the CI. So, we talked of an important theorem of linear variation. Incidentally, this particular theorem is of course nothing to do with the CI, it is related to linear variation. So, it is basically a mathematics theorem of mathematics. So, if you vary the wave function which is expanded linearly in a basis, which means the basis functions are known, these are the only ones which are unknown. So, that is what we mean by linear expansion.  So, you have to change the exponent just like in hydrogen atom or r square, whatever. So, usually they are not linear parameters changing. So, obviously in that case it will no longer be called linear variation. Linear variation means the parameters which you are varying, they appear linearly in the expansion of the function. So, Cs are linear. If there is a C square or one term which is C square, it is no longer linear. I hope it is clear. So, I have a basis and if I had added one more term, let us say k square times some other kai, another known function, this would no longer be linear variation because k is an unknown parameter. I have to vary k which comes as a quadratic term. So, what we are talking about is only for linear variation. The theorem says that if I do a variation by normal way, that is, vary this with respect to the coefficient C i, then the result that you get is an eigenvalue equation which is H C equal to C e in a general form where C is the coefficient matrix which contains all the columns of the eigenvectors and e is the diagonal matrix consisting of all the eigenvalues of this problem. The same and this is something that we have already proved long back. I can again redo it that if I do taking this as a Lagrange multiplier that this let it be 1 and then you vary this coefficient, we have already proved it, we can directly prove it again. So, this is what you get. If you do the method of projection, the theorem says that instead of varying, if you simply do a projection which I did last time, so essentially start with this Schrodinger equation H psi equal to H psi and then put expansion of H psi C i phi i equal to E times C i phi i, then you project with one of the basis functions, one at a time specific phi j, then you will get phi j H phi i C i sum over i equal to E times C j. If phi j and phi i are orthonormal basis, if they are not orthonormal, here also results will change. So, that is unimportant. So, we are assuming that the basis is orthonormal both in both cases. Note that if basis is non-orthonormal, results will still be identical except that it is no longer the eigenvalue equation and you should be able to guess what it will be. The overlap matrix will come here just like we had in the Routhan equation Fc equal to Sc, similar things will come and you can then work on a non-orthogonalized basis. So, then you can see that this equation gives you some over i H j i C i equal to E C j which is again the same eigenvalue equation. So, this is the clear end. We have already proved that what you will get here is in the last class we have also proved this, that by method of projection we again did it. Method of projection is actually very quick, just one line proof that what I want to tell you that we can get the same equations. I hope all of you remember how we got this equation for the method of variation but those who do not I will just refresh the mind that you expand this quantity subject to psi psi equal to 1. So, what psi psi equal to 1 means in an orthonormal basis is it this means that sum over i C i star C i equal to 1. So, this expansion is very easy in orthonormal basis because you expand with a phi i dummy index phi j dummy index but phi i phi j is delta i j. So, you will get this but then of course psi i psi will be sum over i j C i star C j and the matrix element between i and j of the Hamiltonian between i and j. So, you have h i j or h j i does not matter how you do it. So, this is what it is. So, you have to now put a Lagrangian which is sum over i j C i star C j h i j note that whenever I write h i j it means phi i h phi j. So, that is normally the symbol. So, when I wrote here phi j h phi j i wrote h j i but it does not matter you can always change the dummy index I mean to suit it to this form immaterial but this minus some lambda times C i star C i minus 1. So, remember whenever you write Lagrange multiplier make the equation as something equal to 0 and then only write the left hand side that is the trick. So, this is what you will vary with respect to C i and lambda of course if you vary with respect to lambda you will get this back this condition that is trivial and then you vary with C i. So, you get one particular C k let us say you get h k j C j sum over j equal to lambda times C k. So, lambda becomes your E in that case. So, lambda time becomes your E. So, you can easily do this exercise. So, do with respect to let us say C i star. So, you will get so del l del C i star will give you sum over j C i star will be taken out h i j C j equal to lambda times 1 C i will remain only 1 C i will remain specific C i. So, that is the reason you normally do not like to write this C i we will like to write this as some k. So, this will become h k j C j lambda C k it is one and the same thing as long as you understand this is no longer a dummy index here. So, you get the same equation as here please remember this is just i j interchanged otherwise it is the same equation. So, I think we had already done this I just showed that the method of projection provides the same results and this is true in general as a why did I say in mathematics because essentially Schrodinger equation is nothing but eigenvalue equation. So, for any eigenvalue equation whenever you want to optimize the eigenvalue by a variation principle you will get the same result in the case of linear variation by either variation or method of projection. So, that is why in mathematics it is actually mathematical theory nothing to do with quantum chemistry per se we are simply going to use this in quantum chemistry is it clear. So, anywhere there is an eigenvalue equation you can use variation principle to get the eigenvalue. So, it can be used in physics engineering several problems and the theorems are all true. So, I think you should understand the generality. So, certain parts of quantum chemistry are very general we are actually using mathematics to understand certain principles and they can be used anywhere. So, with that what we will do now to derive the CI equations where of course please remember our phi i's are now the basis what are the basis in the configuration interaction the basis is the basis of slated determinants. So, they are n electron determinants this is an n electron function what we did was a general problem where psi and phi can be anything it can be one electron two electron does not matter but for our problem this wave function is an n electron wave function these are n electron slated determinants. So, we have to write the equations and quite clearly if there is n electron two you will get the same equations but to go through the principles of variation would have been more difficult of course now we can directly go to the equation but I will still like to write the method of projection just to show you the nature of this h ij matrix because the key thing now is actually to get this matrix that is the key thing. What is this matrix? This matrix is the matrix of Hamiltonian between the slated determinants now these are the slated determinants. So, all I need to calculate is a matrix of the Hamiltonian between slated determinants and diagonalize. So, the c i problem is extremely easy conceptually once you understand the mathematics that we do not have to go through the formula again but I will go through the proof again the derivation again but the point is that you have to construct this matrix and diagonalize. So, all the energy is and then you have all the other theorems of the linear variation that each eigen value is a upper bound to its own excited states to its corresponding states right the epsilon the the the McDonald theorem. So, remember the McDonald theorem all that will apply now. So, in that case c i is a very powerful method because remember when you did Hartree-Fock we are only talking of ground state we are only talking of improving ground state for perturbation but in c i we will get upper bound for all states. So, c i becomes a potentially good method for deriving excited states not just ground state. So, this is the first time we are talking of a method which is potentially can give you excited states. However, c i has lot of deficiencies particularly approximate c i which is what we will discuss not the full c i and that is where the c i c i has really not been a very good method as it turned out to be. So, we will discuss that later. So, let me go through the the derivation once more but this time I will do only by method of projection to show how this this structure of the matrix and then of course to evaluate this matrix. We already know how to evaluate the matrix right by slater rule depending on the two determinants either they are equal they are one occupancy difference two occupancy difference we should be able to write this later. But remember here the determinants can be anything any j any i s you have to be very careful in writing. So, that is a technical part when you actually write this later rules but we have all the what I want to convince you the entire tools that are required and its consequences have already been covered. So, in a way c i is very easy what we have to really do as a deficiencies of the c i. So, what we will now do is to go back to a c i problem and remind you that your psi was c 0 you can use phi or psi does not matter what you want to use then you have c a r psi a r and so on. When you when you presented the general problem our wave function was a very very easy we can write by one index. Now, what we are doing is that these are my phi i's but they contain other indices a r a b r s that is only to determine the determinant the basis itself with reference to Hartree form. So, that is why all these indices are coming but please remember all these indices together is what was my i here. So, a combination of a b r s was actually one of the i there. So, that is I just want to tell you that nothing has changed it is just that these are now necessary to track your basis itself. So, let us cut this here if I approximate and this is something I want to tell you now if I approximate my wave function just here then of course it is no longer full c i. So, it is no longer exact even in a finite basis. So, it is not even exact in the finite basis I should say other way around it is not even exact in a finite basis it is an approximate. So, there are two kinds of approximate one is basis approximation that I talked of another is the fact that I am truncating c i because even in a finite basis m c n is too large a number. So, to really do a matrix equation solution because then this Hamiltonian matrix will become m c n by m c n and you can very quickly find out what is m c n let us say m is 100 which is a which is a good basis or even 50 and n is only 10. So, you are talking of every modest electron like in a molecule like methane and