So welcome, everybody, for this new day of with many exciting lectures. So before we start, just a reminder of the few rules on how to ask questions. So if you're following from YouTube, you can ask questions in the chat and I'll read them for you. If you are connected to Zoom, you can either post them in the chat or use the raise and the feature of Zoom. Great, so it's my pleasure to introduce again Andrea Rinaldo, who is giving the second of three lectures. So thank you very much, Andrea, for being with us. Please, you can share the screen when you are ready. Thank you so much, Iacopo. And let me go back to the screen. I assume that unless I hear you lamenting that you don't see, I would assume that my full screen would be visible to you all. So I come back to the second of three classes on river networks as ecological corridors. I will subtitle species, population, and pathogens. You may remember, if you attended the previous one, that essentially the light motif of my talks is that we claim that dendritic substrates, like river network, instead, with certain recurrent properties that we have analyzed, however briefly. But those dendritic substrates for ecological interactions bear important consequences for a number of processes that we'd be analyzing. That is essentially patterns of biodiversity, which I haven't done, I'll do today in part. The spread of species along the network is also biological invasions, in a sense. And the spread of waterborne disease, which you will see in my last class, with reference to epidemic cholera and dendritic disease, like proliferative kidney disease in fish. And the idea is that the system is so constrained by the nature of the substrate in the recurrent properties, no local properties embedded in it. But in reality, it would endow the system a certain degree of predictability beyond what was originally thought. And so what we have seen during the first class was that once you put those constraints in place, and you use even the simplest possible model, in that case, was a neutral model of biodiversity. Whether you're using a meta-relation model or a meta-community model, whether you're using nearest neighbor interactions, or you're taking a kernel which goes from a certain discrete length or a mean field approach, in which you average over the whole ensemble for replacing, for getting replacements, or randomly selected species removed from a single site, the system tends to have certain indication. That is, the very nature of the substrate of interactions with the dendritic network has important consequences, which we have later verified by a number of different tools. So the main argument that I put together, and it's a one that said that what these lectures tried to do, were to draw together several line of arguments to suggest that the integrated eco-hydrology framework that blends laboratory field and theoretical evidence has contributed substantially to our understanding of the form and function of the river network. What shall I do today? I shall begin when talking about biological invasions, possibly biological invasions on fractal supports, like a tree, which is the ones that we have seen in the case of river networks. And what you're seeing here is a map of the invasion of the zebra mussel along the Mississippi Missouri River system in the United States. And you see different coders by different colors what happened to a species was completely alien and introduced by accident into the system. We're talking about hydrochery. And to make a first example, we're talking about human range expansions and the population migrations in the past, which is an interesting idea by the group of Spanish physicists which I'll be putting forth today. So first, let me start with the standard things many of you have seen in a number of contexts. And it is the fissure comorbore of a tumbling wave approach to a system. So if you have a model in which you have dispersion role, in this case, it's like a density of a species, or you name it, of any kind, moving along a one-dimensional support, remind you that in the case of river networks, makes absolutely good sense to think of a one-dimensional system in intrinsic coordinates because the width and the depth of a river cross-section are much smaller than the longitudinal length you have to travel. So the assumption that making open channel flows and flows in pipe, et cetera, is a one-dimensional thing. It's absolutely standard assumption verified by hundreds of years of practice. So essentially, what we say is, suppose that the system would obey a simple diffusion with constant coefficient. So the term d square rho over dx square coupled to a significant of the timescale of diffusion reproduction system. But it is, in this case, a logistic equation in which essentially the reproduction of a density follows initial phase, which is the exponential growth phase, the Malthusian so-called dynamics, later on curd by reaching an asymptote. So the growth term is nil, either where the density is 0, or where rho reaches a carrying capacity k. Why this is interesting? It's been studied for a long time and notably from the most gifted applied mathematician of the last century, Kolmogorov, in fact, and Ray Fischer, the inventor of so many results that are crucial now to modern genetics and molecular medicine, et cetera. They started to get under different angles of the same result. What happens if you look, if you suppose that, for instance, you start to generate at a single point in space over a length L, and a single, you inject a single shot of a certain number of organisms of the species whose density we plan to analyze. The system here is known to generate a soliton that is an undeformed wave after a short while that propagates without the constant celerity with the basis equation, which is solely dictated by the value of the growth rate inverse of time and the diffusion coefficient length squared divided by time to generate a characteristic velocity, which is twice the square root of a times d. How do you prove this result? Well, it's interesting point which you essentially take the diffusion equation under this limiting term. And you do that initially by assuming that this term is negligible. And what you have is that you can calculate the expansion radius of the most of a mass or a assigned fraction of a mass, which you have in your system and how this expands in time. Thereby, what you're studying is the behavior that has an important feature for what concerns our capability to describe the network effect. What happens in the vicinity of a low density when this starts propagating actually. So the idea is that if you calculate the expansion radius that in a regime in which this log of a quantity whatever you want to have it pales compared to the term in which you have the square dependence of a square root of a radius. So the velocity of a speed is essentially twice d times r, which is the growth rate in the Malthusian model in which you eliminate the carrying capacity effect. And by no surprise the carrying capacity even if you extend this, it can be shown that the front speed is essentially in the case of the Malthusian dynamic still what happens in the vicinity of this reaction term for which the density approach is zero. And that's not by chance because what we are saying is that so essentially the same result of the Malthusian population which if you take a proper computation of the expansion radius for a Malthusian population and through the curve here and the actual solution of the system which you have, you see it quite soon the system behaves exactly in the same manner. So what is interesting is that in a two-dimensional system for instance or in an isotropic migration system one, two, three n-dimensions, whatever you have it the system will have essentially that the speed of a traveling wave or the argon is generated that will reach a plateau and stay there and propagate on the form it's proportional to be these two coefficients ignoring the effect of the carrying capacity which is immaterial but only depending on the fusion coefficient and the rate of reproduction, reproduction rate one at a time. This thereby in say Eulerian support but is in one two-dimensions, et cetera. And this will have some importance in what follows. Now what is interesting thereby is that what matters and that is important for the particular substrate we are studying which is a tree that is a unique path for any node to any other node it's a directed graph in which there is a sense of direction which is embedded in the structure of a system of those diffusion. And so essentially you can map the evolution of a density of organisms in space and time as a rescale variable of an under form property which is the typical structure of the characteristic curve which I'm in there. So the fact that what matters is what happens in the vicinity of a zero density is important whenever you have to look at systems like this one this is Piano Network which I introduced during the last question there. Why am I using Piano? I'm using Piano because it's the deterministic fractal I rediscovered Giuseppe Piano, the Italian mathematician who wrote a famous paper over a curve that fills the entire plane which was considered like a blunder by mathematician of this area and we're still studying it a hundred years afterwards. When one Mandelbrot, a genius of Mandelbrot rediscovered it to support this idea that mountains are no cones coastlines are not broken lines nor does traveling straight lines. The fact that after 2000 years after Euclid we started looking at the geometry of nature with different eyes was embedded in the curve which is strictly deterministically self-similar because it's created by a process where it's from the originator you essentially do the system which have a broken down half of a segment here adding it into a system of this kind and that allows you to calculate exactly a number of properties. Why this is an interesting feature? Because if you look at topological properties of course if you look at it and say this is not a river network of course it's not but it allows you to calculate certain quantities exactly for instance if you count the number suppose this is a directed graph and you can count and if you suppose you have a seed point like here for instance or in this case it would be here if you assume that the thickness of the line is proportional to the total contributing area it's a tree so in any place you can calculate the number of nodes you have upstream and what is interesting is that you can calculate exactly the number of sites equally distant from the outlet distance being calculated in what is called normally chemical distance that is along the structure of a network itself which is hydrologically is very important quantity because if you suppose that it rains a given quantity in every single node of that the distance if a system behaves in a dynamically constant way which means the arrival time at the outlet so essentially the response of the system will be related to this quantity. And in the case of piano this is an interesting thing because this is a binomial multiplicative process solved exactly. It's an exact multifractal that has been