この実際に実際に使えるのが本当に難しいかもしれない。なので、少し気を付けなければならない。でも、今日はこの問題をお聞きします。ここで、みんなも多くの動物の人々がいることが多く、この反応は普通のストーキャスティックですマテオはこのようなオーディナリーデフランシャルイクエーションを使用しましたしかし、マルキューのリプリケーションがストーキャスティカリーですマルキューの数が少ないです基本的には多くのスピーシーがありますしかし、マルキューの数は蠅数がいなければ、それは少ないですそして、マルキューの数が少ないかとそれぞれの動きがあるのでそれは少ないですまた、このような蠅数が少ないとそれは少ないですでは、普通のスタッフティックを解読してみますこのセットアップについては、どんな種類の種類であるかを考えますか?それが安定されるために、その種類で同じ種類を生成することができます。こちらの質問は、多くのモルキュウスペーシーを持っていますそして、ストラスティカリのリアクションプロセスを行いますそして、デバイトを持っていますそして、そのようなスタティスティカローをスタティスティカローを通じますこのため、私、色々なモルキューのスペーシーを持っていますそして、これほど多くのモルキュウスペーシーを持っています thus,これらのスタティスティカローのこのアバンデンスのモルキューの理由はそれがあまりにんにとって Stealthの理由はそのために、セルモデルは非常に簡単に考えます。そして、これはバージョン1のアイデアセルモデルです。だから、このアイデアセルモデルは非常に簡単です。このアイデアセルモデルのアイデアセルモデルは非常に簡単です。それは非常に簡単です。ただ、ここでは、ここでお話をしてみてください。さて、このアイデアセルモデルのアイデアセルモデルでは、このN0とN1とNkが同時に変化することができます。その後、リアクションが変化することができます。その後、この数が変化することができます。そして必要なのはこの布団に付き合わせるものが2つの中です。他にもモルキューの複数を修正し、このセラリアクションの最大能力や動作のモルキューの行動を比較したのは、これらのエンザイムは基本的にカタライスされていますエンザイムを使うために必要ですそれから、他のエンザイムが多いので他のエンザイムが多いのでそれから、他のエンザイムが多いので他のエンザイムが多いのでそれから、簡単なものを使って簡単なものを使うためにしかし、ここでカタライスされたものを使うためにそのためにアイはアイでカタライスされたものを使うために少し簡単なものを使うために他のエンザイムが多いのでそれから、簡単なものを使うためにそれから、簡単なものを使うために2体の自分のリアクションの場合このエンザイムはカタライスされたものですしかし、このエンザイムは少しずつのエンザイムが多いのでそれが、Xj つまりXlこのXm つまりXj つまりXlそういうのを見ると、Jはサムエアを作ることができます。ここで、ザイムタイプモデルキュールを見ることができます。また、メタブライトの中ではありません。ここで、メタブライトを置くこともできます。ここで2つの簡單なリアクションプロセスをしています。これを使います。これは、Random Reaction Networkをまたどの程度なりとなります。私は just randomly I go to J or okay. If this is one I pick up 3 5 10 randomly and then then I also take a random number.This is cut by 7 or this is cut by 12 or something like that.それを始めたことができますここで、このリアクションは何度も物質が存在することができますKを変更することができますそのため、生徒が増やす必要がありますここでは、ヌートリアンテミカルのシンプリースティーブは0です外側からのサプライズですこのシンプリースティーブはX0が外側からのサプライズですこのシンプリースティーブは5や12などのサプライズです3や7などのサプライズです分かっている人ですこのシンプリースティーブとあってこのシンプリートでそしてx0がありますそして、この 脇の上乗りの数はx0の位置に来ていますそして、脇の上乗りの数は同じです例えば、x0の乗りの数はx0の位置に来ていますしかし、x0の乗りの数は比べるとこれが出てしまうとこの生徒が増やすそれが必要はアウスタサイドXゼロとフローインニングを使うそしてこれが他にあることができますその後これがX、Y、Xゼロとその他の人とそしてその後この現象が出てしまうとこの生徒が増やすそしてその後この生徒はこの流行が必要そしてその後この現象が必要しかしエンザイメイクを使う必要があります5、12、それらのようなものが必要ですこのリアクションは何処に出てくるのかもしこのリアクションが出てくるならこのリアクションが出てくるならそれらのモデルは非常に簡単ですそしてこの数のモニケースがこの体のモデルが増えるとモデルの数のモデルが増えるとそしてまた、簡単にそれらの数をコンピュータにしてこの数は大きな数のモデルが2に多くのモデルが多くなりますそしてこの数は2に多くのモデルが多くなりますそして2に多くのモデルが多くのモデルに多くのモデルが多くなりますこの状況を理解してください私には問題があります私にとってはコンセンテレーションではないかもしれませんそしてこの数のモデルが多くのモデルが多くのモデルが多くなります興味もないならコンセンテレーションだよ我不存じエ Algeriaガムダーに同じ数体などに値段目がたくさん糸を本説明 upbeat粧face voc geschrieben moods年間まで起こっているこれが異なるポーラルイコーテナティースいんじゃないですか全てのモデルが多いです。少なくてもペネットラブルです。ただのネウトレーンはペネットラブルです。他のモデルもここで残っています。はい。あなたは大丈夫ですか?これは2つのモデルを簡単にしていますが、フィジシスは大丈夫です。そうです。このモデルは人間にわかるのか?複数の数を分解するのが、これは、このシーンである。1K、1J、何かの数を分解するのが、この数を繋げることができますが、しかし、シンプレスケースの場合は、全ての場合はシンプレスケースの場合です。しかし、このリアクションネットワークはランダムです。そこで、パフトの位置があります。そして、このパラメーターです。例えば、1,000棟、1,000棟の場合、そして、例えば、Kは1,000棟、Pは20棟の場合です。OK?はい。ありがとうございます。このトランクはXとNの場合、間違っているの?J2、I2に行きます。このリアクションネットは、I2KとKにカタライズでJにカタライズします。このリアクションネットはランダムです。OK。Nによって、Nをアキュミュレーションしていますか?はい。このリアクションネットは、ヌーチランスの場合、ヌーチランスが行くことができます。そして、このフローの位置で、このトランクの数が増えます。このトランクは飲んでいません。もちろん、このフローが大きくなっているので、このトランクが増えます。はい。はい。このシミュレーションを作りました。このシミュレーションを作ることができます。基本的には、例えば、トータリー、10、10,000モリクルを入れて、このモリクルを入れて、このシミュレーションを入れて、X1、X2、X3などを作ることができます。そして、このシミュレーションを作るために、2モリクルを取り付けることができ、これまで回転系を根つけることができます。このシミュレーションに立ち回り、このシミュレーションの位置がかました。それはという讃 habの作業です。並べないと、その方法には、そして、その数が増やすと、2分の2になります。はい。後ろに何がありますか?はい。この反応を考えないと。はい。はい。もちろん、この方法を考えてください。はい。でも、この方法を考えると、後ろ、後ろ、後ろ、後ろ、後ろ、後ろ、後ろの方法を考えてください。この数は、大きく、基本的に、大きく、はい。私は、結果を期待していないと思いますが、エキリリウムでは、外側にも、外側にも、外側にも、この数が、大きく、外側にも、はい。はい。この数が、合わせることができます。それが、他の数が、外側の数が、外側の数が、外側にも、外側にも、外側にも、外側にも、外側にも、外側にも、外側にも、私は、外側の数が、外側にも、外側にも、外側にも、外側にも、外側の個体を操績すること は、私はこそ、外側の、外側の個体を操績することので、それを礼し、奪ったことでは、それを与えることができますそれについては新しいモデルについておりますそれも化学のリアクションこのような今回のプロセスは化学のリアクションプロセスでグラスダイナミックのシンデティカリグラスダイナミックそれも面白いですでもこれがとても違うものですマリアクウンが最後のマリアクウンの可能性がないと全てがモデルに行くことができますマリアクウンがマリアクウンに行くことができますここで一つのモデルに一つのモデルに行くことができますこれがとてもとても変わらないことができますもちろんリアクションネットワークここでは全てのカタリストがありませんそれは一般的なリアクションネットワークとてもとてもとてもとてもリアクションネットワークが表示されているこの accountさらにそれもそのとてもとても凱くとてもマリアクションネットワークをこのリアクションプロセスでヘテロジェネイケーがあるかもしれませんこのリアクションプロセスはここにありますここで簡単にこのセルはスープを混ぜるスタクションはない私はそれを忘れませんこれはスープを混ぜるセルモデルそれはとてもドラスティックなシンクリフィケーションですこれはスペシャルストラクションについてその場合X5が大きい場合X10が大きい場合それはヘテロジェネイケーのヘテロジェネイケーのヘテロジェネイケーのヘテロジェネイケーのその場合何かがあるかもしれませんK1000のスペシャルストラクションそして10か20かもその場合それからこの場合はKは小さくないでもそれについて少し数が必要です1か2かスペシャルストラクションは無くなりますはいあまり次に、コンテニュースオーディオーディナリデフォナッシュアリクエーションを使うことができます。しかし、ここについては、シンプルストラスティックシミュレーションをお勧めします。そして、まずは、シンプルストラスティックシミュレーションを変えます。このシルトはシンプルストラスティックシミュレーションが早くなって、アノメルトフォースレッジが大きいので、グロススピードをコンピュー the growth speed.