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links and quotes are now beautiful just like you, various typos fixed…
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… and many small QoF improvements
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sudoankit committed Oct 18, 2019
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1 change: 1 addition & 0 deletions _posts/2017-04-06-engineering-in-india.markdown
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Let’s analyze the examination results which came out for me last week. In a particular subject (*no, I won’t tell ya*) this was the situation.
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1 change: 1 addition & 0 deletions _posts/2017-04-28-triangulation-primer.markdown
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1 change: 1 addition & 0 deletions _posts/2017-09-04-Research-at-IIIT-BH.md
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Okay, I'll be straight and frank.
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14 changes: 8 additions & 6 deletions _posts/2018-01-01-geometry-lagrange-multiplier.md
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</style>

The Lagrangian Multipliers is an important strategy in mathematical optimization to find the local maxima or minima of a function subject to equality constraints.
Expand Down Expand Up @@ -68,7 +70,7 @@ The point of intersection of the ellipse and the riverbed curve $f(x,y)$. They h

A lot of interesting stuff happens here at the interection point. First, you can easily verify that both the curves have a common tangent equations. Nice. Next, the point has two normals acting on it, in the opposite directions. This is what we care about.

<font color="blue">Normals.</font>
<font color="red">Normals.</font>

Let's focus on normals. As we know the normal is given by the gradient of the curve, (since the gradient of a function is perpendicular to the contour lines)

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$$ \nabla_{x,y} f = \Bigl( \frac{\partial{f}}{\partial{x}}, \frac{\partial{f}}{\partial{y}} \Bigr) $$

So, we never know whether these normal are balanced. It depends on the curve and elipse equations. Thus we introduce a scalar, non-zero constant, <font color='blue'> $\lambda$ </font> (to balance the point of interection, where the maxima or minima lies).
So, we never know whether these normal are balanced. It depends on the curve and elipse equations. Thus we introduce a scalar, non-zero constant, <font color='red'> $\lambda$ </font> (to balance the point of interection, where the maxima or minima lies).
<center>
<div class="boxx">
$$ \nabla_{x,y} f = \lambda \nabla_{x,y} g $$
</div>
</center>

This constant is called the <font color='blue'>Lagrange multiplier.</font>
This constant is called the <font color='red'>Lagrange multiplier.</font>

We continue solving this equation,

Expand All @@ -97,7 +99,7 @@ $$ \nabla_{x,y} f - \lambda \nabla_{x,y} g = 0$$

Note, setting $\lambda = 0$ is a solution if $f(x,y)$ is at the level (horizontal) regardless of $g(x,y)$.

Let us define another function $\mathscr{L}(x,y,\lambda) \equiv f(x,y) + \lambda g(x,y)$ to include all the conditions into one equation and solve for $\nabla_{x,y,\lambda}\mathscr{L}(x,y,\lambda) = 0.$ [ this function is also called the <font color="blue">Lagrangian Function</font>, also note that $\lambda$ can be positive or negative ]
Let us define another function $\mathscr{L}(x,y,\lambda) \equiv f(x,y) + \lambda g(x,y)$ to include all the conditions into one equation and solve for $\nabla_{x,y,\lambda}\mathscr{L}(x,y,\lambda) = 0.$ [ this function is also called the <font color="red">Lagrangian Function</font>, also note that $\lambda$ can be positive or negative ]

As there are three unknowns, $x,y$ and $\lambda$, would need to solve three equations.

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<hr>

References include <font color="blue">my father's lecture notes on numerical methods and FEM at NITC (riverbed) </font>, <a href="https://en.wikipedia.org/wiki/Lagrange_multiplier">Wikipedia</a>, <a href="https://math.stackexchange.com">math.stackexchange</a>, <a href="https://www.microsoft.com/en-us/research/people/cmbishop/">Pattern Recognition and Machine Learning, Bishop</a> and <a href="https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/">MIT OWC Multivariable Calculus. (necklace intuition)</a>
References include my father's lecture notes on numerical methods and FEM at NITC (riverbed), <a href="https://en.wikipedia.org/wiki/Lagrange_multiplier">Wikipedia</a>, <a href="https://math.stackexchange.com">math.stackexchange</a>, <a href="https://www.microsoft.com/en-us/research/people/cmbishop/">Pattern Recognition and Machine Learning, Bishop</a> and <a href="https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/">MIT OWC Multivariable Calculus. (necklace intuition)</a>