you have 50 basis which is about the basis that even today the referees will always demand for any calculation and it is a 50 c 10 and please do that number you will see it is a huge number talking of 50 c 10 say a 50 factorial by 10 factorial 40 factorial fortunately helps you I had to cut lot of things but you still have 41 into 50 41 into and divide by 10 factorial please do that number and how quickly the number blows up. So, you can see I mean people do not realize what is this m c n it is a factorial expansion and and eventually it is simply not doable beyond a point. So, obviously we have to approximate and this is where now the physics comes in how do I approximate. So, obviously the first thing that you will take is the w x at because now I am not going to I am going to approximate based on a physics and I have now realized from m p 2 calculations as well as the synonyl glues articles that we described physically that the most important correlation comes from the pair correlation. So, the two electrons try to avoid each other. So, they get excited they get excited out of Hartley-Fock to form another determinant from another basis remember that excited is again not excited state we are still talking of everything for ground state. So, this is still a function of the ground state it should write size 0 eventually of course we will get all the excited states for a very different perspective in CI but it whether ground or excited it does not matter what I want to show that these determinants are also contributing to ground state. They will also contribute to other states eventually because you have a eigenvalue problem. So, obviously the if you have to take only one class of determinants apart from Hartley-Fock I will choose this that is the first thing because I have learned that then then you have a choice what will be your second class will you take singles will you take tributes singles you will not eliminate because I told you the Brillouin's theorem only shows that the Hamiltonian matrix element between Hartley-Fock and singly x at 0 and you will see that why singles will contribute if you have doubles before I do this let me first convince you that only singles is no good because of Brillouin's theorem. So, let us take an even simpler approximation which I now call it CIS where I write size 0 as C0 psi Hartley-Fock plus sum over AR CAR psi AR. So, that is all I just cut it I call it CIS it means configuration interaction including only singly excited determinants okay the S is an acronym which just says singles. So, I can now derive this the method of projection once again but actually it is trivial I can directly come to the solution but the point is what you will do is first write these as C0 psi Hartley-Fock plus sum over AR CAR psi Hartley-Fock psi AR note that I am just re-deriving okay so this is nothing new E C0 psi Hartley-Fock plus sum over AR CAR okay. So, I continue the CIS so what you do is to project with these basics right. So, first projection would be with psi Hartley-Fock psi Hartley-Fock itself is a member of the basis. So, I project to the psi Hartley-Fock. So, CIS continued so you have psi Hartley-Fock let us see what you get H. So, I am projecting the right hand side H psi Hartley-Fock times C0 right plus psi Hartley-Fock H psi AR times CAR sum over all AR. So, that is my first equation equal to psi Hartley-Fock is orthogonal to psi AR. So, I will only get E times C0 just as I should get okay E times C0 because J is now my phi Hartley-Fock. So, I just wanted to make sure that you get the same thing these are my H, I, J and then the second one would be project to the psi AR but since I am using AR as dummy index let me use the J as BS. So, another set of another set of virtual occupied and virtual orbitals V2 as excited. So, this is one specific determinant out of these basis okay the AR are dummy in this case. So, any particular BS so you will get again H psi Hartley-Fock C0 plus sum over AR psi BS H psi AR CAR right equal to E times C BS. So, that is the reason I wanted to redo it again because it is just that symbols are little bit different you should get E C J.  Coefficient for psi BS which is C J there and that is also easy to see because if you project to psi Hartley-Fock again psi BS will become 0. Here all AR will get 0 except when A equal to B are equal to S. So, exactly that particular determinant that is the only one to survive and then the coefficient will become C BS is it clear it is exactly restating this problem but just in a different language okay this is my equations for which I have to get solutions and you can see my first term is E Hartley-Fock E Hartley-Fock C0 and then the second term is 0 because of Brillouin's theorem. So, I have E Hartley-Fock C0 as E C0 correct this is my exact energy okay whatever E0 or whatever E0 you can say is my exact energy. Now note that without doing anything for the second equation I already have a trivial result my exact ground state is nothing but Hartley-Fock divided by C0 on the left and right hand side. So, my ground state energy at least does not improve okay I can show how by matrix part because this is where the matrix part will come the rest of the part will come but clearly from the first equation because of Brillouin's theorem I have E Hartley-Fock equal to E0. So, at least for the ground state there is no improvement and that is the reason CIS is never practiced for ground state but what about the other states because it is an eigenvalue problem. So, I can get the other excited states. So, that will of course come because of the second equation. So, I will get this so I will I can write this now show this by a matrix structure. So, my matrix of Hamiltonian will look like the following thing so CIS. So, the first part will be E Hartley-Fock right. So, that is your first part then the rest of the HGI will be with psi Hartley-Fock and psi AR. So, these are all 0. So, this entire row of Hartley-Fock to singly excited will be 0. Similarly, when I come here this part is 0 it is just a complex conjugate of this term. So, this is also 0. So, this in a way can be written as all columns are 0. Note that this is a column of psi Hartley-Fock this is the column of all singly excited determinant this is the row of psi Hartley-Fock and these are. So, this is Hartley-Fock and these are all psi AR. So, I have just rearranging the matrix element. So, this is basically matrix element between psi Hartley-Fock and psi AR. This is matrix elements between a particular psi Vs with psi Hartley-Fock and so on and this is the main part which is now new in CIS which is basically represented here. This is a matrix element of the Hamiltonian between one singly excited to another singly excited and they will of course survive. So, let me call this block HSS it just means between two singly excited determinant. So, this is a block this is no longer one term because there is a set of singly excited determinant there is a set of singly excited determinant. I am of course projecting with one particular Vs here but I have to do one by one to get the eigenvalue structure and then I have C0 which is the coefficient that I am looking at and then I have all the C ARs. So, entire C AR whose number is exactly same as this number m by m number. So, all the singles I will get equal to E times a particular coefficient. If I write it in this manner of course this would mean that depending on what is my rho here I will get that particular coefficient. So, in a simpler way the way it is written is that you actually write this as a unitary matrix for all roots and then you can write this way but if I write for one column also does not matter. So, basically have E C0 and all C AR. So, depending on which rho you pick up for matrix multiplication you will get only that number I hope all of you are familiar in matrices I am telling you again. So, all matrices you have to be very familiar. So, we have already discovered that if I multiply first rho times first column and that is what we have done here first rho times first column you get only E times C0 and E is nothing but E hat or E naught is nothing but E hat. So, that is the first equation which is trivial. So, ground state does not improve. However, if I take the other rows let us say second row, third row etc times a column then you start to get an equation which will now give you other roots because you get a full equation. So, basically I have to diagonalize this matrix essentially I am diagonalizing this matrix and you can see this matrix has a very nice structure that the first row and the first column are decoupled from the rest. So, the first row and first column has a number E hat refock but the rest is 0 here, rest is 0 here. Such a matrix is called block diagonal matrix I think we have introduced it before but I want to again restate it is not a diagonal matrix but it is a block diagonal matrix. So, this is a matrix of two blocks one is heart refock another is singles between these two blocks it is diagonal. Within this block of course it is not diagonal. So, this eigen value problem can be easily done by diagonalizing the two separate blocks. So, if I have a block diagonal structure of a matrix. So, for example, give you an example of let us say a 4 by 4 matrix. So, I have a block of 2 by 2 and 0 another block of 2 by 2. So, these are the blocks which exist block 1 block 2 and I have to diagonalize the entire block then instead of diagonalizing 4 by 4 matrix you diagonalize x 1 2 by 2 and x 2 2 by 2 this is much simpler because you are diagonalizing 2 by 2 matrices instead of 4 by 4 matrix I hope all of you know this that diagonalizing a 2 by 2 matrix 2 2 by 2 matrices is much cheaper than diagonalizing 1 4 by 4 matrix and that is very important for you to know that diagonalization is the CPU or whatever is proportional to n q not linear. If it is linear then you would say what do I get I am doing 2 times 2 by 2 instead of 1 4 by 4 but unfortunately it is extremely non-linear. So, if it is 4 by 4 it has a pre factor and it goes as 4 cube if it is 2 by 2 it goes as 2 cube. So, then 2 times 2 cube is much less that is 16 4 cube is 64 right. So, this is a very important part in all the computation and I think one thing you have to remember that the CPU computer time for a step of diagonalization goes as n cube just remember this. So, if you diagonalize a 2 by 2 matrix and a 4 by 4 matrix you will require 8 times more computer time because it is 2 times more. So, the computer time will become 2 cube is it clear and that is the reason this is much cheaper than diagonalizing the 4. So, the recognition of a block diagonal structure of a matrix is a very very important part. In fact, this is something that you will later learn in the group theory course symmetry course that we use symmetry of the basis phi i phi j or whatever such that in a CI problem I can block diagonalize because the Hamiltonian matrix Hamiltonian matrix element between the two basis of different symmetry is 0 just like here it is 0 because of Brunner's theorem. So, if I have a phi i a one symmetry phi j of another symmetry we will not worry about what is that there are representers in irreducible representation etcetera then the matrix matrix element is 