It's mind-boggling when you try to wrap your mind around the fact that we started in California and ended on the Las Vegas Strip I think that was just really amazing It's Baker to Vegas. It's 120 miles It's a relay race and we start just outside of Baker, California And we run through the Mojave Desert up through the mountains in Nevada Back down to the Las Vegas Strip and then we end at the Rio Hotel on the Las Vegas Strip You can't really prep for a run through the desert with 115 degree heat index It's really just for lack of a better word crazy So to kind of have grown up hearing about Death Valley and knowing the climate it was and then being like well I just ran through that The March Service had been doing this race for a long time and at some point They wanted to break off and make it a female only team and not because we didn't want to be with the guys But more so because we wanted to have an opportunity to get all the females together Which is really hard for for our agency because there's a very drastic difference in How many males are our two females in our in our agency because there are aspects of the agency and Aspects of being a female in law enforcement just in general where it can feel kind of lonely So to be able to speak to people who've been in the agency for 10 15 25 years and be like hey, you're not the only one you're not alone We all wear the same star at the end of the day and we are all capable and More than capable. I'm very strong independent fierce women. So I just felt surrounded by fierceness So for us it's not really about the actual race itself The race is what brings us together the race is what allows us to Come together as a team and that's sort of the glue that holds the camaraderie together But for for me and I think for most of the girls This is really about bringing together a network of women who are really strong and powerful and motivated and giving them an opportunity to Number one reflect on what we do as an agency to network with each other and really meet Because we wouldn't have ever had an opportunity to do this in any other means and then honor our fallen and I and I mean that in that You know, we all come together to remember those that we've lost And unfortunately this last year we lost quite a few You never shake that feeling when you're at the starting line and they're about to either start the timer or Hit hit the gun. It's just a thrill that I get out of it I'm from South Texas where it's triple digit weather almost all year round had never seen snow since I moved to the DMV So everyone thought oh, she's got this in the bag like six. You're gonna be fine But I really it I wasn't because nobody in South Texas runs midday for fun You know, we get up early in the morning and say before dawn or you know once the sun goes down It was so hot The heat was radiating up from the pavement There was a point at I heard another racer and their follow team saying there was so many people falling out of this race Because it was so hot and so strenuous on the people running it. I Wouldn't call it nervous, but kind of just like that little bit of like anxiety before like a big event Like waiting to run, but there's so many people there from all different agencies and then my entire team was there So I had my co-workers and all the ladies I had just met who are also involved in the team waiting with me to start running and then When I finally caught the baton and took off for my own 6.1 miles through the desert everyone was there cheering me on and it was it was really cool to be like Hey, I know it's hot and I know you're in the middle of the desert But there's people right behind you cheering you on the whole way If you can imagine running through a desert and up a mountain I'm starting here and you go all the way up here And you just see for miles in the distance the hill that you have to go up a little a little daunting for sure But I just got to keep pushing through that's just something that in our agency in our Job you have to do because you got to you got to push forward no matter what comes whatever obstacles you face You just got to keep moving Our team team too was just so it was full of amazing females and even our support crew Anything we asked for anything we needed they had it they did no questions asked so I just felt very Very like catered to like okay They're here for me because I'm the one putting in the work right now, so let's do this knowing we were there to honor so many people and Getting to meet the female deputies who knew them personally and hear Personal stories about the people we were honoring. Yeah, it was a hot Six miles through the desert, but knowing that we did that for that reason made it really great experience I think for me as we're crossing the finish line in that sense of accomplishment is Yeah, it's pretty powerful These girls have done a lot and this race was Particularly challenging this year for the girls who had not had an opportunity to run these legs before they kind of left in Not recognizing how challenging it was going to be and just killed it And what would you tell these these young deputies? Going forward Yeah, I think moving forward, you know all of my teammates are my family And so I I hope that I get to see them next year and I hope that They serve as an inspiration for other women in the agency to become be a part of something that is as powerful as this I think the message that I'd like to see moving forward for this team is that We as women can really empower other women just by having these connections and these relationships, right? So we can we can light each other's fires and and still burn


This paper reviews the potential of combining hypothermia-mediated photothermal therapy, PTT, and reactive oxygen species, ROAS, mediated photodynamic therapy, PDT, to treat multidrug-resistant MDR bacteria. It explains how the two techniques work together to create a more effective treatment than either one alone. The paper also discusses the mechanisms behind the synergy between the two techniques and introduces advances in nanotechnology-based PTT and PDT agents. Finally, it outlines the challenges and future perspectives of this approach. This article was authored by Atenu Naskar and Kwon Sun Kim.