グロススピード is that, okay, this cell.So maybe threshold is maybe something,1000 or something like that.And when this number increases beyond this number,then cell device.So you can count that how many steps you needto go to this number.And then you repeat thisand you can compute the average division time.So the inverse of this average division timeis the growth speed.So we can compute this growth speedand as a function of D.So as you can see, okay, this growth speedis black point.So this growth speed increases as you increase D.Okay, this is what we expectedbecause this flow is larger.And then at certain critical D,the growth rate drops downand there is no growth beyond this,even though we have a higher flow.And so, okay, initially why this we thought,but now we can then understand this.What occurs here?Okay, it's not here.If the flow is too large and then the cellis mostly occupied, X0.This flow is coming in for very large.And before this reaction is going on.And if this is so large,then finally you have a situationthat this cell is mostly occupied with this nutrients.So it's a very strange situation.This X0 is mostly dominant.And then usually if this reaction going onto buy other X12 or X13 or X20catalyzed by this some other.But at some point, this number goes to zero.And if this number goes to zero, it stops here.So actually this catalyst has to be produced somewhere elsewith some other reaction, maybe somewhere here.So if this reaction process does not work so well,then at certain point, this goes to zero.Then the reaction stops here.Yes.You describe the simulation procedure.You need to have one parameterwhich take into account the present or absent of the catalyst.So because if you go back to a few slides previously,you just mentioned that if you take randomly two molecules,you ask whether they are able to react.And then if they react, then with certain red KIs,they produce a...Yeah.But in most cases, if this is occupied by this,if you just randomly pick up two molecules within,maybe in most cases this is X0, X0.Then no reaction going on.And maybe there exists some X10 or a little bit.Then there is a case that X0 and X10 are selected.But this does not show reaction.Only these pair are selected, the reaction going on.And the probability is, as long as this goes to zero,the probability to have a reaction from here to others goes to zero.So then the reaction stops.Yeah.So actually, so if this D is too large,this no growth condition appears here.So that's the critical point here.So of course this is a very, very simplified cell model.So maybe in the real cell probably such kind of a strange situation would not occur.But anyway, this is the result of this model.Yeah.And I have a question about growth.So does do cells grow exponentially in this case?Over time?Basically grow exponentially.Yeah, yeah.Is it okay?So then, yes.Here is X0 the only permissible species or...Yeah.So it's only X0 that can diffuse in and out.So maybe you can include some other penetrable molecules.But maybe this slightly changes this critical point.But yeah, it does not matter so much.Yeah.Sorry, I have a question regarding the threshold they are choosing.How do you choose it in this simulation?Like a threshold is that this?Yes.Oh, okay.This is I set up initially.And so basically this is the kind of total number of molecules.So actually in the simulation we did is that this is 10 to be, I forget,10 to be quite large.10 to be, I forget.Yeah, maybe somewhere else.10.Maybe I think this is in the simulation.Maybe 10 to be 6 or something like that.And so this is the threshold of the total number of molecules.And molecule species number is also rather large, but smaller than this.So for instance, and this species is 10 to be 4 or something like that.10 to be 4, 5.Is it okay?Initially fixed.Yeah.So you can choose any value, but anyway, this should be rather large.Yeah.Okay.So what do we see from here?Okay.Maybe for this set.I have questions, please.Yes.Please, instead of considering the random reaction, can we consider the Markovian?Or basically Markovian or just take randomly 2 and there is no previous memory.Yeah, but like in the random, we usually pick 2.Yeah, randomly pick up 2.So for the Markovian, I think we are just...Yeah, basically Markovian.So if you, for the next reaction, you can just choose randomly again 2 molecules without any memory of the previous.Yeah.So it's a very well-stared soup and just reaction going on randomly by random collision.So that's a very simple situation.Yeah.Okay.My question was about similarity.I can...Okay.I'll explain that.No.Okay.So then, so similarity is that, okay, when this cell grows and devises, it's going to be like, when this cell grows and devises, so you have initially, so before, so starting, you have this number, N0, N1, Nk.And