0. Once the matrix element is 0 you can quite easily get a block diagonal structure and that is the reason group theory is very very important it simplifies like but I think this is an example of that that because of the entire block of psi ar does not couple with psi Hartree-Fock I get a block diagonal structure. So, I can get downstate energy directly as a Hartree-Fock and then I just diagonalize HSS. HSS is not 0 of course you know there is a structure of HSS we will discuss that. So, if you diagonalize this you will get rest of the eigenvalues and they will be your excited states remember you will get excited states. So, CIS it cannot is not used for ground state I hope now everybody can defend why because the ground state does not improve Hartree-Fock remains Hartree-Fock but it can be used to get excited states because the eigenvalues of HSS block will give you excited states of course you will argue that the states are not good that is a different matter because I have not used doubles or triples I have made a very serious truncation that that only singles. So, results will not be good but at least you will get a results in fact many times in the programs Gaussier or games when people use a very large molecule to get a rough estimate of the excited states this is what is done CIS but CIS is never done for ground state and I think that is the physics that you should remember that the ground state will not improve because of this of this coupling terms being 0 and that is because of Brillouin's theorem. If I would have used non-Hartree-Fock orbitals then of course it would be a completely different matter because there are no Brillouin's theorem is there. So, as long as I am building my determinants out of a Hartree-Fock orbitals and virtual orbitals is orthogonal to the Hartree-Fock orbitals I will have Brillouin's theorem and then ground state will never improve by CIS. So, to get an estimate of first estimate of the ground state however bad it is you must have doubles that is that is very important to realize only singles will not help. The question is do you want only doubles or you want singles and doubles of course singles and doubles will be better than only doubles because more the merry. So, you can get by direct solution of the Fock operator or Routhan equation or you can have some other orthogonal basis which you know are orthogonal then I do not care how. So, Hartree-Fock orbitals are separate after that you can have a separate set of virtual orbitals they need not come from the equation in fact that is an interesting part how will you get it is a different matter but if God gives you no problem you can leave with that but of course this is the better way to get it anyway once you have a Routhan equation. So, the point is the CIS is also very useful to obtain excited state and these excited states also have a variational principle that they are upper bounds just as we said for the McDonald theorem. So, McDonald theorem anyway holds for all variation I do not care how many basis you use. So, they are very nice but then we are interested in the ground state. So, we have to look at a somewhat better method. So, the first method but before I do that let me let me just analyze the HSS block the block of the Hamiltonian matrix element between the singly excited and WX I seen two singly excited. So, essentially this block has psi bs H psi ar for some ar some bs which can be arbitrary now. Now clearly you can see that at all times you can use later rules note that when ar is equal to bs you should use which later rules the first one because that is an average value though it is no longer in the Hartree-Fock but I hope you will be able to do that. So, for example if I have a two electron problem my Hartree-Fock is let us say 1, 2 and one of the excited determinants is 1, 3 another can be 1, 4, 2, 3, 2, 4 these are all excited determinants right and so on depending on how many virtuals are there let us say I have only two virtual spin orbitals 3 and 4 I am talking everything in terms of spin orbitals incident then what I am saying is that if I have one singly excited determinant this is my Hartree-Fock if I have one singly excited determinant here another singly excited determinant there which is identical then I am going to use simply my previous rule 1 but then rule 1 we always use for 1, 2 but now do not get confused rule 1 is general it just says whatever are the occupied orbitals in the determinant right so this will have become h11 plus h33 for example the first term and then you will have rest of the anti-symmetrize matrix you can actually write them down that by i less than j ij ij ij anti-symmetrize so you can write them down very easily and of course then later on when you do spin integration depending on whether this is a up spin down spin you can say if there is a coulomb or exchange I hope you remember that that comes much later when I do spin integration that I will say that for parallel spins I have coulomb as well as exchange for anti-parallel spins I have only coulomb I hope you remember we have done this please revise all this for the end time the entire thing will come it almost looks like ages when you did this though I have done it even in 4 to 5 actually those have attended so that comes in spin integration so coulomb and exchange of integral that we talk of is actually in terms of special orbitals in spin integration right now I have a general form which is half ij ij anti-symmetrize which can be written as i less than j ij ij so in this case it is very easy because there is only one term so I can very quickly write this as 1 3 anti-symmetrize nothing else is there and no half half will take care of the fact that there was a 3 1 3 1 which I did not write so and 1 1 1 1 1 3 3 3 0 so this is just that just to show you this later however there would be terms which is ar and bs are different now there are lots of deep possibilities for example I have a coupling between 1 3 and 2 3 for this I am going to use rule b right because they have only one occupation difference and the result will be simply 1 h 2 and then there is a another term for the 2 electron integral correct on the other hand I can have 1 3 and 2 4 then I have to use rule c because both are different it is a doubly excited and there will be one only 2 electron integral which will survive between 1 3 and 2 3 okay so please even to construct h ss you have to be careful about which rules to apply and how to apply okay do not start writing the formula for heart reform because that is something that comes out of a memory all the time please understand and try to understand the formula what are what are orbitals is what you have to understand and then you have to write so for example if I have to write 1 3 h 2 r determinant which is actually a part of the single x array determinant so I hope you understand what I mean by 1 3 these are all determinants actually just to make sure that you understand okay these are all determinants so what will be the result there will be no 2 electron integral 1 electron integral there will be only 2 electron integral and this will be 1 3 2 r 2 4 sorry and of course then you will write it in regular integrals this 1 3 2 4 minus 1 3 4 2 then if I give you what is spins you have to do spin integration so all that will come up after that so please understand the steps because right now I am writing as a generically as a in terms of spin orbitals and then of course I will specify the spin orbitals in terms of space orbitals with alpha and beta and that will help you to spin integral you cannot spin integrate unless you know that okay so this is how it goes so you have to apply depending on rule BC the depending on the determinants either rule A rule B rule C so HSS will of course not be diagonal or even block diagonal there may be some lots of elements which will be 0 but very hard to identify lots of elements will still be 0 okay even here but that is because of symmetry otherwise if you see the maximum difference between a psi A r and psi B s is how much for any any electron problem 2 it cannot be more than even for any 10 electron 20 electron does not matter because rest of the orbitals are same spin orbitals are same the only difference in here already A is replaced by r so r is there here B is replaced by s so if A is not equal to B r is not equal to s the occupancy difference is still only so I think this is what would be interesting is if A is equal to B r is not equal to s so that is a case where 1314 where A is equal to B that is 2 which is replaced by 3 and 4 so you can see the difference is only 1 in the case A is not equal to B r is not equal to s the difference is 2 but it will never be more than 2 so by slater rule every term will survive actually this is very interesting part for the single single block every term will survive but it practically becomes sparse because of spatial symmetry that is a completely point that we are not discussing that is part of the group theory that is certain integrals like 1323 like this or yeah 1324 let us say it normally should survive by slater rules but it may still become 0 because of the symmetry of 1, 2, 3, 4 that when I actually calculate the integral it becomes 0 that is that cannot be predicted by slater rules that comes of a different symmetry so please understand that there are different levels slater rule directly says certain things will be 0 okay triples 3 occupancy 4 occupancy they are all 0 single occupancy based on Hartree-Fock is 0 because of Brillouin theorem only from Hartree-Fock to singles but not from 1 singles to 1 singles okay so do not use Brillouin's theorem for this because I know a lot of people will use just as 1, 2, 1, 2, 1, 3 is 0 1, 3, 2, 3 is not 0 I hope you understand what I mean because this is no longer Hartree-Fock Brillouin's theorem is only when there is a Hartree-Fock determinant and H and S i n that is 0 so when you apply Brillouin's theorem be careful okay so in principle they may survive but because of spatial symmetry when you actually calculate the integral the integral may turn out to be 0 so there is a lot of sparsity that will come in the matrix I hope all of you know what is sparse matrix what is sparse matrix where most of the elements are 0 okay or many elements are 0 so this sparsity index is very important how sparse is my matrix if the matrix is a very sparse then it is good for me because most of the elements are 0 people should know how to do it because normal algorithms will not work because you do not want to process zeros you want to only process elements which are non-zero and this is a very important technique in C i how to write an eigenvalue equation involve eigenvalue solution involving only non-zero elements so if I write a matrix times matrix you normally write a loop driven code that will not work okay so the matrices are sparse so that is a good thing even for singles to singles block and later on of course you will see much more sparse matrices will come when you go further because of later rule alright so the point that I am trying to say that for ground state C i s is not important and even for excited states C i s gives results but they will not give good results obviously but they give reasonable results.