So, now, we are going to talk about jointly distributed random variables. See, there may be events which need to be described by more than one random variable. So, there may be you know the phenomena, the random phenomena concerned with the event are more than one dimension. And therefore, we need to be able to of course, then we from two dimensions we go to multi dimensions also, but right now to keep it simple, we will first talk about two dimensional random variables and then may be extend the notion to more than two. So, if x and y are two random variables, we define their joint cumulative distribution function as follows. So, probability f of x less than or equal to a comma y less than or equal to b is actually the probability that x is less than or equal to a and y less than or equal to b a and b two real numbers between minus infinity and infinity. So, essentially in this diagram, if this is b then you are asking for y less than or equal to b and then x less than or. So, it will be this whole region, if you can see this line and this line. So, whole of r 2 extending from here to this end, that will be of. So, you are talking of the probability over this region. Then the moment you define the joint CDF, the cumulative distribution function then you can talk of the marginal CDF. So, for example, of marginal CDF of x can be obtained from f a b as follows. Sorry, this should be a b. The probability part comes here x less than or equal to a y less than or equal to b. So, therefore, from f a b we can obtain the marginal CDF of x as follows. So, this is f x a which is probability x less than or equal to a. So, this will be actually therefore, that means this means that y is allowed to take any possible value. So, therefore, y probability x less than or equal to a and y less than infinity. So, now, let me just define it in a proper way in the sense that this is also the same as b going to infinity. So, limit that means if I take the event x less than or equal to a y less than or equal to b and then I take the limit. So, you see what will happen as b goes to infinity. So, x less than or equal to a y less than or equal to b you are talking of this then when say say b 1 then you talk of this y less than or equal to b 2 where b 2 is greater than b 1 then this is a bigger event right this event is contained. So, therefore, now you have a sequence of these events which are increasing. So, increasing sequence of events as b goes to infinity and if you remember my definition of probability as a continuous function, continuous set function. So, then in that case I told you that we can in that case extend I mean when you have a increasing sequence of sets then and you are computing the probability you want to take the limit then the probability of the limit is the limit of the probability. So, therefore, I can take limit outside and this will be limit as b goes to infinity of the this event x less than or equal to a y less than or equal to b. So, you take the probability here and therefore, this will be limit and this is now your f a b by definition.    So, exactly in the same way we will argue out that the b remains the same and then a keeps increasing. So, again you have increasing sequence of sets and so when you take the probability I can you know I can exchange the limit and the probability and get the answer. .. So, now similarly you want to compute and then of course, you see the properties that we had defined for that cumulative distribution function must have for a single variable. So, the same will apply and you can apply them to f x and f y. So, through those you can get the property for the joint. Because, the property that x f x and f y possess combine them and you can you know then put together the properties that your joint cumulative distribution function must have. Now, suppose you want to compute the probability of x greater than a and y greater than b. So, this we can write as 1 minus probability of the complement of this event which is x greater than a y greater than b complement. And then since x and y are independent in the sense that you know I can write this as. Now, this can be written as x less than or equal to a union y less than or equal to b right from if you recall your De Marben's law and so on. So, then this will be 1 minus probability x less than or equal to a minus probability y less than or equal to b. And then you add probability x less than or equal to a comma y less than or equal to b and this diagrammatically also you can immediately see that this is how from here we have to get here. Because, you are computing the probability x less than or equal to a and y less than or equal to b. So, this will be you see x less than or equal to a would give you this region right and y less than or equal to b will give you this region right. So, you see the region extending from here x less than a y less than b is this region which you have subtracted twice. Because, once when you do it for x less than a probability x less than or equal to a. So, it is this. So, then this region is coming into it then when you subtract probability y less than or equal to b then again this whole region is coming right. And therefore, you add this again. So, in words of your I should have written this that means your. So, therefore, I will simply write this probability in terms of 1 minus f x a minus f y b.  So, therefore, to make the equation correct I add this once and then because I need to subtract only see I need this region. So, the valid region that I require is this. And therefore, from 1 I subtract this whole and so this got subtracted twice for I added once to make it proper. So, this will be your that means now one can compute whatever probabilities you want related to these two random variables it can be done once we have made this definition.  So, here again we will just simply diagrammatically look at the equality that we have here. So, x is varying between a 1 and a 2 and y is varying between b 1 and b 2 then f a 2 b 2 is this whole area. In fact, if it is not if it is only non negative variable then it is this region. So, just assume for argument sake that this is both the variables are non negative, but otherwise it will extend to infinity and this will extend to infinity.   So, you see that here you are subtracting this region twice and in this a 2 plus b a 2 comma b 2 you are adding it and then you are adding this. So, that gets cancelled out and this region also gets cancelled out. So, from the whole of f a 2 comma b 2 you are finally, left with this particular region this is the idea I am equating the probability with the area in a sense and that is how I am trying to explain. So, if you keep this picture in mind and you can always make the right computation now in case x and y are discrete random variables the joint mass function can be written easily because here you are simply wanting to compute these probabilities probability x equal to a y equal to b is b a comma b this is how we will define. So, if we can compute this probability then that is the probability a comma b and this for all possible values the pairs a comma b taken by x comma y and then we can also compute the marginal probability mass function of x which will be simply probability x equal to a and this will be your summing these probabilities over. So, fix the x at a and then you are summing it over all possible values of y. So, you are summing up p a comma y for all possible values of y that will give you the probability that x attains the value a because here the value of y is not is a material. So, therefore, you sum it up over all possible values that y will take similarly p y b will be summing up these probabilities x comma b when p x b is positive. So, in this case you want to sum up over all possible values of x to get the probability that y will take the value b and we will go through an example here.    So, now we want to write down the joint mass function or distribution function for x and y.   So, let us I will just compute a few and then you can try to complete the table I think may be I have completed it already. So, when you want to compute the probability of 0 0 that means x is equal to 0 and y is 0. So, which is no red ball and no white ball.   So, this number comes out to be 1 upon 21 which is here. Then I should have computed p 0 1 and I think I have written it here as. So, it is this number is actually. So, it is got mixed up this is 1 by 7. So, that is probability 1 0 is 1 by 7. So, if you want to compute have I done it somewhere here no. So, therefore, let us just quickly compute this number p 0 1. So, 0 1 is probability no red ball and 1 white ball. So, this will be no red ball that means 1 white ball and 2 blue balls. So, blue is 4 c 2 and 1 white out of 3. So, this is 3 choose 1 divided by 9 choose 3. So, let us quickly compute this. This should be 6 3 and then from here you will get a 6 and this will be 9 into 8 into 7. So, 6 3's are 18 and this will be. So, twice twice 4 then 2 and 3. So, this is 3 by 14. So, 3 by 14 is this. So, 3 by 14 is this number and this way I have made some computations. So, 0 2 you have to compute and so on.  