gamma to the D where gamma is strictly less than lambda. Okay, so that's what our first result, which is crucial. And now if we take a correct match, then we know that there is the neighborhood of that correct match in the intersection tree that will be a tree common to the two neighborhoods. And so this tree common to the two neighborhoods is in distribution close to a Galton Watson branching process with Poisson number of springs with parameter lambda times S. That's the, because the intersection graph is another string graph with a parameter average degree lambda times S. So if we pick lambda times S larger than this gamma thing, then we are good because for a correct match, we know that we tend to get a matching weight that is about the lambda S times to the power D. Whereas if we pick two nodes that are far apart, we tend to get matching weight that is gamma to the D for a gamma strictly less than lambda times S. So that's how we carve this little triangle in the phase space. So, okay. So I guess these slides show more or less what I was telling. So we have managed to improve this scheme. So I wanted to describe it because the ideas needed in its analysis, they can be boosted. And so we can construct better schemes. And now we have a better understanding of a large region of the phase space for which polynomial time alignment is feasible. So let me not dwell on the numerical experiments for that scheme. So I'll now discuss more recent results we obtained and where we stand, okay? So I first tell you about some results we obtained with Mark and Luca this year. So remember in the three matching weight algorithm, we have to compare two cases. The case where we have the neighborhoods corresponding to an exact match. So what we tend to get is if we remember the construction of the two graphs, we get two correlated trees and how are they constructed? So you can start from a root node then you sample Poisson of lambda S children in both of them. And then you have an extra number of neighbors you'll get that is going to be Poisson of lambda one minus S, okay? And here as well, independently, okay? And so you have this structure for the two neighborhoods that's when you have a correct match. So and you know how to pursue the construction of the correlated neighborhoods. So eventually you'll have a tree of that will appear in the two neighborhoods that is going to be a Galton Watson branching tree with a spring distribution Poisson of lambda times S, okay? And this gets augmented independently in the two cases. So how is that augmented? So well, each node in the intersection tree gets an additional number of children that is Poisson lambda one minus S independently in the two trees and the new vertices we add, they get a descendants that is a branching process that is Poisson with a parameter lambda. So that's okay. We get a Galton Watson Poisson of lambda here and likewise for all the other nodes. So we know that's the joint distribution of the neighborhoods of two nodes that are an actual match. And so that's one situation. The other situation is two nodes that are far apart in the master graph for which the neighborhoods are independent, okay? And so we have two Poisson lambda branching processes. So what we did in this tree matching weight algorithm, we tried to distinguish between the two situations and we had one statistic to distinguish which was this tree matching weight. Actually we can ask for the best statistic there is to distinguish between these two situations. So this is a hypothesis testing problem in fact that we have to solve. We must distinguish between two hypotheses, whether the two neighborhoods are from this correlated distribution or they are independent branching processes. So once you view it like that, well, you go back to hypothesis testing theory and you have this Neyman-Person lemma from the early 20th century and you know exactly what is the best test that there is, I mean. Just say the Neyman, did this classical result that I should know then? I don't remember this criterion. The Neyman-Person lemma. Yeah, if it's not too wrong. Yeah, yeah, yeah. So Neyman-Person lemma, Neyman-Person lemma is the following thing. So you have, you observe X and under H zero X follows distribution P note under H one X follows distribution P one. Okay, so what you're interested in is you'd like to maximize it. So you construct a test T of X. And when T of X is zero, that means you believe you are under assumption H note. If T of X equals one, you believe you are under assumption H one. And so your test should minimize the errors that you can make. So you have two kinds of errors, of the first kind and of the second kind. So you want to maximize P one that T one of X equals one. So that's the probability of correctly detecting that you are under the alternative hypothesis H one. But okay, if you take it always equals to one, you have something meaningless. So typically you try to do that under a constraint that P zero X equals one is less than some threshold, okay? So to strike a balance between the two types of errors you can make. So Neiman Pearson Lemma tells you that essentially the optimal test is of the form T one of X equals one. If and only if T one of X over P note of X is above some threshold. So that's the actual statement says a bit what you should do when you are exactly at the threshold but essentially this is that. So the best test that there is just considers the likelihood ratio between the two distribution decides for the alternative distribution if the likelihood ratio is above a threshold decides for the null hypothesis H note if you are below this threshold. This threshold is a functional of P zero and P one. You can construct it explicitly. It's a function of this alpha, this trade off parameter that you have chosen. So pick alpha then it will force a value for the threshold. Okay, for a given P one and P zero that you know and given alpha there is a constructive way to get this threshold. Yes, yes. You can look at the cumulative distribution function of the likelihood ratio and the P note and so that will give you how to choose style as a function of alpha. And there are some cases where you have jumps and so you need to randomize where you are at a jump point but that's a detail. Okay, so we know we have this lemma so we know we should not do these three matching way thing. Actually we should face the distribution of these pairs of trees whether independent or whether correlated and do the likelihood ratio computation and then decide whether to put the two nodes as a candidate match or not based on the value of the likelihood ratio. Okay, so I guess that's essentially what it says here. So we'll limit observations of neighborhoods to some depth parameter. We'll take the two neighborhoods if they are tree like, we'll leave aside the neighborhoods where you find loops in your graphs. So if they are tree like, we'll compute the likelihood ratio of the pairs of trees that you get under the two distributions, the distribution of correlated trees and the distribution of independent trees and you'll put the matched pair in your set of candidate matches if this is above a threshold. Okay, so it turns out that this likelihood ratio of the distributions of pairs of trees, you can compute in a recursive manner. And those are branching processes are constructed in a recursive way and you can compute all kinds of quantities of interest on such branching processes in a recursive way. And it is the case here. It's a nice exercise actually that you can compute recursively the likelihood ratio. So that's good for algorithmic purposes because we can implement a test of that kind. We can, the way you would do it is you would start off with depth one and compute likelihood ratios. So you would remember, we'll use dangling trees. So for IJ, then we look at depth one here and then we have UV, we have dangling tree of depth one there. And so we'll compute the likelihood ratio for this pair of trees under the two hypotheses. And then we'll keep increasing the depth and we'll use an induction formula which will allow us to compute the likelihood ratio when we observe at depth D from the likelihood ratios when we observe at depth D minus one. Okay, so it turns out this is a polynomial time scheme but it takes some work to establish it but it is a polynomial time scheme, okay? So let me not dwell on the recursive formula for the likelihood ratio. We just need to know it can be computed. And so, okay, so once we have this angle of attack in mind for this problem of aligning trees we can do some analysis. So I'll not give you many details, all right? I don't know how much time I have, 20 minutes or yeah, okay. So I'll be sketchier and sketchier as I go on. So have I, okay, I went too fast. Okay, so we have one notion that is important for us for analyzing the scheme that we will produce. This is the notion of a one-sided detection. So we have those two hypotheses whether the two trees are correlated or whether they are independent. And we'll say that we have a one-sided detection in this hypothesis testing problem if we have a family of tests indexed by the depth at which we consider our trees such that the probability of correctly guessing the alternative hypothesis when it is true does not go to zero asymptotically as the depth goes to infinity. So we catch some correlated pairs, okay. We don't miss out all the correlated pairs that's what it will mean. But we never wrongly classify as a candidate correlated pairs, some pairs that are not correlated. So the probability under the uncorrelated distribution of deciding that we have something that is uncorrelated goes to one, the depth goes to infinity. So that's a definition. That's a property that we would like to have, okay. And so we can characterize when this holds for this hypothesis testing problem. This holds precisely when the cool back libeler divergence between the distributions of the correlated trees observed to depth D and the uncorrelated trees observed to depth D when this cool back libeler divergence goes to infinity as D goes to infinity, then we have this one-sided detection property. And okay, so in order to progress on our understanding of this phase diagram that I was drawing here, I have this tiny triangle here. We can fill out larger region, any region where we know that we have one-sided detection for this hypothesis testing problem. We know that the algorithm based on computing likelihood ratios using thresholds, et cetera will produce a non-vanishing overlap. Whenever we have one-sided detection. So now the work has been reduced to computing or to controlling the cool back libeler divergence in a hypothesis problem between pairs of trees in these traditions. But why then in the definition of one-sided bounds, you needed the probability to, it's a false positive to be zero because if you, why did you need that? Because if you think of the graph matching problem, we know there are exactly n correct correspondences. So for each node of the n nodes in the first graph, there is only one good match, whereas there are other n wrong matches. So we have other n squared false matches that we need to rule out. And so if we want to produce a non-vanishing overlap, we need a strong control on the number of false positives that we produce. So this is why we crafted this definition. Okay, so now the game is to figure out under what values of lambda and S we have divergence to infinity of the scale divergence as D goes to infinity. So I mean, in the paper I was quoting with Mark and Luca, we came up with a number of sufficient conditions for divergence to infinity of this cool back libeler divergence. So here's one particular, well, this is just a lower bound, but okay, here's one sufficient condition for divergence. There's I guess nothing for you to glean from the formula, but it's just one that can be shown reasonably quickly based on the recursive expression for the likelihood ratios. And so using such arguments, we know that this triangle was a pessimistic region, you can enlarge it. And so we know that there is actually a larger portion. But so the, okay, maybe I'll jump to what we know now. Okay, so recently we started collaborating with Gillem-Semergent on this problem who did amazing computations. And so now we have a much better understanding of when this correlation tree-based correlation detection in trees approach succeeds, okay? And so, okay, okay. I think I should not try to say