studied by many including men of itself. In this case what is specific of that is that even if by looking at this you know that this is not a river network however the topological properties which are non-distinctive in many respects almost statistically inevitable the topological structure of this is exactly indistinguishable like bifurcation numbers, lengths, et cetera for the ones exhibited by river networks. So the message I'm conveying here is that in this case you can study exactly the behavior of a traveling wave along this backbone or propagation for instance because you can calculate exactly the number of bifurcation that the system will experience in its traveling downstream. So if you solve this numerically this is let me show it directly what you see it's a diffusion plus a reaction term a logistic reaction term happening in the sense what you're seeing here and this is how the system propagates. What is interesting is that if you take the longitudinal direction what matters for instance from going from source to outlet I put it for clarity horizontally but it could be even any source term would have exactly the same behavior. What happens is that if you do this so this is how the paw propagates into the system depending of different features in this case you have like no drift I'll later on examine the case with have a significant hydrodynamic drift and what happens here is that you're going to have a system with the jagged part here is due to the heterogeneity is generated by the structure itself but it generates a traveling wave and what is phenomenal is that a walker that is at site on the backbone can spare the certain time of a secondary branch if you go here and you get sidetracked in this direction you spend some time around the system here before you can eventually plug back and continue your travel towards the outlet so the main point is that if you go through a system which is one-dimensional but with significant delays because of the sidetracking of the structure essentially produces a slowing of the speed of a traveling front so if you are only interested in the behavior of the system along the backbone you can interpret the secondary branches as essentially a producer of the delay between sides of the backbone so delays could be chemical, physical, biological reactions but generates essentially a lifetime distribution because that's what I'm interested in into your system and you can do that by a technique called continuous time around the walk I'm just leaving a few slides in here but you have the density of the point is something which you take into account the probability that you have of staying you have a distribution of the delay time in a node a might of a delay time in a node at this point is the time you spend if you get kicked out in one of the side structures how long would you spend in the side pockets before you jump into the mainstream and that's a distribution of a lifetime in here and then you have also a term which describes the jump at every side which in this case we call it reactive random walk because you assume that every time step you have a with probability one half you go back and forth you have the system you have to know bifurcation or if you have z nearest neighbors you have a probability one over z of jumping in one of the other ones you have so a long story short this can be treated by the plus transforms it's called Hamilton Jacobi mechanism and you can calculate in fact fairly well yeah the plus transforms how the system behaves so you can calculate you can do the Kolmogorov Fisher system for the homogeneous and dimensional point in particular one dimensional system the speed of propagation of a soliton that we generated by the diffusion plus a logistic reaction term in this particular case and in the case of Piano Network in particular you can do that exactly so a long story short if anybody's interested I told you that in the book that Marino Gatto, Ignacio Rodriguez and myself just published there is a complete derivation of that that speed in fact turns out to be something which is if you look at the size of a jump which you assume that the system would have in discrete space and continuous time would be delta square divided by tau the mean waiting time of system you can see that this is the equivalent of the speed of the other and this is the equivalent of a coefficient so it's twice the square root of r times or a times d but divided by coefficient which is essentially the convolution of the waiting times you have outside the backbone over which you propagate which is larger than one so a theoretical prediction on an abstract model again on a particular structure is telling you that in principle you should have but in Peano you can calculate exactly when you can do it numerically in any other case the heterogeneity generated by the bifurcation structure that you will face propagating in one direction slows the front and indeed that's what happens so if you take a two-dimensional system this is what you have in the two-dimensional system of this kind like this is the you inject into a particular place oops and you see how these propagates in space isotropically and the speed is twice the square root of a times d and almost regardless of a particular network structure for Peano you have an exact solution for OCNs which you have seen the other time you have something of the same kind you have systematically a slower speed of propagation you may wonder who cares and to do that I resort to something which I find absolutely fascinating a group of spanish physicists wrote on theoretical population biology in 2006 that started our interest in the subject studied a quantitative model for the American colonization of the race towards the west in the 19th century as seen through the lenses of transport of a fractal network so the idea is that the landscape heterogeneities and the need of water forced the settlers about through their courses that is any settler will move along in a fractal in fact because we move along a river and only crossing divides a small time so when they cross the device like a baroque or whatever why do they need the through your courses because they needed the water resources cost for drinking energy transportation whatever and the idea that the exact reaction diffusion model seems like a sensible way about a river network and a say which you would have that the population growth would be a logistic with a rate parameter a for population growth at a single node what is remarkable that the archives of a U.S. Congress allows you to evaluate in fact how the colonization came about and what these guys had is that you had the yearly value of the relative frequency of them that is the distribution of the relative frequency of the distance crossed the year by year by the colonizers in different directions and thereby one of the key parameters that you have to calculate that the system would have been the five distribution of the distribution of the jumps and was actually given and didn't need to be calibrated at all and what is totally remarkable if you take that so you had essentially the growth rate from the archives of the population growth you have the distribution of them the features of them of a random walk in space for distribution of the jumps and the settlers would go about over in an isotropic march towards the west and what you had that the feature bridge which is then you had the parameters twice the square root of a times t will be of the order of 40 kilometers per year what is totally remarkable if you take any simulation any kind of assumptions etc you go immediately to speeds of the order of 14 kilometers per year and mind you that the actual observed speed of the expansion was of the order of 1.3 13.5 so the idea is that the data suggests that indeed even in this case the very nature of the substrate in this case for the population for population dynamics was the one dominated by the features of the river network itself because of the constraints that we have imposed in the system this can be so this is again the picture so the constraints that we have imposed on the backbone of propagation of the tabling waves facing the bifurcation that I will once where you will see inevitably the topological properties that is the properties of the bifurcations that you would face along your path on any particular backbone would be the same in this structure which is statistically identical to a two river network have a replicator replicable etc like we have seen the case of ocean and the piano network if I behave very much in the same manner so yet another indication that the substrate plays a major role in the ecology of the system so like I did like I showed you the other time the first thing that we need to say okay it's a strong suggestion and can we study in the laboratory the what happened so we had developed the the ability in my lab to work with protists and so you have these essentially protisto drones if you want so we made these running places and we see how we can measure it by more or less progressively more refined tools etc how and inject the population one end can invade and the speed at which it invades the system so this looks like a Kandinsky picture but is essentially the trace taken with microscopy done in my lab of individual trajectories of every single protist moving in this direction and mind you that one of the two dimensions were much smaller than the longitudinal one thereby making the one dimensional assumption is so I am interested in how heterogeneity slows the front and one would be to test how the demographic stochasticity pitches in with the respect to the physical Mogorov model of invasion so essentially what we took the model of this kind and we decoupled the sense of space from the intrinsic noise which are having the system mind you that different realizations of the protist run through the system are things of this kind so our application it was absolutely needed to see how the system behaves but the point is that if you do these and you replicate these normally which had a 95% range you see that still in a context in which you have there's nothing neutral in here there's nothing but demographics stochasticity induced by the biology of the system and still what is phenomenal is that the physical Mogorov system proves able to reproduce with a remarkable accuracy what happens in the laboratory so interesting enough we would see okay now can we generate other kinds of heterogeneity in the system and how can you do that when one idea was used photo taxes in biological invasions and and the idea is to use the generalized receptor law because you have a system in which every node essentially you have a reaction in the node and you have transport among nodes so the idea is to use the photo taxes in a system of this kind this is my the runner the drone the stadium for these properties to run the injection point the collection point and what we have in a photo tactic system would be to use leads to generate resources heterogeneously distributed in space which hadn't been done before and slowing invasion by heterogeneous environments is one of the tenets in which I've been trying to get you interested in and as