Towards the end of the previous lecture we started talking about issues related to model reduction and substructuring schemes, so we will continue with this discussion now, so we will quickly recall where do we need you know model reduction and substructuring, actually the need for using model reduction and substructuring arises in several context, one is for example in treating very large scale problems or in dealing with situations when the results from experiments need to be discussed in conjunction with prediction from mathematical models. That means for a given structure we have made both a finite element model as well as we have done some experimental investigations and we want to now reconcile the two and this is an essential step in problems of finite element model updating and in such situations the question of model reduction arises because of mismatch between degrees of freedom in measurement and computational models, typically in a computational model the size of the number of degrees of freedom can be very large and for every degree of freedom in the computational model we may not have a sensor, for instance it may not be feasible to measure degrees of freedom at interior nodes in a 3 dimensional structure or measurement of rotations and so on and so forth, so the number of degrees of freedom that we will be able to measure in an experimental work will typically be much less than the degrees of freedom in a finite element model. Another situation is when different parts of a structure are developed by different teams possibly by using both experimental and computational tools and we need to based on this we need to construct the model for built up structures, so this typically happens in applications such as space applications and automotive applications and this could also occur in problems of secondary systems in civil engineering applications. There is a modern testing strategy known as hybrid simulations where we combine both experimental and computational models for the same structure, so what we do is a part of the structure is studied experimentally and a part of the structure computationally and we want to in some way couple these two disparate studies and arrive at certain conclusions on global behavior of the complete structure. So let us start with discussion on problem of model reduction, so we will be limiting our attention to linear time invariant vibrating systems, so a typical finite element model for a linear system will be of this form MX double dot plus CX dot plus KX equal to F of T and certain specified initial conditions, this is the end product of making finite element model as we have seen in previous lectures. The objective of model reduction is to replace this above this N degree of freedom system by an equivalent lower case N degree of freedom system where the reduced degree of freedom is much less is less than the capital N degrees of freedom here. So for the reduced system the equation will be again of the form MR XM double dot plus CR XM dot plus KR XM is FR of T, the subscript R here refers to reduced model, whereas the subscript M I will shortly come to that, this is the vector of degrees of freedom which have been retained in the reduced model, so in the original model what we do is the degree of freedom is partitioned into two sets, one set is called master degrees of freedom, the other set is called slave degrees of freedom, so this subscript M here refers to the master degrees of freedom which have been retained in the reduced model, the slave degrees of freedom XS of T have been eliminated from this model and a reduced model of this type has been arrived at. So the size of the master degree of freedom will be lower case N cross 1 and slave degree sorry master degrees of freedom, slave degrees of freedom will be N minus N cross 1 vector, XS of T is a N minus N cross 1 vector. Now in all there are several methods for model reduction and in all the alternative method there is a generic form to the problem of model reduction, so what we do is X of T is written as partitioned as already I mentioned as master and slave, and this we take it to be, this X of T is taken to be related to XM of T through a transformation matrix capital psi, so XM is lower case N cross 1 and capital psi therefore will be N cross N transformation matrix, so we can substitute this into the governing equation we get the equation at this stage in this form, and if we pre multiply by psi transpose I get equation of this kind and I call this MR which is psi transpose M psi as a reduced mass matrix, clearly if you take transpose of this it will be since capital M is symmetric this MR would also be symmetric, similarly we define reduced damping matrix and reduced stiffness matrix, we call this quantity FR of T as psi transpose F of T as a reduced force vector, so once this is achieved we can analyze this equation using any of the tools that we already developed, but therefore the question now remains how do we select this transformation matrix, now there could be different criteria based on which we may like to select this transformation matrix, for example the original model would have capital N number of natural frequencies and mode shapes, on the other hand the reduced model will have only lower case N eigen pairs, now suppose I have a 100 degrees of freedom system and I reduce it to a 10 degrees of freedom system, the 100 degrees of freedom system will have 100 natural frequencies and 100 by 100 model matrix, whereas the reduced model will have 10 natural frequencies and 10 by 10 model matrix, these 10 natural frequencies of the reduced model should they be equal to any of these 100 natural frequencies of the larger model that could be one of the criteria or should the frequency response function over a given frequency range of the reduced system serve as an acceptable approximation to the corresponding FRFs of the original system, so here we are matching response, here we are matching only the natural frequency, so if you match FRFs the issues related to mode shapes as well as damping models would be allowed for, similarly should transient response to dynamic excitation for the reduced system serve as an acceptable approximation to the response of the original system, so we can set forth different objectives depending on which one is of crucial importance to a given situation we have to suitably design this transformation matrix, now before we proceed further we can just as there is a model reduction there is a counter feature that is model expansion, for example consider a structural system that is being studied both experimentally and computationally, so this N is a number of major degrees of freedom, whereas capital N is a degrees of freedom in the computational model and this typically far exceeds the major degrees of freedom in the experimental model, so now when we reconcile either I can reduce my computational model to match the number of major DOFs, so let me go back to again the example of capital N being 100 and lower case N being 10, so what I can do is from my 100 degree of freedom computational model I can eliminate 90 degrees of freedom and obtain a model with 10 degrees of freedom and the degrees of freedom can be chosen to match what exactly I have measured, on the other hand we could also expand the measurement model that means I have 10 degrees of freedom model here I will augment it by additional 90 degrees of freedom, so that augmentation is essentially a transformation, so if I do that then instead of calling it as model reduction it would become model expansion because a smaller model is now replaced by a larger model, so the transformation that we discuss can be viewed from both these perspectives, so that is to say reduce the size of the computational model so that only the degrees of freedom which are common to both experimental and computational models are retained or alternatively expand the size of the experimental model so that the degrees of freedom in both experimental and computational model match. Now we will discuss three alternative techniques for model reduction and the names of these techniques are static condensation method, dynamic condensation and there is what is known as system equivalent reduction expansion process, so I will just run through the logic of these three model reduction schemes and we will discuss the relative merits and demerits, so so called static condensation is also called Guyan's reduction technique. So what we are looking for, we have this global degrees of, the degrees of freedom for the larger system partitioned as master and slaves and I want to now relate X of T to the master through this transformation matrix capital psi, so this partitioning of states into master and slave induces a partition on the structural matrices and I can write the equation in this form, so here we assume that the slave degrees of freedom do not carry any external force, okay that's an assumption. Now the idea in static condensation is to relate the master and slave degrees of freedom through a relation which is valid only for under static conditions, that means to establish a relationship between XM and XS I will consider the equilibrium equation, that is this equation I will discard inertial and damping terms and write only the static equilibrium equation, so using this equation now I will be able to establish a relationship between XM and XS, so if this is what we are going to accept as a relationship between master and slaves, the first of this equation gives KMM XM plus KMS XS is FM of T, that we are not considering, the second equation is of interest to us KSM into XM plus KSS into XS is 0, so by rearranging the terms I get XS as minus KSS inverse KSM XM, so this is a relation between slave and master, so the transformation matrix therefore can be written as I into, sorry I and minus KSS inverse KSM, so this will be lower case N by N, this will be capital N minus N across N minus N square matrix, so this is the psi matrix. Now we can also look at now the expression for kinetic energy and potential energy in the original system, the expression for kinetic energy is half X dot transpose MX dot, so X I am writing it as psi into XM, so if I make that substitution for X dot I will write psi XM dot and for X dot transpose it will be XM dot transpose psi transpose, so if I now call this quantity psi transpose M psi as MR I get the expression for kinetic energy in the reduced model as shown here, so this MR is now the reduced mass matrix, similarly the potential energy I can write half X transpose KX, so this again half psi XM here and XM transpose psi transpose here and I get a reduced stiffness matrix KR which is psi transpose K psi. Now therefore the governing equation I can now write for the reduced system as MR XM double dot plus CR XM dot plus KR XM equal to FR of T, so this equation can now be analyzed this is the reduced model that we are looking for, so what are the features of this, so we can work out the details of the MR and KR matrices in a more explicit manner, so psi transpose M psi will give me this, this is psi transpose this is this, and if I expand this I will get now the reduced mass matrix in this form. You must notice here that the reduced mass matrix is now function of the stiffness matrices of the original system, this is unusual because the inertial kinetic energy in the reduced system is now function of stiffness characteristics, okay that's an artifact induced because of the remodel reduction that we have done. Similarly, the reduced stiffness matrix is psi transpose K psi and this by rearranging the terms I get this as a reduced stiffness matrix, okay. Now we can make few observations, now the slave degrees of freedom are related to the master degrees of freedom through relations that are strictly valid for static situations and hence this method is known as method of static condensation. The partitioning of degrees of freedom as being masters and slaves has to be done by analysts bearing in mind this assumption that master and slaves are connected to each other through relations which are strictly valid only under static conditions, so what is the consequence of that? The method is likely to perform better if slave degrees of freedom contribute little to the kinetic energy, so in regions of low mass and high stiffness you should identify the slave degrees of