# Questions tagged [mathematical-analysis]

Questions related to mathematical analysis (often called analysis by mathematicians)

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### Maximizing the product of a set of dot products

So suppose we have a set of vectors $X$ and we want to approximate the maximum of the following: $\prod_{x \in X} b \cdot x$ where the components of $b$ sum to $1$ If it matters the components of ...
3answers
820 views

### Why is the number of comparisons in a BST missing key lookup about 2 ln N?

In (An Introduction to the Analysis of Algorithms) by Philippe Flajolet and Robert Sedgewick it's written that: Insertions and search misses in a BST built from N random keys require ~ 2 ln N (about 1....
0answers
41 views

### Algorithm for detecting a finite limit of time-series numbers

Is there a well known and proven algorithm to find the TOP (finite) limit of a set of points, which are time based metrics? I'm looking for an existing implementation, in order not to invent the wheel ...
0answers
24 views

### Minimizing $E_{out}$ theoretically in linear regression

Related to linear regression with noise I've been given the following functional, depending on the function $h$: $$E_{out}(h) = \int \int (h(x)-y)^2 dx dy$$ I want to prove that the function that ...
0answers
18 views

### Relationship between lexicographic index of size k (tuple) with that of size(k-1) tuple

Given a non-negative integer $n$ such that $X = \{1,2, \dots, n\}$, a combination of k-tuple and its associated index $pos_k$. How to compute the associated lexicographic index for any subset of the ...
0answers
28 views

### Function notation/mapping for this type of functions?

In short, what is the proper function notation/mapping for this type of functions? From Wikipedia regarding maps: In the communities surrounding programming languages that treat functions as first-...
1answer
30 views

### Computing childrens of ith node of a d-ary tree

Assume that we represent a complete d-ary tree in an array[1,...n] (this is a 1-based array of size n). The formula for indices of children of node no. i is given as: {(1-i)d+2, ... , min{n,(1-i)d+d+1}...
0answers
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### Why do many floating point numbers appear compact in base16 and base32 representation? (IEEE 754)

Consider 3 randomly chosen floating point values and their base conversions: ...
0answers
34 views

### If g is a PRG and f is a OWF, is G'(x) = f(g(x)) a PRG?

Just like the title states. If I have a pseudo-random generator $g\colon \Sigma^n \rightarrow \Sigma^{2n}$ and a one-way function $f$, is $g'(x)=f(g(x))$ a pseudo-random generator? And why? My ...
0answers
30 views

### I don't understand formula meaning of computer vision Paper

I am master degree student at Computer Science Department. I started master degree at this year. Now I'm reading two papers about computer vision. Actually before time I didn't have experience about ...
0answers
31 views

### Normalizing the Central Difference Method

How could I normalize the 2nd order central difference method? The original function is F(A,B,C,D) and only one variable is varied at a time. ie \$F'' = \frac{F(A+\Delta A,B,C,D) - 2\times F(A,B,C,D) +...
0answers
56 views

### Math behind path tracing

I seem to remember seeing somewhere (many years ago) a writeup of the math behind calculating the outline of Metafont glyphs. The basic idea is you have a "pen" that is a circle or oval, that you ...
0answers
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### Yarn Resource Allocation

Say for an example,i have Color codes that are : A , B , C I want to repeat this colors so i ll put them as : 5A , 10B , 10C = 25 So now A will repeat 5 times ,B will repeat 10 times and C will repeat ...
1answer
36 views

### Finding the count of 0's bounded by all 1's

Given N * M 2-D matrix find out all the 0's which are completely bounded by the all 1's. ( This is not any online platform question ) (This problem statement I faced during an interview). Sub-matrix ...
0answers
17 views

### What is the Cross Entropy Loss for this output?

Suppose you flip a coin 5 times each with equal probability (let us say 50%, for all 5 coin flips), Would the cross entropy of the function be 1 due to them having no difference in values? Edit: In a ...
2answers
40 views

### Solve T(1) = 1 T(n) = T(n-1) + n^2 for n ≥ 2

I am not able to solve the following recurrence relation: $$T(n) = \begin{cases} T(n-1) + n^2 & \text{if } n \ge 2, \\ 1 & \text{otherwise.}\\ \end{cases}$$ How do I start?