then, then, so total, total N is this Ni.And then this becomes 2N, and then devising to 2.Then the next generation occurs from...So if the cell after division is completely identical, then that means this...So each molecule concentration is completely same for the mother cell and daughter cell.So if we assume that, okay, cell should be completely same after division, this should be equal.But of course, this is random reaction process.Maybe it's perfect identity would not happen.So we can consider that, okay, how this is similar.And so then, so basically you have a, can define kind of n dimensional vector, so here, so define this.And you can define this vector.So this vector is a x1, x0 to xk.And then, in this n dimensional, k dimensional space, if the daughter and mother cells are completely same, that means this and this are same. So, but if this totally different, maybe it goes to different.So you can define this x mother and x daughter.And then if you consider this x mother, x daughter, and then maybe...So that gives this kind of sign theta.And if this is 1, it's completely similar.And if it's 0, it's totally different.So that is the similarity here.So the question, why we introduce this is that we are interested if this cell can reproduce the almost same cell or not.So if this similarity is larger, maybe the cell can reproduce almost similar cell.So that's the similarity.And this similarity is the result, okay, this red one.So around this transition point, this is close to 1.So it means as this growth speed increases, as the increases, you can have more similar cells.Yes?A question on the similarity, like how does it involve the abundances of the chemicals?Because you wrote with x, okay?Yeah, x is that, okay, total...Okay, like this and you just do the inner product.So you can have, okay, basically this cell state is that defined all this k dimensional state space.And so x1, x2, x3, xk.And then the cell state is defined as this position here.So by that, so you can define this mother cell state and daughter cell state and just yeah, compute this, yeah, inner product.Are we assuming anything about the division process?I mean, it doesn't even need to be the same number of molecules in each.It's just a random process in which it creates a line and it divides by two.Or are we assuming something about the process in which the cell divides?When this divides, basically, if you have these molecules, so just randomly pick.So if you have two n molecules, just randomly pick n molecules.But I pick m.They have the same, each of the cells have exactly the same number of total molecules.That's the only constraint we put.Just total number is n and n.Okay.Yeah.But just randomly pick from these two n.Okay.But they both have the same number.That was the question.Thank you.Yeah.Are they likely probable to pick any of them?Like the partition is the same, it's the same to pick one x from another.The same probability.So basically, so just randomly pick up from two n to the randomity of two n cells.With one half.So if you have, of course, so if you have a situation, this is 100 and this is 50 or if you just randomly, completely just equal partition, that means 50 and 25 for each.But if you randomly pick up, maybe this may be 27, this may be 552, and the other is 48 or something like that.So if you have many of them, basically, yeah, you can roughly have so due to this law of large numbers.But if, for example, if some molecule is just two or something, maybe that easily happen, this goes through for one cell.This is just two.Yeah.So yeah.Okay.So I think my question is primarily, I don't see how, for example, with this random picking of molecules, the diffusion coefficient somehow affect the similarity.Oh, okay.For this pickup process of this division, diffusion process is not involved.Division process coming in, is that in this reaction process, reaction and diffusion in.So in this division process, it's not included.Yes, but somehow with your result, you're basically showing that the diffusion coefficient of the molecules coming in and out has some sort of relationship with the similarity of the mother cell and the daughter cell.Yeah.So that means, okay, if this diffusion is large, and then there is some kind of structure.This is more abundant.And this is second abundant.And this is third abundant.So then there is a case that, okay, you have, this is a thousand, this is a five hundred,and this is a three hundred or something.Then you can have, maybe it's quite similar.But in some other cases, this reaction is just very, so randomly, so there is very slow flow.From then, this reaction is, process is just mostly random.So that means this is