you're seeing so the idea is that for instance heterogeneity could be special heterogeneity in which for instance you put some drift in a system so you put a bias in the system not simple diffusion but you add advection which makes it even more heterogeneous of course because advection in this case you assume constant of a system and you have a probability in any node which you have is a probability which is an even probability of splitting in the case of diffusion and it's not even if you have drift of any kind so essentially what you have in the system is the parameter that unifies the drift what you get is that this is the wavefront speed in one case so essentially in the case in which you have like zero drift in the square root of AT like you have it in the color of system up to a system which is completely dominated by advection which is important because I'm interested in studying the persistence of species in a river net or season ecological corridor so they may or may not be important depending on ecologically viable quantities like the nature of the organs we are discussing so anyways what we know is that the Hamilton Jacobi method we have used and the numerical simulations match fairly well and if you instead put drifts you start having negative and positive positive fish waves and you can have approximations which are important in this case we shall briefly talk about the so-called telegraph equations peano then stays in the system with features that are calculated exactly of course I won't test you with the details they are quite involved but but again straightforward and analytically solvable and again significant because peano topological is indistinguishable from the real of your network although if you look carefully you see that other metrics simply do not match the telegraph equation is also something interesting of course now for instance this is what happens if you look at how the system propagates having chosen three different spots for colonizing the system so this is how in fact the system propagation behaves and there's a certain degree of commonality there's a degree of commonality in the system here now why the reaction telegraph model against the diffusion when this all happens if you put a drift what happens is that you have to assume that if you use a reaction random work model you essentially unless you do some provisions for it you would assume that the speed of propagation of the jump will be at infinite velocity which is in fact it's a complicated thing to digest long story short if you put the proper model which overcomes the inconsistency well known inconsistencies of a diffusion model in the case of bias in this case long story short in the computation nothing happens so the reaction random work describe what happens in the system even in the case of the drift fairly well so back to the system which heterogeneity is imposed by me by choosing a certain distribution of resources with a certain correlation length for instance you have like silence resources silence you see it's a prosaum process the one we modeled it with in the system here so we had the ports at the bottom of the channel for changing the distance from the lead the angle of light propagation of the light to use something which is called the Keller Siegel framework for calculating how the resource acts like a sort of an advection in the system and I won't get into details of course if you're interested I'd be delighted to see what what happens but what what is interesting in this case is that we do have a framework so you turn off a light the system behaves and that's very clear from the spectral behavior of the system behaves like a linear e to the minus the wave number square times dt so so it turns out to be a normal diffusion if you turn off the light and it comes up into something different if you generate a light field which aggregates and acts as a drift in the system thereby disturbing the other behavior of the system so individual trajectories here are much larger and as you see in the different realizations and different kinds and yet the coherent picture appears so this is light intensity profile we're using the experiment and you see the one spread experiment was done for each landscape and and thereby you have a a significant way of studying the system what is the punchline of these are relevant to our case is that the mean front propagation that we can compute theoretically through the Keller Segel framework and the experimental one in fact they show that the speed has a new actor it is the autocorrelation length of the resource field so heterogeneity appears in the system and affects the propagation of the speed of propagation of the traveling wave and these autocorrelation does slow the speed as you see here in the case you're having there is which have a mean invasion speed computer directly without any light field included the square root of 2D system of that which is the slope of the system here so heterogeneity whether given intrinsic to the structure of the river network whose architecture recurrent characters were long studying and which I have introduced in my first class have an effect and to jump into something connected like believe it or not I'm going to a giant of the field the late Ilka Hansky craft food price few years back sovereign died too early and whom whom we miss sorely in fact had invented a very important quantity that was key to metapropilation analysis called the metapropilation capacity of a fragmented landscape that is you found out that an ecological measure super sound and quite well established experimentally from fieldwork and from theoretical work that characterizes the suitability of the substrate to effect of heterogeneity in his case was a fragmentation of the landscape and there was a main motivation from the ecological view so technically metapropilation capacity is the leading eigenvalue of an appropriate landscape matrix which I'll explain in a minute and essentially the punchline was that a species is created to persist in a landscape which is the matrix for ecological interaction in my case I would put this in in the other in the case of the other network is larger than some threshold value which is divided by properties of a species and which essentially the capability to disperse and the capability to to to the dispersion capability and the you know whatever the mortality and reproduction rate so metapropilation capacity is a number that can be conveniently be used to rank landscapes or for ecological interactions in terms of their capacity to support meta populations metapropilation of course is another one of those bold statements not unlike the neutral model of biodiversity in that metapropilation essentially ignore interspecific interactions among species that means there's no predator pre-relations etc so essentially it is an intrinsic capacity of one species that determines its ability to survive on this I shall not spend issues time because of the limited time I have but we have discussed that at length for the implications so what happens is that the key to that is essentially a focus on the probability to be at point i in space in time of a focus species the one whose ability to survive is studying which is the probability of being present in patch i at time t which is a balance of colonization extension forces and we just kill out the interspecific interactions over which ecologists spent lifetimes in the past that was a greatness of one of the most in fact gifted field ecologists of our times Ilka Hanskin said so the point is that following the rate of change of this probability in time is essentially a balance of the probability of being colonized by different places at distance at places site j at distance di j measured along the system and and that multiplies the colonization rate and then you have a the extension rate which is birth minus death ratios in the two so the ratio e over c is what determines the teacher that you're having there now the main result is that what is lambda and the the the eigenvalue of the system well it's a landscape it's a the maximum eigenvalue of a matrix which is the landscape matrix which essentially this is the dispersal ability of a species and this is the distance which you have in the system itself so it's a it's a positive matrix it's a reducible matrix in fact so ground for various theorem applies and say and that's what he found out and if it turns out that if the maximum eigenvalue of this particular landscape matrix which is very easy to calculate for a landscape like ours like I show in a minute the landscape matrix for us it's easier and more constraining than in say a savanna ecosystem like we had seen the other day so what happens is the following if you take a path along which an open channel network develops so we started from an any particular system and we say essentially streamline a simplified network by assuming that the system would tends to minimize its energy dissipation approximating the structures that and the statistics that the river network inevitably has but like it or not it's some sort of an unintended consequences with the decreasing energy the second line of energy you have as a bonus in fact the best better viability in abstract terms generated by the river network so the ecosystem in a sense benefits from the physical process that determines the substrate that we are talking about and and then well there are other issues but I realized it's I've been chatting too much so I'll be skipping fields but anyways this is a significant result in terms of the probability and if you take several realizations of the same network etc you have a band a narrow band and if you have like different kind of mean field versus OCN thing you see that this is a significant result from the statistical view so I'm I've the last 10 minutes of my talk will be devoted to can we use the same constant to study river networks and biodiversity and I will leave to the third and last class how this in fact is key to evaluate how pathogens spread along river networks psychological corridors thereby propagating deadly disease deadly or chronic disease so what am I saying is that in a river network is a set of is an oriented graph my my notes and edges edges are physical edges obtained offline by digital terrain maps that we see last time you do have reactions which would be physical chemical or or biological reactions in this case biological ecological reactions and essentially the links are what act as transport models between notes and this applies to individuals this applies to species or to populations so essentially we can talk about rather than make a relation make the communities and the first example I want to show it's a paper which we have Marino and I care very much for Lorenzo Mai is the first author on the metapopulation persistence in in river networks what happens is a following so the to study metapopulation dynamics can be done by if by looking at the system in which you may have like species that live on a substrate of this kind which eventually might if I get off a move off of the network itself so the species we are talking about the metapopulation and that somewhat forces what's going to happen