refreshed. That is absolutely it. And we can even form good habits this way where it's like instead of telling ourselves that we should exercise. Y'all have probably heard the joke, we should all over ourselves. We should exercise. We should eat healthy food. Instead, we can just pay attention and say, oh, what's it like when I exercise? What's it like when I eat healthy food? What's it like when I have one scoop of ice cream and actually pay attention to every bite and savor it as compared to eating three scoops mindlessly and then already planning for my next trip then tomorrow to the ice cream store because I hadn't really been satisfied from today. Yeah, that's what it's all about. And it's amazing how the little things in life can be pretty rewarding when we pay attention.


Yeah, we were here yesterday at around three o'clock and Doing some photographing and this Stream this is the real porco Was in it's was in the stream bed But sometime after three o'clock yesterday here is flooded this entire area Which is totally amazing never seen this kind of flow out of this Out of this stream bed ever. There's a thousand acre lake Below us where this runs into the Rio Grande This thing is just totally unbelievable The USGS is this coral emergency management here that's Checking on some sinkholes that developed here in the in the Bridge and the USGS folks. I think these are USGS folks are measuring the stream flow And these were actually the guys that were here yesterday I think they were in one of the photographs that I took they're checking the stream flow and We're gonna Never ever is this that I'm aware of being out of the in the last 30 years being out of the stream bed like this thing This is a different a different shot, of course, there's my lovely assistant Marie who's Head of emergency management at my home and here are the Coral emergency management The folks there in black and then the orange Orange Blazer, but the bridge all of a sudden Sometime today developed a huge sinkhole, which is you could see where there's a patch Down there at the other end of this, but I suspect this is the kind of flood water That washed the town of San Marcial San Marcial away In about 1922 actually it was the same time of year that that Happened Just a tremendous amount of water running through this thing It's nice to see this thing run. Hey, I've never seen a run. Have you ever seen a run like this? I see a long long time ago. It had a little trickle. Yeah a little trickle I like ten years ago. Yeah Then before that when I was a kid like 16 17 Yeah, we didn't run this much this man. Yeah, there's a big old busy See where they filled it in over there's a huge sinkhole and for them they fill it in this morning I'm surprised this bridge is still here No, did you Well, you know what oh really well we were here yesterday about three it was in this innocent bank I or it might even been later than three because we were getting some We came last night and it was all these little trees right here. Uh-huh water. Oh really? This is the results of the real puerco Overflowing its banks evidently There's an access to the Rio Grande River just east of here that's been blocked and it's flooded Actually flooded this highway Highway 62 mountain air and it's flooded. We were here across here yesterday, too There was not a drop of water in this area and I see the Sheriff and the emergency management folks are Are here and then of course the railroad runs through here and they've shut down the railroad their tracks are We're partially underwater earlier, so I guess I don't blame them for shutting this shutting this down, so This is kind of the long and short of that but an interesting flood lots happening The railroad is I don't know what they're going to do about this. Nothing. I guess the problem the problem with this is it Gets the Red the railroad dead feel wet train rolling over those tracks Can collapse it in it looks like to me down there that that may have happened already if we can zoom in on this It looks like an area down there that the track has Caved in so I suspect that's what's happening. They closed it