freedom. The select slave degrees of freedom such that the lowest Eigen value of the equation KSS alpha equal to lambda MSS alpha has the highest Eigen value, that means between two competing choices for slave degrees of freedom you will get two different KSS and MSS, you perform the Eigen value analysis for the two competing choices and between the two the one in which the lowest Eigen value is higher is a better choice, so I will illustrate that with an example. This again is a consequence of the basic fact that we are relating the master and slave only through static relation, so as I was telling select slave degrees of freedom in regions of high stiffness and low mass. Now we need to ensure that terms of MSS are small and terms of KSS are large, that is I am reiterating the same statement in a slightly different way, yet another way of saying similar thing is those degrees of freedom which yield the larger value for this ratio can be selected as slaves, so you can order all the degrees of freedom based on this ratio and select as many slaves as you needed by assessing, by comparing this ratio. Now it's clear that the error due to modal reduction increases with increase in driving frequencies of interest, that is because with increase in driving frequencies the kinetic energy goes on increasing and we can't ignore mass, a mass which is small at low frequency will contribute significantly to kinetic energy at a higher frequency, therefore the assumption will start breaking down. Now any initial condition specified on slave degrees of freedom would not be satisfied, especially the velocity degrees of freedom and things like even displacement degrees of freedom because where even slave is made to is forcefully related to the master and the initial condition on slave will cannot be accommodated in the further modeling work. The static condensation does not reproduce any of the original natural frequencies of the original analytical model and all the natural frequencies of the reduced models would be higher than those of the full model. Now again let me go back to the example of a bigger model with 100 degrees of freedom and a reduced model of 10 degrees of freedom. The reduced model if you compute the 10 natural frequencies for the reduced model these frequencies need not agree with any of the 100 natural frequencies of the original system, there is no guarantee that that is bound to happen if you follow this procedure. So we can try to understand this through a numerical example, so let's consider a simple example having 6 degrees of freedom which springs as shown here and we will assume stiffness is 1000 Newton per meter and mass is 10 kg, so this is simple you know vibrating system, the only thing of interest is this X1 and X6 are coupled so the stiffness matrix will have certain you know off diagonal terms to reflect that. So this stiffness matrix, this is stiffness matrix for the system as you can see there is a term here which reflects coupling between first and thus the sixth mass, this mass and this mass, this is a mass matrix as one could expect this is a diagonal matrix since we are using lump mass matrix modeling and you can do the Eigenvalue analysis, you can find the, if you perform that the modal matrix comes out to be this and this is the vector of natural frequency expressed in radian per second, so this is, let us say that this is my larger model, now I want to achieve modal reduction okay by using static condensation, so to begin with I can compute this ratio KII by MII, now the ratios are shown here, so let us consider for purpose of illustration 2 alternative choices for master and slave degrees of freedom, in each case we will have, we will try to reduce the modal to a 3 degree of freedom system, so in the first case what I will take the master degrees as 1, 2, 3 and slave degrees as 4, 5, 6, now is it a good choice, it is deliberately a bad choice because we want this ratio to be large for slaves, but I am forcing it to what should be ideally slave degrees of freedom I am making them as masters, just to emphasize what would happen, then I will perform this eigenvalue analysis KSS alpha equal to lambda into alpha and these are the eigenvalues, now the psi matrix turns out to be this and I can get the reduced mass and stiffness matrices and get the eigenvalue, eigenmatter matrix for the reduced system and the 3 natural frequencies, now the 3 natural frequencies we are getting as 5.5, 19.7 and 22.07, so if you go here and see this is 4.6, 13, 13, 19, 22 and 29, so we don't seem to be getting 2 frequencies in this for these 2 frequencies seem to be giving reasonable answers, but the first 3 modes are not captured, well. Now let us now switch the options and I will make now 4, 5, 6 as masters and 1, 2, 3 as slaves, this is what our recommendation you know suggest that this is what we should be doing if you are interested in producing a 3 degree of freedom mode, now let's again do this eigenvalue analysis and I get 290, 419 and 91, now the point I was making was the lowest eigenvalue here is 53.89, the lowest eigenvalue here is 290, so between the 2 model the one which has higher lowest eigenvalue is second model because it is 290, this 290 is much larger than 53, so we could expect that this will perform better and in static condensation the reduced model should typically represent the behavior of the system in low frequencies well, okay. Now the reduced model looks like this and I get the 3 natural frequencies to be this, so we see here 4.6, 13.1, 15.14, so relatively speaking this seems to be a better reduction has been obtained through this choice of master and slaves, so at this stage we should notice that in the reduced model the frequencies that I obtain do not match with any of the natural frequencies of the global model, now the next question I should ask is suppose I demand, okay some frequencies should match, okay how to achieve that, so that takes us to the discussion on what is known as dynamic condensation technique, so let's consider for sake of discussion a harmonically driven undamped system and this is our equation and this we call it a dynamic stiffness matrix, this is minus omega square M plus K this we have encountered earlier, so equilibrium equation in the frequency domain is DX into F, so now what I do is I will again partition X into XM and XS and related to, X is related to XM through this matrix, now this partitioning induces this partitioning of the dynamic stiffness matrix also as shown here, now what I do here is I will again assume the slave degrees of freedom are not driven, so I can use the second equation here which is DSM XM plus DSS XS equal to 0 from which I get XSS to be this, there is no approximation here, okay I am not throwing out any term, so the transformation matrix that I am looking for is given by this, now this omega, okay is now a parameter in your model reduction, okay, so you have to make a choice for this omega, that is in addition to making choices on which of the degrees of freedom should be mastered and which should be slaves, this reduction scheme also demands that you should make a choice on omega, okay. Now again we can do the same steps and obtain the reduced mass and stiffness matrices as shown here, this is what I was saying in addition to choosing slave and master DOF's here one also need to specify the frequency omega it is the condensation has to be done, the method requires the determination of inverse of this matrix, see here this matrix needs to be inverted, again let me point out one more thing the reduced mass matrix here and the reduced stiffness matrix here now depend on the mass stiffness and the driving frequency in the original system, so these reduced matrices MR and KR you have to, they are not amenable for a direct physical interpretation, okay, this inversion of the matrix can be computationally demanding, so we could adopt some simplifications if necessary and while doing so we will also see what is the relationship between dynamic condensation and static condensation. So if we consider the inverse of this I will pull this KSS term outside and I can write in this form and the inverse of product is, product of inverse in the reversed order, so this becomes this, and if you use what is known as Niemann's expansion I can expand this matrix in this form, it is an expansion with infinite number of terms only few terms are shown here, so if I now omit these higher order terms in omega and written only the two terms I get this as my matrix and if I instead of inverting the matrix now I can use this matrix and this method is called the improved reduction scheme, it's an improvement over static condensation method, and it avoids the inversion of this matrix, if you are going to repeat this calculation for different values of omega then this is a simpler approach. We can also of course do something else we can formulate a eigenvalue problem associated with KSS and MSS, and suppose if I consider KSS alpha as lambda MSS alpha, and if phi is a matrix of eigenvectors and capital lambda be the diagonal matrix of eigenvalues such that phi transpose MSS is phi and this is lambda, then if I consider the problem of inverting this I can consider the set of these equations, and if I make a transformation Y is equal to phi U where phi is this matrix of eigenvectors and substitute here and use these orthogonality relations I will be able to show that this inverse is nothing but this, and this is a diagonal matrix so it doesn't require inversion. So this phi can be computed, see this I am while computing phi there is no omega here, so the same phi can be used for different omegas, so that is the idea which affords a simplification. Now we will return to the example that we considered here the same example I will again follow the same choices of degrees of master and slave degrees of freedom, but now what I will do is I have now additional choice to make on driving frequencies, so I have made several choices, I have made seven choices, in the first choice I take omega to be 4.61 which happens to be the first natural frequency of the system, and I make from a 7 degree freedom system I get a 3 degree freedom system, so that 4.61 turns out to be the one of the eigenvalues of the reduced system and there are two more frequencies. If omega is taken as 13, 13 happens to be 13.09 happens to be one of the frequencies, the other two of course are not the natural frequency of the system, so by selecting 13.71 I ensure that 13.71 is one of the natural frequencies of my reduced model and so on and so forth. So in choice 1 this is what I get, in choice 2 that means choice of master and slave degrees of freedom the same thing happens, but of course now the frequencies other than the one that are in proximity of these numbers will be different from what was there in model. So the choice of omega do matter and those natural frequencies which are close to omega are predicted well, that is the observation that we make here. So these 4.6, 13 these are the frequencies they are captured here the 6 degree of freedom not 7 degree of freedom, so there are 6 alternative models and each one works well in the neighborhood of the frequency chosen, and that fact is independent of choice of master and slave degrees of freedom, no matter which is master which is slave the fact that at omega if you select omega equal to 19.93 the reduced model will have that as one of the frequencies in both the cases. So we can make few comments now, so in dynamic condensation in addition to choice of master slave degrees the choice of omega also matters, those natural frequencies which are close to omega are predicted well, in a harmonic response analysis omega can be chosen to be equal to the driving frequency. So if you are varying omega then computationally this form of you know the writing the transformation matrix in this form is advantageous because you have to do only one eigenvalue analysis and you need not have to invert the matrix this matrix for every omega, if the FRFs need to be traced over a frequency range for every value of the driving frequency the condensation needs to be made separately, if omega is taken to match with the driving frequency that is the best option that you would have because at least at the frequency where you are driving the nearby natural frequencies are captured correctly in the reduced model, this