All images are mine and are licensed under CC-BY-4.0. Softwares used include MATLAB, OSX Grapher, Preview.app and Adobe illustrator.
All images are mine and are licensed under CC-BY-4.0. Softwares used include MATLAB, OSX Grapher and Adobe Illustrator.
<hr>

I hope you had as much fun reading than I had writing this up!
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3 changes: 1 addition & 2 deletions _posts/2018-01-26-Head-Fakes.md
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.boxx {
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width: 400px;
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43 changes: 1 addition & 42 deletions _posts/2018-03-09-school-resolution.md
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Expand Up @@ -50,7 +50,7 @@ I needed to try and create some intuition of genetic engineering. I went with CR
My CRISPR slide.</div>
</div>

**Observations:** Visualizing protein structure using AR would be pretty cool. <sup><a href="#first">1</a></sup>
**Observations:** Visualizing protein structure using AR would be pretty cool.

---

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Explaining this kids a simple contraint problem! Copyrights: (NAE Bridge/Lars Blackmore/SpaceX) </div>
</div>

### Sorcery.
---
<div class="imgcap">
<img src="/assets/school/me.png" width="50%">
<div class="thecap" style="text-align:center">
When you allow kids to draw on your photo. Sorcery!</div>
</div>

haha, someone started writing the formular for angular velocity!!?, someone drew horns, someone a hat, someone gave me muscles!, I have no clue what that red thing is on the chair!

The best feeling I got is when someone wrote "come again!".


I will!

<hr>


#### EDITS + UPDATES
<div id="first">

<b>1:</b>

I tried to visualize a DNA strand using Vuforia and Unity and results are great! The only bad review from kids was the 3D model which I had freely downloaded. :(

I hope I'll try to make my own blender, perhaps model and open source this!
<br>
<br>

<div class="imgcap">
<img src="/assets/school/dna-ar.png" style="border:border:1px solid #021a40; width:100%; height: 40%">
<div class="thecap" style="text-align:center">
DNA AR Model using Vuforia and Unity</div>
</div>
</div>


---

More references.

Spring Valley School for allowing me to do this, Wikipedia, Nat and Friends, Google Search,

This was a fantastic experience in my life and I totally suggest you to try teaching at random schools. It's so much fun!

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2 changes: 1 addition & 1 deletion _posts/2019-09-10-Visions.md
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**Note:** This is [a comment I wrote on Reddit](https://www.reddit.com/r/Indian_Academia/comments/cqttnh/best_skillset_to_invest_in_now/ewzmozd/). As I'm right now going extremely slow on an original, quality post -- I hope this will suffice the need reading something new in my blog.
**Note:** This is [a comment I wrote on Reddit](https://www.reddit.com/r/Indian_Academia/comments/cqttnh/best_skillset_to_invest_in_now/ewzmozd/) as right now I'm going extremely slow on an original, quality post -- I hope this will suffice the need to read something new in my blog. I expect the new post to be out around December last week.

---

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40 changes: 32 additions & 8 deletions css/main.css
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h1, h2, h3, h4, h5, h6 { font-size: 100%; font-weight: 400; }

a { color: #6c34ef; text-decoration: none; }
a:hover { color: #000; text-decoration: underline; }
a:visited { color: #C0C0C0; }
a {
color: #6c34ef;
text-decoration: none;
-o-transition:.5s;
-ms-transition:.5s;
-moz-transition:.5s;
-webkit-transition:.5s;

transition:.3s;


}
a:hover {
color: #6c34ef;
text-decoration: underline;
opacity: 0.5;

}
/*a:visited { color: #AEB6BF; }*/

/* Utility */
hr {
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}

.post-content blockquote {
border-left: 4px solid #000000;
border-right: 4px solid #000000;
padding-left: 20px;
padding-right: 20px;
/*border-left: 4px solid #000000;*/
/*border-right: 4px solid #000000;*/
/*border-top: 2px solid #000000;
border-bottom: 2px solid #000000;*/
padding-left: 7px;
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padding-bottom: 7px;
font-size: 18px;
border: solid 2px;
box-shadow: 7px 7px 0 0 #6c34ef;

opacity: 1;
color: #6c34ef;

font-family: inherit;
font-style: bold;
font-style: italic;
margin: 30px 0;
}

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