nsive work an excellent work which they have done to community participation but women's participation and awareness remained an issue in these areas similarly when we looked at some of our studies from the other states in terms of perception of local communities people are well aware of this you know community of the important functions of the mangroves to their lives and livelihoods but the only issue is how they are going to participate what are these models what are these decentralized models of participation for the local communities which are available in some of the areas where intensive work has been done by you know agencies such as MS Swaminath Foundation they have been able to restore and create these institutions but in other places a lot of work in these dimensions continues to remain and if we look at the gaps that exist in terms of research we do not have important indices for different areas in terms either of mangrove species or even of biodiversity again we have gaps in utilizing community knowledge for conservation local local knowledge local traditional knowledge again there are few estimates available at the micro level on the types of goods and quantities extracted process or sold or what value additions are possible and what are being done there are lack of holistic studies in terms of cost and benefit analysis of communities from different parts of the country in terms of technology although we do have platforms for coordination in terms of MFF program or the you know the the Bay of Bengal program for coordination but a lot of impact of these coordination international level coordination at the grass root level remains to be seen there is there is a lot of scope for transfer technology transfer to the communities for adoption of alternate livelihoods you know the government agencies such as Department of Science and Technology have taken very very important initiatives for transfer of technologies for livelihood enhancement and ecosystem maintenance for other ecosystems but there is a huge gap in their work in terms of the mangrove ecosystem again use of advanced technology in ecological studies and few technological intervention in dissemination of information we still rely on the disaster background in fact I'm aware of Dr. Sodamani's excellent work in terms of role of you know information dissemination technology for such ecosystem I think she's done it for disaster but if we were to do it as a normal course of action and we have a lot of example I mean we have excellent example from our country what we can achieve by proper technology transfer in terms of awareness which would require in such areas not only advanced technology but revival of traditional technologies for community awareness and all these information failures actually result in a policy gap which is still a lack of coordination unclear policy objective at different peers and departments of governments again lack of systematic involvement of local communities in decision making still a gap in accounting of income generated by mangroves in state level and national statistics and again no clear linkages of ecosystem services with human well-being and social economic value maybe the only few studies that Dr. Sodamani has been able to demonstrate and the studies by the MS Swaminathan foundation but a huge gap still exists so we probably among other things we need to you know work at various levels at the community level identification of resource lose groups with varying dependency appropriate institutional models for benefit sharing etc harnessing the positive attitudes even when they are fan-sitters is very important and involvement of women again mangrove restoration using advanced technology in terms of awareness and reduction of biotic pressures on these particular habitats cooperation with international partners preparation of scientific management plans we do have management plans existing for almost all these areas working plans but how much it involves the role of policy makers and stakeholders we really need to critically examine and more research on the productivity of the mangrove dependent system and their contribution to the economy so thank you and with this we remain open to questions thank you professor Badullah this was a very very good presentation and ideally like how you kind of identified sort of gap areas some of the failures in information and technology which lead to policy failures and then you highlighted the way forward that that is what we are here to to discuss these and deliberate upon we have crunch of time like yesterday I was thinking I will do better but all the presentations and information were interesting and it didn't feel like you can cut short but we have some time to to have discussion and some questions most of the questions in QA box have already been answered so I thank all the resource people for taking time for typing and answering those questions live once again I like all of our speakers and panel members for a very interesting presentations and information sharing to start the discussion for a limited duration that we have now I'll like to go back to Mr. Vasudevan because there was a comment or a question from one of the panel members who could not post it on QA box and this was from Meenakshi would you like to ask your question Meenakshi or should I would you want me to to ask for you I can go ahead and ask the question was to Mr. Vasudevan about the about the legal status of like mangrove trees in India so I was just wondering because I read in the CRZ but probably this was an earlier notification that mangroves come on their zone one and hence they're not allowed to be cut what is the current status of this and does this mean that there's no like mangroves are not allowed to be cut at all or and what happens if mangroves are growing in private land or revenue land how does the forest department intervene in such cases or I mean it can be addressed to any resource person here I don't see him here so maybe he's there yeah please go ahead I would just comment on this because what I understand from this is it depends on the status of the land on which the mangroves are there if it is a protected area then of course nothing is allowed if it is a forest area it again depends on what is permissible if it is a reserve forest or a protected forest whatever is permissible or not and if it is private land then of course the tree act of the state would apply that is my understanding but if anybody can add on to this private ownership is a major issue in Kerala Karnataka as well as in Maharashtra actually you know in Kerala one BFO he purchased the private lands for the forest department and started protecting them so like that it is very difficult to grab the private land and unless otherwise you know we give some money without incentives it is very difficult to purchase by the forest department this is the current state thank you so much linking question so like in the case of Andaman islands where there was a subsidence because of the tsunami there is like mangrove recolonization and some of these subsided lands so in this case it's growing in like people's agricultural fields that were once there like functional agricultural fields but then at the same time the island protection zone notification says that like these are areas that should be protected so I yeah it's a bit confusing in terms of the gap of both policy knowledge and on-ground implementation so this is where the origin of my question comes from thank you Meenakshi yeah then that's a very interesting question and I actually saw that first and very recently during my last visit to Andaman islands for the sampling trip and Dr. Neruk and perhaps say something he has a much longer experience about Andaman islands on this one but my understanding is that the previous farm lands or agricultural farms which got subsided and mangroves are coming up in those cases there was some I cannot vouch for the efficiency of the process but some sort of reset like you know settlement happened government did provide some compensation for those farm owners whose land was subsided or hence made unproductive we can talk about whether it was a fair compensation how good it was then and all those things but there was this process and once that is sort of settled then they do not have an ownership of that land and then whatever the norms or regulations are under the coastal zone protection or mangroves that can take place however I do know not everyone agreed in terms of getting that compensation and they still hold that land so this is a little bit complex issue but Dr. Neruk wants to add something to that like Rupesh has mentioned it's a kind of a complex issue and more or less it is even some people have given up their land and got the compensation but as far as my understanding goes they when others who did not claim the compensation they also joins with them to reclaim their lands so and there is a probably a gap in implementation of policy so that may be pretty much common in many places as well so as far as in Andaman those who haven't got their compensation the policy is still kind of it's in a kind of a gray area so it's like there is no clear steps have been taken so the situations in mainland India could be quite different than how it is in Andaman because this is a kind of a very unique situation where croplands or human settlements were taken over and it does become intertidal whereas in the mainland you don't at least see that kind of situation or you don't have the land use what this land is so in Andaman you have lands that are still you know you don't know where to put them in the records so you don't have the issues in the mainland so the issues in mainland are quite different yeah Thank you questioner I think we can continue with our conversation it's an exciting topic and we all are mango lovers so I know time time is not crunch essentially for us but for a lot of participants and a lot of busy people I know we need to come to a closure of this interesting session so what I'll do is I will quickly do a wrap-up of today and then we will call it a closure and we have to meet again tomorrow to continue our discussion so this will give us some time for reflection so today's team was mangroves for coastal resilience and biodiversity conservation this is where we wanted to sort of bring together some voices people who are working in mangrove ecosystems these coastal areas on aspects which are not directly focusing on carbon sequestration and I think we did it very successfully we had a wide variety diversity of speakers talks, experiences covering not only biodiversity aspects from say bento to pelagic in Dr. Poonsil of father's talk but also about the social economic aspects that was covered by our speakers in their talks as well as in the panel discussion we started off with a very good welcome address by Professor Sivakumar and he presented his own personal anecdote from his visits and his work which was very encouraging he also identified some of the key aspect when at a landscape level water is damp or freshwater supply is curtail it not only hampers the estuarine environment because of freshwater diminishing freshwater supply but also suffocates the life because the essential nutrients are also trapped and that has implications on biodiversity on livelihoods the whole food cycle the food chain and food that ecosystem so with that with that great start then we moved on to our keynote speaker Dr. Vasudevan who has a great experience working in working or we say establishing the mangrove the only mangrove settled in India in Maharashtra and we continued there for eight years and although he was very modest in claiming this as a success story but we all know it was a great success story in terms of increasing the mangrove cover in Maharashtra what are the legal and policy and institutional changes that has to be made or creative solutions have to be derived to achieve that so this provides a good primer for other states or even countries how do you tackle those complex issues because as such these landscapes these coastal seascapes are heavily populated in many many many places and a lot of services or benefits are derived with people so they are these contesting claims on these resources and how do you tackle them something with a good political support it seems easy but it it takes time to to gather that political support to to drive that confidence and then carry on this so we thank Mr. Vasudevan for sharing that story then we had our first speaker Professor Punsilov Baderi from ISA Polkata and he dealt deeper into the complexity at the biological level looking sort of at the at a finer detail level I would say microscopic to a little bit microscopic level connecting the benthic and pelagic organism how these flow of nutrients energy occurs at the juncture of this where freshwater meets the coastal in this very productive ecosystem that's where the mangroves thrive and he shared examples from his work from Sundarvans and he highlighted the importance of long-term time series data if we need to understand these ecosystems in a better way in a holistic manner we need to