is expected to lead an acceptable results if modes are well separated and damping is light, okay, that's very clear because once you make a choice of omega and you are driving a system harmonically at that frequency the response contribution is dominated by a single mode then the method is likely to work well even for force response analysis. Now we can ask this question in dynamic condensation in the reduced model we are able to capture only one mode correctly, so the next logical question that we can ask is can we retain a subset of the natural frequencies of the original system in the reduced model in an exact manner, okay, suppose in a 100 degree freedom system there will be 100 natural frequencies and if I am looking at a reduced model with 10 degrees of freedom the reduced model will have 10 natural frequencies, the question I am asking is can we select these 10, all these 10 natural frequencies can they be the natural frequencies of the original system, need not be the first 10, it can be any 10 that you can arbitrarily specify, so if you can do that then you are achieving something substantial, but then you have to input lot of details into the reduction scheme, so such a scheme indeed exist and that is known as system equivalent reduction expansion process and abbreviated as SCREP, so I will be using the term SCREP, so the main features of this reduction scheme and also as the name indicates it is an expansion scheme as well, but we will focus on reduction aspect of it, so it preserves a collection of normal modes during the reduction process, suppose we consider a n degree of freedom model for a linear vibrating system and let capital Phi denote the N cross P modal matrix that include the first P modes, okay, as before we partition X into master and slave degrees of freedom, this partitioning on X induces a partitioning on the partially known modal matrix as Phi M and Phi S, so what are the different sizes here, this Phi is N cross P, Phi M will be lowercase N cross P, where this N is the size of the master degrees of freedom and P is the number of modes retained, so in dynamic condensation P was 1, now P can be more, Phi S is N-N cross P and also when I say P it is not just the first P, by selecting the appropriate vectors in the modal matrix I am also specifying which of the P modes I am looking at, now we will assume that N is greater than P, that means the size of the reduced model is larger than the number of modes that you have in the global model, now we want to introduce a N cross 1 vector of generalized coordinates Z of T through this relation, okay, this is X is equal to some modal matrix into Z, that part is fine, so this is a relation, now XM of T is we can put it in the, you can expand this I get this, so from which I can, I can solve for Z of T using this equation, now the number of unknowns and number of equations in this case would not match therefore I cannot use inverse directly, I will have to use what is known as pseudo inverse, I will just shortly explain what pseudo inverse is, but if you right now will accept that there is an operation known as pseudo inverse as indicated here and this is this, that is Phi M plus is this, where plus indicates pseudo inverse, now if this is acceptable then X of T can be written in this form that is Phi M Phi S into this, this, so the Psi matrix which relates X to XM is now given by this, mind you this capital Phi here is the modal matrix of the complete system, so before you do modal reduction you should perform the eigenvalue analysis on the large system, okay, otherwise you cannot use this method, so the reduced mass matrix and reduced stiffness matrix are obtained as shown here, now let me quickly describe what is pseudo inverse, it is not a thorough discussion but it tells you what the idea is, so the motivation is suppose if you consider a linear algebraic equation X1 plus Phi X2 equal to 1, so we have one equation in 2 unknowns, so there will be an infinity of solutions, you draw this line any point lying on that line is a solution to this equation, however if we decide to pick the point that is closest to the origin as the solution, see by that I mean, so all points lying on this straight line is a solution but if I decide that I will take this point which is closest to the origin as the solution, this one, right, then I get a unique solution, okay, so let's consider what that means, so let us consider AX equal to B where A is N cross M and X is M cross 1 and B is N cross 1, okay, so this is the equation, now let us consider the case where M is greater than N, that is number of unknowns is greater than number of equations. Now what we do is the solution that minimizes the norm X that is a distance from the origin to the line, this is given by this, this distance, so we can show that this is given by what is our ARM, ARM is A transpose, AA transpose inverse, so ARM is known as right pseudo inverse of A, now on the other hand if number of unknowns is less than number of equations then I can find A solution X naught that minimizes this norm that is the error in satisfying this equation is minimized and we can do the simple calculation and show that X naught that is the solution in this case is given by A LM into B where A LM is given by this and this is known as left pseudo inverse of A, so what does these things mean, what do these things mean? A simple example suppose I consider a 4 cross 6 matrix A and define B as pseudo inverse of A, so I will use these definitions and compute the pseudo inverse, B is computed like this, now if I multiply A and B I get an identity matrix, so in that sense B is a pseudo inverse of A, although this matrix is not a square matrix I am able to define another B matrix so that AB is an identity matrix that is why it is called a pseudo inverse, now if this is 6 cross 4 instead of 4 cross 6 the pseudo inverse will be 4 cross 6, so AB in that case is again a diagonal matrix, okay, so this is a notion of pseudo inverse that we are using in developing this SCRAP transformation. Now I have been mentioning, I am referring to experimental models, so it is better at this stage to understand what is the difference between modeling in an experimental work and in a computational work, so in a typical computational loop we start with a continuum, we discretize and suppose we are dealing with time invariant linear systems, we discretize and form the structural matrices MCK and load vector F and write this equilibrium equation with this specified initial conditions, then I will perform the eigenvalue analysis and determine the natural frequencies, mode shapes, model participation factors and model damping ratios, so this analysis is known as modal analysis, that is given the structural matrices how to find the natural frequencies, modal matrix, damping ratios and the participation factors, so this is the modal analysis in a computational modeling approach, where we solve an eigenvalue problem, once this is known we have seen already how to compute the frequency response function or impulse response function and either use this algebraic relation or this convolution relation and obtain the response either in time or in frequency domain, this we have seen, so here it is in time it is a convolution in frequency it is a multiplication, this is what we do in a computational modeling, in an experimental work this loop is reversed, we start by measuring the response, okay, so the story is here, we apply known excitation to a test structure and measure the response, and what we measure we process and get the matrix of impulse response function and frequency response function, from this we extract natural frequencies, mode shapes, damping ratios and participation factor, this process of obtaining the modal information from measured responses is known as experimental model analysis, this is in contrast to the modal analysis in computational modeling where we knowing the structural matrices we perform an eigenvalue analysis and find these quantities, and that we use to compute the response, here we measure the response and we extract this information from these measured responses, and from this we would like to construct models for the structure that means mass stiffness damping matrices and so on and so forth, so the loop is you know the directions are reversed here, so there will be fundamental difficulty whenever we use these two alternative approach to the same problem, that is where this question of model reduction and expansion become crucial. Now let me return to the example of that 6 degree of freedom system and now apply SCREP, so let us retain now first three modes, so to implement SCREP I have to again declare certain degrees of freedom as masters and certain degrees of freedom as slaves, additionally I should specify which are the modes that I want to replicate in my reduced model, how many of them, so what I am selecting is I am taking three modes and I am taking the first three modes, so I can get phi M and phi S by partitioning the modal matrix of the 6 degree of freedom system that's what I have done and this is a transformation matrix, okay. Using this I will construct the reduced mass matrix and reduce stiffness matrix and perform the eigenvalue analysis on the reduced system, it's a 3 by 3 system, so that system now has these three natural frequencies, 4.60, 13. this and this, now if you look back these are exactly the three frequencies of the larger model, okay, so there is no, it's precisely mathematically exactly this, this is a reduced modal matrix and I get the reduced structural matrices as shown here, that these are actually this is nothing but, this is psi transpose M psi, this is reduced, this is psi transpose, okay, similarly if I now declare 4, 5, 6 as master and 1, 2, 3 as slaves, there will be certain changes in my features of the reduced model but the three natural frequencies will be identical again. So this is phi M and phi S, this is a transformation matrix, this is slightly now different from this transformation matrix, so again I will perform the eigenvalue analysis, no surprises, the first three natural frequencies exactly match, the reduced modal matrix of course is now different, okay, and reduced structural matrices are obtained here and the interesting thing is this pair of care and MR and this pair of care and MR although they are different they share the same eigenvalues, okay, so that is the achievement of this method. So what are the features of this? To implement SCREP the user need to specify the number of modes to be retained, the mode indices which modes and also the slaves and master DOFs, the choice of normal modes to be included in the reduced model is arbitrary, for example in a 100 degree of freedom system you want to select 10 modes, you can select 1, 18, 32 and 76 and so on and so forth, it need not be first 10, nor they need to be in a cluster, the scheme preserves the collection of normal modes during reduction, whatever you identified as the natural frequencies which should be retained in the reduced model they will be faithfully retained. The transformation matrix is deduced from the modal matrix here, the modal matrix can be incomplete, you need not have a square modal matrix, even you can work with a rectangular modal matrix, this is what would happen if you do experimental modal analysis, in an experimental modal analysis the modal matrix is seldom square, it will be always you know a rectangular matrix, so it will be incomplete, so knowledge of K and of course is needed if you are doing computationally because you need to find the modal matrix, this could be of value if modal matrix is obtained experimentally, that in which case K and M need not be known, Phi can be directly measured experimentally. The natural frequencies of the reduced system matches with the full system natural frequencies irrespective of choice of master and slave together, the method can be used for modal reduction or for modal expansion, so I am not discussed what exactly happens if you use it for modal expansion but in principle it can be done. Now we have now talked about modal reduction, the next topic that is related to this type of questions is questions of what are known as coupling techniques, again here this is a device to treat large complex structures and the problem is large complex structure require handling of large size