So, now the whole idea is that once you have completed this then as I was saying that if you want the marginal distribution for x then. So, for example, if you are looking for the probability, let me just take it from here. So, if you add up the numbers here this is what probability x equal to 0 then you are giving values to 0 1 2 and 3. In other words you are adding up probability. Let me write it as 0 0 plus probability 0 1 plus probability 0 2 plus probability 0 3.   So, this all these probabilities add up to the probability x equal to 0 and so this will be right. Similarly, when you add up the second row that will give you probability x equal to 1 second third row will give you probability x equal to 2 and this will be probability x equal to 3, but since this is all 0 because there are no the number of red balls is only 2. So, you cannot have number of red balls in the sample that you pick up as equal to 3.  So, these are the only numbers and you see this now finally, because this is probability x equal to 0 probability x equal to 1 probability x equal to 2 which are all the possible values that x can take in your sample of 3 balls because there are only at most 2 white balls that can appear in a sample. So, this must add up to 1 and similarly when you add up see when I add up these probabilities this will give me the probability of the y is equal to 0. That means there is no white ball in the sample when you add up these numbers this will give you the probability that y is equal to 1 and similarly this. So, all these 4 when you add up that should also add up to 1 and that will give you a good check. So, again that means when we are defining the marginal pdf's and so on then we must continue to check the validity and so make sure that your calculations are because otherwise you will know that you have made a mistake somewhere. So, you can go back and check. So, all these numbers so the numbers here will give you the marginal distribution of y here the numbers will be marginal distribution of x and so on. So, this is how you write down the joint probability distribution of 2 random variables. Now, take another example so that I want to make sure that you understand how the calculations are being done. Now, this is an example in which there is a community in which 15 percent of the families have no children 20 percent of the families have one child then 35 percent of the families have 2 children and 30 percent have 3 children. Now, the probability of the children being a boy or a girl is same that means it is half half. So, once you pick up a family at random. So, the experiment that we are doing here is that you pick up a family from the at random that means any family is equally likely then you want to find out the number of boys and girls in that family. So, both of them are random variables that means number of boys in the family and the number of girls in the family the family that you have picked up at random. So, here again let us see I have made a few calculations. So, if you want to compute P 0 0 then that means no children. So, of course, this is straight forward you know that 15 percent of the families have no children. So, this is simply 0.15. So, which we write here then when you want to compute P 0 1 that means no boy just one girl. So, this is the event probability of one girl child now I will write this as a conditional probability saying that probability one child into probability one girl given that there is one child in the family. So, that will come out to be 0.20 into half because there is only one child in the family P 0 1. So, that means only one girl and no boy. So, this the total number of children in the family is 1. So, that probability is 0.20 then it being a girl or a boy the probability is the same therefore, it will be into half. So, that is 0.10 that is the number you enter here. Then similarly, if you want to compute P 0 2 then it will be two children and so I am writing the conditional straight away. So, two children probability of that and then two girls given there are two children. So, this is 0.35 from here families having two children that is 0.35 and then two girls. So, 1 by 2 into 1 by 2. So, 1 divided by 4 and so that is 0.0875. So, 0.0875 then when you want to compute I have done it here it is not very this thing, but anyway it is coming up may be I can just show the calculation in a better way. So, when you want to have 0 3 that means all the children are girls. So, this again will be probability 3 children which is 0.30 then into 1 by 8 because all the three are girls. So, 1 by 2 raise to 3 and therefore, you divide by this by 8. So, this is 0.0 then 3 will be 24 then 6 then 8 7's are 56 and then 40 and 8 5's are 40. So, 0.3 0.0 3 7 5 0.3 7 5. So, when you add up this numbers this will here will be the probability that x is 0. So, that means no probability when you pick up a family at random from the community it there are no boys in that family. So, that number will come out to be this you can add it up. Similarly, this will give you the probability that x is equal to 1 that means 1 boy in the family probability x equal to 2 and this will be probability x equal to 3. And here also you can see that this these combinations and of course, because the boys and girls are equally likely. So, the tables so once you have computed this part then this is symmetric because whether having a 1 boy and 2 girls or 1 1 when you have 2 children. So, it is whether girl or boy is same therefore, this will be the same then 1 2 see this one we are having yeah this is 2 0 I am sorry 0 1 and 1 0. So, that was the number then this number for example, 2 1 and 1 2 1 2. So, these two numbers so this is symmetric because boys and girls are equally likely similarly here whether all the 3 children in the family are boys all the 3 children are girls is the probability must be the. So, I am sorry this should be 0.375 so make that correction. So, this will be 0.0 375 and then again as we said when you add up all these probabilities they should be add they should add up to 1 and here also you will get the marginals. So, this will be probability y equal to 0 probability y equal to 1 probability y equal to 2 and probability y equal to 3. So, I would like you to complete the tables I have made some computations for you this. So, this is the same now you have to make just these two computations and then you can complete the table. So, this is this should give you an idea as to how to go about computing joint when the variables are discrete how to compute the joint distribution function for discrete random variables. So, let us continue with the jointly distributed random variables suppose x and y are continuous. So, I will now define another way in other way in the sense that now I will define this through your joint pdf and so we are saying that if there exists a function f x comma y real valued function which is defined for real x and y having the property that for every set c a subset of r 2 that means all pairs of values the pairs of values which are there in c then x y belonging to c that means you see the convention is that the first these are pair of coordinates then the first value is for x and the second value is for y. So, then probability x y belongs to c is this. So, now this is different from the way we define the cumulative distribution function right in the beginning. So, of course, the two will merge to the same thing. So, you have the probability should be f x y d x d y for a continuously distributed joint you know jointly distributed continuous random variable. So, f x y is called the joint pdf of x comma y and if a and b are two subsets in r square then probability that x belongs to a and y belongs to b will be integration over a with respect to d x and actually see what you should make a convention that this must refer to the later one here. So, I should have said this is d y and d x because just a convention. So, therefore, when you are writing the limits you know the ranges then it is nice to remember that this one refers to the second integral and this is the first. So, the order has to be maintained. So, therefore, this is a b. So, I should have written d y d x of f x comma y.  