too much about the, well, okay, let me try. So I've skipped many details. There are several ways in which you can describe those trees. So we are dealing with rooted trees. There's one way which is quite natural, which is to assume you label in some order the children of each node. So this is a representation in terms of labeled trees, okay? And I did not mention it, but this is how we approach the problem initially. And so when we observe the neighborhoods of nodes in graphs, there's no intrinsic notion of an order of the children or of the neighbors. So what we do is we assume we label them uniformly at random. So we worked on that. And so the expressions I wrote for the likelihood ratio were based on this representation, okay? So that got us that far, but actually we are dealing with unlabeled trees, okay? So rooted trees that are labeled, but changing the labels would make them identical, they are isomorphic, and we are dealing with classes in this equivalence relation. So we are dealing with unlabeled rooted trees. And so what we wanted to understand in particular is how does this region behave as lambda becomes large? And if I look at neighborhoods to depth one, so I have one node here. I have here Poisson of lambda s, that is a common number of nodes in the two rows. And then I add Poisson of lambda one minus. Okay, so when lambda becomes large, I can subtract, so a tree to depth one is just a number. It's a number of children, okay? So I can subtract its average, I can rescale it. And when lambda becomes large, I know that this properly rescale will admit a Gaussian limit, okay? That's just the central limit theorem. And I know that under the correlated model, after proper centering and rescaling, instead of having two independent Gaussians, I'll have two correlated Gaussians. The parameter s will show up in the correlation of the two Gaussian random variables. And so what we did with Gilem is push this idea of their existing Gaussian limit to arbitrary depth D, and which allowed us to understand exactly how this region behaves as lambda is large. And so, well, to get a Gaussian limit, you want to apply centering and rescaling. So you'd better be in a vector space to rescale things, subtract things. So it will be helpful. It turns out that unlabeled trees, they can be seen as objects in a vector space. So for instance, unlabeled root tree of depth D, you can view that as a counting measure of unlabeled rooted tree of depth at most D minus one. So, you know, you have the space of depth D minus one. Each of the children of your root, which has as its downstream tree of depth at most D minus one, then particular tree, you put a Dirac mass for the corresponding object. You do that for all the children. And so that's an equivalent way to consider unlabeled rooted trees. So we are in a vector space, okay, measures. We can add measures, we can multiply measures. And so that's actually the right way to consider this hypothesis testing problem. And using this, we can actually show that for our joint distribution of trees, if we let lambda go to infinity, there is a Gaussian limit. We can, it's a, it's a delicate operation, but we can center and rescale the measures that stem from those unlabeled trees. And we get limiting objects that have a Gaussian distribution in an infinite dimensional space, but vector space. And we can also compute the KL divergence for the limit, the Gaussian limit. And we can also show some continuity that as lambda goes to infinity, the KL divergence we are interested in will converge to the KL divergence in the Gaussian limit for which we have an expression. So putting all these together, we get, okay, what have I, all right, so, okay. So maybe let me stick to the slides. So what do we know about the, limiting Gaussian objects? Okay, so the KL divergence for the limiting Gaussian objects diverges to infinity as the depth goes to infinity. If S, the correlation parameter, is larger than the square root of a constant alpha that is known as the Otter constant. That's 19th century in mathematics. Otter worked on combinatorics of counting the number of trees rooted trees unlabeled with a given number of nodes. And so this is a number which grows exponentially with the number of nodes and the exponent, well, the generating function has a radius of convergence that is this Otter constant alpha. So that's, we know that for S larger than square root alpha that is larger than 0.582, the KL divergence in the Gaussian limit blows up, whereas it stays bounded if S is smaller than a square root alpha. So eventually what we know today is the following. We know that the region in which this approach produces in polynomial time a partial alignment, probably so, is a region which as lambda goes to infinity is asymptotic to square root of alpha. So we know exactly the boundary of this domain for large lambda. And we know that this region lies above the line at square root alpha, okay? So for lambda large, we know reasonably well what goes on at square root of alpha. We know reasonably well what goes on. We don't have an exact characterization of the boundary for any finite lambda, but asymptotically, we know where it lies. Okay, so that's where we stand. So and in between, you know that it has to stay above the square root alpha because? Because we know that the KL divergence in the original model converges to the KL divergence in the Gaussian model, but we know it is bounded by a quantity that stems from the Gaussian model. And this quantity does not diverge if we are below. So we know the KL divergence in our original model can never blow up as D goes to infinity if we are below this line. Okay. All right, so conclusions. Okay, maybe you have to catch a bus, right? Okay. We took the time enough so that... Okay, okay. So take the time to conclude. So as for information theoretic feasibility, as I said, we believe that the true condition is lambda s larger than one, but it is still open. So if you are interested, you can try and improve the result of Su, Wu and Yu from lambda s larger than four to lambda s larger than one. So that's an open question. Okay. We are trying to understand even better this region where this algorithm I described based on likelihood ratios succeeds. But we have now a good understanding and this Gaussian limits that I mentioned are really a good way to learn more about this, but okay, we are trying to improve our understanding of what happens for finite lambda. You conjecture that your algorithm is optimal in this intermediate region? So yes, I guess that's my third point. We did conjecture that when it would fail, it would not be polynomial time feasible to achieve partial alignment, but we don't have a strong argument for that. So this is a gut feeling or something like that. But that's completely open, showing that no polynomial time algorithm can succeed in a region. This is, okay, we will never or we can't do that in general, what could be done though is to show that if you limit yourself to a family of algorithms, say you have those low degree polynomials that you can construct from the observations, if you limit yourself to a family of estimators, maybe they are not powerful enough in some region. So that that would be, I guess, when we're to approach that showing that below this square root alpha line, and no algorithm of bounded polynomial degree can succeed. Okay, something like that. But this is not done at all, this is totally open. Okay, and so, right, so there are open questions as well for the graph clustering in understanding this hard region in showing somehow that a whole class of algorithms will not succeed in the hard region. This is something I think that is quite interesting and that will improve our understanding of what these hard regions are. And, okay, so as a general conclusion, I'll just say that statistical physics brings a rich perspective on computational complexity. I mean, these hard regions, hard phases, this is very intriguing, but this is something I think we have tools to progress on. So better understand, and this is exciting. Okay. We have time some question, no stress. I can't believe that we're actually such in time. You use the recursive solution for the generative regular pair of trees to obtain the likelihood parameter L. So is there any other solution to solve this problem, to achieve the likelihood parameter L or not? You mean to compute this likelihood ratio? Yes, except recursive solution. It has a lot of structure, so we could produce several formulas for it, but I think in terms of algorithms, the recursive formula is the one that is the most practical. Or if we consider non-generative trees, is it possible to use the recursive solution again or not we have to switch off? So the algorithm can be implemented no matter what.  So that's not the two trees, there's a value for the likelihood ratio, no matter whether they are sampled from a distribution or another. So that's always doable to implement the algorithm. The guarantees we can prove are going to be limited to the cases where the trees are sampled from these, well, the graphs are sampled from these correlated data. But it is not possible to use the recursive solution for non-regular trees. Oh, typically they are not regular, okay? These Galton-Watson branching trees, each time you have a node, you sample at random the number of children and you use Poisson distributions for that. So these are not regular trees at all. Yeah, the number of children does vary from node to node. Thank you. There's a question. Can you speak a little bit about the practical use of these results in the social networks? Like if you manage a social network, what can you do to avoid people making these graph alignments? And so what would you do if you find out that you can de-anonymize, say, Twitter or? You try to align the graphs and what if you try to prevent that from happening? The reverse problem. Well, yes, okay. So you could say how many fake friends do you need to make in the anonymous network? So you want to be below the green region and maybe we can tell you, okay, here are the parameters, here are the numbers of fake edges you need to create so that that could be a way, I guess, to exploit those results. I can also comment on the algorithms that have been used typically in order to de-anonymize social network data. They typically start from what they call encore nodes. So if you know that a guy in that network has this identity in that other one, you have a correct match granted. And so you are in a better situation to de-anonymize. So I've discussed the case where you don't have those encore nodes, but in practice, the successful de-anonymizations have always been based on those encore nodes. So the real-life situation is more complex. Okay. Okay. I think it's time to thank the organizer. Yes. Thank you very much. Thank you very much. And thanks for, thanks to Vianne, Parché and Sondrin Péché who unfortunately could not be here, but they helped greatly on many aspects, including financially. So thanks to them. Also, I mean, ICTP staff, I didn't mention them, but really they did most of the jobs. So, but I mean, I had personally a lot of fun and a lot of pleasure this week. I really miss that. I don't know about you, but I mean, you forget during these two years that having these kinds of events really changes many things. So thanks for being there and making it happening. Also, I mean, I got tons of new, too many new ideas of new projects. Thanks to these great courses. I hope this is the same for you. And so you are always welcome to ICTP to come back. Events are taking place all the time. And I can advertise, for example, the youth in high dimensions, which is a conference I organized with three other friends, which is concerned with a generic, with many fields related in some way or another to high dimensional statistics that goes from statistical mechanics to computer science to mathematics to neuroscience. It's very broad. We give a main need of floor to young researchers, PhD students, postdocs and young faculties. It's a very nice events until now it was online because of, you know what? And it's now starting to take place in a hybrid mode, exactly like this. It's a bit bigger, the size, it will take place in June. But I mean, keep it in mind for the next years because we will make it a yearly event. So that's one occasion for you to come back here. I hope there will be many others and so we keep in touch. Thank you very much.