matrices, so can we do something about that, similarly in a manufactured product parts of the structure could be modelled experimentally in parts computational, now the question is how to develop model for built up structures based on models for these substructures, now the coupling techniques answer these questions, a good coupling technique needs to possess some desirable features, it must be versatile enough to accept data either from experiments or from FE model, say part of the structure can be modelled experimentally and part of the structure computationally, the computational modeller will be able to give structural matrices, mode shapes, natural frequencies and so on and so forth, an experimentalist typically would be able to give FRFs impulse response function and if modal information is extracted you will be able to give the natural frequencies, mode shapes, damping ratios, participation factors which is experimentally measured, but the experimentalist will have difficulty in specifying the structural matrices. Now each component can be treated by an accurate and refined model, you can use each component each substructure can be modelled with any level of refinement and detailed modelling, any level of detail can be included in a model, components may have to be broken into small enough subsystems which permits suitable experimental tests or analytical modelling to be carried out, that means the substructuring scheme should not constrain the user in terms of you know if user wishes to do this it should not be a constraint. Any structural modification which has to be applied at any time only involves the re-analysis of the affected part, suppose there are ABCR 3 substructures and if A is modified then we should not end up analysing B and C, okay, then the technique must permit analysis of different components at different times and by different teams, this is what typically happens in a you know space structures or automotive systems and so on and so forth, and even you know mechanical systems in civil engineering applications like a turbine or a piping in an industrial structure, okay, so the different people will be doing different products. Now typically what are the steps involved in this? The steps involved are we partition the physical system into number of substructures with a proper choice of connection and interior coordinates, we need to decide upon the method of analysis for each of the substructures that means analytical or experimental, we have to derive the respective subsystem models either by a theoretical or experimental approach, then we need to carry out condensation of degrees of freedom at the subsystem level and we need to assess the effect of neglect of certain modes and coordinates. Next we need to formulate the subsystem equation of motion either using spatial coordinates or modal coordinates, analysis of one substructure should not require the knowledge of dynamical properties of remaining components, then we arrive at the reduced order equations for the global structure by invoking interface displacement established for different component models, okay. So this is what will lead to the coupled system, so the coupling techniques can be classified based on how you model the subsystems, for example for modeling the subsystems we could use structural matrices that is mass stiffness and damping and spatial coordinate like displacement degrees of freedom and so on and so forth, or you can model each subsystem in terms of a set of natural frequencies, mode shapes, damping ratios and participation factors, both are equivalent. So depending on how you choose we can have different types of coupling techniques, in one of the scheme of classification we classify this coupling techniques as impedance-complete techniques and modal coupling techniques. In impedance coupling techniques reduction within the substructure is performed in terms of spatial coordinates or with the help of frequency response functions of the subsystems, we don't use modal information, in modal coupling techniques reduced model for the subsystems are obtained in terms of subsystem normal modes. So we need to develop the formulary for dealing with you know these coupling techniques and we will take up these questions in the next class and specifically we will be talking about a method known as component mode synthesis which is widely used in practice, so with this we will conclude the present lecture.


Great. Welcome to digital asset news. Take a top stories and crypto break them down into bite-sized pieces. So today this is the big story and We've been talking about this for a while and finally it's going to happen We've got Simon Dixon here from Bank of the Future and he's gonna help us understand what this is as far as a Celsius recovery plans We're gonna go over a lot of things today. So just stick with us The first thing we're talking about is who is Simon Dixon? Why is Bank of the Future his company even taking part in this and a little disclaimer? Also the big question, how do we get Celsius and users money back? I think that's what everybody's here for Also when talking about what have you done so far to try to help Simon and the company? Then we'll talk about what's a bad result. What would you consider a win? And then what's the next step because we can talk how we want to what we got to take action We're gonna take action fast And that's what the plan is and then we'll finish up a little final thoughts mental health And we're gonna take your questions that you submitted to Slido, which we have over 260 or 300 upvoted to the top one so first one Simon First of all, thanks for being here, and I recently lost a family member. I know it's a very tough time So thanks for taking the time out to do this. This is gonna help a lot of people. I really appreciate it Okay, yeah, obviously I really wanted to give this interview to you because I think you know We did some interview about three months ago Firstly, I've just got to say I've got like a loz injured in my mouth if that makes an annoying noise My throat is dead I'm this is not ideal conditions. I've been you know mourning the loss of my father But the DM's just got so heartbreaking The I just needed to do something because I knew I could so You know, that's really the situation right now. This is less than ideal I haven't so, you know, that's that's really the precursor to this but many people are asking for interviews, but I wanted to give it to you Rob because I think you've been doing the Most for the community And and I think it's deserved Well, I'm trying my man I'm trying and then also I just want to say it to everybody that we've got three screens up here We had a little issue technical So you're gonna see the video of Simon as he's hanging out in the nice background and then the audio is coming from a better source So Simon, let's get down to it Your time is valuable my times everybody's times valuable. Who are you? Who is Simon Dixon and why is bank the future taking part in this any disclaimers you want to throw out there before we get going? Yeah, sure. Okay, so I Gave really an overview of me the past present and future of Bitcoin I was involved in Bitcoin from speaking at the very first Bitcoin conference in the world Writing the first published book in the world to include Bitcoin over a decade ago bank to the future And before my life kind of went into turmoil recently I was writing my next book on the future of finance and the surviving the Great Depression of the 2020s and so the reason that I'm here and talking about this right now is because I Am a shareholder in Celsius And the company that I co-founded bank to the future.com is the longest standing company in Bitcoin And it's the world's first crypto securities business We funded over a hundred different companies from Kraken the Phoenix bit stamp Coinbase blockchain.com circle and some of the largest names in the industry and We also did a funding round for Celsius the series a and so that was really my first involvement and What I do want to say in Everything that I talked about today. Firstly, I'm not actually a lawyer, but I paid tens of millions of lawyers over the years surviving Every single, you know, regulatory crackdown that we've had so far in crypto over the last decade So but I'm not actually a lawyer. So you can't take anything as legal advice, right? I'm not I'm not a financial and investment advisor. I have done all my qualifications. I used to work in investment banking I was actually a qualified financial advisor, but I'm no longer registered to give investment or financial advice So nothing that I say in my opinions about What I'm saying it's about purely what do I want for my deposits at Celsius and my shareholding that Celsius There is going to be tax consequences in what what happens here. I'm not a tax advisor So I just got to say that right and I don't work for Celsius I was offered a role on the board of Celsius, but I am not a director of Celsius. I'm not an employee of Celsius I am I believe from my understanding one of the top depositors at Celsius I've always taught diversification Approximately three years ago. I released a video series on retirement plan B.com where I shared Life how I'm investing because I was forecasting a great depression Everyone thought I was crazy back then because the market didn't go into a depression But I was trying to prepare everybody for inflation deflation economic decline economic growth bank failure wars pandemics And how to be okay, whatever happens including crypto and Bitcoin bear markets So part of how I invest is diversify And so I try to prepare for all outcomes and one of my strategies is yield So I had a percentage of my wealth on Celsius as part of my yield strategy And I published, you know, the rewards that I was receiving to be transparent about that And I was so in shares in Celsius. So When this disaster happened, I was forecasting a yield and defy crackdown And letting people know that the net's boom market from this after a yield and defy crackdown and would probably be a securities boom And that happened sooner than I thought it would happen and obviously my deposits are on the line And my shareholder value was on the line and I knew that I could try and do something about it and the all of a sudden The direct messages just started coming through and they were heartbreaking I started to realize that people had actually put their entire life savings in Celsius And people were dependent upon Celsius for their retirement and their financial future and While I cannot do anything about that, you know by the end of this I'd like to really give some tips from Someone that's been completely broke Somebody that's lost their life savings and retirement in the past And I'd like to cover some of that as well But really the main topic I'd like to cover is what can we do about Celsius? So who I am? I'm a depositor I'm a shareholder. I've involved in the industry. I deeply care about this industry I do believe that Bitcoin Is going to play a huge role in the future of finance? And I do believe we need an exit from the traditional financial system. I lean more to Bitcoin than Alternatives to Bitcoin But I also diversify in order to prepare for any outcome and one of the outcomes that I need to prepare for is Bitcoin failure And so that's one of the outcomes I prepare for even though I don't believe it will happen I always invest in maybe me being wrong Gotcha. Okay. So that covers the big stories or the big parts of it who's Simon Why are you guys involved and a little disclaimer? So now let's get to The bigger question How do we get the Celsius users the money back?  