So, this is the relationship between the cumulative joint cumulative distribution function and joint pdf and then of course, the marginal distributions here. So, this will be x belonging to a and y is from minus infinity to infinity. So, in that case you are integrating with respect to y from minus infinity to infinity and this integral when you are integrating with respect to y will be the marginal. Just as I showed you in the discrete case that you add up for all the possible values of y to get the marginal and the probability of you know x for a certain value. So, same here the marginal with respect to x will be you integrate the joint pdf from minus infinity to infinity and for the marginal of y pdf of marginal y this would be integrating with respect to x from minus infinity to infinity and of course, depending on whatever the region of actual definition is fine. . Let us take up this example. So, if you have this function defined here which is defined for all values of x is from 0 to infinity and for all values of y from 0 to infinity and it is 0 otherwise. So, it is in the first quadrant that the function is defined then verify that this is joint pdf. So, therefore, the integral total integral from 0 to infinity and this should be 1. So, suppose I just integrate with respect to y first. So, the derivative here the integral is minus e raise to minus y from 0 to infinity that gives you 1 because at infinity this is 0 at 0 this is 1 plus 1. So, then this is this now you differentiate integrate with respect to x. So, this is minus 3 upon 3 e raise to minus 3 x going from 0 to infinity which is equal to 1.  So, this time I have taken care of the order. So, this is 2 to infinity for x and for y it is from 0 to 1 and. So, again the same integral you do it with respect to y first take the limits and then this is 1 minus e raise to minus 1 then you integrate with respect to x and this will be. So, the final answer will be this and so you can go on. So, this is nothing new except that your dimension has increased and the same concepts are there the same axioms will be followed. So, we will now you know continue developing this theory and then talk of independent random variables jointly distributed independent random variables then we will talk of some of random variables. So, of course, the thing is that this concept can be extended to more than 2 and except that the writing part is a little tedious, but the same thing will follow. So, I will just revisit this I had shown you this probability try to well computing this probability I had drawn the diagram. So, let me just make it more clear because I had a feeling that I did not do a very good job last time. So, let us see probability x greater than a and y greater than b then if this is my origin this is x equal to a this is y equal to b then this is the area that you want to compute the probability on your region x greater than a y greater than b is this event represented by this area. So, now we said we will write it as x less than or equal to a. So, x less than or equal to a is this whole area extending on this side whole area and then y less than or equal to b will be this area. So, therefore, all this and all this gets covered and you see that this area the area that is x less than a y less than b this is. So, this portion because when you are covering x less than a then it is all of this y less than b then it is all this.  So, you add here and therefore, you get this. So, therefore, 1 minus of all this that means if I write probability x less than or equal to a plus probability y less than or equal to b minus this then I will get the region corresponding to this and therefore, so 1 minus of that and that will be the probability for this. So, just wanted to revisit this thing and here also in the other example that we had taken when we were talking of a community in which there are families and there were probabilities associated with the families having no children, one child two children and three children. So, I thought that though I had asked you to compute I had computed some probabilities for you and I asked you to compute the remaining one, but I realize that probably you need a little more working out and so I thought I will give you the hints here. For example, when you are computing 1 comma 1 then it is the probability two children into the conditional probability that it is either a boy girl or girl boy. You see when you are saying 1 1, so then it can be you know the first child is boy and the second is girl or the first child is girl and the second child is a boy. So, therefore, this will be 0.35 into because the probability of two children families having two children is 0.35 then into actually boy girl will be 1 by 4 because each of them are equally likely, but since there are two possible cases. So, 2 into 1 by 4 therefore, this is half and so this number comes out to be 1 1 this is 0.175 now for 1 2 when you want one boy and two girls then the that means three children. So, the probability of having three children is 0.3 30 percent of the families have three children. So, this is 0.3 then the conditional probability of having a boy and two girls and then with three children having three children and then one boy and two girls. So, now here again you need to say that see it could be the first child who is the boy other two are girls then it is first girl then boy then girl and girl girl and boy. So, these three possibilities are also there therefore, it will become 3 by 8 because each of them is half. So, then when you have these three possible cases you know favorable for your event then this is 3 by 8. So, 0.3 into 3 by 8 that comes out to be 0.1 1 2 5 and then the rest we had computed and then these are the marginal. So, that means this I told you is probability x equal to or b equal to 0 and probability b equal to 1 probability b equal to 2 and probability b equal to 3 and similarly here this is the marginal for probability the girl the probability girl is 0 no girl in the family of course. So, probability no there is one girl in the family two girls and three girls and then you see that this adds up to 1 because they are marginal pdf's or probability mass functions and so on. So, once you find out the joint then you find out the marginals and then you can do all other computations that are required the expectation variance and everything you can compute as we have done it for you like even for the joint also you can do it expectation x y you will do it and so you will multiply I think I have given you the expression p x y this we worked it out this into your the values that x and y take some y is positive and so on. Now, I will continue with some more examples of the continuous random variable. So, here let us see you take a circle of radius r and let us say it is centered at the origin. So, the equation of the circle is x square plus y square equal to r square. So, when you are taking the inside of the circle then it is less than or equal to r square. So, this is the circle given to you then let us and we just pick a point on inside the circle then that is a random because and we are saying that all points are equally likely to be picked up in the inside the circle then x let x represent the x coordinate of the point that you have picked up y is the capital y represents the y coordinate. So, now both x and y are random variables and since any point in the circle is equally likely therefore it will be a constant the p d f of the x comma y that joint p d f of x comma y will be a constant inside the circle and 0 outside and this is an example of a two dimensional two variable uniform distribution. So, this represents a uniform distribution because any point in the region in the inside and on the circle is equally likely right and then now you want to find out the value of c. So, we will have to say that this must integrate to 1 the whole thing and since this is simply minus infinity to infinity and minus infinity to infinity d x d y this is an element of area. So, when you integrate over the whole of the circle you will get the area of the circle by everybody. So, this is you have already done it in your class 12 and so on. So, then c into pi r square is equal to 1 therefore your constant is 1 upon pi r square which is expected right for in one dimension also I told you that when you had a uniform random variable then this was the length of the. So, if this was point a this was b then the probability density function for any for this uniform random variable was 1 upon b minus a which is 1 upon length of the interval in which the random variable is defined. Here the random where the pair x comma y is defined inside the circle when it is uniformly distributed this pair and that means that the p d f must be 1 by pi r square the area of the region. In this case it is the area of the circle now you want to compute the marginal of x and marginal p d f of x and marginal p d f of y. So, for x you will integrate from minus infinity to infinity f x y d y and this is what I want to point out that. So, you have fixed value of x if you have fixed a value of x then how does your y vary y varies along this chord right and the length of the chord is because this length is x this is r the radius of the circle. So, this length is under root r square minus x square. So, therefore, this point has the coordinates x comma under root r square minus x square and this point has coordinates x comma minus under root r square minus x square. So, your