not just have one or two sampling event taking snapshot but a long-term monitoring of these systems how these systems are changing how the organism are behaving across the seasons or at an annual or by annual level and if we have a good time series data we show the graph on salinity which is an important predictor of a lot of functions in that area so those kind of efforts need to be taken then we have a recorded presentation from Dina Resguana she's a doctoral student and she talked about the importance of mangroves taking us to Bithirkanika area Bithirkanika and Gahid Matha essentially that part of eastern India ISA affected quite a lot in today's discussions which is very good because that's the area I personally visited and also and that some work so very close to my heart and she shared the important value of mangroves as a firewood provider of firewood or fuel wood and other users that it is used she highlighted three important aspects one is the livelihood security second is the conservation value and then strong sense of space or place for the people's perception toward mangroves then we moved on to our panel discussion where first talk was by Professor Sadamini Das and her pioneering work in putting an economic value of mangrove is legendary as was highlighted a couple of times that we hardly see good number of studies putting some values economic valuation of these mangroves what kind of security or what kind of role they play in events like a super cyclone of Orissa and how learning or knowing more about wind pattern wind damage called by cyclone and how mangroves can protect against that gives us a good understanding a solid foundation for policy makers to formulate protection and conservation laws for mangroves then Dr. Ramasubramanian presented some of his experience and learnings from the practical aspect of restoring mangroves so he started off with some of the reasons how mangroves can be degraded destroyed anthropogenic as well as sometimes natural causes natural causes which are highlighted due to climate change which is because of anthropogenic reasons so and some of the successful areas of restoring mangrove sites how do you identify which are the sites where restoration should place that should take place and what needs to be done how do you mobilize community how do you find ways to generate livelihood option for the community while you are restoring mangroves so looking this as more associated logical complex system not just working mangrove individuals and then lastly we had Professor Chitatola from WIFI and she highlighted the provisioning and regulatory services many ways for sustaining the communities that live in these coastal environment the economic valuation of mangrove services therefore provides a very good reason to formulate policies that are helpful in long-term sustenance of these coastal environments she highlighted some of the technological and knowledge gaps and how we can address them to to basically address the policy level gaps so to make informed decisions to ensure that mangroves are accounted in national accounting the incomes that they provide the services they provide are not forgotten so we had a very sort of wholesome presentation and a good amount of discussion I believe in question and answer in the form of question and answer a lot of interesting questions were asked a lot of responses provided so I feel this is a very good second day and I before concluding this this day I would like to thank all participants for their active engagement and participation asking questions and trying to show their interest in learning more about the information and the knowledge about mangroves I also like to thank all our speakers and panel members for their time their contributions sharing their wisdom knowledge and I like to say that we have one more day of this interesting discussions tomorrow tomorrow's theme will be about recent advances in mangrove research in future perspective so we'll try to look from the lens of what we know already and what we still need to know so what are the directions we need to follow to advance our understanding of these ecosystems and how do we forge new collaborations new partnerships and how do we address some of the challenges that lies in front to achieve that successfully so with that I would like to thank everyone and I will call this today's session to a close thank you all


We mentioned the range and that today, of course, kila mahali wa tuwaki kuwa na ukuwa pekiya.  No, let me not talk about my relationship right now. As I said on social media, I want to keep it private for some time. For some time? Yeah, for some time, sasa. Maybe you can, you know, so do give marriage advice? Marriage works and love is a beautiful thing. Never give up on love. Yeah, that's all I can say. I'm a caribu now officially now. Yes, thank you for having me. Mm hmm. Unende lehaji. Nikosalam, I can't complain. Yeah. Alright, now maybe we get to some stories about maybe the online thing, of course. Amber, kidogo tunneza sem hawa kenya, kidogo alkuwa mikuwa mulia. Sasa, if you need to talk about love, you're meant to help first, so that comes first, are you doing? Yeah, yeah, yeah, I'm okay, I'm okay, yeah, yeah, I'm good, yeah. Okay, maybe Amber, I mean you've been on social media, our haters work whole, as you know, how do you deal with this? Because you've seen, I can ask you to go through the same thing, so how does Amber think? You just ignore, you know?  And you just realise these are people who are miserable in their lives and they're trying to pull you chinni so that you can feel whatever they are going through, but never let them, never let anyone pull you down. Yeah, it stay focused, yeah. At some point maybe have you ever gotten to this point where you feel like no, I really need to deactivate my maybe Instagram handle because we also, like the other day of real, I need to deactivate, okay, how has it ever gotten to that point for you? No, it got when, it was Kitambo before I got famous and it was something very sensitive, it was to witchcraft and all because I was not ready to handle all that pressure.  Nojwa, I finish up with them and then I move on and that's what I did. And I thank God I did that because that's why I'm here today. That's why you people know me as Amber, that's why I'm very famous because it has made, it was a blessing in disguise. Disguise, sorry, yeah. And maybe talking about what happened, I would say many years ago, that's your now witchcraft allegations and things like that. Of course, it's something that resurfaced again yesterday. I don't know whether you came across that. Oh really, what happened? So there's someone, a blogger who actually posted the same and he or she claimed that you, Likwanga Nare City, kumba you are filing an affidavit to tell the court that actually Rapudo is not violent and also defend yourself in the allegations about witchcraft and a quote and quote prostitution. Oh okay, I didn't know about that. I haven't seen that. No, I haven't seen that. You know, a lot goes on on social media and you know so many of these bloggers tried to use my name because they know, even when you go through the stories, anywhere I've been posted, the comments section is, the comments there is a lot. Like people love talking about me, whether negatively or positively. For me it's a plus because it gives me work and that's why I'm who I am, yeah. So for me, I have nothing to say about that, honestly, yeah. So these allegations are actually false? I can't say that, some of them are true, but I don't want to go into details, yeah. Okay, and maybe just to know, you know, most of the celebrities occur first and things go out there, they feel the need to address is told in witchcraft. I mean, that is unique to your faith. Why as Amber Bonojif Kiriamebe should address it out there and I say, I'm not part of that, me, me. Actually, I've done videos on my YouTube channel if you can go through Uteza Pata before I was not able to address it because it's something that really got me unaware, let me say that, because I love God and I've always been, you know, even if my lifestyle doesn't portray like I'm a Christian, the society wants us to be, I love God and I know God loves me and then it really affected my relationship with God. Like at some point I had to stop believing in God, but yeah, but you know, I healed.  And I've addressed it all, yeah.  Is it something that maybe I'm going to approach one day, these two? No, no, no, it has never affected my family. Let me start there, because one thing I'm very true to the people that in my life, the people that I love and value, that's why we addressed it.  So I've never had any problem with people that I love or even people that I work with, yeah. I'll say that for sure, yeah.   Daily expense, I mean, but it's not like I'm an inflector, not like I'm a dog, I don't want to go there, yeah, but yeah, we are surviving, you're living, yes, yes. You're living, yes. We'll say how to pay at a range level. No, no, no, I'll start at the next time. For now, I'll start at the next time, yeah. You mentioned the range and today, of course, kila mahaliwa tuwaki kwa na ukwa pekiya kwa. For example, today, actually, you drove yourself in and nilkwan miskewa together around wakilisa labda, tajere yu ukwa api, how jafi kani? No, let me not talk about my relationship right now. As I said on social media, I want to keep it private for some time, yeah. For some time? Yeah, for some time, sasa. Maybe, you know, so do you give marriage advice? Um, marriage works and love is a beautiful thing. Never give up on love. Yeah, that's all I can say, yes. Never give up on love. Yes. We don't see ambare glowing any anakavizuri. What is keeping, you know, ambare look this good? Ah, first things first, of course, you have to use legit skin care products, naizonesas, but atupale kwa all things face and you have to take care of yourself, Pia. You can never pull from an empty cup. So, take care of yourself first so that you can be able to take care of other people. Yes. So, we could also say that maybe beauty products or other people we say ma ma futa. Yes. It's an investment. I'm willing to go, yeah. Big and heavy on it, yeah. Right. And of course, the need that you went out there to kuwonga, ya ni ku indeed to clarify that you're not broke as people think, maybe did it affect your brand or something when you went out there to say that? No, the reason why I did that is because the people that I'm working with, Pia and Anishanga, not just sometimes, and they want answers. And then, actually forget about that, there are people that love me genuinely and they want to hear my side of story. Me, I don't care about what people say. You can say whatever. I think I've heard the worst about me by now and it has never affected me and it will never. And I'm still who I am. Najwa. Mtimunye una matunda una tupiwa mawesana. If I was nobody, people would not want to talk about me. But almost every day I'm trending and the funniest thing, some people are buying to be talked. Let me say, yeah. They pay to be talked about. But me, I don't. Najwa, naikuongelaida nipatia kazi like I say. So kazi kwao, kazi kwaungu. Najwa, yeah. So me, I'm good to go. At the end of the day, pesa nikuwako. Pasa ina ingiwa, I'll continue glowing, living the good life God wants me to live and being an inspiration to other people. Yeah, to never give up, to never listen to what people say. It's all voices, it's all coinge. You block them as much as you can. As long as you know who you are, as long as you know your intentions are pure, then just focus. Wacha umba zendele kubak. You focus, Najwa, yeah. One last question before we let you go. No, you're talking about you trending. Sometimes it's not even planned, najipata too. And of course sometimes... It has never been a plan for me, yeah. Of course sometimes it comes with trolls and negative things and things like that. Is it something that you feel that you are also at a point you really worked on maybe? You tend maybe and people won't trouble you? No, people will always talk. But you know, like I said, nwale wa tuwako kuchini. Wanakuongelia vibha because their life is very miserable. They don't have a job, you know. They can't believe. They don't think you deserve the kind of life you are having. So for them, since they cannot undo what God has already done in your life, they try to pull you down to make you go to where they are who feel kamawa, but that can never happen. Yeah, me I always say I'm God's favourites. Yeah. And if you have never seen God in my life, then I don't know what you're doing following me. If you have followed me keenly, I swear you'll see God. Yeah. But maybe just one last question.  Do you think you can agree with that? For me, I always advocate for not, I'll never date a broke man. The reason why I say that is because me, myself, I'm not broke. So I don't want to layer manome mwingine. Like, come with what you have, I come with what we have. We grow. I don't want to be dragged behind. So yeah, date someone who has pesayake. Yeah, because me, I can comfortably sustain my lifestyle. Yeah. Thank you so much, Amber. Thank you too.