So, welcome to this course on mechanisms and organic reactions. I would be your instructor for this course. My name is Professor Nandita Madhavan. I am from IIT Bombay. You can find more about me on the course webpage and also on my department webpage. So, my interest is in general in organic synthesis and in this course we would be looking at a large number of organic reactions. So, when you think of organic reactions, typically these are reactions involving chemistry of carbon compounds. So, if I give you a very simple reaction, any organic reaction, so what you would see is this is a very simple substitution reaction and you might have seen this in your 12 standard textbooks. So, if I have say an alkyl chloride and I react it with a hydroxide ion, I end up getting an alcohol. Correct. So, you might have seen this in your 12 standard textbooks. So, now what I want to ask you is for this particular reaction or for that matter any other reaction that you have seen, what do you understand by the term reaction mechanism? So, what I would like you to do is you can pause the video for a bit, take out a sheet of paper and write something which comes in your mind when you think of the term reaction mechanism. So, you can go ahead and do that exercise. So, when I do the same exercise in my classes, some of the responses that I get are a reaction mechanism is something which describes the pathway of a reaction, it also tells you how the reaction takes place. Now to give you a little bit more detail into definitions, one can define a reaction mechanism as actual changes undergone by reacting molecules to reach the product state or sometimes people talk about chemical steps necessary for one molecule to be transformed to another. So, essentially if you are thinking of going from say destination A to destination B, you can even think of travelling by road to one destination to another. Reaction mechanism essentially is something similar where your two destinations are your reactant and your product and the road essentially is your reaction mechanism. Now having said this, I want you to think about one more question. Now that I know a reaction, is it possible for me to say with 100 percent confidence that this is the only mechanism for that reaction? So this is another question where I want you to think about it for like 30 seconds. Now what you would see is, one can propose what you would call a most probable mechanism but it is not definitely possible to say with 100 percent confidence that this is the only mechanism for the reaction. Again just like I told you for the earlier example of going from destination A to B, you can take one road to reach from A to B but that might not be the only road. You might have different roads which take you from A to B. So you can say with 100 percent confidence that this might be the fastest road to reach from A to B but what you cannot say with 100 percent confidence is this is the only road to reach from A to B. So now what we will be doing in this course is we would figure out ways for you to propose a reasonable mechanism for a given organic reaction and how you would check whether this mechanism works by designing experiments. Now again if I give you the example of going from destination A to destination B. Suppose there are two of you, you and your friend and you have this discussion, you say that to reach from destination A to B the quickest way is to take a bus especially if you want to reach at 5 p.m. So now let us assume your friend says no, no, no the quickest way to reach from destination A to B is a train again at 5 p.m because as you know traffic conditions vary. Now how will you both check who is correct, the best way to do that would be at 5 p.m. one of you goes by the bus and the other person goes by the train.  If you want to check whether the mechanism you are proposing is correct, what you would need to do is design experiments which tell you which would be a reasonable mechanism. Now once you do the experiment what would you check? Does this match the hypothesis? So in the example I had given earlier you would check who would reach faster you or your friend who took the bus or the train. Now if you find that your hypothesis matches the experiment then you can say this is the most probable mechanism. So in your case whoever reaches faster their hypothesis was correct alright. Now if it does not match what you would do is you would again go back propose a new reaction mechanism and again check the hypothesis with experiments. So that is how this goes, so this is a continuous cycle you start with a reaction mechanism you check the hypothesis if it works great if it does not work you keep repeating this cycle until you get a good mechanism. Now for this to work in the first place you need to be sure that you are able to A propose a reasonable mechanism and B design experiments to figure out if this mechanism is correct. So the learning outcomes for this course is by the end of this course you should be able to propose or write a mechanism for a given organic reaction. So we would be giving you tools to help you write a reasonable mechanism for a given organic reaction and the other thing is you should be able to design at least some basic experiments to determine whether your reaction mechanism is correct or not. So with this let us start into what we were telling earlier how you would be able to propose a reasonable mechanism and check the hypothesis with the experiment. So the first part is proposing a reasonable mechanism. So now if I were to broadly classify organic reactions so what you see here on this slide is that I have used a very very basic classification of reactions it is not overly complicated and you will also not see many structures here. So one type of mechanism is a polar mechanism. So now in a polar mechanism just like the name suggests you have two intermediates which are charged so one would be positively charged and the other would be negatively charged and they would come together to give your product. The second one is a radical mechanism. So now in the radical mechanism you do not have charged intermediates what you have is radicals which would come together to give you your product and the third one which is concerted reactions in these reactions all the bonding changes occur at the same time. So essentially there are no intermediates involved in these reactions. So what we will be doing is we would be looking at each of these mechanisms a little bit in detail so that you have a general picture of how these reactions work. So coming to the first one which is a polar reaction. So polar reaction is one where a negative region of one molecule reacts with a positive region of another molecule. So essentially you have charged intermediates. You can have a positively charged intermediate reacting with a negatively charged intermediates. So many textbooks you will see terms like nucleophile, electrophile, Lewis base, Lewis acid, donor, acceptor. Essentially what all that means is you have some electron rich species and some electron deficient species. So since we are talking about organic reactions which essentially involve carbon if I were to look at carbon and another species now if X right now if X is carbon so if you are thinking of C, C what you see is both of these atoms would take the electrons of the bond in a similar fashion to each other. So now if you have two atoms CX where X has a greater tendency to pull electrons to itself now what will happen is X will end up having a small electron density over itself and carbon will have less electron density with itself. So even with a neutral molecule what you end up generating is a small positive charge and a small negative charge alright which is very essential for polar reactions. So what we need to look at is what are ways in which there is this kind of a charge build up in organic molecules. So there are three effects which you would have come across even in your 12 standard books they are inductive effect, resonance effect and hyper conjugation. So when you talk about inductive effect it is essentially the phenomenon of withdrawing electrons through sigma bonds and here comes a very important concept of electronegativity. So I have shown you in the previous slide where you can have essentially so you can have this right. So now if X is an electronegative atom what electronegative means is that X has a greater tendency to pull electrons towards itself from this bond that I have drawn here. So as it pulls electrons what you end up getting is you end up getting a delta negative or a small negative charge and a delta positive which is a small positive charge on the carbon alright. So it is essentially imagine if you have two friends standing next to each other and you have a bag of chocolates the stronger one would end up pulling it pulling more of the chocolates towards themselves. So similarly here instead of chocolates we are talking about electrons. So if X is more electronegative it will tend to grab more electrons towards itself and as you know electrons are negatively charged hence you get a delta minus. Now so that you can compare like two friends I said one is stronger to compare which is more electronegative there is a scale called as Pauling scale and what Pauling scale does is it ranks atoms based on their electronegativity. So shown here is I have just shown you a few atoms you can look at it in any textbook you would get the Pauling scale for all atoms and as the number goes up the electronegativity increases. So as you must have studied in your 12th the most electronegative atom here is your fluorine. So it has the greatest electronegativity value of 4 on the Pauling scale. Now related to fluorine if I were to compare carbon has a lower electronegativity of 2.5 correct? Now hydrogen has now a lower electronegativity of 2.1. So if you imagine a bond which has a carbon attached to a fluorine or a chloride for that matter what would happen is because this is more electronegative you would see essentially a situation like this where you have delta minus on Cl and delta plus on carbon. Now it is not important for you to actually remember all these numbers but what is very important for you just like the two friends I told you about you need to remember which is more electronegative. So what is more important is understanding the relative electronegativity and this is something which you must have studied in 12th along the periodic table as you go down the row the electronegativity increases which is why fluorine is the most electronegative atom there. So as you go there electronegativity increases similarly as you go down the group electronegativity decreases which is why chlorine is less electronegative as compared to fluorine. So one thing you need to remember is when you talk about inductive effect it is only the pulling of electrons through sigma bond. So it has to be through a bond alright not in space. Now having this concept in mind let us try to do a sort of game or an exercise together and I will help you out with this. Now I have shown you a table here and this concept is called as group electronegativity. So instead of one atom what we think is suppose we have again I will try to draw it out to you so that it makes sense to you suppose we have carbon alright and we have this group attached to it whatever I have shown you here alright I am just calling it GR for group. So as I change the group how does the electronegativity change and as I said relative values are very important. So I have given you the value for methyl. So for