with more complex compartmental models for a number of different phenomena will be like you have like in every note you have two ecologically distinct developmental stages so we split the population living in the node which is a reach if you please and in the young non reproductive individuals why and the adult reproductive individuals movement from one node to the other can occur for different pathways but along the structure of the network either along the same network if you are a fish or even overland if you are an amphibian for instance in certain stages of the life you take into account local demographic processes birth growth and death and the dispersal dynamics in each node of a river network which again using the full constraining power of of the system of this kind now this is important to explain what's called the drift paradox because to explain the long-term dispersal in system in which the drift could be very significant effect there's there's something which ecologically puzzled ecology for a long time for instance to explain the long-term persistence of populations for instance empirical documented examples came in for instance for Scandinavian freshwater ecosystems insect species that compensate the larval drift that is transported passively along the river network with upstream directed flight of adults prior to OV position and it's called the Mueller's colonization cycle otherwise an excess production hypothesis has been forth in which drifting organisms would be exceeding the balance of demography of the local scale which implicitly assumed that the drift essentially represents an extra mortality terms of these kinds but anyways all I'm saying is that what is new here is not the ecology which is well known but it's the fact that you're using a subset of this kind and to give an example of how coupled are these in this case two for every node at node I you have the young the number of young no reproductive individuals and the number of adult reproductive individuals they have a certain mortality term possibly density dependent you have them in what you have the most important you have the probability of dispersing from any j site so you may have adults at site I can be taken because of the connectivity matrix for any side j by simple proportion and transport that you're having in the system whereas in the case of the adults in addition to that you have reproduction terms it's not important actually how you do that of the specificity of that which is very well known system that we're having in this place here but what I'm showing you is the fact that how do you study those systems is two equations per end nodes of a river network so you can actually assume that those matrices dispersal matrices are probability which depends on the connectivity structure something which you assign and give offline and which you can study by studying the stability of the the metaprolation persistence is actually related to its stability of the population that is if a state x0 is stable the population cannot persist in any river network nodes if it is unstable juveniles and adult abundances grow and they grow the multivalation persistence so you can study the global equilibrium of those matrices which is essentially it's a super Jacobian in which you have two n by two n matrices that can be done exactly and calculate the survival and the non-survival of the different ranges of the system and what for instance one particular case which was particularly interesting was the study of salamanders for which you had the critical data from I think it was in Virginia some place in which you can relate the conditions from manipulation to persist and manipulation not to persist counting on the fact that the juvenile and the adults have different ability to jump off the river network itself I am almost done regretfully so I will compensate next thing but give me three minutes to complete with another example the invasion of the zebra muscle which paves the way of something which I'll be showing you Friday that is what you're seeing here it was the zebra muscle was by accident introduced in the Mississippi Missouri river basin by introduction it was taken from the veligus without the the larvee that were introduced in ballast water of cargo ships that came in from Europe where it was native and it started spreading through the system reaching the DTAs even embedded hydrologic units in the system have been growing dramatically over the years so up to a point what is totally remarkable about this is the fact that at a certain point it didn't even simply diffuse or disperse downstream all of a sudden you started having places where you started having flare-ups of invasions in completely unrelated places far away from it that introduces the fact that we can study river networks fairly well in those systems and essentially the local reaction equation is the local local age growth model in four stages which have lava production transport of lardy is a passive larvae are small the veligas are essentially passive scalars so they diffuse and they are vetted to the river network for the river network but most important you have to introduce what is called more than a multiplex network why because in those recreational ponds in which you put some boats what happens is that if a guy picks up a boat doesn't empty its ballast water properly put it on the trailer and brings a thousand kilometers away then in as much as COVID-19 spread through human mobility so did the spread of this system here so the long story short on which I shall stop in time regretting that I have dedicated too much time to the early phases but I will be saying this what I miss from here next Friday so EGAS is the computer that simulated values in like in this case that is a measure and is a computed as you're seeing here only by our ability to introduce those long range flights generated in the injection by a different network which is not related to the topology of a river network but they're related to the road infrastructure in a certain probability of making a distance in the system you are able to calculate one of the most devastating because zebra mussel grew at the level of density that generated significant damage not only ecological because it displaced every other native species of that kind but it also generated clogging of hydropower plants production and the likes and this is an example of how in fact that biological invasions reach the place yeah this is a good point to stop in here so the point line is that and now we've been taking on the next class to see how this in fact becomes the essence for studying through the same environmental matrix and possibly multiplexed network in which pathogens disperse waterborne I mean through the network and human mobility spreads the disease how in fact they can use oriented graphs and other reactions and hydrologic analogic transport to tackle individuals to make up relations or make up relations now I'm ready for your questions great thanks a lot Andrea for the very very nice lecture so we have time for questions so please if you want to ask one you can use the arrays and feature or you can type it in the in the chat yes please Monday can we emi then Monday can we emi yes I do barely but yeah okay yeah can you hear me sir I I do okay I'm okay so I I'm I'm looking at the last the last point you presented in this slide is it or do I join the class not to at the point to start it is it that the the network of of of of the the model that you brought was but it but it did before you presented the result of the data or is it it it directs imputes without validation but it's a good question actually Monday what happens is the following okay there are networks and networks in this case if you're talking about the transport of you see the main point right you have nodes in which have physical chemical biological reactions right and then and you have transport along the network structure now if you're talking about the dispersal of the organism in the in the larval form for instance they are small seeds they behave like a passive scholar so they diffuse and they are affected and diffuse a lot of the river right but if you get a bunch of them and you take them from a node and you transport that completely artificial into another node like you do if they with the veligas they get trapped in the ballast water uncleaned of the boat then is the mechanism that can explain why you can actually have a flare up of the of a proliferation of a zebra mussel hundreds of kilometers away without any in between why this is interesting because it's like receding the infection if you want or the density of a population somewhere else now in one case the network is essentially the physical substrate which we know directly right because that's unavoidable digital terrain maps allow you to extract those connectivity matrices that is how I know to connect to any other node in the system and you can actually distinguish whether you for instance you can also go you have a preferential transport downstream but you may even go upstream with a probability which is different so you have a bias transport I'll be talking about that Friday but in the case of a of a mobility network generated by the other have time something else so in that case what we did was to evaluate the kernel of dispersion but it was calibrated on the data actually which is the displacement of commercial boats into the place through some proxy which is a data on the number of boats parked in different positions when Mississippi Missouri were basing so when whereas in the case of a river network it's a given the connectivity matrix is given once and for all because it's extracted objectively it's added remotely and objectively manipulated if you have a case that you may have to make assumptions when we'll be talking about human mobility for instance to spread disease which is not unlike these you will have two possibilities one assume one of the models for like normally used like gravity models radiation models and then or you may use cellular phones and track individual mobility of large numbers now you can now in that case you may wonder whether the use of a telephone in certain places where color spreads is socially biased or not if you're looking only a certain segment of a population but mind you high experiences that's not the case that's actually socially neutral the ownership of a phone even in the most dilapidated place on earth and I've seen it in my eyes and I'll tell you next week okay thank you so much for the explanation I will appeal if there's maybe a kind of a reference material then I will like to to read more into it I'd be delighted well actually if I'm not I'm not selling anything because all the money we go to Cambridge University Press but the book that I just published that with Marino Gatto and Ignacio Rodriguez-Turbez called the River Networks as Ecological Corridors Species Population Pathogens had everything where we have done the past 15 years on the subject and I think hopefully a good review of a literature as well thank you Mande great thanks a lot for the question and the answer so we have time for more questions if any also on YouTube you can type the question if you want otherwise I think we are actually on time so otherwise thanks again very much Andrea for the for the lectures and looking forward for the next one if you want to listen to Marino can I stay on here absolutely yes so what we're going to do now is that we are taking a break before the before Marino