twenty, this is also, maybe this is thirty, or this is twenty, or this is fifteen, or something like that.Then after division, maybe it can be more deviated.So this is the structure here, influences on this similarity.Yeah.So there are two daughter cells, right?Yeah.So with which daughter cell are we calculating this similarity?Oh, okay.So I can just choose randomly one of the two daughter cells and continue this reaction process.But we repeat this process so many times and compute the statistical average.So which we choose do not matter so much.Okay.Okay.Now it's fine.Okay.So now we consider, okay, what d value is good for this cell?So that means, of course, it's better for higher growth.And so that means the cell state around this transition point is maybe good for this cell.And around this point, maybe similarity is large.So if d is closer to this critical point, maybe this cell is good.So maybe, so this is a kind of constraint from a biological constraint for a good cell or in this model, means that, okay d, but this is a little bit tricky because if thisapproaches dc, then by a little bit increasing that this cell can no longer grow.So this is a little bit dangerous.But so maybe, maybe if you have, maybe around here, maybe this will be good for this cell, for this simple cell world.Okay.Then, okay, so what we did here.So, okay, so I mentioned that, okay, in this case, so there are maybe X0, N0 is 1000 and N1 is 500 or so.So there is some kind of structure in abundances.So is there some kind of statistical structure in this abundance?So some are more abundant, some are less abundant.So what we did is that, this is just plot the ranking versus abundance.And that kind of, yeah, plot is often used in some statistical model and maybe you may have heard of this similar thing.So in this case, so basically what we did is just simple because since X1, X2, X3, X4, thisnumber index is kind of has no special meaning.So even if you plot this against this number index, that does not mean if you choose a different random reaction network, this may be totally different.So what we did is that, okay, so if you have X, okay, maybe you can.So for instance, if you have this situation, X1 is 300, X2 is 8000 or something like that.We just put the ranking.So this is the most abundant, this is the second abundant, this is the third abundant, this is the fourth abundant.So what we plot is that ranking versus abundances.And so this is the result, ranking versus abundances.Of course, we plot this in this order, this should always a decreasing function.But what kind of the structure of this function depends on the case.So what we plot here is that, okay, this ranking and if this small, maybe more like, so every molecule rather have a kind of similar abundances.So everything is 20, 30 or something like that.So that's the case when D is small.And then as D is increased and near the critical point, we have this situation, this ranking and abundances, and this is log-log plot.So this is the slope minus 1.So abundances ranking minus 1.So this is what we observed in this simple cell model.So when this simple cell model can grow well and reproduce almost the similar cell, then we have this situation.And now, okay, this is a kind of two simple model.But as we, as I said, we can check this kind of law in the real cell.And in the real cell, of course, we have many, many different chemical.So maybe you can compute, for example, each protein species or messenger RNA species.And for experimental reason, there are easy technique to compute this messenger RNA.So from this messenger RNA, each protein is produced.So there are many different protein species, and corresponding to that, there are many different messenger RNA.So you can have, yeah.So from that, so we measure.So actually, this is a little bit old data, and there may be a little bit better result.But yeah.So we take, for example, in this case of human liver cell and human heart cell.And again, ranking versus this abundances of each messenger RNA.There are actually 5,000, what, messenger RNA species.So this is the slope minus one.So it looks roughly okay.And of course, there may be some deviation here, but actually the measurement too, usually if this is too abundant, maybe there is a saturation in the measurement.So this may not be maybe such result, or there may be real saturation, something like that, deviation from the power law.But basically, this is minus one, and okay, this is also, maybe this is slightly different, but this may be slightly different, but we are not sure.But globally, this is minus one, and this is also minus one, minus one.So although this is a very, very simple model, maybe