# Questions tagged [mathematical-analysis]

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

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### Maximum number of similar groups of a given size that can be made from a given array

I am given an array of numbers, not necessarily unique, and the size of a group. Let the array be denoted by $B$ and the size of the group be $A$. I need to find the maximum number of groups with the ...
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### Replacing 0x1021 polynomial with 0x8005 in this CRC-16 code

I have some highly optimized code for a CRC-16 implementation. It focuses on speed rather than flexibility, and as a result, it is hard-coded to model the specific unreflected polynomial ...
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### How does the forget layer of an LSTM work?

Can someone explain the mathematical intuition behind the forget layer of an LSTM? So as far as I understand it, the cell state is essentially long term memory embedding (correct me if I'm wrong), ...
41 views

### Coinduction in mathematical analysis?

Coinduction is a logical principle that is somehow dual to induction. I'm struggling to understand it. Are there any interesting examples of coinduction in analysis? A few examples seem like they ...
69 views

### Algorithm to find best solution

I am writing a software as small project in TypeScript/JavaScript and got to a problem i cant solve: A Company makes a new contract with a customer and wants to order materials. There are serval ...
12 views

### Growth of n/logn vs n^(1+e) [duplicate]

Is $\Theta(\frac{n}{log(n)})$ faster growing function than $\Theta(n^{1+\epsilon})$, where $\epsilon > 0$?
43 views

### Can most programs (except the IO part) be re-written as a sequence of matrix operations?

I got this idea recently. If we do not consider the data IO part of software, imagine the data is in the memory and we need to come out with some decision (which product to recommend to a user, how to ...
59 views

### Computer Vision Techniques to find Slope of beach in the 2D Images?

What I am planning to do is to calculate the height and estimate the slope of the segmented Object. The camera will be static and the Object of Interest is the slope of the beach. I am finding harder ...
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### Algorithm Analysis of Insertion Sort

Why is the recurrence formula for insertion sort is T(n-1) + n? I understand the T(n-1) part but the why does the cost for ...
85 views

### Can we find every 216 digit number combination? [closed]

This question popped to my head when I watched Pi where the mathematican told the Jews "Didnt you calculate every 216 digit number allready?" So I want to find every possible 216 digit number ...
64 views

### How does sum of first $k$ integers equal $k(k+1)/2$ [closed]

According to this video, he explains $$p = k(k+1) / 2$$ Where $p$ is the sum of the first $k$ natural numbers. I understand $k$ means times of repetition and $k+1$ is how it increments, but why does ...
35 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 ...
56 views

### 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 ...
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### The equation for how much data is produced every period [closed]

I am trying to find out how much data we produce to project how much we will produce in the future. I find stuff like this and this: There are 2.5 quintillion bytes of data created each day at our ...
175 views

### What is the depth of recursion if we split an array into $\log_2(n)$ with each recursive call?

We have a function which takes an array as input. It breaks an array into $\log_2(n)$ parts with equal sizes where $n$ is the size of the subarray. It keeps breaking each of the subarrays until there ...
197 views

### Fixed point of hash

Are hashing algorithms constructed to guarantee that no fixed point exists? My assumption is not, because I don’t see what utility that would have. (Please correct me if I’m wrong.) As such, purely ...
58 views

### Is $f(cn)$ always $O(f(n))$ for constant $c$ and any function $f$?

This seems to be true for any function I can think of, but I'm not quite sure how to prove it. Is there a proof of this proposition for any such function or a counter-example?
53 views

### Real RAM computational mode

Given a real value $M>0$, I want to compute the greatest value of $\epsilon$ strictly smaller than $M$. Given the assumption that the computational model is Real-RAM, how to find a real number ...
114 views

### Complexity of computing the antiderivative of a given function

Disclaimer: I don't know much computational complexity theory. I am nevertheless curious. If function $f(x)$ has a certain level of computational complexity (which I actually don't know how to ...
504 views

### What is the exact definition of undirected graph, directed graph, unidirectional graph, bidirectional graph? [closed]

I've read many literature papers, but I still cannot understand their exact formalization definitions. Is their any difference among them or is there any relationship among them?
354 views

### Average number of comparisons in sorted insertion

The questions is pretty simple: Given a sorted array of N elements, what is the average number of comparisons made in order to add a new element (let's call it x) in its correct position? I am using ...
55 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 ...
152 views

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### Amortized analysis for doubling resizing array is ~3n

I'm brushing up on stuff related to analysis of algorithms. And I have a question about this PDF I found. This is where I'm confused: Question 2: What if instead we decide to double the size of the ...
83 views

### A totally-ordered set of functions

When we analyze algorithms using the $O$ notation, we usually use only a small set of the space of all functions. E.g., we use $\Theta(n)$ but not $\Theta(2n)$, as these two are equally well ...
289 views

### Looking for an algorithm to generate an identicon/avatar from genome data

I am looking to develop an app that generates a single identicon image that summarizes the genome information in visual form. Identicons are essentially a visual hash of of data. usually string data ...
953 views

### Is Big-Oh notation preserved under monotonic functions?

I was just looking at the big-Oh notation. I wanted to know if the following is true in general $$f(n)=O(g(n)) \implies \log (f(n)) = O(\log (g(n)))$$ I can prove that this is true if $g$ is ...