y varies from minus under root r square minus x square to under root r square minus x square. So, this is it this reduce because there is no other mass outside this. So, this is c into d y and the c is 1 by pi r square. So, this becomes twice under root r square minus x square and this is defined for all x between minus r and r right because your x varies from this point to this point along this and as your x varies along this your y varies along this. So, the whole circle gets covered right similarly because there is symmetry. So, your marginal of y will be twice under root r square minus y square upon pi r square where again y varies sorry this is mixed up this is minus r less than or equal to y less than or equal to r 0 otherwise. Now, suppose you want to find out the distribution of random variable d which is the distance of the point from the origin. So, this is under root x square plus y square. So, you take any point here and then this is the distance the length would be under root of x square plus y square. So, we find out the distribution function of d which will be f d r. So, that means probability d less than or equal to r. Now, since everything is non-negative distance is a non-negative number r is non-negative. So, this event is the same as squaring up both the sides that means x square plus y square less than or equal to r square. The two events are the same and again by the same argument that for x square plus y square less than or equal to r square. So, all points inside the circle having radius r all these points will satisfy this or define this event. Every point inside the circle of radius small r and therefore, the area here is pi r square small r square and divided by the p d f which is pi r square. So, you can you know want you can do it from by integrating and everything, but this is a straight forward because everything is uniformly distributed. So, therefore, the probability of a point lying inside the circle small r is pi r square just as we said that the you know this is the that means this is the area which is favorable to our event and then the density of the function is of the two pair is 1 upon pi square r square. So, therefore, the probability the distribution function of d is r square upon capital r square. So, now, if you want to find out the p d f of d p d f of d would be differentiating this with respect to small r. So, 2 r upon r square and small r varying from 0 to capital r because now d is a non negative random variable and the value of d will vary from 0 to r because the point is here then this way and this way. So, it can go up to capital r and similarly you can find out the expectation of d which will be 2 by 3 r. So, you know just by you know geometry helps you draw pictures then you can you know get a good idea as to how to go about solving a problem. So, in the moment you have more than one you know if you consider a pair of random variables and you can see that the complexity will increase the moment you consider higher dimension you know that means 3 random variables together joint density function of 3. But as I go along I will try to solve some more problems relating to 2 random variables joint distributions of 2 random variables. So, another example on joint distribution of random variables suppose f x y is a function given like this 6 by 7 x square plus x y by 2 x is between 0 and 1 and y is between 0 and 2. So, then you want to verify that this is this represents a pdf of the variables x y. So, I will just integrate from 0 to 1 and 0 to 2 and the working out shows that this is x square y plus x y square by 2 if you are differentiating with respect to y because I have written the limits with respect to y first 0 to 2. So, let us integrate with respect to y first and therefore, this is what you get and then you this you look at this then integration with respect to x 0 to 1. So, that will give you this function and finally, you get the integral to be equal to 1. So, therefore, the function does represent because it is a non-negative function since x and y are both non-negative. So, this is a non-negative function the integral in the defined in the specified area integrates to 1. So, it represents a pdf. Now, to compute the marginal or the pdf of x or the marginal of x, you see I have already done it here because you have to integrate this integral from 0 to 2 dy. So, this integral gives me the marginal of x therefore, this is 2 x square plus x 0 less than or equal to 1. And you see that if I now integrate this from 0 to 1, it will give me the answer 1 and hence this is also a pdf. It is non-negative in the specified region and of course, I should also say 0 otherwise. See it is very important that your definition of the pdf must be complete in the sense that you must specify the region on which it is defined. So, here it is in between x 0 and 1, this is the pdf is defined by this function and it is 0 otherwise. Then you are asked to compute x greater than y. So, if you have to compute x greater than y, then see I have written down this is the line which represents x equal to y. So, this is the region over which you want to compute this probability because you have to specify the event. So, then it will be see here if you are integrating with respect to x, then you fix your y that means when I am integrating with respect to x, my x is varying. So, y is fixed. So, when you fix a y in this region, how will your x vary from y to 1 because this represents 1 here is this line. So, that means you are integrating from here to here for a fixed y and as y changes from 0 to 1, you will cover the whole area like this. Therefore, range for the variable x is from y to 1 and y varies from 0 to 1. So, this is very important and again I will keep repeating this that draw the diagram we can two dimensions you can always do it and then you get a feeling for how the what are the ranges of integration and so on. So, integration with respect to x gives me x square x cube by 3 plus x square y by 4 from y to 1 and that is important because I must integrate with respect to x first since the limits for x are in terms of y. So, then I will first integrate with respect to x and then get the function as a function of y and then I integrate with respect to y. So, this has to be the order and you must keep this in mind and so finally, this comes out to be 15 upon 56. So, the arithmetic should be correct. Now, here what I was saying is that suppose you had to compute the event probability y greater than x. So, in that case you see what will happen is it is this region over which you have to do it. So, then you see you will have to break it up into or what you can do is maybe no it is not necessary because then if y is greater than x you will want to write the limits for that means for a given x how will your y vary that is no problem. The y will vary from here to here that means it will vary from x to 2. So, I will integrate with respect to that means if y is varying from x to 2. So, we will have to integrate with respect to y here. So, the limits would be x to 2 and then x varies from 0 to 1. So, this will be the this will give you this probability. If you integrate first with respect to y x to 2 the same function and then you integrate with respect to x because for a given x. So, this is how when you have the diagram you can immediately see that given a value of x the corresponding value of y can range from x to 2 and that is it. You can compute this way right. Now, just look at another example and maybe we do not need to compute it fully, but I will give you an idea here. This is f x y is defined as c into y square minus x square into e raise to minus y. Now, the limits for x are from minus y to y and y varies from 0 to infinity. So, therefore, to draw the diagram see what I said is that when y is fixed then my x is varying from minus y to y. So, it has to be between the lines this is x equal to y and this is x equal to minus y right or minus x equal to y whatever whichever way. So, this is this and this is this this line. So, your x is in between these two lines and your y varies from 0 to infinity. So, it is this region extending to infinity right this is the region. So, once you know this then there is no problem because anyway you was first want to find out the value of c. So, find value of c such that this defines a pdf. So, then you can integrate and you see the what will happen is that you come up to here. Now, this is y cube e raise to minus y. So, you will have to you know do integration by parts and it will have to be done three times because you know you this will be your first function this is second. So, you will have to in the first iteration you will get y square then you will have to do it again to get y and then get rid of the y. So, therefore, it will be three times you will have to repeatedly apply integration by parts to get the value of c. So, that this integral finally, has to be equal to 1 and this yeah.