I got a bunch of DMs messages heartbreaking and we talk about Only investing what you can afford to lose never leaving too much on your anyone exchange We have the rules right there, but people get ahead of themselves. We're human, right? So now we got a lot of people stuck Simon, how do we do that? What's the plan going forward? So how does this all work out for Celsius users depending if you got three percent like me on the portfolio of their portfolio on Celsius Or like a hundred percent like some people Yeah, okay. So the first thing is we can look back in history having been involved in this industry for over a decade We've been here before So the first time I experienced this was when I spoke at that first Bitcoin conference It was sponsored by a company called Mt. Gox And Mt. Gox had pretty much 70% of all the the tradable bitcoins on their exchange In they tried to get out of they created a bull market And they created a bot to try and trade their way out of a hole because Mt. Gox purchased an exchange from the creator of ripple and that exchange was missing 80,000 bitcoins when Marco Pella sported They then got hacked and they were missing a lot of bitcoins. So essentially They became inadvertently a fractional reserve bank without having a license to do so And so we've got that experience to go by What we do know is that they did a few things right and a few things wrong Some of the things they did right is that they didn't sell the Bitcoin they kept the Bitcoin And it moved into bankruptcy and liquidation and eight years later There is billion dollars of Bitcoin. So it went from being bankrupt to having hugely valuable assets and dollar terms and It's still at this moment being resolved eight years later And a company that I invested into was a small startup at the time called Kraken And Kraken was the company that put together a plan with the liquidators in order to try and Unwind and support all of the depositors in seeing what they could recover and what the financial situation was So that was wave one that took us from Bitcoin, you know up to 1,300 dollars and crashed us right down again to 250 dollars Then we had a sideways market where we tried to reconcile that And we moved into another one The other situation that I was directly involved with was we were in a sideways market in 2016 and Bitfinex lost a hundred and nineteen thousand bitcoins as a result of a hack that was recently recovered from the crocodile of Wall Street. You can follow that story and And The situation there was that they didn't want to follow Mt. Gox. They learned from Mt. Gox and They put together a plan that we were involved with that we can go a little bit deeper in yeah where they haircut users They gave them a token and that token represented a debt. They traded their way out of the issue They repaid some of the debt and people converted it into equity Which is later went 16 and times up on bank to the future dot-com And paid out hundreds of millions of dividends and they got a right to all of the billions and dollars of bitcoins It was later recovered many years later in this year actually 2022 So Bitfinex used financial innovation And really it was comparing those two different stories And people get this confused as well because Bitfinex had two disaster recoveries We did the equity part of that The second one was when 815 million dollars was seized by the government from one of their banking partners by the tether And they had to issue a billion dollars of a token in order to recover the funds that the government had seized As a result of that and that was the Leo token so people get confused The first recovery for Bitfinex was called the BFX token and we can go a bit deeper into that The second one was called the Leo token. They both worked and they both recovered Yes, perfect. So yeah, let's dive deeper next. There's a big distinction between what happened with Mount Gox They kind of want to try to fly away at a bunch of lawyers involved and now we're eight years out 2014 hack I believe right in 1911 12 so we're I mean we're coming up on a decade and we're still in flux But now we're talking about Bitfinex and how it works. So walk us through that those distinctions. You just talked about Okay, so Mount Gox went into bankruptcy went into you know years and years and years of lawyers paying lawyers millions trade by route And eventually the price of Bitcoin went up because there was one very fortunate thing Which is the the the way that the the proceedings worked in Japan meant that they didn't have to sell the Bitcoin Bitcoin went on the bull market for years and years and years. It was a force huddle There was hard forks with Bitcoin cash and Bitcoin SV and all these other ones And so they were able to sell off some of the hard forks and they kept the valuable asset, which was Bitcoin Now the liquidators played it very well um The but you know that went if you move into bankruptcy proceeding is essentially You're relying upon Tradfy's belief in Bitcoin Right and traditionally they are very risk adverse now Japan was The only country in the world that was supporting Bitcoin regulations It was a the the highest level of merchant adoption in Bitcoin And it had a very different mindset, you know Without being stereotypical, but you know, they have 100 year games plans versus three to five year game plans And that was a stroke of luck that made that work, but it still took eight years to get the funds back Okay, so that was number one um with Bitfinex They had to move really fast and this is my original approach to Celsius and I'll go through what we actually did and how we approached them Okay You have to move really fast because the longer you go on The more fud comes out the more bad pr comes out. Yes Predatory offers comes out the more the community stopped believing in what they originally believed in um, so to give you context from the moment that Bitfinex was hacked Um, they were immediately the enemy of the world Everyone was giving me my money back. They were scammers You know take them to prison all of that stuff Um, and but they got they said about releasing after two weeks some press around what they were going to do um within a couple of weeks after that they executed it and essentially Every advisor would never have advised them to do what they did, but they decided We have to find a way or make a way. Um, and they did it Um, so here's what they did Okay, they were they realized that so they took the value of the bitcoin 119 000 bitcoin at the time was valued at 72 million dollars now 72 million dollars compared to hacks that happen today Is a reasonably small number, but back then it was a disaster number True 72 million in our industry back in 2016 was this is before the ico boom You know this was a big hole a really big hole um And what they said is that 72 million dollars is the value of what we can't repay so they opened up They allowed for trading they allowed a bunch of people to withdraw Um and get the rest of their money and they were haircutted by about 33 percent of their deposits um What they did is they then issued a token And that token was called the bfx token The bfx token was essentially a security. It was a promise to repay one dollar and there were 72 million tokens And those 72 million tokens you could either sell them on the market if you thought I went out with this ship I don't believe bitfinex. I think there are a bunch of scammers I'm out and so you could sell it and immediately it started trading at about 30 cents on the dollar But somebody else said I believe bitfinex can recover. I'll buy that one dollar a debt for 30 cents Um, and so immediately that's what happened. This is very different to just issuing a token like luna or something like that You know, this is a security. It represents a debt Um, and in accepting that token you had to agree not to sue bitfinex so if you wanted the recovery then you had to give up your right to see Um, and uh, you know and most people accepted the token and decided that that was the route forward Speculators came along and said well, I'll buy it up I believe the bitfinex has a future and it became a prediction market For the likelihood of bitfinex recovering Now as this 2017 bull market came along a stroke a lot came along Tether tether started to get traction Binance was launched And binance didn't have any banking facilities and it used tether as it's pretty much a crypto to crypto exchange Right and binance became huge because it didn't need to get banking and essentially used bitfinex and tether as their bank account Which led to the later issue that arose the second time round But anyway, binance grew because of that that you know, they they didn't need a banking and bitfinex and tether took on that responsibility The market recovered. They started paying down the debt They also said if you want to convert your Your token No matter what the price of the token is even if it's trading at 30 cents We'll give you a dollar of equity at a set valuation in the company And so we launched a pitch on bank to the future and bank to the future is a securities company and so people were buying tokens at 30 cents And converting them to a dollar of equity. So they were getting a 70 discount on the valuation Wow bitfinex Now as more and more people did this they were buying it for 30 cents and then converting it to equity at a dollar The price of the token started to come up. It went to 40 cents. It went to 50 cents. It went to 60 cents And more and more people realized and then they started repaying more of the debt And then approximately 50 million dollars about 55 million. I think the final number was Was converted into bitfinex equity At a dollar and people could either you know buy that at a discount and they got a deep deep deep discount in the valuation of bitfinex Gotcha This created that prediction market allowed people to make their choice between a token debt or equity And then the 55 million that was converted to equity Went on the bank to the future secondary market The one dollar went up to a price of 16 dollars when it hit at this peak on bank to the future So there was a 16x upside on the equity And there was also they took all of their profits from the whole Ball market that happened in 2017 and 2018 and paid it out in dividends, which was you know to the tune of hundreds of millions Um throughout that time and they also gave people the right To if the hack funds were ever recovered You would get your piece of that and uh, and that was really the first Uh recovery story. Um, it worked well because people acted fast People were given choice And the market recovered Gotcha. Okay. So that's a good lesson as far as like the history of what's happening so then that leads me to Actually, we'll have to back up and kind of talk about that So are these the ideas that you guys are having to move forward potentially with celsius? And not that this is actually happening right now, of course There's a lot of things and talks are in flux But is that some of the some of the of the Rationals of what you're trying to do here or you would just put out a celsius recovery plan and it was uh all about The three proposals So do you want to get into that now or do you want to just give like a brief overview of how the bitfinex Is or is not some of the proposal you're trying to do now with celsius Yeah, so um When we were putting proposals forward, um, we knew that so there was a few things firstly We thought traditional finance are going to take it down to mac boxery But they might take it even worse. They might sell the bitcoin Um, they might sell a lot of the cryptocurrency causing a further crash in the market Yeah, um, they also Would take a risk adverse approach. So There's three issues with celsius that we were trying to find solutions for The first is disclosures. So um, the challenge that that I was putting forward Is that celsius was sold in the wrong way from my perspective Um, it is my belief that the the guild product is a security We know that because block fi Just settled 100 million with the sec And you know, all of the yield platforms as nice Were in challenges around whether you know, there was publicly disclosed things. Here's the challenge of this We were working on their funding round. NDAs have been signed I'm trying to make sure I give as much information as possible represent The right solutions without breaching some of those NDAs and creating legal trouble for myself But sometimes you just got to go for it because The the consequences are too disastrous if you don't go for it. All right, so that's the situation. So disclosures I believe that the yield product is not a low risk savings account It is a high risk security And that became apparent when the bull market ended um, and so Many people took money out of their bank bought stable coins Thinking it was the a different type of risk So it's not a low risk saving account from my perspective. So I believe that that was sold in the correct way And instead it is a higher risk security And that means that when you