methyl the value is 2.3. So now what I want you to do is as you can see I have given you a list of groups on this table you can press the pause button on your video and take out a sheet of paper and then try to figure out as you see in these groups for example here I have CH2Cl, CHCl2 and CF3 alright. Let us first look at these three and then I want you to figure out how the relative electronegativity would be. And I will give you some time to work this out or you can take your own time by just pressing the pause button on your video. So now let us see if your answer matches with what we have here you need not have the correct answer exactly. So what I want you to understand is as I go down here what is happening is that the electronegativity is increasing right and I want you to now think about if for those of you who did not get the correct answer for this I want you to again look at this trend and try to again think why could this be a trend. Now to give you a hint as I am increasing as I am going down this table the number of halogen atoms is increasing. So here I have 1Cl here I have 2Cl and here I have 3 Fluorines alright so this is a hint I am giving to you. Now let us look at the next group. The next group has phenyl right and alkene and an alkyne all of these are now attached to the carbon and we are trying to figure out the relative electronegativity of these groups again you can press the pause button and try to work this out. So let us check our answers so what you would see is compared to methyl and even to the alkyl fluorides what you see is if you compare CH2Cl with the phenyl what you see is the phenyl is more electronegative and what you would see is both of these are almost equal whereas if I have a C triple bond C the electronegativity again increases alright so these two are almost equal and what you notice now is in the last set where I have NH3 plus NO2 and OH so this is the last set what you would see is here you have the maximum electronegativity values. Now why is this so so what I would like you to do is look carefully at these trends and try to understand it yourself before I explain it to you because that would be more effective for you alright so what I would like you to do is I would like you to see and understand the trends that are given here alright and the hint I am trying to give you is that remember we are only talking about withdrawing electrons through sigma bonds alright. So now to understand these trends now that you have had some time to think about it what you see is when you go to phenyl and the alkene both of these are sp2 hybridized so these are both sp2 hybridized as you see the percent S character increases that means the nucleus has a greater tendency to grab the electrons because the percent S character has increased which is why it is more electronegative remember the stronger friend so in this case the nucleus percentage is increasing the S I am sorry the S character is increasing in the nucleus so it can grab electrons. So the biggest effect you can see is now when I have an sp hybridization the electronegativity goes up. Now in all these cases where I have NH3 NO2 OH a common mistake which students do and I see this even in my classroom is that they confuse this with another effect where the lone pairs actually play a role but in this case as I told you again we are only talking about the effect through the sigma bond. So here what would only look at is the electronegativity difference so nitrogen and oxygen are more electronegative than carbon which is why they have a greater value of electronegativity of 3.8 and 3.4 of course in this case the value is very high because you are talking about a charge species. So now that we have some idea of the inductive effect another effect now in this effect the lone pairs play a very important role this effect is called as resonance effect. So resonance effect is where you have multiple Lewis structures for the same compound and you must have seen this again in your books so what you must have seen would be benzene. So if you have benzene you would have seen an arrow like this shown to depict resonance and these would be the two resonance structures of benzene and the actual structure is actually shown as the hybrid of both the resonance structures. So the actual structure is the hybrid of both the resonance structures and in some books the actual structure is shown as a circle to show that all these electrons are moving along these are very useful for conjugated systems. So conjugated systems means systems for example where I have say a positive charge here so resonance structure for this would be also it involves p orbitals so lot of times what you would see is you would have structures so this is the structure of an intermediate a resonance structure of that would be now do you actually need to memorize all these structures to be able to write multiple Lewis structures no these are very logical and you just need to remember how to show movement of electrons right. So one way or the convention to show movement of electrons is what is called as arrow or electron pushing this depicts movements of electrons or electron pairs so how do you show the movement of electrons this is very useful in writing multiple Lewis structures in a very systematic way. So the arrow pushing or electron pushing depicts movement of electrons in a way such that you go from an electron rich species which is your source add to the sink which is electron poor just like it suggests source means it has lot of electrons sink means it is very poor and you show it by a double headed arrow so double headed arrow indicates you have two electrons moving so now if I were to look at the structures that I showed you before if I have so here it is very clear what your source is it is these pi electrons so you start by drawing an arrow from the source to your sink so now that these electrons move this carbon becomes electron deficient so what you end up getting is you end up forming a new double bond and a positive charge here make sure you draw the direction as I have shown you here otherwise it would be incorrect you can also think of the earlier structure which I showed you CH2 minus so here this would be your source so the source will come here now carbon cannot have so many electrons so it will push the electrons onto oxygen so your resonance structure would be alright so you can try practicing this arrow pushing picking up any examples from textbooks where they show you multiple resonance structures just remember that there are some rules that you need to remember only electrons move around when you look at the new structures the nuclei have to be in the same position so similar to the example that I had given you earlier suppose I take and then I write another structure now what has happened is the hydrogen has moved here so these two are not resonance structures so be very careful when you write resonance structures also remember that the net charge of the structures remains same right so in the previous example what we had seen is the only difference was that a negative charge had moved from a carbon to an oxygen but the net charge will remain same which is logical because only electrons are moving so if you write a resonance structure for a neutral molecule if you have a resonance structure which shows some sort of charge then you know that you have made some mistake in drawing the Lewis structure the other thing you need to remember is some structures are more favorable and contribute more for example if I have so now I can write resonance structures where alright I can also write a resonance structure where I have that would be if I were to push electrons where I am pushing in the reverse direction now out of these three structures so I have structure one structure two structure three this would be the most stable because there isn't much charge separation now between these two this structure would be more favorable because you have a negative charge on an electronegative atom whereas here you have a positive charge on an electronegative atom so it will be a very minor contributor alright the other thing is resonance involves delocalization or sharing of electrons as you see in all these cases it's either pi bonds or lone pair of electrons which move so all the atoms must be in one plane and this is an example which you would have seen in your textbooks where if you have a molecule like this because of sterics this molecule is not planar so no delocalization alright and of course whenever you write all these structures you have to ensure that you remember the octet rule for example if I were to write the structure so if I were to write the resonance structure of this one plausible resonance structure could be again because we are moving from this center I generate a positive charge here now I cannot push any more electrons on to nitrogen because I would be violating the octet rule alright so these are the rules for resonance and as I said some structures contribute more than the other so before we stop this lecture what I would like you to do is I would like you to do this as a mini homework where you try to draw plausible resonance structures for the three molecules that you see on the screen and what you should figure out is which resonance structure will contribute more for each of these molecules so remember the rules of resonance which I showed you in the earlier slide and use the concept of arrow pushing to clearly show each of the resonance structures you can if you have any doubts you can take this up in the discussion forum but initially I would like each of you to spend the effort yourself in trying to write all possible resonance structures for the following molecules and find out which resonance structures will contribute more so thank you and we will see you in the next lecture where we will look at answers to this problem


