Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing Segmented Differentiable Quadratics to Determine
  Algorithmic Run Times and Model Non-Polynomial Functions   We propose an approach to determine the continual progression of algorithmic
efficiency, as an alternative to standard calculations of time complexity,
likely, but not exclusively, when dealing with data structures with unknown
maximum indexes and with algorithms that are dependent on multiple variables
apart from just input size. The proposed method can effectively determine the
run time behavior $F$ at any given index $x$ , as well as $\frac{\partial
F}{\partial x}$, as a function of only one or multiple arguments, by combining
$\frac{n}{2}$ quadratic segments, based upon the principles of Lagrangian
Polynomials and their respective secant lines. Although the approach used is
designed for analyzing the efficacy of computational algorithms, the proposed
method can be used within the pure mathematical field as a novel way to
construct non-polynomial functions, such as $\log_2{n}$ or $\frac{n+1}{n-2}$,
as a series of segmented differentiable quadratics to model functional behavior
and reoccurring natural patterns. After testing, our method had an average
accuracy of above of 99\% with regard to functional resemblance.

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics