# Takeaways from “Never Split the Difference” by Chris Voss

HBO charged me $15 via Amazon for my subscription that I forgot to cancel after the Game of Thrones was over. Upon writing to Amazon, the representative said: As per policy we are unable to issue refund for the previous month charge (September) for your HBO subscription. However, I am able to make an exception for you and have issued you a promotional credit of$15.14 in your account.

Walmart manager said he would not accept my returns (worth $107) without a receipt. Although the first guy said he would give me a gift card, the system didn’t let him proceed. The manager came in and told me they wouldn’t take these returns. Why? Because they have recently changed the rule: without a receipt, I can return items worth only up to$25.

# Impagliazzo’s Hardcore Lemma: a Proof

Informally speaking, Impagliazzo’s hardcore lemma says that if a boolean function is “hard to compute on average” by small circuits, then there exists a set of inputs on which the same function is “extremely hard to compute on average” by slightly smaller circuits.

In this post, I am going to explain how I understand the proof of the hardcore lemma presented in the Arora-Barak complexity book (here). Because the formal proof can be found in the book I intend to write in an informal way. I think some subtleties are involved in turning the context of the lemma into a suitable two-player zero-sum game. Doing so enables one to use von Neumann’s minimax theorem to effectively “exchange the quantifiers” in the contrapositive statement of the lemma. Although the Arora-Barak proof mentions these subtleties, I am going to explore these in more detail and in a more accessible way for a beginner like me.

# What Is Your Excuse Today?

I changed my mind before entering the blue doors of the weight room in my gym. There was the soothing sound of water trickling  down from the fountain. I felt more thirsty as I waited.

— “Hey, Saad!” exclaimed a low voice. I looked to my right. He just came out of that blue door of the weight room.

— “You used to be my TA !” he said. It always feels good to meet your past students, especially ones that still remember you. I looked hard. Remembering my students’ names used to be my forte, but probably not anymore. Continue reading “What Is Your Excuse Today?”

# Const-Pointer and Pointer-to-Const in C / C++

You must have known it already, but I can’t stop myself from showing off the interplay of const with pointers in C/C++.

Here goes the code. It’s simple.


void main() {

int arr[]={1,2,3,4}; // data

const int *p1 = &arr[0]; // non-const ptr to const data
int const *p2 = &arr[0]; // non-const ptr to const data
int* const p3 = &arr[0]; // const ptr to non-const data
const int* const p4 = &arr[0]; // const ptr to const data

p1++; // ok
p1[0]++; // compile error: modifying const data

p2++; // ok
p2[0]++; // compile error: modifying const data

p3++; // compile error: modifying const ptr
p3[0]++; // ok

p4++; // compile error: modifying const ptr
p4[0]++; // compile error: modifying const data

}


# Eigenvalues of the Laplacian Matrix of the Complete Graph

We will show that the eigenvalues of the $n\times n$ Laplacian matrix $L$ of the complete graph $K_n$ are $\{0,1\}$ where  the eigenvalue $0$ has (algebraic) multiplicity $1$ and the eigenvalue $n$ has multiplicity $n-1$.

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