Welcome to digital asset news. Take a top stories and crypto and bring out a bite-sized piece. It's today Just as the thumbnail asks what would happen if traditional equities or stocks just took a big nosedive Would it bring down bitcoin and the entire crypto digital asset market? So we're gonna take a look at what? Bitcoin stocks we're gonna talk about getting ready now through education because that's so important to get that ready right now Before everything hits the fan. We're also going to talk about blockchain gaming and NFT TVs And before we get into that, we're gonna get into the market itself before we get into that Let's take a look at this nifty meme that I put out on Twitter Which is Karen and I did this because it seems like a lot of people They've been asking me in questioning like hey, I heard on Twitter. I heard on YouTube I heard on Instagram. I heard on tiktok that once we get out of 2021 Everybody sells off for taxes and everybody's gonna get everything into a row and they're gonna start 2022 Q1 off with the bang and we're gonna start to see moons and lambos and everything else and it doesn't work like that So right now, I know everybody wants to get rich fast This is not a get rich quick overnight. This is a get rich financially stable over a long time But it's not a get rich quick scheme crypto digital assets the same theories apply And what we really need to do is get everything together So we know what is about to happen by taking a look at not just what's going on to our crypto market But what's going on in the whole macro ecosystem as far as finances? So first, let's take a look at my favorite market, which is Crypto and digital assets. So just so you know right now, we're going sideways It's still 2.2 trillion somewhere around there as far as total market cap. We're down almost the point Bitcoin price is 46 for everything else is down around the board There is a couple of different cryptos that are up. Congratulations. If you're one of those guys But the sentiments as far as sentiment we're using trade the chain link in the description Is still pretty down high. I think people feel like this is going to be a good year But remember, it's not about feelings. It's about data and the things that are actually going on around us So what I like to do is there's a great newsletter I get every day. It's called the daily upside And uh, there's a link in the description. It's a hundred percent free newsletter All they have to do is sign up for that is give you information And what I like to do is just take a look at what exactly is going on So they tell you like super easily. Hey After a blockbuster year, well, here's the three points at a blockbuster year Markets are facing a complicated outlook Nuclear energy is posed to be labeled green and sustainable by the EU They're also taking a look at natural gas that would actually help with our esg problem That some people have with bitcoin and different proof of works and 5g network deployment hits another bottle of turbulence So what's important here is pretty much those first two that we talked about And when I take a look at this and I'm like, okay This is what's going on in a macro environment because we're not in a fishbowl Crypto is not in a fishbowl. We actually have other components and institutional investors are here So here's what's happening markets face a tougher 2022 after last year's record run The s&p 500 has efficiently doubled since new year's 2018 doubled since 2018, which remember Traditional finance equities stocks. They don't double very quickly. It's a very slow growth process So when this happens, it's like a big thing over there. I mean in crypto, we call that a Tuesday We don't really care But here it's a big thing and is it sustainable the first time the index has produced a three-year return of 100% since march 2000 and now as far as last year the s&p hit 70 record highs 2021 70 record highs For the first time every single s&p 500 sector posted double-digit gains In 8 out of 11 rows at a least 20 percent to cap off the year the s&p 500 turned in the best December since 2010 which is kind of interesting because we had kind of a junk December I think we all remember december and crypto. We were hoping for a big bang didn't really happen s&p did pretty well to cap off the year the s&p I already said that early 2022 will likely feature some hawkish pronouncements from the federal reserve fourth quarter earnings reports that underline ballooning inflation and the fed tapering asset purchases so you have to remember right now what is going on in the macro environment is that Traditional finance had a pretty massive run. Can they keep it up? And if they can't keep it up and we see a decline because of the Fed is starting to taper Then they may and they've already talked about this about raising rates interest rates What will happen with the stock market? Well, it'll probably not do as well as 2021 because there's such a monstrous year And if that's the fact and we know that institutional players are here What's going to happen with our market? And I got a little concerned until I took a look at this great article Uh, why portfolio managers will need to look at altcoins in 2022? And actually this goes along in lines with what we talked about yesterday and yesterday's video about hedge fund managers need to get on board With crypto and time is up for them actually and this was written by uh, lorence Louis tin and managing editor and he did a great job here With this opinion piece and just to break this down in the simplest way possible They've got four lines here You got green red black and gold Okay, and then for this right here where it says, uh the black line It's all about correlation and this is the correlation between bitcoin and the s and p 500 for correlations anything that's positive, especially like up to one Means that it is doing the exact same thing So if you have something that's uh very the more positive it gets the more correlated is meaning if bitcoin and s and p 500 We're at a one that means if the s and p went up Bitcoin would go up and now if it was at a zero it means it doesn't really do too much together And if it's at a negative number and the lowest is negative one it means it does the exact opposite So in this case if it was if bitcoin and the s and p 500 was at negative one Then that means that if the s and p went up then bitcoin would go straight down that is negative zero and positive And to get that you can just see here that in the black It's really not as correlated as some might think even me I talk about how there's a little bit more correlation than it used to be and I thought I was a little bit being more correlated But not so much so over the last year the correlation coefficient between bitcoin and s and p 500 peaked at around zero point three one So yes, it is positive But not too much in june the coefficient was negative point zero four meaning there was statistically No relationship between the price of us stocks and bitcoin. So why is this important? Well, this is important just because what I talked about if the stocks start to crash Or they take a pullback Maybe this is the time for some of these players to go, you know what? We knew this was going to come so where do we put our money and bonds have done nothing for us I mean, it's pretty much negative negative yield and if the Crypt and if the stocks aren't doing so much where can we put our types of funds? We can do the us dollar, but I mean there's this thing called inflation. That's just eating everything up alive But there's other other different asset classes looking pretty good Why don't we put it into crypto now? If it was me And this is years ago. I might think about real estate but real estate's on fire and is going up tremendous amounts So I can't even say that you can put your money into traditional Real estate because there's just the price is going up so high So where do you have you got crypto at its paltry 2.23 trillion market cap, which is absolutely nothing So that's just one thing to look at now going forth. It says bitcoin's correlation with gold Uh, the correlation between bitcoin and gold saw its 2021 peak in early january at 0.3 So in actuality, there was a little bit of correlation, which was surprising to me The lowest point was negative 0.18 back in august and it's a measly 0.07 So not really correlated to what's over which makes sense to me. I didn't think it was going to be that well correlated And if the cryptocurrency isn't trading with stocks or gold, surely it's tight with bonds Nope, that line is sticking to zero. So bonds, which I don't know why anybody would get into that these days Especially that uh, traditional 60 40 split 60 stock 40 bonds I think that's dead in the water and then uh, lastly it talks about the upside for a portfolio manager and this is where It's nailed What he's talking about here. This really makes sense the upside For a portfolio manager is that low correlations with other asset classes in the crypto Something that must be at least considered Or a portfolio to boost diversification and we talked about this yesterday And we're going to take a look at another uh topic But they need to start looking at these things because as time goes on What would it hurt to put one to two or even three percent if you're a portfolio manager into crypto It's only pretty much gone up in the top. Well, just take the just take the top two that go into theorem Even though it's volatile has gone up over time. So that's the part where my man here Lawrence nails it. Here's where he gets it wrong The downside is that non stablecoin crypto, even its safest one Is dreadfully volatile so The word dreadfully I think is a little bit of much Lawrence, but There is a a certain Positivity to what he's talking about here or the correct statement. It is volatile, but not dreadfully The volatility Is what gives it its magic because if you don't have too much volatility What can that really do for your portfolio? Yes, it'd be great if we just went up, you know One percent every month and at the end of the month. Hey, we got 12. Sorry in the year we got 12% That's not the that's not the magic with what crypto is.  