Life is about constant evolution. Always better today than we were yesterday. There are no shortcuts to a successful fitness regimen. Only hard work and consistency. And to navigate through the mountain of fitness advice available, candidates must learn to separate fad from function. I'm Daniel Fletcher. Welcome to the Only Easy Day was Yesterday, the official Navy SEAL podcast. In this extended series, we'll speak with select special warfare performance experts to clarify common training misconceptions and provide insight into areas of focus specifically important to special warfare candidates. Today, we extend our fitness series with a discussion about push-ups, sit-ups and pull-ups with director of fitness for SEAL and SWIT training, Mike Capiston. Let's get started. Well, Mike, today we're talking about push-ups, pull-ups, sit-ups or whatever order you want to put it in. Usually following the order of the PST is I'd have to guess. Obviously, there's movement standards that they're going to have to hit during these tests and it's a big part of what people are kind of staring down the train tracks that they know that they're going to be tested on. Touch a little bit on people maybe falling into the mistake of overtraining in these areas and how that impacts people's programming. Well, if it wasn't for the PST, the physical screening test and the requirements to do certain standards in push-ups, sit-ups and pull-ups, I really wouldn't talk about them at all because those three exercises fall within the overall framework that we've talked about previously for training the upper body and the core so those are exercises that should be part of your overall balanced routine but in a perfect world, they wouldn't be emphasized or overemphasized exclusively. The reality is that people have to pass the standards for the PST and so they're going to have to spend a little bit of extra time working specifically on those exercises. We want to try to walk the line between developing the ability to meet the standards without violating the principles that I've talked about previously in terms of over-developing certain areas. There are actually reasonable ways that we can do that. So maybe you can unpack that a little bit. I know pull-ups are a big, I guess, hurdle for people that may be just starting to work out and they want to try to nail it until they're really good at it. Well, so if you can't do even a single pull-up, that's kind of a problem. Ideally, to get into budge, you want to be able to do in the upper teens, you know, 20. I actually wouldn't encourage people to do more than that because the statistics show that people that do large amounts of pull-ups in the 25 to 30 range are much more likely to get injured and not any more likely to get through the program without quitting. So more is not necessarily better, but you got to get past one. So how do you recommend people kind of scale that or kind of assist themselves? Yeah, a couple of different ways. You can do assisted pull-ups and so different people have used bands so that they can take out part of their body weight and if you can't lift your entire body weight one time, you can lift part of your body weight one or a few times. So what do you mean by that when you say using bands? I don't have an example right in front of us here but on elastic bands, such as over there, so you put it around your feet. Like a large elastic band. We're talking about something that's maybe two inches or so, different colored bands. Even probably more realistic or easier to do if you're in a gym that has a lat pull machine where you can use the plate stack and use less than your body weight. Are you talking about one of those where you would rest your knees or part of your body with it? There are a couple different ways. So you're talking about what I think it's a gravatron that will do that. So there are different designs that allow you just the actual weight stack machine where you grab the bar and you sit down and you put the weight stack to an amount that's less than your body weight. I got you, okay. So a couple of different ways you can approach it, but one way is to do several reps with less than your body weight until you develop enough that I can do 10 at say 70% of my body weight, then eventually you can do one or two with your body weight. But another even simpler way that you could do it is to do negative pull-ups. So you would get a pull-up bar, get a step or a stair or some sort of platform that you can step onto so that you can put your chin over the bar and then lower your body weight down. Kind of like an arm hanging. An arm hanging and then resist gravity. So the negatives are the important thing. If you can't do one pulling yourself up, you can still do one lowering yourself down. And so you can do one rest for a few seconds, do another and in the beginning you might only do that five or six times, but after a few sessions you'll get enough strength where hopefully you can eventually do one. If you can do one complete pull-up, then you can do it and take a little break and do another complete pull-up and eventually get to the point where you can do two or three. And then once you get up to where you can do five or six, you're on the way to being able to do even more. And then kind of incorporating that in smaller rep counts and kind of building from there. Yeah, but the biggest stumbling block, again, if you can't do one, then that's a problem. You've got to figure out a way that you can at least do one and then gradually build from there. Now I read in your training guide kind of changing up the variety of grips for yourself. Is that more of an advanced thing? You recommend that? It's not an advanced thing. And I think that over the years I've probably come away from that. I don't say never do it. It's actually fine to do it occasionally, but it's probably not the most important aspect. Do you think that's because people kind of can fall down that becoming a specialist that pull-ups kind of attract? Yeah, exactly right. So I'm just, I'm trying to discourage people from spending too much time on pull-ups as an example. And my recommendation for push-ups, set-ups and pull-ups is to try to get the most benefit out of the least amount of training that you can do. And so you're really trying to be streamlined and efficient. And so if you're on the pull-up bar, exploring all sorts of mixed grip and wide grip and narrow grip and different grip, then you're going to be spending too much time on the bar altogether. So that's something that's not necessarily over-developing your pull-up but not developing other parts of your regimen. Yeah. Okay. Is that an area where you think applying, like we talked about this briefly in terms of training the core, adding resistance, whether it's weight, weighted vest. Well, you can get to the point where if you can do pull-ups in the high teens that you might want to add a little bit of extra weight. So yeah, you can do that. Again, I don't necessarily encourage people to strive for that, but if you can do 20 perfectly executed controlled pull-ups with your body weight, then rather than doing 30 perfect controlled pull-ups with your body weight, I would say you can add a little bit of resistance so you can put on it. Start with a 10-pound or a 15-pound weight vest. Or if you're on the lap pull machine, you can pull down more than your body weight. You know, you can adjust the plate stack so it's less, but you can also adjust it so that it's more. So there's other ways that you can create a little bit more resistance. Do you echo, I guess, that same recommendation throughout the other movements of push-ups and sit-ups as well in terms of adding weight or resistance, however you see it? It's probably a little bit different for push-ups and especially sit-ups because it'd be a rare person, especially somebody that was seriously considering budge that couldn't even do a few sit-ups or a few push-ups. And so if you've got something that you can build off of, then you can get started. If you literally couldn't do a single push-up, you would do the exact same thing. You would start in the