Byddwn yn fwy o'r gwirionedd o'r sefydliadau sydd yn ymddangos, ond mynd i chi'n meddwl i'ch gwirionedd fel gwaith bod nifrwys. Felly mae'n cael ei gwaith o'r fawr ac yn ddod. Fel hynny'n gwybod, mae'n gwybod i'n gwybod i'n gwybod i'r byw sydd yn ddod i'r gweithio Michael Matheson o'r cyffredinol. Mae'r gweithio yng nghymru yn ei gweithio o'r gweithio. Mae hi'n mynd i gweithio ddod i'r gweithio o'r gweithio o'r gweithio, I'll just give a few moments for the front-benchers to resume their seats. I now call on Michael Matheson, cabinet secretary. Ten minutes. I welcome this early opportunity to update Parliament following the publication today of the report on police call handling that I directed HMICS to undertake three months ago. I want to start once again at offering sincere condolences to the families of John Ewing and Lamara Bell for the tragic loss that they have suffered. I have previously highlighted in my belief that the foundations of policing are strong. This is reinforced by the latest statistics that show that recorded crime is at a 41-year low, supported by 1,000 extra officers that this Government has delivered. Of course, the credit goes to the hardworking officers and staff across Scotland who regularly put themselves into situations that many of us would not. However, there is more to be done, which is why the programme for government set out a series of measures to strengthen policing. In September, I held a summit to support the further development of local scrutiny and over 80 stakeholders attended. The chair of the Scottish Police Authority has already begun his review of police governance, and that is on track to report in March 2016. We will shortly embark on a refresh of the strategic police priorities, giving communities the chance to have their say. The process to appoint a new chief constable is also well advanced, and the chair of the Scottish Police Authority has set out a clear expectation that the new chief will put a strong focus on addressing issues highlighted in the recent staff survey. I want to spend my time today focusing on the HMICS report that was published this morning, and I thank Her Majesty's Inspector Derek Penman and his staff for their work. This comprehensive piece of work has involved more engagement than any previous HMICS review. It includes a public online questionnaire, an audit of calls and more than 85 interviews and 34 group discussions with police officers and staff. Police Scotland Contact, Command and Control centres manage 500,999 calls and 3.24 million 101 calls per year. The HMICS report provides a number of welcome assurances. Staff levels are now stabilised at Bill St Glenn, Motherwell and Govern, and staff are committed to providing a good service to the public. The grading, prioritisation and dispatch of officers works well for emergency and high priority calls. Risk and vulnerability assessment is strong within the area control environment. New training is now in place for all new staff and the interim ICT solution in place are fit for purpose. The report contains 30 recommendations and Police Scotland has assured me that they will implement them all. The report confirms that significant progress has already been made but gives a clear direction to the SPA and Police Scotland where further improvements are needed. Those include in governance and programme management, staff communication and training, technology and in quality assurance. I will deal with each of them in turn. Firstly, the report contains a series of criticisms of programme management and governance in place around the restructure programme. Well performance is now stabilised. It is essential that those issues are addressed before the remaining phases of the change programme are progressed. I have discussed this with Andrew Flanagan, the chair of the SPA and Police Scotland. They have confirmed that independent experts will be brought in to provide strong assurance before any decision is considered regarding the implementation of proposed changes to Aberdeen, Dundee and Inverness centres. Police Scotland will establish a reference group of senior independent change and call handling professionals who will provide on-going oversight and advice as the restructuring process progresses. The report also highlights concerns about how staff expertise was captured in designing the change. It also echoes findings from the Police Scotland staff survey around communication and engagement. I have made clear to Police Scotland my expectations around that recommendation and my strong conviction that investment in staff is as important, if not more important than investment in systems. To address that, Police Scotland has confirmed that it will establish a programme dedicated to shaping the future of C3 and that will support clear and transparent engagement with all affected staff from here on. I am also encouraged that Police Scotland has now put in place a training programme for all new entrants that will improve consistency across the country. Moving on to technology, the report concludes that the interim solution is generally fit for purpose but poor reliability and the ability to bypass certain aspects of the system is a risk. Police Scotland plans to invest £15 million in a new IT solution, which will be a major step forward and which I am assured will be subject to the stronger programme management approach now in place. I have also been assured that Police Scotland has already put new processes in place to monitor compliance with procedures. Ensuring strong quality assurance is the final theme that I wish to touch upon. The SPA has continued since April to monitor performance on a weekly basis. In future, any dip in performance such as experienced in Bilstein Glen earlier this year will become quickly apparent and will trigger rapid intervention. The report confirms that a regional approach to call handling can deliver an effective service for communities across Scotland. The overall direction of the programme therefore remains fit for purpose, but the management of the change programme must be strengthened. In welcoming the assurances provided by the HMICS report on the quality of customer service called handling and grading, I want to make sure that the standards are maintained and the improvements being implemented by Police Scotland deliver the required improvements. I therefore asked the HMICS to undertake a further programme of unannounced visits to call centres across the country. That will begin with immediate effect and will be on-going until the restructuring is complete. I have requested that the outcome of those visits is reported back to Police Scotland, the SPA and to myself, clearly identifying any actions that need to be addressed. The report recognises that the Scottish Government acted swiftly on the recommendation in the interim report by making £1.4 million of new money available. That has already supported an active recruitment campaign in the north, which has attracted a significant level of interest. New money is also being used to deliver improved system reliability. I want to close by stressing once again this Government's commitment to ensuring that the public can have confidence in police, contact, command and control functions. That is why I directed the HMICS to undertake a review and why I have sought at the earliest opportunity to update Parliament on its final report. The report includes some hard messages for Police Scotland, and I have been assured that all 30 of the recommendations will be accepted and actioned by them. The report provides confidence that staffing levels have stabilised in the east and west and calls are being answered and actioned. The new training is in place for all new staff and recruitment to support the next stages of restructure in the north is actively under way. HMICS has provided assurance around the ability of a regional model and both the SPA and Police Scotland to ensure independent checks are in place to monitor contact, command and control from here on and oversee the next stages of the restructure. As I said in September, there are challenges, but the fundamentals of our police service are sound. The actions that I have set out today will build on those fundamentals to deliver a stronger service. Be assured, Presiding Officer, that this Government will continue to work tirelessly to strengthen policing in Scotland even further. The cabinet secretary will now take questions on issues raised in his statement. I intend to allow around 20 minutes for questions after which we move to next site of business. It would be helpful if members wished to ask a question where to press a request-to-speak button now. The minister has already expressed his condolences to the families of John Mule and Lamarra Bell. I know that that is shared by all of us across the chamber. I am advised that the case is now a live investigation and I will therefore take no other references to the particular circumstances of the tragic case. Questions should therefore relate to the report on police call handling and the minister's statement. I am grateful to the cabinet secretary for sight of the statement prior to this session. Even in the language of management speak and acronyms, the HMIC report is damning. The report refers to weaknesses on 20 occasions. Two years since Police Scotland was formed, we are still seeing systemic failures in the important aspects of policing. The report boasts of savings of £1.8 million on policing while submitting the force had to spend an additional £1.4 million on overtime. This is a massive failure in strategic management. The report uses the word assurance on 103 occasions but we have heard so many assurances on policing that have come to nothing. The litany of failures listed in the report are extraordinary. IT systems offering only basic functionality with questionable stability. A lack of resources for front-line staff, weak local management, inadequate oversight of call centre personalisation, the narrow approach to the scrutiny of major projects by SPA and Police Scotland, no framework to measure stated benefits, key staff on the project board lacking experience in training, a lack of staff and those who are there reporting low morale. 41 per cent of officers and civilian staff responded to the HMIC survey and spoke negatively about the 101 service. We need so many improvements. On 12 July this year, the cabinet secretary blamed the M9 tragedy on an individual failure, rather than a lack of resources. We now know that this is completely false. Mr Pearson, can we just get to the question? Will he now apologise to the Bell and Yule families? Cabinet Secretary, would you like to address the other points of Mr Pearson's statement? Mr Pearson made reference to a number of points within the report. The important issue is that the very reason for directing HMICS to undertake this review was in order to provide us with assurance of the process that Police Scotland had in place in managing the change around the call centres. The 30 recommendations that are now set out in the report are absolutely key. We will wait until the minister finishes his section then. I will take your point of order, Mr Findlay. They are absolutely key to making sure that the lessons from the management of this particular area of the restructure are learned and that these mistakes are not made again. What I think is now important is that Police Scotland implements every aspect of the recommendations that are set out by HMICS. In order to make sure that that has been taken forward, is that there are no further steps within the reform programme and the restructuring of the call centres, it is taking place until all of the necessary assurances have been put in place. That will be checked not only by the SPA but also by HMICS before there are any further steps taken forward in this particular area of restructuring. What I am determined to make sure is that they build on the progress that they have made in recent months in improving the situation within their call centres to make sure that the public can have confidence when they contact Police Scotland that their call will be dealt with appropriately and as quickly and effectively as possible. Mr Findlay. Those are very, very important issues that every one of us has constituents speaking to us about. The minister has just had longer to reply to Mr Pearson than Mr Pearson had to ask his question, and he did not have the opportunity to finish it. I would hope that we could be a bit more tolerant in the chamber and allow the lead spokesman for the opposition to have his say in which, after all, are extremely serious matters. Mr Findlay, I am well aware of the seriousness of those matters. Every opposition spokesperson knows how long it is that they are expected to speak, and that is 1 minute 30. The reason I stopped Mr Pearson from going further was that I had only moments before explicitly said that I wanted no references to that particular tragic case because it is a live issue. Now we move on to Margaret Mitchell. Ms Mitchell, 1 minute. Thank the cabinet secretary for early sight of his statement. This is a report full of management speak, which nonetheless reveals a system in chaos summed up by one of the key findings, namely, the