That's a rank number 1247 I can't help you But if you're sticking within the blue chip cryptos chances are you're doing pretty good So I think the volatility is what gives it those types of magic as far as it's returned And I like to see those types of things and then lastly to finish this up Bitcoin and ether the 90-day correlation coefficient is at a very high 0.8 Even though other trance bitcoins return in 2021 is the matter. So really what we this is just saying what we already know Yes, bitcoin is correlated to pretty much everything as bitcoin goes up. So does everything else But in relation to it, you're going to see some that R exceed bitcoin as it goes up. Solana, ethereum, cardano avalanche I mean those types of plays We've seen just go up polygon maddock. I mean they've they've gone up Exponentially higher than bitcoin because market cap. So that takes care of that little piece and then also just so you know Just to follow this up This is what we talked about yesterday and laurence is right These portfolio managers need to really take a good look at crypto because as a reminder As far as hedge funds portfolio managers hedge funds only three beat the s and p 500 three Send best and paul on srs. All the rest of them were below the 28 percent gain that s and p 500 did last year So if you're an investor, why are you using all these guys? All they're doing is just taking fees from you Just go to just buy into the s and p 500 and that's it because that's all you need to do It's just a hedge. It's just a fund and you don't need these people to tell you anything because you can beat them Just by going into a buy and hold situation. Anyhow, that's what we have for that Let me know what you think about that in the comment section Now let's talk about getting ready right now and when I talk about that You have to understand that for my What I'm trying to do here is the majority I've been doing is I'm dcaing dollar cost averaging in I'm going to dollar cost average out I'm going to take profits and I'm going to stick to my plan Even more so than I did in 2021. I'm going to continue to buy these dips Not just the blue chips. I'm going to get into some very low low cappers because I think there's some really massive Asymmetrical gains and then you can make a lot In as far as in terms of investment, but that's a very small sliver. That's in the gamble and trade section Mostly what I do is just hold on hold on for dear life and just kind of make it make it go that way But to do these things you need to get ready and to do that You need to really know a little bit of like on-chain analysis Me and kiyongju who is the CEO of crypto quant. We're doing this great video where we talked about these five or six different Six as far as on-chain analysis and what to look for and how to read those charts and then also If you're taking a look at like the new projects that are out there Take a look at my second channel digital asset news clips. We've gone from everything from kevin allari's wonderfi to everdome to kinsikishi online and some other different ones that are like the new emerging type of Platforms that are out there that could I think be monstrous gains and lastly if you're looking for just the overall appearance Or overall education just go to dan teaches crypto. It's the thing that spins out of my head constantly It's 100 free. It'll never I'll never charge it. It'll always be free And I'll we go everything over everything from like the basics of crypto Safety because it's not how much you make it's how much you keep how you don't get scammed Investing reviews like all the things that we just talked about is like the different products I put them there also and then uh module five is how do I whatever you think of that you need to do So Link is always in the description, but it's super simple dan teaches crypto.com So check that out And that I think is a big thing as far as like getting ready because on days like this not much to do Just get yourself prepared for the upcoming Year, so let me know anything about that in the comments and let's finish up with two articles that I thought were pretty interesting Blockchain gaming I think is going to be huge And we talked about this at length in this channel if you've got Gamers who are just free to play now. They're saying hey, we're gonna Hey you to play I think they're going to go on that route, but there's a caveat and I'll get to in second so Square onyx president talks in fts metaverse blockchain gaming nearest letter first of all. What is this place? This is uh the company that brought you like final fantasy Some other games that I've never heard of in my life because I'm not I'm not a huge gamer I'll just be honest with you. I'm just an investor. So all's I take a look at is Which place and which investment is the best one for me? Which one has utility? Which one has pretty great teamwork? and if I'm looking at uh Different projects. What's the tokenomics, but I thought it was interesting that Square onyx has been around forever is now talking about nft So how does that work into you as an investor? I'll get to that in a second So to fit to go and get into this This is from the president of uh square onyx He says uh as this abstract concept talking about nfts Begins to say concrete shape in the forms of products and service offerings I'm hoping it'll bring about changes that have a more substantial impact on our business as well And this is a guy. I think who's starting to realize like, you know If this is being asked for maybe we should get into it The president pointed that the company is conducting aggressive research and development efforts and investments in areas that include blockchain gaming and ai Excellent from having fun to earning to contributing a wide variety of motivations will inspire people to engage with games And connect with one another. It's a blockchain based tokens that will enable this by designing Viable token economies into our games. We will enable self-sustaining game growth and that sounds pretty great I mean right there. I'm like, well, that sounds very positive. However, you have to remember To get the traditional gamer over from one format Gamers are just like the rest of us They they like a little bit of change but not crazy change and there's a dichotomy going on and I can see it and I can understand why So what it says here? To finish up the inclusion of these new elements in traditional gaming has been received negatively thus far by gamers Gsc game rolled a small company had to recently abandon its intention of including nft of elements in stock or two And ubisoft another leading developer major game developer Faced a similar problem when the when the reveal of its nft marketplace courts Received 95 negative reactions on youtube and I get where they're coming from because these traditional gaming companies They have been squeezing The the funds out of their gamers for a very long time The games cost quite a bit of money For some of them But if you're playing like the like the free to play it's not so much that cost that doesn't cost money at all but To buy things within the game to buy skins and to buy weapons before you know it A game that may have cost 40 50 bucks Just cost you 300 400 dollars that you just poured into it for all these different Add-ons that you can't take anywhere that you can only play in this one specific game So when you've got games where you've already had to pay for it And now they're going hey, we're doing this great nfts Now I get why the gamers are like we hate you Because you're screwing us because we just bought this game And now we got a bay for all these power ups and if we don't pay for these power ups Then of course i'm going to get slaughtered in this game. That's not fun for anybody So I don't want to do that. I think These traditional gaming platforms are going to have a real problem Convincing these gamers that nfts is the way to do it. I think To get away from that stigma These new version of games, I mean you'll have like big time and the sandbox and all these different cornucopia is You'll have these different uh place Places go, you know what are you know ginsokishi never done? We're not like those guys We started off with free to play and nfts and we're going to give you these tokens and you can actually earn Earn to play and there's no real There's there's no rug pull or anything like that just come in here and play and we'll make this whole ecosystem. So I think These traditional game platforms are going to have problems. Anyhow, maybe we should think about that in the comments and then uh, lastly This one is crazy I never saw this coming, but here we are samsung The uh pretty big, uh south korea company says they're going to announce nft platform for smart tv's South korean tech giant samsung building smart tv lineup Uh, which is going to be micro led neo q led and the frame We'll have an nft platform app that can be used for discovering Purchasing and trading digital artwork and they stay with demand for nfts in the rise The need for a solution of today's fragment of viewing and purchasing landscape has never been greater I thought that was interesting that these guys are getting that big into nfts The upcoming platform will enable viewers to browse and also trade nfts without leaving the couch Which i mean you can do that anyhow with your film or whatever It's unclear exactly which nft platforms or marketplaces will be included for aggregation But uh, this has been actively investing or see me, uh, samsung has been actively investing in nft and metaverse projects Through its venture capitalist arms samsung next and the firm participated in an investment round for a metaverse Gaming platform and I was thinking myself and like well, that's interesting. How big are they getting into it? Well, if we take a look at samsung, there's a website called samsung.com Ford slash global Ford slash galaxy they have their own wallet Their own samsung blockchain simple and trust proven, but it's mostly it's a wallet They say it's their their blockchain, but I didn't see anything about the blockchain itself Just wallets and now you can do all these things and you can use daps and There's the central land right there and all the different games and so yeah, okay Keep private gotcha and then also They also have a Uh blockchain phone samsung makes it easier to use blockchain and galaxy devices With support for other hardware wallets. This is on may 13th. So they're really into crypto samsung And then also if you haven't noticed Theta one of my holds. Yes, I'm biased if you scroll down here and talk about uh enterprise value their nodes Well, there's sony google and there's samsung so When we kind of try to put the dots together That's where you want to start to think to yourself is like, where is the hockey puck going? And if you're really thinking about well, I don't really know where to get into it If you just go to coin gecko and you click on Categories When you click on categories, it breaks it all down into smart contract platforms You have the salon of the ethereum is the cardon was the avalanche or something like that polygons avalanche Blah blah blah blah and there's one called non fungible tokens and if you click on that It'll tell you like all the non fungible token platforms. So axi is the game sandbox shirt. There's theta network There is the central land engine coin. I think it'll be a pretty good play. I hold that myself. So that's why wax I don't hold that but I know Wax is great for minting nfts That's like super cheap and a lot of big big players are using it Audius is for uh nfts as far as like uh music So you can just take your pick and start to do your own research And that's why it's important to really get into these To either research that you can do and get yourself prepared now and lastly, I just want to leave you with this I tweeted this out because people are they were getting kind of ticked off at the whale situation people getting dumped on Oh poor as me. What was me?  It's true But I just said very simply If you dollar cost average in you buy the dip and dollar cost average out by taking profits When the price is climbing and not getting too greedy What difference does it make when whales what whales do if they dump or pump? You could just piggyback off of what they do and have a symbiotic financial relationship So you're never a victim. So that's investment advice from me I can't give you investment advice my investment advisor, but that's just the things that I do Dollar cost average in dollar cost average out. It's a profits along the way I don't allow myself to be too emotional. It was a little emotion in uh investing But that's it for today. Look, I know it was long So many things are going on right now But um, look he found a little value in the video. Give it a thumbs up I'll consider subscribing as we talk about and on this channel are time sensitive, especially what's going on right now So thanks so much for watching. I appreciate it and I'll see you on the next one