invest in a higher risk security You need to comply with securities laws now people hate compliance. They hate laws They claim me are being a lover of regulations and all sorts of stuff There's only a reason why banks of the future survive the decade is because I personally believe there are good regulations and bad regulations Good regulations are investor protections And so when you're dealing with a centralized company, it's good to have checks and controls on that company Because there's all sorts of things we have to do liquidity requirements, you know, audit Transparency all sorts of things that are involved in investor protections other things are suitability We anyone that signs up a bank to the future we have to test that they understand the product They have to actually pass an online quiz I'm showing what happens if they issue more shares What happens if I lose my money should I be investing in all my money in one thing? So you do a suitability None of this was how people invested. So I believe that they had a deep misunderstanding of the product And so disclosures transparency All of those things need to be addressed Because is this a security or is this a savings product? That's a that's a question that needs to be answered and addressed and if there is a recovery The second one is regulations. So So Celsius was originally started as a peer-to-peer system And they said you put your bitcoin in and then we'll take that bitcoin And we'll lend it out to somebody else and we'll pay you the yield Um, and uh, you know, that was a peer-to-peer model In having that model There was a reason why it was a peer-to-peer system because it's treated differently from a regulatory perspective when you do peer-to-peer If you then start making investment decisions It's more like a security at that stage because you're investing in the ability for a fund manager to make investment decisions But every piece of every bit of money or crypto that goes into Celsius If it's back one to one, then there's more of security at that stage if however, it's not back one to one And someone you got hacked for example, that's the mount gox scenario At that stage you're engaging in fractional reserve banking Right you need to have a banking license In order to be able to you know lend out more deposits than you have Um, so, you know it evolved as it were what it seems from a peer-to-peer model to a securities model To what looks like a banking model now and therefore there is regulatory consequences now What we saw with block fi is that they settled with the sec And they said we're going to turn this into a security which would imply That it's back one to one and it's not engaging in any kind of fractional reserve If there were month funds missing and then it's an liquidity issue.  Yeah, we got to go over all of it Yeah, so really there's three ways of solving that right Either it's in liquid if it's in liquid Then the my perspective again not financial advice is just wait it out HODL Wait for the system to unwrap itself Um, you know s eave converts to eave when it moves to improve the stake and you just simply wait it out and unfortunately There's reputational damage right There's anxiety financial anxiety in the time that you haven't got your deposits. There's lots of lessons learned But if it's illiquid If nothing major happens with those investments Then eventually you should be in a position where you can slowly withdraw withdraw some now more funds come in withdraw more more funds come in withdraw more And that's really the illiquid solution There's a difference between illiquid and insolvent Insolvent is when you actually don't have enough deposits to meet all of the demands in which case everyone is demanding for Celsius Give me my money back Um, there isn't the money there And so you really have two ways of dealing with it when you're in an insolvent situation Mt. Gox or Bitfinex Right and those are your two choices You either say i'm out we move to bankruptcy And then trad fi lawyers advisors all take over and the board no longer have any decision making in that process Bankruptcy is that solution Insolvency is where you say I believe we still got something that we could do as a board And so my job was to try and get those solutions in front of the board while they could still make that my belief Speculation i'm not a board member of Celsius Um, I'm not privy to the inside conversations I believe that the board wanted to do recovery. I believe trad fi wanted to take the conservative route And I believe that's all based upon You know not buying into the ethos of the crypto industry not buying into the future of bitcoin Trying to protect From certain issues and challenges Um, I'm really not the right thing So when we launched the the web page, which I think you'll be sharing in a bit We tried to articulate some of these thoughts around belief systems become important here Um, I did not want my deposits to be put in the hands of trad fi and bankruptcy proceedings I thought it was best for my deposits Um to actually do a combination Of an illiquid solution for the assets of the liquid And a financial innovation solution so that we can benefit in a very high risk way Like the bitfinex from any upside of what's left over in order to do that It required regulatory transparency financial transparency a willingness to move fast to act fast And to communicate and put pr there about the actual recovery plan So this is when I came out. So what did I actually do? Um, I was mourning my father's loss. I was I publicly said I'm no longer creating videos Um, I've got other things I need to deal with Um, and so I when I realized that this was happening Um, I silently said Right, you've engaged these advisors. I'll tell the advisors what I think they should do Um, and so that was my first approach and I hope that that was going to lead to something When I realized that that was not leading to something I then said we can do it engage us to do it. We've done this before we got the experience We'll take our entire team And put all of our efforts into doing what we think would be the best solution that we can come up with We had a belief That our shares were worthless If depositors were not given a good solution So our solution was focused on depositors And then there'll be shareholder value. And if there's shareholder value, I don't own the tokens Then there may be token value, you know, but my priority was depositors first shareholder second And then if there is a company Then the token might have something to do But there that wasn't really my priority Gotcha And so yeah, that that was I wanted to avoid bankruptcy for that reason. So that was my advice Now when I realized that We weren't really getting anywhere. I started to detect speculation again That there was a bit of a power play between what the board wanted and what the advisors wanted and what tradfire wanted and At that stage I decided that the only thing I could do here is go on to twitter And when I went on to twitter, I wanted to harness the community to let them know that there are solutions and That we need to unite and put more influence and pressure Because we have over five percent share in the company And we can call a shareholder meeting and force a vote again, not legal advice We just believe I've been moving as fast as we can That we could use our shareholding in order to force this And this is when I started to get an offer to become an internal member And then I took the opinion that me being an internal member meant that I'd have to go silent I wouldn't be able to support the community in the way that I'd like to support it And it would give me less influence to do What I thought would be right For depositors would then retain some shareholder value So that was the point when I decided to go public and go on twitter And everybody was asking me who the hell is Simon Dixon? You know, um, what axis he got to grind?  I didn't want to do any videos Um, I wanted to use this time as downtime But the community called And the dms just broke my heart quite frankly. There is a human element to this. Yes People were contacting me saying that they're suicidal They don't want to tell their partner that they've lost all their life savings Um, and then really at that stage it kicked into me Um, I have to push to the final hour and do everything within my power and influence in order to try and come up with a better solution Um, and that's where we are right now. I'll push to the final hour Um, we have certain tools. We have certain influence. We have a team of people Um, we've completed a year of due diligence because we're about to launch the series b funding round for celsius It didn't get quite past the due diligence because of this You know insolvency or stroke Regulatory stroke Yeah, the community issue and that started to happen Um, and so, you know and people are asking us why is this taking so long to do the next round? Well, you know, there were these challenges and they uh, and The stars and the moons all lined up and um, and now everybody I think gets a bit clearer I do also want to say that it's a very very challenging thing for the board It's not my job to judge here. My job is to come up with solutions There's many things that the board did that I wouldn't do Um, but you know, that's not for me to judge. I'm just here to try and get the best result that I can give Um, and use my experience to do what I think is best and why do I care? I've got tens of millions on the line and deposits If I lose those tens of millions, honestly, it won't make any difference in my financial position because I prepared for that But there are people that have all of their savings and that breaks my heart They need to learn the lesson and at the end of this, hopefully they can come out a wiser investor Um, but however, if we could do something to prevent that and that's why we're on this call right now And so it was a human element that kicked in Um that made me want to come out. Yeah, and that's and that's that's huge And then the big thing right here is I will just say this for me move on the next part is the experience So because you've had that experience with the mount gox with the biff index You can say look I can tell you what doesn't work And I can tell you what can work and I can tell you we can do a hybrid or we can take a look at a new approach And we're going to talk about that in a little bit as far as the three proposals So to me it makes a lot of sense and that will kind of answer You know, how do we get the users the money back? We'll talk about that And then what are you doing so far to try to help the human factor makes a lot of sense So here's the next question before we get to you know, the proposals and what we can actually do What's a bad result here? And what would you consider a win and that would be a win for like you talked about The depositors the shareholders the people involved in Celsius and also crypto in general So what would be something to be positive? What would be like or what would be just a big bad negative? Yes, so from my perspective and again, I'm talking from my deposits and not from your deposits You have to make your own decision about what's right Um, and we'll have a way where you can express your opinion about what you think is right for you And but from my perspective the worst result from my deposits would be that bankruptcy takes over They sell all the the my bitcoin And they sell it at the bottom of the market. They create further pressure down with pressure on prices from people that have no belief in Bitcoin And then they take Whatever whatever decent assets Celsius has left And sell it to Goldman Sachs That would be my idea of a worse nightmare Now I I did do some again. Um, I I know many people at Goldman Sachs When the Goldman Sachs rumor came out I asked all my contacts at Goldman Sachs and the people from the relevant departments and I tried to bust that as just misinformation Because all of the people that I spoke to at Goldman Sachs that will remain Unnamed and said that it was just fired. It was just there was nothing to it So I take that for what it is. It doesn't mean that there's not a secret team working on this or you know I just take that for what it is. I try to bust that fud But I do believe that traditional finance want to get into this industry and those that have banking licenses Are them perfectly positioned to take all of the decent assets And as somebody that's been on the other side of many of the conversations that are happening with deals related to You know, gotta be careful what I'm saying here But there's many companies that have challenges right now And I've been on the phone non-stop and my team has been on the phone non-stop with all those companies and all those investors And all those people that putting in solutions There are really predatory solutions that being offered right now and I don't like them at all And you know, so I I want the the reason we put this whole hashtag depositors first I'm a karma guy. That's how I operate.  