front-leaning position and lower yourself carefully down to the ground. Maybe you can't lift yourself up, but you could lower yourself down. So lower yourself down, take a little break, lower yourself down, and get to the point where you can do at least a couple of regular full-scale push-ups. And it would be a long time later, although as part of regular strength training, you're going to be doing some resisted chest-press exercises anyway. You're going to be doing some dumbbell presses or some bench-press or something like that. So you're probably going to be doing some resisted chest-press motions in addition to the push-ups that you're doing to prepare for the PST. I know that push-ups is an area specifically where there's a little bit of variety in terms of hand positioning that can be either beneficial or potentially detrimental. Maybe you can unpack that a little bit for us. Well, two things. I would say make sure that you investigate the current standards for the PST so that if you show up to take one that you'll know exactly what they're going to expect you to do in terms of what your hand placement is, how far your range of motion is, where, if anywhere, you can rest during the test and recognize what all the requirements are so that you can practice that. But besides that, my encouragement is to keep the hands pretty much below the shoulders. If we look at the website Sealswick.com, we've got some discussion on that and I've pointed out some technical things that I would encourage people to consider. But the important thing about the push-up is that you keep the hands relatively shoulder-width, maybe only slightly wider and not very much wider, and that you incorporate proper body position, back position, identical to doing the front plank. And it turns out that people that are struggling with push-ups, a good compliment to preparing for the push-up is to do a good core strengthening program. We talked with, if I can remember, I think Steve Drum at NSW Prep, and he kind of hammered home perfect push-ups, perfect form, and I think it was him that recommended recording yourself and watching yourself. I think that's a really great idea and I just kind of want to throw that in there because I'm never hearing that from you. But again, it's important to recognize the standards that are going to be enforced when you're doing your PST. So you might think you're doing a good push-up, you better make sure that your view agrees with the official view. Do your research, do due diligence to make sure that you're not wasting your time training improperly. In regards to sit-ups, I think this is kind of an area that I've heard potential for, you know, rink in your neck or maybe the back, maybe potential injury there. Talk a little bit about maybe some of the stuff that you see specific for ab training and core training that you would maybe incorporate, whether it's some lumbar support or foot clamp type apparatus. The thing that I would recommend for abdominal work or for actually a variety of different exercises that are involved in core and even some lower body exercises would be awareness of the pelvic tilt.  You want to try to maintain a fairly neutral pelvic tilt. And if you're doing a sit-up or if you're doing an exercise like the leg lift on the ground, if you lie on the ground, the small of your back should be pressed against the ground. If there's an arch or a space that you can put your hand underneath, that's improper. That's a forward pelvic tilt and that'll create pressure on the spine that you want to avoid. So a good general thing to learn to apply to all the different exercises that you do is how to control your pelvis and how to make sure you keep it in the neutral position. And so whenever I have guys on the ground doing sit-ups or leg lifts or any sort of exercise like that, we'll talk about the pelvic tilt. And I'll have them imagine pressing the small of your back against the ground. If I see daylight, I'll put my hand under there and I'll say press against my hand. And when they're doing it, keep the sensation of your back pressing against the ground because once that daylight opens up again, you're tilting the pelvis forward and that's going to create problems. That's a really good thing to bring up. I think that's really overlooked. It's a common thing that you see with squatting all over. It's just kind of a lack of awareness of the position of their pelvis in general. Maybe recording yourself if you don't have a buddy. Maybe just take a look at some information to kind of at least bring your awareness to that. And in terms of training and volume with sit-ups in general, are there any numbers that you think, you know, when you're able to hit this unbroken or something it's like maybe it's time to not focus as much. You have the specific recommendations in the physical training guide available on salesweek.com. And so again, the goal for the PST specific exercises is to accomplish your goals with the least number of reps possible. And a general guideline I throw out there for pull-ups is not do more than 50 in a day and not do more than 200 in a week. And for push-ups and sit-ups it would be not do more than 200 in a day and not do more than 1,000 in a week. And so what you want to focus on is doing the best quality you can maybe in sets of 50. For example, for push-ups, you know, a little bit more if you can. For example, you're going to do four sets of 50 making sure that you're maximizing the quality of each push-up. And then if you're getting in better shape then you can reduce the rest in between your sets. And if you can combine them into, you know, sets of 60 or 75, that's fine. But when you get to the point where you can do like 100 consecutive push-ups with good form, that's enough. What are some of the general faults or what are people not doing right in terms of movement standards to have their reps not count during these tests? Is it, you know, something specific that you see over again for the different movements, for the pull-ups, push-ups? Well, for the pull-ups it would be not getting the chin over the bar so the chin's got to go over the bar and for the descent not locking the arms out completely and it's got to be controlled and there can't be kipping. So people are used to it. And what do you mean kipping? Kipping, like kicking the legs, trying to pump with the legs to get the torso up. Like a swinging motion. So yeah, so you're not allowed to do that. So you've got to be able to keep your body completely still and only use your arms to get the chin up all the way over the top of the bar and then back down to full extension. For push-ups it's making sure that the back stays straight and making sure that the arms are fully locked out at the top and that the chest comes all the way down to the ground in the bottom. For sit-ups it's making sure that the knees are kept at 90 degrees and then the arms have to be crossed across the chest and grabbing the shoulders so if the elbows don't come all the way to the knee or if the hands lose contact with the shoulders those will be discounted. So pay specific attention to yourself when you're doing your movements. Not just counting reps but making sure that you're not doing any of those faults. Correct, it's not just counting reps it's making sure that each rep is correct. Or else that's likely to be a slip-up for you. It won't be counted in your PST and you won't get credit for doing the exercise. Again the data shows that contrary to expectations if you get very high numbers of push-ups and pull-ups you're less likely to succeed and you're more likely to get injured. So everybody always thinks more is better but I think more is good for push-ups you want to be able to do in the high 90s maybe 100 more isn't better. For pull-ups you want to be able to do in the high teens maybe 20 more isn't better. So when you can do that stop and go on and do something else. Well Mike I think that's a pretty comprehensive look at pull-ups push-up sit-ups. Obviously these guys are going to be hammering these when it comes to the PST and throughout their training. And hopefully they'll train smart as well as hard.