this kind of result may be at least to, yeah, approximately of this value.Yes.In the previous slide, I saw cancer.The graph of human group is also cancer have a minus one slope.It seems.So this part is minus one, roughly.Yeah.There may be deviation here, but I'm not so sure.Because as I said, this is just totally 10 messenger RNA species, and so very small fraction.And also, maybe this is maybe due to this measurement, yeah.Okay, but my question is more about, isn't cancer trying to grow without any limitations or something like that?So shouldn't it be a bit different from other cells?That, yeah, so we know cancer is more higher growth, but yeah, we are not sure about that, yeah.And of course cancer somehow depends on each type of cancer has a different characteristics often.So it's a little bit dangerous to say from that we can expect.Yeah, we initially thought that, okay, if we could find that this results for usual cell, and if cancer cell does not follow this, that would be great, but maybe not true.Yes.Hi.For the zips, zips lost.Yeah.I saw that we have varying values of the number of molecules.So does that mean that if we've also vary big D, the big N also kind of changes for different.So in this model, you mean?No, for the slide, previous slide.This, okay.That one, yes.Yeah.In our model, this is valid if D is close to critical point.Right.So in some way, also the N changes because of D.Is that the case?And you mean the total number of molecules?Yes.So actually in this model, so we fixed this threshold for division.So the total number of N is fixed.Okay.Yeah.Right.Yeah.Yes.Did you mean, did you first think of the model and then realize that it, how it was, or you first knew the experiments and you knew the distribution and you said, oh, this is a power law.This must be a statistical feature.It was like, more of how was the process of realizing.Initially, we did this simulation, and then, okay, then we tried to, actually this is 20 years ago or something, and then we tried to find some kind of a, yeah.Actually this is the data, so actually this real data, this is not our experiment. So there is some kind of in some database, and we, okay, then we try to see, okay, if this may be okay for the real data, and then check, so.But the data this was prior.I mean, this data already exist.Yeah.Experimentals show this, okay, this messenger and a data, all these, but they are not, at that time they are not working on this kind of statistical, yeah, to find a statistical law.At that time, maybe now more people are going in that direction.Maybe just a comment on the growth of cancer.I mean, I am not the expert, but what I understand is that, like the limitation on cancer growth is more about, like the cell trying to, like make, it's more in the, how do you say, like not following the constraint of the environment rather than the fundamental difference on the cell itself.But I'm not sure about this, so.Yeah.At least, so we cannot, in this simple model, we cannot discuss, okay, this is true for cancer, or this is not yet for the usual cell, or that we cannot discuss it, so this is too simple, yeah.Going back to the model, did you find some, when the results, when you were, like, looking for them, some cells that didn't have the necessary things to keep on living, like, you have, like, that state appear in some frequency?Because when you're near the DC, the cortical diffusion, I think that affects the similarity. You would have a lot of proteins, but very few of some of the other proteins that can make the network breakdown.Yeah, network breakdown.Yes.Yeah.Did you find that in the right frequency?Yeah.For example, beyond the DC, or near, very close to DC, that can happen, so.In some sense, this is a little bit interesting, how it starts to collapse, so then at some position, so maybe, so maybe you need X20 or something, too, for this catalyst, and then maybe this is a little bit far from this network path.And then, initially, okay, all molecules exist, but at some stage, maybe, they lack some part of molecule X30 or something like that, this seems, this is more abundant than X30s, but maybe X30 is necessary to produce X20, then X20 disappears, this, and then finally stops.So, the network somehow shrinks, so initially they have all these, but maybe, so it's some part supporting this is disappear, so in the order of this collapse, what happens here is that you have some kind of network layer, network layer, some something like that, and then at some stage, this disappears, and when this disappears, maybe this reaction path disappears, and then this reaction path disappears, and then finally this path disappears, so it's successively