There is a scenario as we saw where man gots where they don't sell the crypto And I hope that that's I'll use my influence if it goes into bankruptcy to try and push for that Um, but that would be the worst result. Yeah, the best the best result is that we transparently say Okay, this is not illiquid. This is insolvent Um, it's insolvent. Here's the whole Okay, and we put together a way for people through time um An illiquid solution for people to gradually and slowly withdraw their deposits as investments online And then a solution a high risk a speculative solution using securities Is put together um for the whole to try and see if you can recover those funds Um, and there is still a company at the end of this um, and the company at the end of this is either Celsius is a tarnish brand And a tarnish board And therefore they hand over to another board and a brand that can take this on that can deal with um, the regulatory challenges securities banking Whatever this is at the end And there is an upside in that business opportunity That takes care of the whole Um, and some kind of mergers some kind of acquisition and those types of solutions are put together to try and make deposits as whole With the best effort You know team that can do that Gotcha Well, you know what so this would just let's just get down to brass tacks and talk about what that entails So that's going to be the next step. This is where we take action talk is great But talk is cheap. We need to action. So here's what has been given to me So there is this website. There's a link in the description It's bank to the future bnk to the future doc co forward slash Celsius again You don't have to remember that just go in the description click the right one and there's three proposals This is what the team has come up with from bank to the future And sonam needs you to walk me through this as we talk about each one. So here's the first proposal This is a restructuring to relaunch Celsius and allow depositors to benefit from any recovery Through financial engineering. This involves risks and full recovery of funds is not guaranteed I'll go to the all three a pool of the most influential wells in bitcoin to co-invest with the community that'd be pool number two This is see the previous series a fundraise when we can when we completed for Celsius here And proposal number three is an operational plan that allows a new entity Which we just talked about and team to rebuild and make depositors whole this again involves risks and full recovery of funds So let's talk about this very first one here a restructuring to relaunch Celsius and allow depositors to benefit from any recovery through financial engineering What does that look like? What is a time frame and what kind of risks are we talking about? Yeah, so um in terms of time frame Let me check. I've got 20 percent battery. Hopefully that's okay. We should be good. Yeah, um In terms of time frame, that's 100 percent dependent upon the board and the advisors and the internal flights that i'm not privy to at the moment um So that's the first solution which has been phoenix the brand survived The brand's had a lot of damage The brand recovered And financial engineering was used in order to make depositors whole um My fear is that we've come too far for that solution That was my first solution of at fast communicate put out press Tell people the whole Read the haircut Suck it up and put together a plan and act fast So that was proposed to one Gotcha So let's move down to pros and it sounds good get in front of it put out the fire move forward FUDs coming make sure you stamp that out. Here's the number to the second one a pool of the most influential whales in bitcoin to co-invest with the community previous era series everyone And you talked about biffin x in 2016. So talk to us about that time frames those types of things Yeah, so you take the same approach in part one But immediately I got on the phone to i've spent the last 11 years Being a shareholder in many of the most influential companies in the bitcoin and crypto space I got on to the phone to as many of those as I could and said would you be interested in participating in their recovery? Is not going to be a predatory one It's going to be one that gives upside reasonable valuation Um, and if you start investing Then we could see what we could do. So with the big phinex one when there was 55 million Initially, it was the big whales that came along and said, okay, we'll convert junk And that gave confidence and then the smaller people came along and we gave them the solution We had a pitch on bank to the future. You could spend those tokens convert them to equity Um, so immediately we had a bunch of people that wanted to participate in that What I did find is that a lot of There were some that were Interested if we had more Financial information and the regulatory plan that worked right And there were others that were like what we're already putting together a predatory offer And so there were a bunch of those out there. Gotcha. Okay. So that moves us to pros number three This is what we just talked about operational plan Board gets reshuffled put something in there with trust that allows a new entity and team to Rebuild and make depositors whole just they also involves risks. What does that look like time frames if you got them?  Um, then I'd back that Um, however, I do believe that bank to the futures are in a unique position in that we already have a securities business And for the last two years Um, we were working on how to do Celsius's business in compliance with securities laws and we beta tested it with Celsius Uh, and that was our retirement plan B portfolio builder solution that we were beta testing um, so, um If it turns out that there is no faith in the board I know that there are a lot of people that still have faith in the board solution one proposal one then great If that's the solution But if it turns out that somebody else needs to come along and try and get the shareholder value for their haircut Um, then we've been working on investment banking licenses. Um, we've been working on a security solution Um, we have a competent team that survived every single market like this. Um And uh, we would be interested in supporting Some kind of structuring that allowed the haircut shareholder value to try and get some kind of upside Um with the business that we've built Or somebody else's business Um, this capable of doing that Gotcha. All right. So those are three proposals make sense We break them down into the easy pieces that they can be So now it comes up to you for everybody watching this video live and of course the replay This is where you come in it's time for you to make your voice heard. So if we scroll down a little bit more A little more and more This is where you can vote And talk to us or talk to bank of the future about what you would like to see happen You can submit it right here the link again bank to the future.co forward slash celsius You don't remember that all's you got to do is click on the link in the description And let your voice be heard and that is the next step to take action


ay kapangyarihan. Now, let's put that power to the test. It's time for K-Check! Everyone, I'm Gaby Koncepcion, the attorney, not the artista. At ako po si Jonella Bor, and this is K-Check. Weeks of competition, questions and answers, teaching and learning. Paramihan, pabilisan and pagalingan, it all boils down to this. Welcome everyone to the first ever K-Check Grand Finals. Dumating na tayo sa wakas, sa pinakahihintay natin araw. Samahan nyo kami dahil ilang minuto na lang, kontin tanong at sagot, malalama na natin kung sino ang tatang kaunahunahang K-Check champion. Wag na natin patagalin pa, kilalanin natin ngayon ng ating apat na finalists. Having come this far, they are all winners. Pero isa lang sa kanila ang pwedeng maging K-Check champion. Sino ba sa tingin ninyo ang magiging champion natin? Will it be our soft-spoken film major Charlene? She almost whispered her answers but her impressive rally was loud enough to make her our first grand finalist. Or it will be Asher. Ang nagakalang ang K-Check ay game show tungkol sa K-Drama but he survived an opponent's comeback attempt to secure his place in the finals. Pero malaki rin ang chance ng BS Camp student na si Hanna. Dahil kahit ang minor niya ay paggala, nakumpo pa rin niyang deigin ang kanyang mga Kapo contestants to become our third grand finalist. And finally, BA creative writing student Tamara now has something to write about using her second shot at the competition to make it to the K-Check finals. Of course, these four will be competing under the watchful eyes of our esteemed K-Check panel of experts. Professor Glessia Tienza of the College of Arts and Letters UP Diliman. Professor Neil Santelian, Chairperson of the UP Diliman Department of History and Professor Marian Roque, Professor of Mathematics at UP Diliman. And now contestants, papasok na tayo sa K-Check Paramihan where each correct answer is worth 10 points. This is your chance to bank as many points as you can and take the all important early lead. Let's begin. Charlene To the nearest whole number, how many kilometers is the Olympic marathon? The correct answer is 42. Asher In 2021, she won the Grammy Award for Record of the Year for the second straight year. Who is this female singer who had a concert at the Mall of Asia last August? Oliver Rodrigo. Malik. The correct answer is BLH. Hannah, what mineral is rated at 10 in the most hardness scale? Diamond. K-Check. Tamara, which common Mexican flatbread from flour or corn is used to make an assortment of Mexican dishes? Tortilla. K-Check. Charlene, also known as break bone fever, what viral infection is transmitted to humans through the bite of the 80s Egypti mosquito? Dengue. Dengue? K-Check. Asher, not applicable to the Philippines. How is the legal dissolution of a marriage called? Of divorce. Hannah, what racket sport shares its name with a starchy vegetable? The correct answer is Squash. Tamara, which much-hated leader was named Time Magazine's Man of the Year for 1938? Adolf Hitler. K-Check. Charlene, Captain Hook is the adversary of which flying boy? Peter Pan. K-Check. Asher, what does UV stand for if we are talking about light and waves? Ultraviolet. K-Check. Hannah, how many degrees is an angle that perpendicular lines form? 90. 