Where in the world is that part? All right, The Great Search brought to you by DigiKey and Adafruit, Ladiator, user, PowerZone, nearing to find things that you're looking for on digikey.com. It is hard to find parts, but with Ladiator's help, you could probably find the things that you need. Ladiator, what is The Great Search this week? This week, sorry, I was expecting you to say something else. I was expecting to say something too, but then I figured I was kind of done. I was like, you know, I think I've said it all. Okay, so this week we got a little bit of a mail bag. Someone wrote in and they said, I want a 16-bit DAC, and I think you should have a Stemic UT board because we have a 12-bit DAC board. And I was like, you're correct, we do. We don't have a 16-bit DAC board. And there are some times where you want 16 bits of resolution. We have 16-bit ADC, so let's go to the computer and I'll show all this stuff off. So, we have the, a couple of different, we have 12-bit DACs, the MCP4725 is a fine DAC. We also have the Quad version. Not in stock because you can't get this chip anymore. The 4728, actually these are our two DAC boards, but there are people who want to use our ADC boards. We'll notice that we have 12 and 16-bit ADCs. So, you know, they're more expensive. Like, once you get past 10 or 12 bits, you're definitely gonna be paying more. But if you really need that resolution, you know, you want 16 bits, you want 16 bits. So, let's find a DAC board. So, I'm actually just going to search for DAC. And there's a lot of DACs. And here's something to watch out for when you're searching for DACs. First off, there's a two-bit DAC. That's just like a single resistor divider, guys. Like, do you really need a whole chip to do that? So, for DACs, you know, there's 13,000 of them. So, let's filter what we want. So, you know, we want 16 bits or better. And we want to be surface mount because we want to put it in our Stem IQT board. And we want it to be I-squared C, ideally, so that we don't have to have any sort of, you know, converter or translator. So, let's go to number of bits and let's select, well, there's like a weird 12 slash 16, but we pretty much want 16 and up. So, let's apply. Okay, so now we've reduced it to, and let's also look at only active chips because I don't care for the unactive stuff. So, oh, and then, you know, there's a lot of, like, look at these beasts, these monsters. But we don't want these. We actually really want surface mount only because we're gonna put this on the board. Okay, so now we're back to normal. So, one thing to watch for is a lot of DAX. In DAX, there's actually kind of like two kinds of DAX. There's more, but there's kind of two kinds of DAX. There is, you know, if I sort by price, there are, you know, the CS4, 334, which is actually kind of a famous I2S DAX. So, when you're looking for DAX, there's basically like three interfaces for DAX in the most part. There's the I2C, kind of slower DAX, but you know, if the I2C is very easy to integrate. There's SPI, and we've used SPI DAX before, like our wave shield to play wave files. We could, you know, you basically pump in SPI data and the 16 bits gets converted to analog output. And there's I2S DAX. So, technically anything that is I2S to audio is a DAX, but you do have to, you know, you can't just send and set data with I2S. You know, one thing is that they're quite inexpensive. And so there's definitely gonna be cases, by the way, if you are constantly setting an analog voltage, you probably could get away with I2S if you have the interface and you can stream that data out, but you have to continuously stream data or you're gonna get like popping. Most DAX, I2S DAX, do not like it when you stop sending data. They're not gonna hold that last value. Also, you know, some of them have limitations on the voltage range. Some of them have limitations on how fast they can update. So there's a lot of, you know, a lot of times when I was looking at these DAX, there's a lot of I2S DAX. I'll tell you another thing. Sometimes, you know, it's very easy to people mistype when they're categorizing these and I2S and I2C, like, you know, I make the mistake of I2S, I2C, I confuse the two. So just be aware when you're searching for these, like, you know, this top one is labeled I2C, but it's not, it's definitely I2S. So the first thing is I'm actually going to remove and only look at 16-bit and maybe, you know, Dash DAX, because the 24 and 32-bit DAX are all the I2S DAX. So let me apply that. And then the next thing I want to look at is the interface, the number of converters, so I want, like, one or two. And then the interface down here, because I want this to be for a STEMI QT board, I really do want it to be, you know, only I2C. I'll also pick up this Dash here, but I don't want parallel or SPI or serial. Okay, so this is what I came up with. And so all of these were actually pretty good options. I'll say that none more in stock pretty much, except for this one from TI. I did search, you know, and this is, you know, once in a while it's like, you know, it's like I'm trying to pick a part that's in stock, what were these, like none of them were. So given that none of them are in stock, I thought let's pick one that would be a really good option and then I'll just sign up to be notified when it is and then when it's ready, I'll, you know, I can get samples and then I can maybe design it in. So for pricing, once you get to the higher pricing, there's basically the two options that seems pretty good are, you know, if I want something in stock right now, this is the only one that was in stock right now, but this ADI won, the AD 5693 actually looked like a very, like a very nice design. It has I-squared C, the voltage, analog and digital supply is up to a 5.5 volts, which is really nice. It's a voltage buffered output, it's 16 bits. I also know that ADI makes really, really good analog stuff. So I think if I'm going to design a 16-bit DAC board with STEMIQT for I-squared C to 16-bit DAC out, I think that this is what I'm going to go with. So I'm going to, I can't order it right now, but what I will do is I'm going to add this to my, you know, so you can subscribe to get told when it will be back in stock. I think it was going to be a while. I don't know, it doesn't have, it doesn't have a lead time even. And then when this is available, you know, I can design the PCB and get it ready, and then when it comes into stock, I'll be able to design something with this. So the AD 5693, so the nice person who mailed, this is the 16-bit DAC that I would pick. That's a great church.