current C3 performance framework that lacks detail on quality of service, cost and outcomes. That deficiency has resulted in a huge disconnect between what is happening in practice and what should be happening in theory through what should be stressed, absolutely no fault of the call handlers themselves. The report is peppered with overly optimistic and justifiable comments about improvements already made. My question, therefore, is this. Given that we have heard all those assurances uttered by the cabinet secretary before and restated today, what possible confidence can the general public have that a call handling in Scotland is fit for purpose to ensure that history is not repeated? Cabinet secretary. I know that members may wish to question the way in which Police Scotland has taken forward the remodelling and restructuring of its call handling system. I must say that I am somewhat surprised that a member would seek to attack the inspector of constabulary for producing such a detailed report into this matter. I do not think that that serves in anybody's interests in actually looking at this particular issue in itself. The report highlights a whole range of areas where Police Scotland has not addressed sufficiently how it should have taken forward the change, management and reassurance that was necessary in taking forward this level of change. It also identifies areas where there have been improvements made in how they are dealing with calls. I would have thought that any reasonable member would have welcomed the fact that Police Scotland has improved the way in which we are handling some of those calls. The HMICS report provides us with clear reassurance on how that has been taken forward. What we now need to do is to make sure that in areas where they have identified deficiencies in their management of this change is that they are then taken forward. However, bringing it into question the quality of inspection undertaken by the inspectorate, I do not think that does anybody a service in here. Roderick Campbell, followed by Willie Rennie. Thank you, Presiding Officer. Can the cabinet secretary provide further information on the impact of the additional £1.4 million of funding provided to Police Scotland following the interim report of HMICS? Cabinet secretary. One of the actions that we took at the interim report that was published in September was to provide immediately additional financial support to Police Scotland in order to allow them to take forward the interim recommendation that has been set out by HMICS at that particular point. That supported Police Scotland and was able to accelerate the recruitment of staff in Dundee as well as increasing the number of staff that they have within their virtual service centre in anticipation of the additional workload that will deal with the future change within the system. That has also allowed them to take forward some further work around providing stability around their IT system as well. What I would now expect is for that work to continue to make progress. Alongside that, there has been a recruitment campaign in the north of the country that has attracted significant interest in recruitment within the Dundee area control room. It has also allowed them to provide additional staff within their virtual control room, which are based at both Glasgow, within Government Motherwell and Bilsengline. Willie Rennie, followed by Eileen Murray. It is a shocking indictment of the Scottish Government that it took tragic deaths before the problems at police call centres were taken seriously. There is no acceptance from the minister in his statement that they ignored the warnings, that they paid little heed to the complaints from hard-working staff across the country, that they brushed aside my pleas in this Parliament. That is a powerful report. Does he not regret ordering that inquiry sooner? Will he finally agree to a fuller inquiry into the whole of Police Scotland? Cabinet Secretary. I want to deal with this particular issue that Mr Rennie raised about the point that he raised within Parliament, and given the impression that no action was taken following those particular issues that were raised. I specifically raised those matters with the chief constable and with the deputy chief constable, Rose Fitzpatrick, and also the assistant chief constable, Val Thompson, who all have lead up policy responsibility in this particular area. That resulted in changes in the way in which they were managing the way in which they were taking forward the restructuring of the actual call centres. Let me just refer the member specifically to the findings within the HMICS report, where he clearly states that there has been significant action taken earlier in the year to address a number of the issues that were raised in Parliament and where concerns were raised with Police Scotland. The executive summary produced by HMICS makes particular reference to them. One of the aspects that came from that is that it was clear that those issues around poor performance identified early in 2015, this is at Paragraph 29, and that there has been, as a result of that, a stronger engagement from the SPA with oversight and evidence around those areas. The report highlights improvements that were then taken forward in internal governance in the spring and the weekly reporting that was introduced in order to address some of those issues as well. I am not saying that that was everything that was sorted and HMICS report identifies that further work is required, but it is wrong, factually wrong, to suggest that nothing happened from the point when he raised the matter. HMICS itself identifies improvements that occurred as a result of that. I welcome that and the recommendation from within the report will build on that progress in order to address those issues further. Lee Murray, followed by Christine Grahame. HMICS report states that staff engagement and consultation during the C3IR process could have been more effective, that initial levels of C3 staffing were insufficient and that the address, look-up gazetteer and Police Scotland's internal directory did not meet operational requirements. Staff in the Dumfries control room and their trade unions raised these very issues when the closure of the control room was announced in January 2014, but the previous cabinet secretary drove past and wouldn't even speak to them. So why were the views of experienced staff ignored and what has the Scottish Government learned from these mistakes? Let me deal with two issues that the member has raised, two very valid issues. The first one I want to turn to is the issue of the gazetteer, which has been highlighted in some of the difficulties that the control centres, the contact and commanding control centres are having with the police gazetteer system at the present time. What is also highlighted is that the fire service has a gazetteer system as do the ambulance service. One of his recommendations is that we should look at bringing these three systems together in order to provide a much more comprehensive system for delivering for blue light services in Scotland. That is something that I intend to make sure is now taken forward across those three blue light services. As I said in my statement, the issue around the way in which staff do not feel that they were properly engaged by Police Scotland in taking forward this reform, the way in which too much of it was also dealt with through email and through the internet, I do not think are acceptable. That is why I have made it very clear to Police Scotland that investing in staff is as if not more important than investing in IT systems in themselves. That is why I want to make sure that the issues that are highlighted in the report and the recommendations for addressing them alongside the findings from the Police Scotland staff survey are all addressed to make sure that staff are much more effectively engaged in that process and the mechanism that Police Scotland is now putting in place is to assist staff in being able to support that work in moving forward. I want to see improvements in the very areas that the member has highlighted to make sure that the valued voices of members of staff within Police Scotland get an opportunity to be heard and for their views to be listened to as well. Christine Grahame fall by Gil Paterson. Supplementary Cabinet Secretary to the issue of the Gazetteer on a recommendation 19. Can I ask him to ensure that, as a matter of urgency, a bespoke emergency services address Gazetteer for Scotland is dealt with given that paragraph 294 of the report states, quote, staff told the inspectorate that the internal directory was inaccurate, poor quality, inconsistent and of limited use, close quotes. That's some indictment, so I think this is a simple matter that should be remedied as soon as possible. Cabinet Secretary. Well, as a member will recognise, access to up-to-date information is vitally important, particularly local knowledge for those within emergency services. As the report rightly highlights, it would be prudent to consider greater collaboration and development of a purpose-built emergency gazetteer. As the report also recognises across the blue light services, there is development work taking place in different elements of our emergency services. What I will be doing is directing my officials to make sure that there is now collaboration across the blue light emergency services in Scotland in order to look at developing a Scotland-specific gazetteer service that could be used right across our emergency services in Scotland in an effective way. Gil Paterson, followed by Lewis MacDonald. Thanks very much, Presiding Officer. In September, the cabinet secretary held a summit with stakeholders to discuss the development of local scrutiny of policing. What steps will the cabinet secretary take to further strengthen local scrutiny of Scottish policing in the future? Cabinet secretary. That is an issue that has been raised with me on a number of occasions. As I set out my statement, I held a summit on scrutiny 23 September with members of the SPA at Police Scotland and local authorities. The next steps will be to explore the detail for improvements that have resulted from that particular discussion. The Scottish Government will be working over the coming months with the Scottish Police Authority, Police Scotland and our partners, particularly those within local authorities in taking those forward. The other aspect that we will be taking forward is our intention to have the national policing priorities reviewed. That will strengthen local policing and community engagement. Members of the public, communities and local police scrutiny committees will have an opportunity to discuss and develop those when we publish them in the coming weeks. Lewis MacDonald, followed by John Finnie. The cabinet secretary talked of bringing in independent experts before any step was taken to close the control rooms in Aberdeen and Inverness. Will those experts be free to recommend that the Aberdeen and Inverness control rooms should not close if they judge that that is the best way to assure a high-quality service for the future? If not, what does the term independent experts actually mean? Cabinet Secretary, what the report from HMICS does not say is that the end model that has been set out by Police Scotland should not be pursued states that it can offer the service that is intended to. What the purpose of independent experts will be is to provide a gateway review and assurance at the time when Police Scotland bring forward their