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Diastema closure using BRB matrix technique Steps: 1️⃣Take a silicon impression from initial situation 2️⃣ Cut silicone in diastema area creating space for composite 3️⃣ Restore palatal aspects of proximal zones 4️⃣ Use sectional matrix to restore teeth one after one 5️⃣ Finishing and polishing #AboutDent

15,206 views • 9 months ago •via X (Twitter)

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There is a concerted effort by rival parties and the press to oust Nigel Farage as leader of Reform. It would be a mistake for Restore Britain to join in. Farage faces scrutiny from the Parliamentary Commissioner for Standards following a Times investigation into his association with “Posh George” Cottrell, and an undeclared £5 million donation from crypto billionaire Christopher Harborne. If found to have broken the rules on reporting gifts, he could be suspended as an MP and face a by-election. The likes of Fraser Nelson and Boris Johnson are salivating at the prospect of sabotaging Reform, replacing Farage with a Tory defector or performing political necromancy for the Conservative Party. Persecution might further endear Farage to the public. It suggests the establishment is afraid of him, and could encourage him to continue his recent strengthening of rhetoric on immigration and anti-white racism. But some in Reform are eager to purge the party of nationalist sentiment. There are already traitors talking to the Observer, detailing their efforts to remove “trigger-happy” Zia Yusuf from his role as Home Affairs spokesman. “Zia’s a big problem,” one said, with others arguing “privately that the use of racial politics was necessary to see off Rupert Lowe’s Restore, but the party ultimately needs to appeal to the centre to have any chance of winning.” With the right on the ropes, it is unwise for Rupert Lowe to promise to “throw everything” at a by-election in Clacton. Restore can’t afford another self-inflicted wound, after weeks of Rupert making needless rhetorical blunders about ethnonationalism and multiculturalism, causing infighting among the base. Joining a witch-hunt would reinforce the narrative that Restore is purely motivated by vengeance against Farage — which is not what most of Restore signed up for.

Connor Tomlinson

39,638 views • 2 months ago

Discrete Fourier Transform by hand ✍️ ~ 12 steps walkthrough below Here is a little-known secret about the DFT and the inverse DFT: it is just matrix multiplication in both directions, one the transpose of the other, exactly like the forward pass and backpropagation I drew in other examples. Goal: recover which cosine waves a signal is made of, using nothing but multiplication and addition. = 1. Given = Three signals written as sums of cosines, and a fourth, X, that we do not know yet. = 2. Frequency matrix F = Let us write the coefficients as a matrix. Each signal is a row, each frequency a column, so A = cos(w) + 2cos(2w) becomes [1, 2, 0, 0]. = 3. Sample the waves = We read the four cosine waves at ten discrete time points. That word "discrete" is the whole difference between this and the continuous transform. = 4. Cosine matrix W = Let us write those samples as a matrix: each frequency a row, each time point a column. = 5. Frequency to time = We multiply F by W. That combines the four cosine waves in the proportions F specifies, and the result T is the three signals as they would look in time. = 6. Transpose = Let us stand each signal up as a column. = 7. Time to frequency = We multiply W by that transpose. Every cell is the dot product of one signal with one cosine wave, which measures how much of that wave the signal contains. Zero means none of it. = 8. Scale = Let us multiply by 2/n, with n = 10. The projections come out five times too large, and this is the correction. = 9. Transpose back = We turn it back around, and it is F again, exactly. That is the check: the transform recovered the coefficients we started from. = 10. Now solve for X = Let us run the same multiplication on the one signal whose recipe we never knew. = 11. Scale = We divide by 5 again. = 12. Transpose back = And X reads [0, 0, 3, 2], which says X = 3cos(3w) + 2cos(4w). Note: I originally drew this to show that the DFT is a special case of a convolution layer, its filters fixed to sine and cosine waves rather than learned. No wonder, then, that a convolution layer free to learn its own filters can be trained to process signals. 💾 Save this post!

Tom Yeh

25,684 views • 1 month ago

Discrete Fourier Transform by hand ✍️ ~ 12 steps walkthrough below Here is a little-known secret about the DFT and the inverse DFT: it is just matrix multiplication in both directions, one the transpose of the other, exactly like the forward pass and backpropagation I drew in other examples. Goal: recover which cosine waves a signal is made of, using nothing but multiplication and addition. = 1. Given = Three signals written as sums of cosines, and a fourth, X, that we do not know yet. = 2. Frequency matrix F = Let us write the coefficients as a matrix. Each signal is a row, each frequency a column, so A = cos(w) + 2cos(2w) becomes [1, 2, 0, 0]. = 3. Sample the waves = We read the four cosine waves at ten discrete time points. That word "discrete" is the whole difference between this and the continuous transform. = 4. Cosine matrix W = Let us write those samples as a matrix: each frequency a row, each time point a column. = 5. Frequency to time = We multiply F by W. That combines the four cosine waves in the proportions F specifies, and the result T is the three signals as they would look in time. = 6. Transpose = Let us stand each signal up as a column. = 7. Time to frequency = We multiply W by that transpose. Every cell is the dot product of one signal with one cosine wave, which measures how much of that wave the signal contains. Zero means none of it. = 8. Scale = Let us multiply by 2/n, with n = 10. The projections come out five times too large, and this is the correction. = 9. Transpose back = We turn it back around, and it is F again, exactly. That is the check: the transform recovered the coefficients we started from. = 10. Now solve for X = Let us run the same multiplication on the one signal whose recipe we never knew. = 11. Scale = We divide by 5 again. = 12. Transpose back = And X reads [0, 0, 3, 2], which says X = 3cos(3w) + 2cos(4w). Note: I originally drew this to show that the DFT is a special case of a convolution layer, its filters fixed to sine and cosine waves rather than learned. No wonder, then, that a convolution layer free to learn its own filters can be trained to process signals. 💾 Save this post!

Tom Yeh

13,124 views • 4 days ago

Gilbert Strang taught linear algebra at MIT for fifty years. His last lecture is on YouTube. It has fewer views than his worst lecture. Nobody told students it was the last one. He just walked in, said "the final class in linear algebra at MIT," and started reviewing old exams. Google built a $2,000,000,000,000 company on one concept from this course. He is 88 years old. He still answers emails. This is MIT 18.06. Linear Algebra. The most watched mathematics course in history. Then the Markov matrix. Strang writes a transition matrix on the board. Three states. People moving between them every step. After enough steps - the system locks into a steady state that never changes. That steady state is an eigenvector. Google's PageRank works the same way. Websites are states. Clicks are transitions. The importance of every page on the internet is one eigenvector of one enormous matrix. Then least squares. Three data points. No line passes through all three. So you find the line that minimizes total error. That is how every AI model on earth is trained - including the ones running inside Goldman Sachs trading desks. Then the projection. The closest point on a plane to a vector outside it. Strang draws it in 30 seconds. That same operation is how Netflix decides what to recommend to 280,000,000 subscribers. Watch the moment he gives back the final exam answer and asks students to work backwards to the question - the room solves it in silence faster than any other lecture all semester. A software engineer told me 18.06 was the course that got her from $90,000 to $200,000 in two years. Same company. Different title. Bookmark this and watch later - after this lecture every dataset you touch will feel like a geometry problem waiting to be solved. MIT 18.06 Lecture 34 | Linear Algebra Final Review | Gilbert Strang

Zyphor

56,433 views • 11 days ago

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

Ochob

130,818 views • 1 month ago