shrinks, so this is a result, because every molecule needs other molecule species for to grow, so everything mutually supports with each other, so if some part is, so if one is too dominant, and then maybe finally, they collapse that had supported this growth, so if you consider some kind of very rich people, and rich people can grow, and this can grow, but usually rich people need some other people for their growth, so if they are too rich, they suppress this other who would support this reaction, and finally disappears, so actually it's interesting, initially, so when this occurs, so we have this rank and abundance, this ziploc, and when this collapse appears, this is something like that, so this is too much, and then some are too less, and then finally, supporter for this will disappear, and finally it goes, and then at some stage, this is quite dominant, but there is no more they can support, and then stops there, okay, this may remind of this how kind of disparity in capitalism, so people say that, okay, some disparity is necessary for capitalism to sustain and for growth, maybe this is true, but if this is too strong disparity, then finally it collapses, and actually this kind of law is also seen is, so this is generally called Zip's law, and Zip is originally found this law in the linguistics, so when you measure maybe this frequency of each word and or over maybe in the English, that is the most common than the end or over or something like that, then frequency abundance brought, they brought this and they Zip found this, and also this is in many cases, this is true for also in this kind of wealth, so maybe some are very rich guy, and the second rich guy, so you can have this wealth and ranking, so I do not know who is the most who is the richest guy,I don't know Elon Musk or I don't know, but anyway somebody here, somebody here, and then and so often this shows this, but probably maybe now the capitalism going to this, and then maybe we may maybe collapse, I don't know, but anyway as long as this system, the system for this growth, they need some others and mutually support each other, then maybe some balance is necessary, and if it's too much disparity, then it will collapse, so maybe this is true for sales and then this economy also probably, yeah, okay,okay, so I did not explain why this minus one, but maybe this is a little bit too detailed calculation, so if you are interested in you can check this paper in this physical review letter 2003, but basically the structure that in this case, so the highest ranking and second ranking, so this catalyzed, so this lower next level layer catalyzed this and this catalyzed this, and that structure is yeah self-organized near the critical point, so this is zips okay and some yeah, okay, so maybe this kind of power near the transition point, maybe you know already in many of these statistical physics examples, so that that is also appears here, okay, so okay, this structure is an assumption, right, it's a it's somehow organized near the critical point because it's just initially we put this random reaction network, so such kind of structure does not exist in the network itself and as for instance if this d is small we cannot have this structure and if d is large then more abundant of this nutrient and then there's some other layer that can be produced from this and catalyzed by others and so that structure emerges near the critical point, yeah, okay, so more than yeah, but but anyway it's interesting to consider this kind of yeah, zips all in general and maybe maybe probably the explanation for this cell by this simple model may not be true, the real cell is more and more complicated, I initially said all this reaction rate is unity, but maybe this reaction rate itself is distributed in a very yeah broad range, so that that may be important to have this zips in the real cell, but anyway this is just a simple model and simple model prediction may be okay or something like that, okay, so maybe I have 20 minutes so I have another point here, so near this critical point so similarity is large, but still it's not perfect, of course this is random, this reaction process is stochastic and so that means so maybe you have this cell and divides into two and you have another cell, you have many cells here computed and then and then set up, pick up some special specific chemical, so you compute ni of this cell and then you compute it ni, so then you can compute the distribution of this chemical across cells, so now we consider the distribution across cell, previously we discussed this distribution across species, multiple species, but now we consider the distribution of