Yes, I mean, I'm not sure I'm going to do that. But at the end of the day, I'm going to be doing this one. OK.

That's fine. That's good. That's fine? Oh, you're welcome. So good evening, everyone. My name is KJ Kawa. I am a professor at a particular architecture in Lisbon.

Actually, I'm a mathematician, so I use the mathematics. So maybe you don't find my work very practical from the point of view of architecture, but for example, attempts to help architects.

So the work we said here is a part of the research, in that developing the design tips for architects that can be particularly useful in the design of large buildings with complex and specialized programs like hospitals.

So if you think of an architectural layout, especially in case of the housing, these are the design risks. We have T1, where it is given by the users. So it's the number of the rooms, and then the shapes of the rooms, which is generally rectangular or orthogonal, the shape of the layout,

and then there are some dimensional constraints, which are based on the area of the rooms and the area of the layout, and the topological constraints. So if you see mathematically, so the dimension constraint is already an optimization problem,

and the topological constraints are quite interesting. So normally, this is how the topological constraints are given. So we have given a graph, which we can see on the left-hand side. So for example, in case of house, we can say that we have given the dining room

goes to the kitchen, and at the same time, there can be negative adjacencies, like the playing room should be away from the library. So these are given to the adjacency graph. So even if it's given in some other way, we can put it in the form of the adjacency graph. The idea is to have a convolutional schema satisfying

the adjacency relations set by the even adjacency graph. So we can already see that there are two solutions first from the given adjacency graph. So there can be many solutions, and then we can restrict the solution on the basis of the shape of the layout.

So the first one is kind of a brush shape, but the second one is rectangular. And then on the right-hand side, we have the adjacency graph of the design solution, which cannot be similar to the even adjacency graph. So this is the right-hand side.

The adjacency graph is called the deep wall. And if we consider the adjacency among the exterior, like here, if we consider like this is north, and we consider the adjacency among this exterior, then we call it the dual graph. So the dual and the dual graph.

So this is what the space observation problem is that we have given the end rooms, and then we have given the width and length of each room, and the adjacency relations among the rooms. And the problem is basically in terms of rectangular problems. The problem is to fit the even rooms

inside the rectangular, while satisfying the dimensional and the topological constraints. So if we see the dimensional constraints, they are both end of the optimization problem, and if we see the topological constraints, it's more of a graph theoretical approach. So already two big mathematical domains are involved here.

So front-round design layout, so obviously it's a multi-constraint problem, so we have the topological constraints, dimensional constraints, and then there can be many many other constraints which are put by the user or by the architects,

like the view and the daylight and many other things. So initially we are concerned with the topological and the dimensional constraints only, and then maybe we can lead to the architect that they can modify the results which we are proposing.

So there can be two approaches, one is to consider the dimensional and the topological constraints simultaneously, and the other is to first concentrate on the topological constraints, and then consider the dimensional constraints. So what I am working is

I am using the second approach. So now we introduce the concept of the best-connected rectangular formula. So we have seen that we have an adjacency graph and then for the adjacency graph we can obtain a rectangular formula. So this is not like we have the design brief given adjacency graph

then we can obtain a rectangular formula and then it has the the design solution adjacency graph which we call the DVQL. So now I put mathematically that this brief dual-organ design social adjacency graph can have at most

3A-7 edges where n is the number of D moves. So idea is to to obtain a solution which has the maximum connectivity because connectivity is I think very important in any design so which has the maximum connectivity and if we look directly for this

so at some point of time the idea is that that all the given adjacency graph should be contained in this solution if it is possible then we do not have to look for the given adjacency graph we can directly say that we are already considering this solution which has maximum connectivity

so that's why we do not have to look for the connectivity every time. So for example if we consider the 4 roots then y is equal to 4 3A-7 is equal to 5 so if you see both the solutions and if you draw the graph for them the number of edges would be 5

but in the first solution now for 5 roots the number of edges should be 5 but in the first solution now for 5 roots the number of edges should be 8 so in the first solution the maximum number of edges can be 5 and in the second solution

the maximum number of edges should be 8 so if we have to move from 5 to 8 it means that we have to put the next room in a way that it should be adjacent to 3 of the existing roots so if we see first solution where we put the rectangle room it can be adjacent to

at most 2 rooms and in the second solution it can be adjacent to 3 rooms at least in this side or not on the other side so what I want to say is that the idea is to design an algorithm which always guarantees that at the end

independent of the number of the rooms we have the best connected rectangle 4th one so choose the number of the rooms and then there should be a compositional schema which should be generated automatically such that it should be best connected so there are

2 very common approaches which has been used for the derivation of the rectangle 4 class so one is what we call dissection and the other is the addition and in both we can see that at the end we are getting the same dissection so we are using

the second approach so this is the algorithm which we developed to have the best connected 4 plans for any given number of the rooms so we call it CRLAB algorithm so in this algorithm we start with

first 2 rooms in the center so you can say that first and second rooms are in the center then the third will come on the right the 4th will be left then above and then below so that's why the name is CRLAB algorithm and it can be always verified mathematically that the

compositional schemas which we obtained from this algorithm are always best connected so I am not showing how they are best connected but it can be best connected so the what approach we discussed earlier is that first we look for the topological constraints so that means that the best connected solution and then we

introduce the dimensional constraints so we introduce the dimensional constraints so if we have the rooms of the different areas so it means that at the end we have some extra spaces if the area of all the rooms are different and that's why we

produce the extra spaces in a way that the composition always remains rectangular but at the same time we have developed some optimization techniques so that the area of the extra spaces should be minimum

so these are the two two techniques which which we developed so one is the order of the ellipsoid the way in which the rooms are arranged because like suppose we have the five rooms so you can start with any rooms and you can end with any of the rooms

so there should be some order in which the rooms are arranged and then we can swap the width and height of the rooms to reduce the extra spaces so at the end of the day the area of the room will be constant so by swapping the width of height and by considering the order of the location the solution which has

the minimum extra spaces we get the best connected extra floor plan which always guarantee the minimum area extra spaces so this is the example that we have been looking for rooms their width and height and using the CRLAV

algorithm we developed this extra floor plan so again using the algorithm I am just showing you an example of the before rooms but using the algorithm we can design very complex buildings like the hospitals which have 50 or 100 rooms so using the CRLAV

algorithm we can develop the item of time dependent of the number of the rooms and then using the okay prediction techniques we can see the difference that both are developed through CRLAV algorithm but the area of the first one is 968 and the area of the last

the second one is 1786 so we can see that by just having the two operations we can reduce the area of the extra spaces that much so the future work is to identify the other best connected computation

schema so that the user can have the many different choices and the idea is to consider the other architectural constraints that's why now I am in the architecture department so that I can know other architectural constraints and to identify the circulation

paths these are the references thank you very much clapping