# Questions tagged [heuristics]

The tag has no usage guidance.

28 questions
0answers
23 views

### Can time-scale calculus be used to derive a counterpart theorem of discrete-time dynamic systems directly from continuos-time dynamics systems?

From what I read of time-scale calculus literature, most results of continuous-time and discrete-time systems can be generalized to arbitrary time-scales by considering the generalized derivative ...
0answers
21 views

### Generating Biconnected Graphs from Spanning Trees

Background of my question is an idea for generating an initial subtour for general symmetric TSPs: Add to a MST a set of edges with minimal weight sum, that renders the resulting graph free of ...
2answers
549 views

### Heuristics behind the Circle problem?

Is there a heuristic argument behind the exponent in the circle problem? The problem that I am referring to is the following: Consider a circle of radius $R$ centered at the origin in the plane and ...
16answers
5k views

### What are examples of books which teach the practice of mathematics?

One may classify the types of mathematics books written for students into two groups: books which merely teach mathematics (i.e., they present theorems and proofs, ready-made, as it were) and those ...
0answers
317 views

### why do we mainly integrate with respect to martingales?

Although my resarch focuses on PDEs (optimal transport, these days), I am currently trying to learn stochastic calculus and integration. I am just beginning in this topics, but I was wondering: why do ...
1answer
109 views

1answer
94 views

### Worst Case Region for a Convex Hull Heuristic

I am currently implementing a heuristic algorithm for planar convex hulls hand would like to know, for which kind of strictly convex region it exhibits worst performance. I know that there are many ...
1answer
140 views

### Heuristics for counting degrees of freedom

I have recently learned about the representation theorem for isotropic, linear operators, which says the following: Defintion: Let $M_n$ be the vector space of $n \times n$ real matrices. We say a ...
0answers
32 views

### Performance guarantee of RLF [closed]

I cannot manage to find the performance guarantee of the Recursive Largest First (RLF) algorithm for approximating the chromatic number of a graph. I know DSATUR has a $\mathcal{O}(n)$ guarantee, ...
1answer
562 views

### Heuristic probabilistic argument for the Navier-Stokes existence and smoothness conjecture

The Collatz Conjecture is a famous conjecture that has never been proven; nevertheless, there exists a simple heuristic probabilistic argument which supports its truth - in Wikipedia's words, "If one ...
4answers
3k views

### What are reasons to believe that e is not a period?

In their 2001 paper defining periods, Kontsevich and Zagier (pdf) without further comment state that $e$ is conjecturally not a period while many other numbers showing up naturally (conjecturally) are....
2answers
528 views

### Categories with binary relations as objects

For the category of functions, pairs of functions making commutative diagrams are the canonical morphisms $\alpha:f\rightarrow g$. For binary relations there is an alternative, to consider the ...
1answer
346 views

### Cohen-Lenstra heuristics for totally complex fields

If a number field $K$ is a Galois extension of $\mathbb{Q}$, and $G = \operatorname{Gal}(K/\mathbb{Q})$, then the class group of $K$ is a $\mathbb{Z}[G]$-module, and since $N = \sum_{g \in G} g$ acts ...
0answers
137 views

### Reduce a Combinatorial problem

It is given n sets with k vectors. (k is element-wise positive or zero) Choose one vector of each set so that the biggest element of the sum of the chosen vectors is minimal. What i also know but is ...
1answer
63 views

### Heuristic for choosing n-vectors from n-sets

my given problem is: choose n-vectors from n-sets (one vector from each set) so that the biggest element in the sum of the chosen vectors is minimal. Unfortunately the problem is NP-hard. So I'm ...
18answers
4k views

### Non-rigorous reasoning in rigorous mathematics

I was wondering what role non-rigorous, heuristic type arguments play in rigorous math. Are there examples of rigorous, formal proofs in which a non-rigorous reasoning still plays a central part? ...
0answers
173 views

### unfolding as resolution

Has anyone described 'unfolding' as used in mathematical physics (e.g. on-shell AND off-shell) as analogous to a resolution in algebra - higher derivatives are unfolded in terms of new variables?
2answers
260 views

### Formula in common: How to search for same/similar equations in other knowledge domains?

Hi people In a recent presentation by Sedgewick, he recounts in 1977 Flajolet noticed that they had a formula in common, both in different domains (see slide 4 in http://www.cs.princeton.edu/~rs/...
0answers
678 views

3answers
2k views

### Groupoids vs Pseudogroups

(Warning: I'm not an expert in the topic) Let's work in a "geometric" category, for example the category $\mathfrak{Diff}$ of "manifolds" (without the requirements of connectedness and second ...
1answer
200 views

### Possible semantics for categorical co-constness

In category theory a morphism is constant IIF it is absorbing (for left composition). That is a morphism $k$ from $k:A\rightarrow B$ is constant if an only if for any two parrallel (same domain and ...
6answers
68k views

### Fourier vs Laplace transforms

In solving a linear system, when would I use a Fourier transform versus a Laplace transform? I am not a mathematician, so the little intuition I have tells me that it could be related to the boundary ...