across cells, so we divide this process and then we take many many cells in this simulation and so maybe for the cell one this x1 chemical is 10,000 and for cell two 8,000 or something like that and then we can compute the distribution by so using this kind of simulation, so what we found is that distribution is something like that, so ni, so this is a distribution for different chemical species, so previously what we discussed is average of this and average of this average of this across chemical species and that follows this law, but here we take some specific chemical species and compute the distribution across cells and this shows this kind of distribution, so you can see this is rather different from usual Gaussian distribution because this has a long tail over the abandoned side and then we take make a transformation instead of just plotting in as a pn we take log n and then plot this and then this is the result, so this is a more abundant chemical and less abundant and much less abundant chemical, so if we take log n, so the distribution is almost symmetric and only by that we cannot say this is log n is really Gaussian distribution or not, but actually this is close to Gaussian distribution, so this kind of distribution is calledOK, maybe this is log normal distribution, so basically in the original n this shows long tail, but if you take log n this is more like Gaussian distribution, so basically you can have this log, so this distribution is that average and maybe you need some kind of normalization constant, so in the original distribution that, so you can consider just Gaussian distribution for log variable and then transform to this original and then the distribution is something like that, yes, analytically you mean thisOK, from where, it's a, oh OK, log normal distribution is just a transformation, so it's a, if youOK, how to derive log normal distribution? The whole model trying to solve it not numerically, but analytically, so far not possible, it's, yeah, we did this numerically, and OK, near the transition point and assuming some kind of, so this kind of distribution structure, we can derive some kind of deep flow and also maybe log normal distribution, but that's, that's not analytic derivation, it's some kind of approximated estimate or something like that, so but if you're interested you can make a kind of analytically solvable model for this kind of thing, yeah, OK, soand again, OK, in the, oh, I forget, forget to put this, OK, experimental result, I'm sorry, I forget to put this, butexperimentally this kind of log normal distribution is mostly observed for chemical species, of course there are some deviation that if this depends on, depending on some specific, so low molecule number species, there may be some deviation or something like that, but roughly as a very rough estimate, this is close to log normal distribution, so I forget to put this, but now what they did Actually experimentally, there is a technique for this cell, sort of something like that, so you put this cell into some kind of machine and this flows in and then cell, each cell comes in one by oneand then you have, for instance, laser something and then from this diffraction you can compute, observe the abundance of E, so for instance put some protein, so to put some proteinand often there are many techniques experimentally to make this protein fluorescent, so there's some fluorescent, so then you put this and then the fluorescence is measured and then you can so measure this fluorescence for each cell and from that we can compute the distribution of fluorescence across cell and actually this technique is very fast and so you can measure thismaybe 10,000 cells and then distribution so quite easily and of course in some cases okay maybe the cellvolume may be different and then if this has a larger cell volume maybe fluorescenceis accordingly increased, but in that case, so actually they can measure this and some from some scattering they can measure this volume and fluorescence and then you can compute volume, fluorescence by volume, so that corresponds to this kind of concentration of each proteinand so if you make one protein fluorescent then you can compute, measure this kind ofdistribution like this and I forget to put this, but actually this experiment showsrather lognormal type distribution, yeah. I have a question, so the zip we saw before it's a sort ofconvolution of this distribution with the distribution of the averages, so if you look at how broad or what isa distribution of the averages of this of this distribution here, so basically the case is okay this isokay this value and this value and this value and this value, so