final proposals for the changes in the north of the country is that they will go to independent experts to be assured that everything that is necessary in order to facilitate that change can then be taken forward. All of the assurances which are necessary are in place. The second part to that will also be is the independent expertise that will be fed into Police Scotland directly by those who have an expertise in this type of change management. The end model is still the approach that is being taken by Police Scotland. However, there will be safeguards put in place to make sure that before that final stage in the north is taken forward, the independent expertise has fed in both to Police Scotland in their final approach and also in the SPA in their consideration of that before they agree to its final sign-off. John Finnie, followed by Bruce Crawford. John Finnie, followed by Bruce Crawford. Thank you, Mr Penman, for his report and the Cabinet Secretary for every site for that report. I want to pick up on Mr McDonald's point too there because my attention was drawn to the independent experts who will be brought in to provide strong assurances and I think that language is very important. To many, myself included, that reads like decisions being made and the experts are being brought in to confirm a predetermined decision. I have to say that I read the report with further evidence in the interim report that suggested in my mind that there was a compelling need to retain Aberdeen, Inverness and Dundee. Will the cabinet secretary agree to ensure that unison are at the forefront of meaningful consultations about this with nothing predetermined? As the member will be aware, the report does not recommend that the final model, as I have already stated, should not be pursued and that it cannot deliver the type of service that Police Scotland are attending to achieve with that. The approach, the intended model, which is the end point that Police Scotland wants to get to with its call centre arrangements, is still the direction of travel that they are taking forward. What the independent expertise will put in place are the additional safeguards before any further steps can be taken forward in moving to the closure of any other call control rooms at the present time is that they will have to go through an independent process of scrutiny to be assured that all of the necessary steps have been taken before that change can actually take place. In relation to unison's point, I welcome the statement that has been issued by unison today, and disappoint others who have not welcomed the report but welcomed the report, and the progress has been made in improving the situation within the call rooms as well. What I have made very clear is that I expect good engagement to take place with all stakeholders as this process moves forward, including important stakeholders such as unison, who represent so many of the staff within our control rooms within Police Scotland. I can give them assurance that Police Scotland will be left in no doubt about the need to make sure that there is good effective engagement with the staff side in taking forward those issues. I would be grateful to know if the cabinet secretary would agree with me that any individual who raised a formal complaint about police call handling since the beginning of July should be sent a copy of the report to Police Scotland that was published this morning and offered the opportunity to discuss its contents at the appropriate juncture. That will enable the relationship between those individuals and the police to be rebuilt and re-strengthened and deepened. I think that that would go some way to helping the process to move along. I can say that HMICS has made provision to provide copies of the report to a number of individuals who had some contact with them regarding the control room with issues around the way in which Police have handled certain issues around control rooms and the dispatching of police resources. If the member is aware of any other individuals who has not received a copy of this report I would be more than happy to ensure that they receive a copy of it at the earliest opportunity. My apologies to the two members that I simply did not have time to call. The next item of business is a debate on motion number 14766 in the name of Roseanna Cunningham on the trade union bill. Members who were


So guys, I am back with another Halo Infinite video and today I bring you six collectable locations within the tower Area within the campaign. We have a multiplayer Armour cosmetic piece. We have a couple of audio logs We have a couple of Spartan cores and we also have a school. So let's go How's it going guys? My name's DPJ and if you do enjoy the video leaving a like really helps out And if you like what you see I want to see more be sure to subscribe also guys I'm giving one lucky person a chance to win any game of their choice no matter platform They're on to being the chance of winning this giveaway simply drop a like on this video leave a comment down below Make sure you are subject and have those notifications turned on winners will be announced at the end of the week. So good luck Okay, so the tower as you can see right here located on the map this absolutely enormous Building and it's actually relatively start close to the start of the campaign And we're gonna start this is actual entrance. I use that to scale these walls So make sure you come to this point to make things a little bit easier on yourself to know exactly where I am coming from And it's actually the point we'll come back to you to get the school Which is at the very top of this building which I will state You're probably gonna have to upgrade that grapple hook a couple of times And that's why I've left the school and the location to it till the end of the video because you may need to Sparrow and cause you get from this actual this area to upgrade that grapple hook So first of all you want to mount to this whole this wall. So Compass this red room on your right and This is actually the first audio log. We're gonna be collecting today So yeah, it's just in this little small room on your left or right here So pick that up guys. That's the first of six collectibles from this area Next up guys, we have that multi-player Armour piece cars Metic so you want to come out of this room where this audio audio log is come back on yourself and come over to wash His cliff edge. So run underneath this part here Come around Right to the edge of this cliff be careful not to throw yourself off and there is right They're pretty straightforward guys get that armor locker. You're good to go Next up guys, you have our first of two Spartan cause So from this armor locker, you want to come back on yourself and follow through I take now now Obviously, I clear that this area before doing this which I probably suggest will be wise to do on your behalf So clear that the entire area I've rescued the Spartan at the top of the actual mission and I've come back to do all these collectibles So you probably want to do that as well. So there's the Spartan core right there the first of two Next up guys, we have a nova audio log.  We now guys have another this second of a two Spartan core so from the last audio log you would have collected Still within these dark red maze of a building You want to rotate around to the right again? You want to go up this ramp here?   I mean this may not Be something you definitely definitely need to do this But I mean the quick shot which reduces the cooldown of the grapple by 40 percent for me Absolutely helped a ton because you have to get on the very very top of this massive building And it is pretty difficult So come back to the very start Of where we actually started this video and just want to scale up here as I'm doing I didn't want to scale up one of these massive legs But that's actually where we've got to get to we've got to get up there So you have to bend around it's quite difficult to do. I tried it without the upgrades on my grapple I just couldn't do it. I kept falling down and it was just driving around the bend. So yeah So make your way up here. You can actually just walk up this part. You don't have to grapple hug I just thought I'd do it to make it a little quicker And once you get to here guys this part is a little bit tricky Because you have to actually get up a little bit further before you can actually get around on to do You have to slingshot yourself around then grapple hook again. Actually almost fail I think I failed the first time trying to get up here.  Now, like I said that 40% cooldown reduction helps at an absolute turn You just don't have time to do it again sling yourself again You don't have to cool down. Well, I didn't anyway. So yeah, follow here guys and there you go There is the school And there we have it the six collectibles within the tower area Halo infinite people if you do enjoy the video and it helps you out Leaving a like really helps me out if you're new around here want to see more halo Be sure to subscribe. I've got plenty more guides underway. So stay tuned for those But thanks as always for stopping by guys and hopefully I will see you on that next One


You too. What's up, man? I'm here with salary cap action This was on the last chance leaderboards and I was playing McKinley status So I believe is on this YouTube channel earlier in the year playing a good game And so McKinley status definitely one of the trickier players to play in Madden Doesn't run the bunch trips tight end through three five or whatever, you know, you guys deem as the meta He's definitely always ran his own stuff Offense and defense so it's definitely somebody different to play and if you haven't he can't catch you off guard With a couple things and we'll see how that goes in this game If you want to watch these games live man a link below twitch.tv Slash dub that make sure you guys check that out man. Awesome I want you guys start following my Instagram that link is below in the description and make sure you do it I want to make sure I keep growing that as he hits me with a little baby hits right here to tie Recall you see when I say he doesn't run the normal stuff He's in tight doubles and this was one play hit me with early where he puts Both his receivers on flat route and then swings it off to his running back So it's kind of a makeshift screen something I saw him doing a lot You see him doing it here again with the wheel route goes for the corner out up top and Ronnie lot got smoked This is salary cap. These players are not that great. That is out of position Ronnie lot the corner 12 cap gay Martin and all you guys should know if you play salary cap is a goon making that stop there But he no huddles me and then he quick snaps catches me on Josh Jones over here who I don't want to be on Then rolls out rolls out everybody's pretty much covered. I send the spy early Throws it back to his running back and we saw Ronnie lot get burnt Then he doesn't get physical with Ricky Williams right there This was probably the last game that out of position Ronnie lot played for me He got burnt then he didn't get physical on with the running back catching the ball. So that definitely a Frustrated me big play up here to Calvin Johnson made him pick between Julio Jones and Calvin Johnson first and ten Sends some heat off the edge there man really gets to me hits me as I throw the ball Jalen Smith and but we come back and hit Vernon Davis on the corner route right there Nice little game get me to the 20 yard line got a score touchdowns and man He sends five throw it over the middle. He good job hits thicken Randy Moss make some drop his second and ten I get screamed at by Jalen Smith Third and 17 years just in a bad position. No where really to go with the ball.  