Hello, my name is Frank Hwang and I'm here today to share with you how to rapidly navigate through your scores on the Henley app Which is available on the iOS and Android tablets. I hope you find this tutorial to be helpful The Henley app provides a number of different ways for page turning If you like to go one page forwards or backwards simply tap once on the right or left part of the score like this You can also easily turn your pages if you have a Bluetooth pedal that is connected to your device Let's say if you want to jump to a later section of the piece or quickly navigate to a different movement of a larger work That can easily be done Go to the tiny dots here on the bottom of the screen and simply drag and swipe And as you can see here, you can control the speed depending on how fast you're swiping Another rapid navigation option is to tap the bar indicator which is located on the bottom right corner Here you will see that the bar numbers are organized in 10 measure increments As I mentioned earlier, you can also jump to another movement if you prefer One of my favorite and useful features of the app is the ability to rapidly go back to the beginning of a repeated section It is very easy to do this when you reach to the page of the repeat Tap with two fingers anywhere on the screen to go back to the beginning of the section Alternatively, you can also accomplish this with a Bluetooth pedal Simply tap the left and right pedal button simultaneously And for those of you that are wondering how this works for movements that include decapo sections, Henley makes it really convenient for the performer Here in the electronic version, you will find that the full repeated decapo section is reprinted in its appropriate place I love that they do this because then you don't have to worry about turning several pages backwards as you would if you were to use the printed edition As you can see, there are a number of different and easy ways to rapidly navigate through your scores Particularly useful is the option to jump back to the beginning of a repeated section I hope you enjoyed this video and that you will consider using this wonderful app To read my review and overview, please see the link below Thanks for watching


In this video, I will be sharing the top reviews of the book, The Paper Palace, written by Miranda Cowley Heller. This book is on the list of New York best-sellers for the last three weeks and overall rating of 4.05 which is pretty great. It is a perfect July morning, and Elle, a 50-year-old happily married mother of three, awakens at The Paper Palace, the family summer place which she has visited every summer of her life. But this morning is different. Last night Elle and her oldest friend Jonas crept out the back door into the darkness and had sex with each other for the first time, all while their spouses chatted away inside. Now, over the next 24 hours, Elle will have to decide between the life she has made with her genuinely beloved husband, Peter, and the life she always imagined she would have had with her childhood love, Jonas if a tragic event hadn't forever changed the course of their lives. As Heller colors in the experiences that have led Elle to this day, we arrive at her ultimate decision with all its complexity. Tender yet devastating, The Paper Palace considers the tensions between desire and dignity, the legacies of abuse, and the crimes and misdemeanors of families. Karen from Roseville says my goodness. I loved this book. Perfect to read right now too. A family spending all their summers on Cape Cod. A family that has dealt with some devastating history. There's so much more to this story than what the synopsis states. So many layers, so much that many of these characters have endured. You'll laugh, gasp, feel enraged, so many emotions. The perfect read for me. Oh, and just beautiful descriptions of the land and sea. Claire from the United Kingdom says I loved this book. The proof, thanks to the publisher, had sat on my shelf for far too long, and when I finally pulled it down, I read it in a day and a half, because I couldn't stop. One of those books that I read while walking around the house, attempting to do other things. Published in July. Every summer Elle goes to The Paper Palace, with her family, husband, three children and mother. A series of cabins in the woods on the Cape. She's been going there since she was a child when she became friends with the neighbors, including Jonas. Ellen Jonas have a complicated history, which we learn in luminous and illuminating flashbacks. The present day narrative takes place over the course of 24 hours, at the end of which Elle must make the hardest decision of her life. In rich and sensuous prose, Cowley Heller, cracks open the human heart and exposes her character's choices, the paths not taken and the devastating consequences. I smelled the old cabins and the backwoods, felt the pond water lapping around my ankles, the love and loss of family.  Barbara from Florida says the story begins with Elle beginning her day after consummating a lifelong crush relationship with a man, Jonas, who she's known since she's been a child. Elle and Jonas came to this family compound, named The Paper Palace since they were children. Elle is two years older than Jonas, which is not a big difference in age now that they are adults. But as children, he was a mere boy. The beginning scenes are a bit, racy, in the description of their trist. Author Heller is direct. This is an extramarital affair. Elle then narrates her history, beginning as a baby, including the volatility of her parents' marriage. The structure of this story is Elle going through her present day, after having sex with Jonas, and the history of her life bringing her to this moment. She, at the current time, is contemplating if she should leave her husband and go to Jonas, the love of her life. Yet, through the ruminations of her history, she sees her husband, Peter, as a good stableman, a man whom she loves. Lou from the United Kingdom says The Paper Palace is a story of summer, secrets, love and lies. In the course of a singular day on Cape Cod, one woman must make a light-changing decision that has been brewing for decades. When the novel opens, it is 6.30 a.m., the present day. Elle Bishop, a 50-something happily married mother of three, wakes at dawn and heads down to the pond for her morning swim. She is staying at her mother's summer camp, nicknamed The Paper Palace, on a freshwater kettle pond in the backwoods of Cape Cod. As Elle plunges naked into the bracing water, she thinks about what she has done the night before. How? In the middle of her mother's dinner party, she and her oldest friend Jonas crept out the back door into the darkness and had frantic breath taking sex for the first time while their spouses chatted away inside. Over the next 24 hours Elle will have to decide between the life she has made with her genuinely beloved husband, Peter, and the life she always imagined she would have had with Jonas, if only they hadn't had to carry the shame of a tragic event from their youth. Kelly from the States says After having a fail with everyone else's summer faves seven days in June I had sworn myself off of Reese's book club pics. I thought I could easily pass up The Paper Palace after taking a gander at the blurb that talked about how these two married people snuck out of a family dinner while on vacation to bang because no thank you very much. But then people were commenting that it was disturbing and well. And for the content? Yes, disturbing, is an accurate word. I am not one who wants a sensitivity reader or trigger warning so I am not going to spoil the contents contained within this book's pages by saying anything aside from if you don't like dark, then stay the hell away. All you need to know about this one going in is at the story of Elle and Jonas who have been friends most of their lives, spending their summers together vacationing with their families in Cape Cod. This book is all about secrets of the past and what they can do to a person. As far as I'm concerned it proves once again that. Resources of this video are available in the description. Feel free to check them out.