Bobby, the new thin girl home permanence for a casual wave, presents transcribe my friend Irma, treated by Fly Howard with Mary Shift as Kay, and starring Marie Wilson as Irma. Not far from the town of Marblehead. But now my home's in New York and I live with Irma Peterson. So here's the question. Why did I have to leave one Marblehead to come to another? You think I'm exaggerating? Listen to this. Irma, I'll just... That's simple. That's the man who comes to read the gas meter. Smooth hair, silky hair. This can be your hair if you use white rain shampoo. White rain is a gentle lotion shampoo, as gentle as softest rain water. White rain leaves your hair softer, smoother, silky or too, sparkling with natural highlights, brighter sunshine. Remember this promise. Use new white rain shampoo tonight, and tomorrow your hair will be sunshine bright. White rain. White rain. Miss Peterson, why are you late? Well, there was a big fire downtown and the taxi cab I was in couldn't get through. Taxi cab? You always take the bus to work. I know, but the bus wasn't going anywhere near the fire, so I had to take a taxi. Very interesting. Now would you please sit down and take some dictation? Oh, all right. Wait just a minute. Okay, I'm ready. This is to my gardener. These are instructions about cutting back my roses. Be especially careful about pruning the Cecil Bruner so we will not win a prize at the show. Have you got that? Yes, sir. I'll read it back to him. Oh, if you want to. Um, tell Rose to be especially careful about winning a prize, even if she has to put prunes in Cecil's bloomers. No, no, that's not quite right, Miss Peterson, but never mind. I'll do it myself. Yourself? Aren't you going to bar me out? No. The way I feel, I don't really care. I don't care about anything anymore. Why don't you take the rest of the day off? Oh, Mr. Clyde, you're crying. There are tears in your eyes. What's wrong? Oh, please, Miss Peterson, there's nothing you can do. It's strictly a personal affair. Well, you can tell me. I'm a person. My wife wants to divorce me. Divorce? Yes, and I can't understand it. I've tried so hard to measure up to our expectations. Let's no use. She thinks I have no depth. Why, that's ridiculous. If you put on another pound, you'd only look sloppier.  No, Mr. Clyde, I'm not going to leave you alone, because I know how badly you feel, and I feel the same way. I think divorces are terribly sad. We would have been married 25 years next January. Congratulations. Thank you. Miss Peterson, if there was only something I could do to bring her back to her senses, I haven't done anything to deserve this. Of course you haven't.  Thank you, Miss Peterson. It's comforting to hear you say so. Now, I've never forgotten a birthday or an anniversary. In May, I bought her a Picasso, but does she appreciate it? No. Well, maybe once she takes lessons and learns how to play it, she'll like it better. Picasso is a painting, Miss Peterson. I cater to her every whim.  Well, don't you know the first rule of marriage is never leave another man on the house after you go to work? You'll be a favor, Miss Peterson. Go home. Oh, no. You need help, Mr. Clyde. I'm sure your marriage can still be saved. I don't see how. Well, I'll think of something.  Oh, if I could believe that, I'd never forget you. No, Mr. Clyde, I don't want anything. The only reward I want is that when you and Mrs. Clyde are together again next Christmas and are looking for things to hang on the tree, just think of me. Irma, what are you doing home so early? Don't tell us you lost your job again. Oh, no, worse than that. Mr. Clyde's wife is going to divorce him. When did this happen? Are you sure, Irma? Mr. Clyde told me so himself. Oh, the poor, lonely man. He's going to be saved again. But what did you say his telephone number was? This is all right. I don't start jumping for the boat before it reaches the pier. You can at least wait until the other passengers get off. Oh, now stop it, the two of you. How can you joke about a thing like this? Well, Irma, these things will happen. But you don't know what they're doing, Kay. They need each other. Man is meant for a woman. And they must go hand in hand down the highway, ever alert for the pitfalls and curves that lie ahead on the road of life. Who puts out this song, the automobile club? Irma, I don't like the look in your eye. Just what are you planning? Well, I'm going to get Mr. Clyde back together again. You? Yes. What makes you think you're in a position to tell two grown-up people what to do with their lives? Kay, do you know what the marriage ceremony says? Well, so far I haven't had the pleasure of hearing it, but I'm trying like man. It says, these two who have been joined in holy matrimony, let no man put a sonder. No. These two have been joined together in holy matrimony. Let no man put a sonder. Yeah, I understand you. What does a sonder mean? A sonder? Yeah. Is that noise you hear after lighting? Oh. The Clyde has run into a storm and it's up to me to clear the weather. Well, continue, my little smudge bot. Oh, Kay, you don't believe in anything. You're just a natural-born septic. Well, thank you. It's only me, Professor Kropotkin. Hello, Kay Irma and Mrs. O'Reilly, my three little natural beauties. You, Kay, as fresh as a cool mountain spring. Well, how sweet. And you, Irma, with the curves of a winding brook. Thank you. And you, Mrs. O'Reilly. Old mudbank. That's human pipe cleaner. Oh, my God, that's it. After I gave him an electric heater with a fan in it. Who asked you to? The fan blew a hole in the wall. The snow came in. The heater melted. The snow and I almost drowned. We love enough as it is. What's the better with her, Kay? Well, the Clyde's are getting a divorce. Divorce is a terrible thing. I don't believe in it. Well, I'm glad to hear that. Only because it lets a woman freeze so she can hook another victim. Now that's a jaded, selfish way to look at marriage. How else could a person look at it? Oh, like my late husband Clancy used to. To him, our whole romance was a glorious adventure. He was the hunter, and I was the beautiful bird of paradise. Looking from tree to tree until he finally trapped me.  That's your wife's crack. Can't you see poor Irma's upset and worried? There must be some way to stop this divorce, and I'm going to do it. You can count me out, honey. You can play Cupid, but I want to be out of the way when you let loose with those arrows. But, oh, glory be look at that wind. I bet it gets me pretty cut off the line before it blows away. And I better go with you. If the wind ever gets that thing up in the sky, we won't see the sun for three days. Well, I don't know how successful Irma will be in changing Mr. Clyde's mind on this divorce business, but I have a young lady here whose mind is definitely made up when it comes to permanence, because she has a Bobby pin girl permanent. And what is your name? My name is Molly Gribkoff, and I live in Alhambra, California. Would you like to tell us about your Bobby? I've had several Bobby home permanence, and I like them very much. They are soft and casual, and so easy to do. That's the part I like. Well, of course, we say that if you can make a simple pin girl, you can give yourself a Bobby. It's fast, and you don't have to worry about the results. You're going to look good as soon as you brush your hair out. Yes, with a Bobby, you have soft, casual waves from the very first day. No kinkiness or fuzziness, because Bobby was created especially for today's popular casual hairstyle. Everyone who saw it, my family at the beginning and others as I went out, have had very favorable comment on the Bobby. They like it. So your mind is definitely made up in favor of Bobby? Many times as I need a permanent, it's going to be a Bobby permanent. Well, thank you very much, Ms. Grepkoff. And remember, if you want your hair to have Bobby, to be manageable, and if you want to have soft, casual waves, so important for today's casual hairstyles, make your next permanent a Bobby. Bobby pin curl permanent.   I sure did, and I've been moving with the speed of a pickpocket who's just lifted a cop's wallet. Oh, so how are you doing, Joe? Simple, beautiful. I got my friend, Mushi, trailing Mrs. Clyde. Oh, Joe, do you think that's nice? Surely hope, doll face, and she is suing Mr. Clyde. It's up to us to get something on her, which will make her afraid to open her mouth, you see? Now, you've been around, Ms. Clyde. Do you think she's promiscuous? Oh, no, she dresses very conservatively. Doll face, promiscuous means, as the French say, chercher la femme, bewitched, bothered, and bewildered. Oh, I always get a confused with c'est la guerre, which means keep off the grass. Open the end. Hello, woman. Oh, there you are, Joe. Well, Mushi, how did you make out? Let's have your report. Can I give it to you like them private eyes do on the radio? Don't waste any time. Let's have it. Oh, it was like this, chief. It was a cold. As I sat in my office, I got a call to tell this day, Mrs. Clyde. I went immediately to her home and entered through the window. There was a shot. A shot? Yes, so I drank it. Then I sat down with the early time. Can you say that? No, the bottle, and I had another drink. Suddenly, I heard footsteps. Yeah? I quickly identified they was mine and decided not to follow them. Mushi, will you stop with the dribble and get to the point? Okay, chief. I looked around the room and suddenly saw a cigar. With lipstick on it. A cigar? Yeah. And I figured I had Mrs. Clyde dead to rights. All of a sudden, a hairy arm reached out through it. Yeah? It was the maid. She smoked cigars. Can I realize I was wasting my time? There's only one thing to do. I'm going over and see Mrs. Clyde myself. No, no, no, wait a minute, Alfase. Don't go getting yourself involved. But it's my duty. It's my duty, Joe.  