He can a couple times. He returns the ball Pretty decently in this game. Once again, he hits the running back on a wheel route Use a flat zone a flat or a flat route somebody to take away the flat zone And then hits the running back man You see it again the wheel rat sort of running back and he wants this corner out to the 2y receiver side That's something I learned by playing a man He wants to go to the running back also wants to go to that corner route or wheel route on the 2y receiver side Hits the running back again this time Ronnie lot gets out makes the tackle So as the game went on I went fourth and nine we really sent everybody at him right there, man He went to crossing routes there and it really Didn't have enough time to get one of them off So we get a stop right there man stopped them from throwing the running back route Stopped them from picking up yards as Michael Vic makes a great play and Rod Woodson saves it from being a highlight Get inside the arm on the 12 yard line now first play really boxed up Know where to go good lurky was in a good position right there second and ten We're gonna go ahead and scramble with Vic and get sacked this bad plays I got going down here Antoine, but they third in 19 gonna give Moss a chance on this one one time for the Not coming down in traffic with that Randy Moss Field goal so that's two trips inside the 22 field goals man That's definitely hurting me But like I said man, I want to make sure I don't give up the running back pass And I want to make sure I put my good corner on the 2y receiver side because that's where he's got the deep fade And he has that deep corner route So I want to put Ronnie lot on the running back side and put my good corners You see Jalen Ramsey on that side to worry about that wheel route a corner route or fade Got everything covered pretty well man I guess I want to make sure don't let him get big yards early or short yards early So he has to get into a long yard situation and we're able to get there just in time before the playmaker Force him to a fourth and four There we sit man, we got everything pretty much covered good But the high ball hitch man good play first time he went to a high ball hitch right there I had a flat zone wish I would have had a yellow zone Next plate those over the top Jamal Adams put Julio Jones in the dirt. That's the physicality I need gay Martin with the stops get them to third and long those his little hitch to Dallas Clark And we pull him forward. I think no fourth down He no huddles runs the ball Ricky Williams air trucking away got the first down there man first in 10 Good job right there getting some pressure was that no miles Garrett 25 cap miles Garrett always liked him There we go throwing that corner route We have Dion over there and knocks it away from Dion Dion on Dion crime right there Get them to a third and 13 he's looking for the running back again But my good running my good corners over there Janelin Ramsey knocks it out of Ricky Williams hands fourth and 13 we're gonna give pressure again But he actually gets outside and that's one mistake. I made man if he's gonna be rolling to the right I have to go to the right Because he's that it's gonna be harder for him to make that throw back across the left Even though it might be open this one would just be a harder though I have to make him make the harder throw here. I'm not really using my time out Just to make sure it doesn't score a touchdown here.  I have two timeouts 20 seconds Let's see if we can make something happen as he kicks the field will go up 10 to 6 Let's see what we got first and 10 Looking for Calvin Johnson. Just throw it high big catch right there by him So I can call time out nine seconds left man nine seconds He sends five or six stand out with Vic get around catch a nice block playmaker up Randy Moss Throw it to him to one step out of bounds and field will range with one second left That's Michael Vic man. Just staying patient in the pocket. That's definitely my offensive line holding me down Allowing me to get that field was we start high loaning him over here to the tripside hitting that out route Once again next play I get the same look but I get actually get hit by somebody I believe Javon curses on his defensive line Second and ten just throw the flat right over here to Vernon Davis He gets hit a big hit, but he's been a horse for me not dropping the ball Out route again. Like I said man, it looks like the same play It is the same play because he's in the same defense every play. It's pretty much just covered three That's the defense he calls all the time man And that's the thing about man when you find a play as I go to a little Pat sale look out of this tripside And hitting that poster over top man If you find a play that works and their opponent continues to want to run the same defense Then do the same thing that works man.  Come out here. He's in goal line. I know that means man to man coverage I know I'm gonna have Julio Jones. I block an extra person. Ah Just don't get the right animation man turn the ball over just devastating right there Like a goal line is gonna give you a lot of pressure But you know, it's man coverage behind it and he was able to just get enough pressure not allow me to get a good throw there Gabe Martin again making a play Third and 12 goes to a quick little out route over here in front of Ramsey That was a nice play to get his back up against that or off of that field goal post Goes for the playmaker Terrell Edmonds. Give me all of that. Never stumble get up Julio Jones saves another highlight man But that was just anticipating the playmaker and being tall enough, you know We talk about obviously your height is good for for you know reaching balls that are over your head pause but Also to have the arm length as we throw a laser right there to Randy Moss for the touchdown But if your players taller they're gonna have longer arms So he's able to reach out a little bit further there to row Edmonds goes for the corner out here And of course Dion on Dion crime went in my favor earlier in the game and that his deans is shitting on my Dion right there Those were the little hits right another pass to running back gets to the point of game where I want to start Manning up my running back as we get a big sack right there pressure by Ron Parker and Joey Bolsa cleaning it up Goes a lot around Ronnie lot man I started using him in the cover two didn't want him going deep as much anymore And this was a just a user fart by me. Just go right by He got a different animation right there. It went more to the inside He's got man up the running back really boxed that play that he's trying to run Nothing else for him to go to man. He throws a ball away But that play man He's just got he jumped more into the inside than I thought gave up a big play to Julio Jones But we're gonna hold him out of the end zone here get him to a third and five What's he go to a little curl over here to Tyreek Hill bang inside the tennis should be the two minute warning but he snaps quick Throws the little play over here to Dallas Clark He no huddled me there and I should have kept that in the game because I really once again Caught me off my user hits that nice little curl route to Dallas Clark man But here we go. I got the ball all I need is a field goal That first run was pretty much just get it as a two-minute warning next play pretty boxes me up pretty good I get lucky right there that it was an incomplete and not a sack hit the quick out route though on 39 To Megatron steps out of bounds still plenty of time in this game The time is actually almost my enemy. There's so much time flat route to Vernon Davis Getting out of bounds again Almost would love to stay in bounds to run some clock once in a while here playmaker right up the middle Randy Moss gonna just hold our B fight pretty much infill will range now So I'm gonna take this down to pretty much as I have to get into his timeouts the worst case scenario right here is that he um He gets the ball back down to with no timeouts left man If I get one first down the game is definitely over But I'm gonna take this all the way to one second because he didn't choose to cause timeout there So I definitely got to use all this time make him pay for not calling timeout I'm guaranteed gonna run just to get into one of his timeouts early and that's what's gonna happen if I Just from running I'm gonna get into his timeouts But we see a hole cut back so he misses that block and you know We're gonna two-step on him into the end zone Joe Mixing touchdown man Obviously, I almost could have fell right there and not scored But I'm gonna go ahead and score my touchdown because I can hold him out of the end zone I've done it all game cover three. Look, I want a quick pass right here But that yellow zone snuck out there picked me off and could take it to the crib But you got a Julio Jones that could have been devastating because that would have mean a field goals ties the game Hard to keep somebody out of field range, but it's easy to keep him out of the end zone No big plays everything in bounds is what I want right here He goes underneath actually finally drops one with the running back I would have loved for him to catch that and keep the clock running next plate goes out in flats Jukes back inside and gets tackled in bounds clock is running I would have used one of my three timeouts right there He chooses the no huddle 31 so it was at 57 seconds then he audible so why he's doing all this the time is running You know if you're gonna know how to at least quick snap then he runs the ball Okay, cool gets his first down longer animation bang clock still running calls timeout 26 seconds that wasted about 15 seconds at least those the ball over the middle again nice little game But has to call a timeout one timeout left and we get to the quarterback That's what I need Miles Garrett again Gabe Martin fighting now He has no timeouts can't really even do anything in bounds. Those are the pretty much lobs I strafe up with Dion no pick knocks in the way 20 seconds left just got to keep him out the ends on a lot of deep blues Those are out wide down Sanders strafe Incomplete again should get one of these picks fourth down game on the line And of course Ron Parker is going to go end it for me great game man way to hold up way give up that touchdown early and Just try to limit his running back touches and go ahead and continue to score on that cover three man Defend all Madden is about sevens and threes man. If you can get sevens and threes Sevens instead of threes you're gonna win man. So make sure you guys hit that like button and comment below


This paper discusses the use of an unmanned aerial vehicle, UAV, for environmental remote sensing applications in Morocco. The UAV was equipped with a Panasonic Digital System camera and flown over various study sites with varying extents and altitudes. Two different methods for Jorferencing were used depending on the scale and extent of the survey. The resulting images were processed into digital terrain models, DTMs, ortho-image mosaics, and 3D models of gullies and badlands. These data products were then used to quantify erosion and analyze the surrounding areas and landscape development. This article was authored by Johannes B. Reis, Irene Marsolf, Sebastian D. and Hashtag 039, O'Lear Oatmans, and others.