Hi everyone, my name is Aleksandr Gladysh and today I will tell you about rapid back-end prototyping for a geolocation based mobile game with OpenResty, Radis and Docker. I will tell you a little bit about the case, about the technology stack in general and in details about the nuances of this stack. I will tell you about how the game world architecture is laid out. Hopefully I will show you a very brief demo because the time is really short. I will mention a little bit about the client side and after conclusion maybe we will have a little bit of time for the questions, otherwise I will be here. A little bit about me, I am developing software since 2002, most of the time in game development and lots of things beyond the game development now as well. Well, I am a Lua person, Lua programming language, it is my favorite one and we are holding a conference in Moscow this March on Lua. There would be hopefully some topics on the game development, so you are welcome to come here. What are the games with geolocation? Anyone knows what this is? Okay, everyone knows. So those are the games with geolocation. Well, and given the success of that game, we decided to try a little something to prototype a number of ideas on the gameplay we had and to figure out what is fun, what is not, what works out, what doesn't. And well, figure out what are the technical limitations of the thing too. And well, as a result in less than two calendar months and about 100 hours we have a playable prototype, mostly for the service side technology, but with a small client. And it's enough to get us rapidly iterating on the gameplay. Well, what does this talk about? This talk is about technological side, not the game design, not monetization, not something like that. So some of the examples will be silly from the gameplay standpoint. I am talking about technology. And well, right now it's easier than ever, I believe, to develop the geolocation based games. And I believe that there's quite a lot of space for creativity there. Quite a lot of space for new things, not to repeat the other major brands, but just to have fun. Since it's so easy, it's easy to have fun here as a developer too, not only as a player. And well, here's a gameplay for the prototype. It's quite simple really. The player with his phone in his hand walks around and he searches for mobs, monsters, that is, which are placed on the map. If player finds a monster, he can try to collect it. There's a certain chance that the monster will escape. Otherwise, well, a statistics counter gets increased in player's profile, monster vanished, and then it responds after a certain time. And basically that's it. Other than that admin users may add new mobs on the map, new spawn points. For the initial prototype, that's quite enough. You have to start small, but not so small that you don't lay down the foundation for the next new features. So start small, but generic. The stack we choose is something we used earlier on other projects. It's something we are familiar with. You can choose, of course, something else, but I'm talking about what we did. It's Redis as the database. OpenResty as a web server and application server. Docker as a thing to hold it all together. That's for server. And for client, that's a single page web application in a browser. We have HTML5 implementation of the client code. Well, why Redis? For us, it's a reliable proven solution, which, luckily, supports yellow positioning out of the box here to commands for the Redis related to that. You can Google them up. And Redis as well has a nice set of primitives to store the game object data. And well, since we're coding in Lua, our application on the server side, it comes as a nice bonus that Redis has stored procedures in Lua. Never use them, actually, for this project, but there are a few places that can be useful. And why OpenResty? OpenResty, what it is first? OpenResty is an engine X, a web server, distributive, which supports out of the box Lua, Redis, and many other useful things. And Lua there is, you have an option to install plain Lua, but for the fastest performance, not that it's needed for the prototype, of course, but still, you can use LuaJIT, which is much faster. And well, so OpenResty is something very fast, quite friendly, at least to me. And while maintained, there are some large corporations behind it. Let me move the cursor though, sorry. And it's useful for quick prototyping as well as for the production environment. We use it on production on other projects, as we use Redis too. And the Docker is a good thing for us because usually when you have a complicated ecosystem on the server side, it's a pain to set it up for each single developer. Okay, for a prototype, there may be a single one developer, but then you have to deploy it somewhere. And let's do the same thing again. With Docker, you have a reproducible environment, which you just write once the Docker file, and after this, you can set up the Docker containers you need just with a few commands. But the problem with Docker for us is that, okay, it's really good for developers. You don't have to teach every single developer to set your project up. But it is arguable if it is suitable for production because there are certain performance problems, certain reliability problems, which can arise still, unfortunately, on the higher loads, so to say. But that's a prototype that doesn't matter. So you can set up Docker environment on your server really quickly for the prototype and then decide what to do with it. One point though, Docker usually is outdated on Linux, at least on Ubuntu, not to say about Linux. In general, so you have to update it to sufficiently recent version. I don't know, maybe it's changed with the last Ubuntu release. I haven't seen it. And the browser, well, it's for this project we are prototyping the server side first. So the client doesn't matter much, but still the game has to be playable. You can, of course, as a developer, send CURL queries from the common line, but it's not fun. And it's hard to do from the mobile phone while you're working around and playing the game. So some client has to be there. And well, you have to have a map, you have to have a list of game objects. But if you remember this original title we were talking about in the first place, there's certain kind of combat there. You can imagine this in your head. In general, don't implement anything you can imagine at least at first. So you are sure you can implement later. For us, it's not a problem to well do this kind of thing, not tied to girl location. And the girl location is the main topic here. So we skipped the battles. We skipped other frills and the client is pretty basic. And well, another problem here is that girl location data access is rather limited on the browser, but it's okay for our purposes. And well, I will skip some of the slides. You can read them later, given that we have little time. So on the developer machine, Docker is quite simple. The client, which is browser, connects to the local host port. And there, those two square boxes are sitting Docker, OpenResty sells the HTTP request and talks to Redis, which it resides in another Docker container. Here's a configuration for the Redis. It almost works out of the box. And I will not read it to save the time. Here's a configuration for nginx, the interesting parts. Basically, you serve the static here from the index. And you serve the REST-like API for your application at another URL. And well, that's it. One thing to note here, though, is you have to disable the lower code cache for fast reloading. So you change the code on your computer and it's there on a server. It drops the performance a bit, but you don't care that's a prototype. And here's a Docker file for the OpenResty. Basically, it just copies all your code there and launches it. One little trick. So the OpenResty sees another Docker containers. You have to tell it that the DNS server from the Docker resides right here. So you have to adjust Resolvers Conf. Anyway, how the API works, there are only three player calls to get the game real estate, to get the specific game object status a bit redundant because the objects are here as well, and to call the game object action. And there's a few system calls to create a new player to reset everything to the factory