They need the care of a specialist. Goodbye, Joe. Beautiful. Where are you going? I'm wanted in surgery. I'm ready to call on Mrs. Clyde. She's putting on her best outfit. The red hat, a white dress, and a blue coat. Very effective. Besides, when she walked down the street, all the servicemen salute her. You know what she's taking with her? A statue of Cupid with a clock in its stomach. This is to show Mrs. Clyde there's still time for love. Of course, the clock doesn't work, but it's got its cuckoo along. I'm going to talk to that girl. Irma. Yes, Kate? You know, as long as you're determined to go to Mrs. Clyde, you might as well listen to a few facts so you don't make a fool of yourself. It's too late. I've already made up my mind. Now, Irma, listen to me. I imagine that Mrs. Clyde is just as upset about this thing as Mr. Clyde is, so you'll have to be discreet, huh? Well, your approach must be subtle and tactful, so I want you to remember my words carefully. Oh, all right, Kate. I'll try to remember everything you tell him. Good.  Well, I'll remember that. And secondly, Mrs. Clyde is an old-fashioned model wife, but being a wife is the only trade she knows. So you must convince her that if she loses him, she loses everything. Oh, I won't forget it. Well, I'm off to the peace conference. Good luck, Mrs. Dallas. And I do mean, doll. I hope I can bring them together. Oh, Irma Peterson, come in. Thank you. This is rather an unexpected visit. Won't you sit down? Oh, thank you. My, here, a place looks lovely. Oh, I see you have wallpaper in the entrance hall. That's right. I think wallpaper makes a room look so smart. I've papered my bedroom and I did it all by myself. Yes, I saw it. And I knew you hung the paper yourself. How did you know? Well, a bumblebee generally sits on the rose. The rose doesn't sit on the bumblebee. Well, we all make mistakes. Gee, your living room is beautiful. And I see you have new pictures. Uh, is that general Grant? That's my mother in a blue hat.  Oh, gee, I'd better close this door. I didn't see that gentleman sitting in the corner without a shirt on. Any relation? That's a Chinese Buddha. Well, I'm so glad that you're telling me to what I owe the honor of this visit. Oh, certainly, Mrs. Clyde. I'm going to have to be a little personal with you. Well, go on out with it. Well, now let me see. What was it I was to remember? Mrs. Clyde is a lace-headed woman who would like to put a point in her husband's chest. No, no, no, that wasn't it. Oh, I remember.  I beg your pardon? No, no, that's not it. Why can't I remember things? Well, this next thing is very important. Now, was it, um... When Mr. Clyde takes a model to his house for old fashioned, that is trade, and his wife should get lost. No, no, no, it doesn't go like that. Oh, Mrs. Clyde? Yes? I don't... And if Mr. Clyde trades you in, he won't lose a thing. I didn't mean it like that. I was just using somebody else's word. But I'd like to tell you what I feel in my heart. Thank you, Mrs. Peterson. But I must say you're intruding on something that's very personal and of no concern to you. But I... I don't see why we can't speak as woman to woman. After all, I... I have a man here. His name is Joanne. He's a gentleman from head to tail. But I told... I've met the man. You needn't have corrected yourself. Now, if you'll excuse me, Mrs. Peterson, I have some things that I'm scared about. Oh, but, but, Mrs. Clyde, you must listen to me. Mr. Clyde loves you. How would you know? Well, a secretary often knows more than the wife. Oh? Oh, indeed. Well, you see, Mr. Clyde talks in his sleep.  Well, don't tell me you eavesdropped. Oh, no, that would be vulgar. I just turn on the dictaphone and go out. Mrs. Peterson, if you don't mind... No, no, you must hear me because I know what's wrong with your marriage. Something is missing. You have no children, nothing to link you and Mr. Clyde together. So? So I want you to think of me as your daughter, the missing link. Much if it, but I'll try. Now, if you'll please go, I'd be very much obliged. All right, I'll go, but I'm... I'm very sad because I know what's going to happen. What's going to happen? Well, you and Mr. Clyde will separate, and then some man will come and steal you away. What about it? Well, then it will be too late for Mr. Clyde to do anything because there's no point in closing the barn door after the horse has been stolen. And now a word from Tony Gilden. May I tell you about a new cream deodorant that actually vanishes when you rub it on your skin? You rub it in, you rub odor out. You rub it in, you rub perspiration out. It's the new arid with non-staining chlorophyll. Just try this amazing test.  Now take arid with chlorophyll and rub into the same spot. When the light green color vanishes, all odor is gone. And that's exactly what happens to perspiration odor and perspiration, too, when you use arid with chlorophyll daily. No other deodorant can give you arid's exclusive rubbed-in protection. Arid has a vanishing cream texture, which gives you one and a half times the protection of any leading deodorant. Safe for normal skin and fabrics, non-staining, washable. Don't be half-safe. Be completely safe. Rub in arid with chlorophyll to be sure. Only 43 cents per pack. Milton J. Clyde, attorney-at-law. Hello? Yes, Martha? No. No, your attorney hasn't spoken to me yet.  What?  Oh, here she is now. I'll talk to you later. Oh, uh, who was that on the phone, Mr. Clyde? A pointy-headed woman that you said I was trading in for a new model. Sorry about that. I got all mixed up. Has she changed her mind? Changed her mind? Her attorney's on her way over here to discuss a separate maintenance. You mean like alimony? Yes, it's something like alimony. Oh gee, that's too bad. Mrs. O'Lily always says that alimony is like laying a wreath on the grave of a departing soul. Not Mrs. Clyde, I know her. She won't be satisfied with a wreath. She'll want the whole flower shop. Look, when her attorney gets here, will you help me out? How? Mrs. Clyde is claiming I'm a spendthrift, so I want you to tell her attorney that I'm extremely conservative. Yes, I know. Cheap. You just tell him that I shined my own shoes, bring my lunch to the office, and never spend the nickel on entertainment.  Oh, you couldn't find a more dependable person. Yes, I know. Imagine that wife of mine claiming I'm extravagant, well, I've just arranged a $25,000 trust fund for her she doesn't even know about. Oh, well, what's the difference? Take this box of cigars down the hall to Sam Brooks. His wife just had a baby girl. Do you think she should smoke so soon? Well, I can only remember where she put that dictation. Are you Mr. Milton Jay Clyde? Yes, yes. What can I do for you? My name is Drake. I'm from the Department of Internal Revenue. Oh, fine.  What's on your mind? We're just making a routine checkup on your returns for last year. There's some pretty large deductions that we'd like to have you verify. Well, I'm sure that everything's in order. I'll be glad to cooperate in any way I... excuse me. Hello? Oh, Martha dear, I'm sorry I didn't get a chance to call you back. I was... no. No, your attorney hasn't gotten here yet. What? Tell him to forget the whole thing? You've changed your mind about going through with the divorce? Oh, darling, well, you know I love you. What's that? Do you think the world of me is attractive? Do you think I'm cute? Well, I am a little pudgy. So what? Do you think I'm sweet and adorable? And you found the receipt for the trespart? Oh, Martha darling. Look, why don't you meet me downstairs at Tony's? We'll toast to our reunion and go out to dinner. I'll run right down and order champagne. Goodbye, my angel. Uh, what about me, Mr. Clyde? No, no, haven't got time, son. I just made up with the biggest tax deduction a man ever had. Mrs. Community Property. Goodbye, Secretary. I'll tell you everything you want to know. Just remember, I'm a businessman. I have large expenses. Goodbye. Ms. Peterson, tell this man everything he wants to know. Goodbye. Who, when you're dancing and you're dangerously near me... Well, Miss, are you ready for me now? Oh, yes, we were expecting you, sir. You were? Well, good. Now, we get the general impression of the office that Mr. Clyde is a very extravagant man. Person you can meet. You don't say so. Yeah. Well, there's no point in going through this list. Just give this to Mr. Clyde when he returns. Oh, I will. I think this should clarify matters. You have no idea. Goodbye. Goodbye. Well, it's the, um, $14,000 payable to the government. Gosh, where's Mrs. Clyde going to live in a White House? Who, when you're dancing and... Oh, oh, Mr. Clyde. I forgot my overcoat. Congratulations, Mrs. Peterson. Mrs. Clyde and I are very bahatchy. Isn't that wonderful? Yes, but why does her lawyer want all this money, especially after I told him how cheap you were? Her lawyer? Yes. Let me see that. $14,000.  You didn't tell me. Well, why didn't you ask? But I thought, oh, you must want to shoot me. I bet you want to throw me out of the window. You probably want to murder me. No, but keep talking until you come to something legal. I heard it out, Patras, by proving the expenditures he listed on his income tax returns were authentic. As for Irma, this whole thing has made a profound impression on her. Kate, yes, what is it? After Joe and I get married, there'll never be a divorce in our family. Well, I'm glad to hear that. Yep, I think marriage is a 50-50 proposition. If I do anything wrong, I'll apologize. And if he does anything wrong, I'll ask him to forgive me. This girl hasn't got any divorce problem at all. Why? Well, because most divorces are based on mental cruelty. And there isn't a person in the world who can prove there's anything mental about my friend Irma. Here's a scene that could happen in your doctor's office. A doctor speaks to Mrs. Smith. You're in perfect health, but there's no need for you to take laxatives three and four times a week. No need, doctor? None. Five New York doctors now have proved you can break the laxative habit and regain that wonderful feeling that goes with natural regularity. 83% of the cases tested did it. So can you. I'd love to, doctor, but how? Stop taking whatever you take now. Instead, every night for one week, take two Carter's little liver pills. Second week, one each night. Third week, one every other night. Then, nothing. Every day, drink plenty of liquids. Put yourself on schedule. But how can Carter's help break the laxative habit, doctor? Because Carter's little liver pills not only relieve irregularity, they also improve the flow of liver bile that is needed for natural regularity. When worry, overeating, overwork make you irregular temporarily, take Carter's temporarily, and don't get the laxative habit.  Only 43 cents. Break your laxative habit. Restore your natural powers of regularity. My friend Irma is transcribed and directed by Park Levy. Marie Wilson is starred as Irma with Mary Ship as Kay. Benny Rubin as Professor Kropotkin. Gloria Gordon as Mrs. O'Reilly. Alan Reed as Mr. Clyde. And Hal March as Joe. Also included in the cast for Bonnie Phillips, Virginia Gregg and Luke Rubin. Script was by Park Levy, Stanley Adams and Roland McClain. This is John Heason speaking. My friend Irma has been brought to you by Carter's little liver pills, proved by five New York doctors to improve the flow of liver bile and break the laxative habit. Be sure to tune in next week at the same time to My Friend Irma. This is the CBS Radio Network.