dispersion across chemical speciesso the variation doesn't matter here, so you yeah, so the averages are over, yeah, yeah and actuallythis is also agrees with this experimental technique, so they usually measure, so when they measuremany different chemical messenger RNAs, they usually average out many many cells, so basically thistechnique is used for measuring specific molecule abundance over cells, but if you have10,000 chemical molecules, it's difficult to put these different fluorescence and put this, then it'svery very difficult, so you can measure only just a specific molecule or maybe two or three andand then compute this distribution across cells, but in the previous case you can compute thisso this across species instead usually across species in this measurement what they did is that youtake many cells and then so start and then then from that you can so compute a measure messenger RNAone two something like that, so this is in this case average over cells, so if it's of course it's ideal thatyou can compute a measure every different yeah molecule number for each single celland there is some kind of recent technique advances yeah for that single cell RNA6 or something like that, butbut of course this is much more yeah more takes some more time or money or something like that yeahok so ok so the question is why log normal is appears here and thisok before that we know that normal distribution Gaussian distribution is quite commonin nature and that is due to central limit theorem if you have some kind ofrandom process and adding by that this many many this process you get some kind of Gaussian normal distributionso then why we have this log normal distribution because we have many many reaction processes and manycomplex reaction networks so we can consider that this may be similar to just follow thisyeah no so central limit theorem and going to Gaussian distribution and the reason for thisis that basically if you consider some reaction process and a x is produced with some otherhelp of this a this is multiplicative and so this is the simplest case of this explanationx increases by a and then this is something like that and if n is distributedand fluctuating then this follows log n is shows some kind of Brownian motionand then maybe log n follows the central limit theorem and in this case so actually you have many reaction process is going on so catalyzed this this is catalyzed this and this is catalyzed by something else then you can have successive catalyzation by this is catalyzed by something else and this is catalyzed something else so extra catalyzed by why and z and then why is catalyzed by something他のことを考えてみてください。基本的には、ランダムプロセスが多くあります。そのため、ローグを取り付けると、そのために、マルティプリケーションは、アディションを取り付けるために、ローグを取り付けるために、ここにある大きなアイデアは、ランダムアディションを取り付けるために、センターリミッドフェレムとガウシアンディステビューションを取り付けます。ここにあるXがY、Zがキャラクターで、YがAPがキャラクターで、それを取り付けるために、XはY、Zがキャラクターで、これを取り付けるために、這描きに入り切れてそれを取り fe マルティプリケーションとしてローグを取り付けるために、それを取り付けるために、ランダムアディションが多く、その後、中央の限定のアルメントが使用できる。そのため、この場合は、この場合の解説をするために、この場合の限定のアルメントが使用できる。そのため、この場合の解説は、この場合の限定のアルメントが使用できる。実際に、そう、実際には、人間の温度が高くなっているかもしれません。そして、ログノーマルディスティビューションは素晴らしいです。そして、高さは素晴らしいです。これは、私は知りません。最終的な理由は、これを説明します。しかし、もちろん、温度が高くなっているかもしれません。そして、温度が高くなっているかもしれません。そして、温度が高くなっているかもしれません。このような、多くのファクターのアディションを説明します。そして、Gaussian Distribution Center Limit Theoremを説明します。それは、人間の温度が高くなっているかもしれません。日本では、少し小さな温度が高くなっているかもしれません。しかし、温度が高くなっているかもしれません。そして、少し大きな温度が高くなっているかもしれません。それは、非常に高い温度が高くなっているかもしれません。そして、ログの後に、この温度が高くなっているかもしれません。それは、非常に高い温度が高くなっているかもしれません。しかし、このログのディスビューションは、このような温度が高くなっているかもしれません。そして、エコシステムでは、若干の温度が高くなっているかもしれません。では、もう少し多くの質問がありますか?ディスビューション・コフィッシャント・シミュラリティ・セルの影響についてお伺いしますか?はい。このディスビューションは、このような温度が高くなっているかもしれません。それは、このような温度が高くなっているかもしれません。このディスビューションの発酵は、この表現である程度、このディスビューションの発酵は、この性格が低いと思います。この体を選択すると良いですが、このクリティカルポイントを選択すると良いです。しかし、この体が少し大きくなります。かもしれません。それは簡単に死ぬことができます。それは良いのです。一つの問題は、この体の中にあるメカニズムがあります。この体を自動に設置することができます。そして、この体をクリティカルポイントに自動に設置することができます。それは、たとえ、フライデーやな。そのため、この体を応じて、この体を追加することができます。ここにも追加することができます。この体を中心に操作していることができます。簡単なプロセスを作るために、それを確認することができます実際、コンプレックスが多くなっているのでコンプレックスのメカニズムを使用するために、この良い状態を使用することができますお疲れさまでしたいです。どのようにネットワークのジョマティカルを使用するか、ネットワークの影響を感じますか?ネットワークの影響を感じます。そのため、ネットワークのスケールフリーなどのようなものを使用するために、そのようなものを使用するために、このモデルのインシャルモデルで、このクリティカルを使用するために、ネットワークのスケールフリーなどを変えることができますでも、このスケールフリーは間違いません。そのため、ネットワークは多くの効果ができます。そして、その後、ネットワークのスケールフリーが変わっているなら、もちろん、このようなアバンダーのストラクターが必要かもしれません。そのため、ネットワークのストラクターが必要かもしれません。そのため、このようなモデルから始めたら、ネットワークを選択し、ネットワークを早く増えるために、その最後に、スケールフリーネットワークを選択し、そのため、ネットワークのストラクターが必要かもしれません。そのため、アバンダーのストラクターが必要かもしれません。その後、ネットワークのストラクターに専用することも可能です。それはとても面白いです 先ほどの遺跡は少し残っていて 今後のストラクチュアもあるかもしれません可能性もあるかもしれません 経験もあるかもしれませんそれはとても面白いですはいどうぞどうぞ もう少しの問題があるかもしれません