90. K-Check. Tamara, Honolulu is the capital of what U.S. state? Hawaii. Hawaii. K-Check. And that's it for our first round of the K-Check para mihan round. Talagang best of the best na itong round na ito. Kitamang yung scores nila, di ba? Dikit-dikit sila, pero siyempre, si Tamara ngayon ang medyo. Angat ng konte, but not by much. And it's too early to tell pa, di ba? Correct. Round one pa lang. Speaking of round, warm up, may mga katanungan ba kayo sa aming lahat? Siyong gusto magtanong una? I think I'll go first. Sure, go ahead. Since I mentioned in the previous episode na yun nga po isa sa mga role model, kasi ator ni Gaby, I'll ask her. So what is the legal question internet versus ornita? Charit. It's for our final project, pero like kailahan talaga namin ng tulong, pero to be honest, a serious question is like what would be your advice for youth like us who are being disillusioned with the flaws of our legal system and how it approaches inequalities and our problems in our society? Ang bigot-bigot naman ang katanungan ng internet final. Thank you very much for that question. Unfortunately, the problems that trouble our legal system has been there since time immemorial. Yung din ang sabi ng tatay ko sa akin magkanang maglo kasi it's a marketplace. But if you think about it, ko hindi tayo sa sabak, sino iiwan natin ang mga korap kaya ang mga tulad natin na malinis at patawid dapat pa rin sumabak at makipaglaban. Slow clap. Thank you. Slow clap tayo. Thank you for that question. Just ko, hirad naman mag-contest at post dito. Reading ready ka sa kasagutan mo yun. At kaya yun ready na ba kayong lahat for our Pabili sa round next here on K-check. Tuloy pa rin ang ating karunungan check grand finals. And after the first round, meron tayong nangunguna na si Tamara with 30 points. Charlene, Asher, and Hannah closely trailing behind with 20 points each. Kaya maganda ang laban pa rin. Maganda ang laban. Mahirap talaga kung mga best of the best ang naglalaban. And since it's their opportunity to ask questions now and probably the only opportunity, Charlene, meron ka bang gustong tanungin sa isa sa ating mga panel of experts? At si no ang gusto mong tanungin? Si Ma'am Glessie po. Okay. Question mo kay Ma'am Glessie. Hi Ma'am. Ano po ang play ang gusto niyo po makita adapted into film in your lifetime? Siguro gusto kung gusto kung makita yung play na tungkol sa migrant teachers. Ito yung isang play na ginawa namin yung teacher ng bayan kasi covered nito ang lahat ng issue ng lipunan na hinaharap natin ngayon mula sa brain drain, unemployment, middle level service education and I think it's something na kailangan natin makita kahit saan. Maraming salamat. Ang mga contestants natin hindi lang magaling sumagot ng mga katanungan, magaling din pala magtanong. Parang gusto ko yung silence na parang seriyos talaga tung pangayaring ito ngayon. We're now going into K-check pabilisan. Buzz in first for the right to answer the question. Correct answers are worth 20 points pero sa round ay ito minus 10 points ang maling sagot. Kaya contestants now more than ever think before you press it buzzer. Let's begin. This is it, guys. Question number one. Who became the first president of the KKK or the Katipunan in October 1892? Hannah. Andres Bonifacio. Malit. Asher. Teodoro Plata. Malit. Ang tamang sagot Giordato Arrelliano. Question number two. The phrase an eye for an eye originated from what ancient text or book? Charlene. Nakuda Famurabi. K-check. Question number three. In sports, which team won the first TBA conference championship in July 1975? Ang tamang sagot Toyo. Question number four. What Spanish song by Luis Fonsi became a number one hit? Asher. Despacito. K-check. Taposin ko lang sagot. One hit more than 40 countries in 2017. Question number five. Which city in the western hemisphere is second only to Paris as the world's most populous French-speaking city? Charlene. Montreal. K-check. Montreal. Question number six. Which president declared the Philippines under martial law on September 21, 1944? Hannah. Justado makapagal. Malit. Asher. Josepiloral. K-check. Question number seven. What is the name of the longest river of the USA? Which is also the name? Charlene. Mississippi River. Malit. Which is also the name of the 24th state of the Union? Asher. Colorado River. Malit. Correct answer is the Missouri River. Longer by 100 miles than the Mississippi River. Next. Question number eight. Corredor Island politically belongs to what province or city? Asher. Bataan. Malit. Charlene. K-check. Question number nine. Which former colony was handed over to China by Portugal in 1999? Asher. Macau. K-check. Question number ten. In anatomy, what do you call the colored tissue at the front of the eye that lets the proper amount of light through an opening and into the eye? Tamara. Pupil. Malit. Charlene. Pratina. Malit. Asher. Iris. Question number eleven. Who received almost three million popular votes more than Donald Trump? Asher. Joe Biden. Malit. During the 2016 U.S. presidential elections. Okay. Sorry. Okay. Time's up. Correct answer is Hillary Clinton. Last question for this round. Nitrogen and oxygen are the two most common gases in the Earth's atmosphere. At slightest less than 1%, what is the third most abundant gas in the atmosphere? The correct answer is and that's it for our K-check Pabilisan Round. At talagang nakakastres atong round nato as of now ang ranking ng ating mga contestants Charlene and Asher are tied at 60 points each. Tamara has 20 and Anna has zero. Except that it's still too early in the game. Correct. May round three at maraming ang ating mga expert. Pero I understand meron paring ka tanungan. Ang isa sa ating mga contestant, si Tamara has a question for one of our experts. Tanong ko po kay Mamro kay Dal. Kayo po yung prof ko datin and like malapon masyadong chance na makausap kayo ng ganto and malakong seryosong tanong specifically pero naisip ko sa Dal kanina mention yung sagot na squash yung gusto nyo. Like yung favorite na food nyo. Pwede ng dessert, pwede ng savory dishes, kayo po bahala. Di ako ganong matakaw. Pero siguro ano something I like, I crave lechon or paksiyo na lechon. Wow. Parang biglang na gootong din, Yatta. Yung pang panganga na ko gusto ko nang masasarap na food. Kaya nga, par. Gooting po lechon paksiyo. Dal na namin ko lechon. Wow. Yung anong, kusaka saan na kay gawan na in one time. Kaya natakot ako na lechon. Masama kami sa dalong. Natakot ako sa lechon. Paano ko gagawin ni lechon? Gusto ko kumain. Lechong paksiyo. Ang pwede nga win ni Tamara. Sige, kaglaluto mo ako. Paglaluto mo ako. Pumpkin soup gusto. Pwede na rin nyo. Pwede na rin nyo. Pumpkin soup and paksiyo na lechon. Correct. Basta kasama tayo. Basta kasama. Lahat ng nandito sa mundong ito. Thank you. Thank you. Kasi hindi ko siya pinahirapan. Hindi niya ako pinahirapan. Sa tanong. This time, our contestants will face their toughest challenge yet. Yalang ating ultimate pagalingan round. Susunod na. Here on K-check. Welcome back. Mag points recap mo na tayo. Charlene has 60 points. Asher has 60 points. Tamara has 20 points. At si Hannah ay hahabul yan. And it's still early. Pwede pa talagang humabol. But ito na ang final chance for one of our contestants to ask a question from one of our panel of experts bago natin umpisahan ang round. Kung saan sila ay tatanungin na talaga na mga experts sa ating final round. Si Hannah ang magtatanong sa isa sa ating mga experts. Sino ang tatanungin mo at tanong question mo. Kay, Prof Neal po. Okay, so my question is in your opinion, ano po ang isang historical event sa ating mundo na nagshap ng kung anuman ang nangyayarin na ngayon sa ating political climate? Sa akin yung digital revolution. Yung ICT. So basically, yun yung nag-define ng globalization sa kasaluku yung contexto. Short and sweet, yung sagot niya. Napaka short niya. Pero malalim. Pag-isipan mo na natin. Pwede, no? But we don't have time because now, it's time for our Kcheck Ultimate Pagalingan our last for this season. In this round, correct answers are worth 30 points. Wrong answers get a 15-point deduction. At para mas madagdagan ang kalaman ng ating mga contestants at viewers sa round na ito sa mga professors na ating panel of experts mga gagaling ang mga tanong. At the end of this round, malalaman na natin kung Sino ang first ever Kcheck Champion natin. And for the last time in this season, contestants, let's begin. And now for the first question for the last round of this season, Professor Glesy ang tanong. Eto na, usa pang language. Right? This language is often called the bridge language or the common language between speakers who do not share a common language. What do you call this social language? Charlene. Lingua Franca. Kcheck. The answer is Lingua Franca. Professor Neal. Ano ang naging pinakamalaking hamon sa Munich Olympic Games ng 1972? The boycotts during the Olympics from particular participating nations. Maling sagot. Yes. The apartheid. Maling sagot. Ang tamang sagot ay dapat terrorismo. Maling sagot na 11 atletang hudyo at ginawa ito ng isang grupo na mga terrorista ang arabo. Prof. Marion. I'm sure masakit ng ulo nyo sa usa pang gamot. One classification of drugs is through their route of administration. How do you call drugs which are directly applied on affected areas and affect HANA. Topical. Examples will be ointments and creams. Topical. Kcheck. Ayinit ng painitang laban back to Prof Glesy. Tapang pelikula ulit. Okay. This Lino Broca film exposed the fanatical paramilitary groups which terrorized Charlene Oropronobis. Should I continue the question? Okay. Which terrorized barrios in the hinterlands of the country during the post-ed sa revolutionary period. It has been screened privately and has not been commercially screened since it was banned ajuto its subversive message. It has won international awards such as the director's fortnight in Cannes, 1989. Correct answer is Oropronobis. Kcheck. Kcheck. Nako nakikita natin na merong lead but still we have many more questions to go. Next question, Prof Neil. Ang bansaang United Kingdom ay may tatlong babaing prime ministers. Ang tanong ay magbigay ng dalawang babaing dagsilbing prime ministers ng United Kingdom. Margaret Thatcher at Theresa May. Tatlong posibling sagot na sabi na ni Asher. Si Margaret Thatcher mula 1979-1990. Si Theresa May na humarap sa Brexit mula 2016-2019. At ang pinakahule ang predecessor na kasolokoy ang prime minister si Liz Truss na nagsilbilang less than two months. Salamat, Prof Neil, back to Prof Marion. Usapang math. What number between 2020 and 2030 is divisible by nine? Asher. 2025. Okay. A number is divisible by nine if it's digits. Okay. The sum of the digits is divisible by nine. So between 2020 and 2030 2025. Okay. The digits are 2025. The sum is nine. That's divisible by nine. So 2025 is correct. Okay, Jen. Talagang umi-init ang labanan dito. Prof Glacey. A usapang literature mula si regions. Okay. Filomena Hubaldi is one of the last singers of the La G. An ancient song which is traditionally recited in community occasions. Where is the home of this ancient song called La G? Untamang sagot ay ang pinaka-northern part ng ating bansa sa batanes We learn something new every day. Prof Neil ang tanong. Anong bansa sa Asher ang dumanas ng genocide mula 1975-1979 na nagresulta sa pagbaslang ng halos dalawang miliyong tao. Hanna. Myanmar. Balinsagot. Charlene. Cambodia. Untamang sagot ay Cambodia, Kate. Naku. Question. Professor Marion. Okay. What sugar in beer undergoes metabolism by yeast during fermentation? Hanna. So gross. So, um, the main sugar in beer which undergoes metabolism by yeast during fermentation is maltose. But there are other sugars like fructose, glucose and sucrose. So, K-check. So, eto na. We now enter the last round of questions from our panel of experts. At malalaman na natin kung sino ang first ever K-check champion natin. Prof Glesy. Okay. Tongkol sa political theater. Okay. What is the title of this famous seditious play by Aurelio Tolentino which chronicled the challenges of colonial rule in the 1900s? Sagot ay kahakon ngayon at bukas. Salamat sa tanong ngayon. Next, Prof Neil. Ano ang tawag sa Philippine Army contingent sa United Nations Command sa Digma Ang Coriano ng early 1950s. Tamang sagot ay Philippine Expeditionary Force to Korea or PEPTOC. And for the last question. Na ito. Mat na. Okay. A pentagon is a polygon with five sides. A pentadecagon has 15 sides. How many sides does an enyadecagon have? Asher 200. Malay. So baka dapat utawagin ding no na dekagon? The correct answer is 19. Thank you, Prof Marion. And that's it for our K-Check Ultimate Pagalingan Challenge. Wow! And that wraps up our K-Check Ultimate Pagalingan Challenge. To award the prizes, we'd like to call on the Executive Director of TVUT Professor Emeritus Great. Javier Alfonso. Para okay pa. Natin kung sino ang nanalo, congratulation star. First-ever K-Check Champion, Char Lane with a final score of 150 points. She will receive a laptop, courtesy of TVUT, and a trophy designed by Professor Alfonso herself. Thanks to Asher, Hannah, and Tamaro for joining and to our members ng panel of experts natin ang Professor Glesy, Professor Neil, and Professor Marion. And of course, maraming salamat po sa yung lahat for staying with us all season long. At habang nakakasiahan dito, gusto ko rin magpasalamat sa you, Janelle. Sana ay magkasama pa tayo ulit next time sa next season. This is K-Check. Thank you, Natori Gabi. I'm sure may next time pa ito, di ba? Dalit sa K-Check as a TVUT na niniwala tayo na paggating sa teaching and learning Thank you again, everyone. It has been Janelle Bore. And this has been Attorney Gabi Concepcion. Until next season, here on K-Check!