state. It's often needed when you're prototyping. And to upgrade the database that's B to the current version, so if you just deployed your code in your version and have to change the data. And we are not implementing any kind of back office UI to save the effort, but we're using the in-game mechanics for in-game, well, game management. So certain users can be made admin and through game actions, sorry, they can change the relative, they have the proper permissions. How much time do I have? Seven minutes. Good. GameObject. Well, for server, GameWorld consists of game objects and game objects only. GameObjects has numeric characteristics and a list of actions. It may have coordinates and if it doesn't, it's either a prototype for another game object or it's inside another game object like an item in inventory. And the prototypes are there to save your work on the setting up the objects in the same way each time. So basically prototypes object includes its properties and actions from its prototypes and a prototype can have a prototype as well. So that's like inheritance in programming. Characteristics. Well, this slide talks about how they derive from the prototype doesn't matter. GameObject actions as well. So here's an object. It's a green torot monster. Well, here it is the torot itself. It has a unique ID, sorry. It has a position and it has a reference to a prototype. Here's its prototype, which is a specific prototype for this kind of monster. It sets the escape chains for it and it has a prototype in itself and that prototype, well, it sets the respawn time. And here's the implementation of the action that catches them up. We'll skip it. One interesting thing in Redis that you can, using the sorted ranges, you can implement the delayed action execution. You don't need any kind of cron. You just add each query to your server. Check if there are any actions to be executed by this time and execute them. In production you will have to limit this by the number of actions to execute right now, but for the prototype it works. And here's player. Here's an interesting item. It makes anyone who wears it administrator. It grants user admin rights. Here's how we give the admin hat to player and, well, here's how the stored inventory items work. Here's how the objects attach to another object work. Sorry for skipping this. No time. Here's a spawn point. Well, what else? A demo. Let me show you the demo quickly. As I said, it's quite basic. You can open it yourself and play a little bit on a mobile phone. Don't forget to change the user ID, otherwise you will be jumping around. As you see, no authorization. It doesn't matter because it's a prototype. Only people who know it played. And there will be link later in slides. As you can see, there's a map. Here's a green tot and me underneath it. And here's another green tot I placed yesterday. There's me. I have an admin hat. I removed it. Let's don it if the internet works. Ah, no problem. And there's a green tot. Its name is Bradley Perry. The names are randomly generated by a JavaScript library based on this as a seed. It's very useful because this seed, you can't remember it. And here's another user nearby. Anyway, what else? Here's how the client worked. Not interesting. You will read the slide. No problem. Here's a trick how to launch the Google Maps. I found that all the examples in the internet lock, one line or another. So I have to compile it together. And, well, the problems. The problem here is noisy deposition data from client and extremely low precision of geolocation in buildings. But there's no other problems. Actually, that's technical limitations you have to adjust your gameplay for. Well, what's missing? The event system is solely missing. It has to be added to the engine. And lots of small functions like pedometer, the number of steps you take and the meters you walk. So you can tie some gameplay mechanics to it. Well, that's a prototype. After you're done with the prototype, after you understand how it should work, throw everything away. Well, it doesn't work. But okay, at least start over and thoughtfully move parts, good parts of the code there. Not just reuse and hack around. Because in the end, close to release, it would not work at all. And thank you. That's it. Sorry for skip slides. We have a moment for questions. Yes, your comments. Oh, good. Anyone? Please? Can you detect if I am in the city, in the forest or in the sea? Depending on what date. Sorry. Can you figure out beyond the coordinates if I'm in the city, the player in the sea or somewhere else? Yes, you can. But you have to get the coordinates to the zone data somewhere. There's OpenStreetMap project, which I believe does something like this. So if you will tie this to this, that will work. Please? So there were three parts here, Redis, Docker, I'm sorry, I didn't understand what the third part is for. I'm sorry? What are the technologies mentioned here? Is Redis, Docker, and Sonya? OpenResty. There are three parts of technologies here. Redis, Docker, and OpenResty. OpenResty is there, the application code is. The code and law that defines your server-side game logic. Next question, please. No questions? Yes? Is this a game you're trying to... The goal of the prototype is to experiment with the technologies?  What's the goal of the prototype? The question? Well, for us, the goal of the prototype is to understand how the games, the girl-location games work. We have like a list of ideas for several pages, which try this, try this, try this stuff. And without something easy with which we can rapidly iterate, we cannot try those ideas, of course. The technology is second, and that's important only because you have to filter those ideas by the technology limitations, but that's it. This... No, I'm sorry. I don't have the URL on my... Or do I? I probably called all the... Come on. That's a pity. Everyone write down this URL, geo.logic editor.com, if you want sources or talk slides, they are there. I will publish the English language talk slides there today, and the game there as well, it's available for everyone to play. So it's a little small open-source game, patches and contributions are welcome, I will publish them as well. Well, so another question. Are we done? No, we have time. I think there's a question. Yes? You mentioned this is not a pretty secure authentication part. No authentication at all. We trust that you are the one... I may ask what would be a good start for implementing this? Can you do anything out of the box with Redis? It depends on the platform... Sorry, how to do the authentication properly in this game? It depends on the platform you're targeting, because users don't like to type in passwords. You have to type into Facebook or Google+, sorry, or whatever. So basically, the proper client would not be just a patient browser. It will be an application. It can stay in HTML, no problem, if the technology suits you, but you will have some framework, and you will tie the authentication from this framework to this game. If you worry about this prototype being secure, just add basic half there at your engine X config and that's it. Well, in Servit and HTTPS, as I did because the Chrome limits the geolocation data on plain HTTP. Another question, please? Yes, please. How can you be sure that the coordinates, the client send you are correct? It doesn't matter. Can you be sure that the coordinates client send you are correct? Like I said, it doesn't matter much because, well, it will be probably a problem for the final game, but then you will have the proper application where it would be harder to hack. Right here, it's easy to hack, but you're just trying it out. So if you worry about hacking this, first the people have to start to care about your game enough. And as long as you don't pay money to people who come to a certain place, you can forget about this until release, or until better at least. Thank you so much. Thank you.


Kings drops in back at the 21er to be a loss of 10. He's gonna be sacked. And coming on the blitz was Darren Hall. Matt on a straight drop, gonna loop it for Gage and the end zone flag down. Russell caught it though. Falling to the ground for the Atlanta touchdown. Holy smokes, what a catch by Gage. Gonna taste the deep shot looking for OZ. And Zackeus makes the catch at the 10.