Questions tagged [applied-mathematics]
the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)
13 questions from the last 365 days
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First time reviewing an applied mathematics paper: how to evaluate it?
I am in the pure math camp but was invited to referee an applied/interdisciplinary paper because I'm a specialist in the underlying mathematical tool. I want to ask for general guidance about ...
- 565
5
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1
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Under what circumstances Is a symmetric matrix representable as a Coulomb matrix?
Question:
I am exploring a neural network architecture inspired by physical interactions, where each neuron has associated "mass" and "position" vectors. The weight matrix between ...
- 3,054
2
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Ashkin-Teller Model
Consider the two-dimensional Ashkin-Teller model on the square lattice $\mathbb{Z}^2$ with Hamiltonian:
$$ H = - \sum_{\langle i,j \rangle} \left[ K \sigma_i \sigma_j + K \tau_i \tau_j + k \sigma_i \...
- 21
1
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Regression models as local sections of a chain complex
Let's say we find some regression equation $\ell$ (best fit / linear / whatever words you need to put here) for a sample $D$, subset of population $P$. This equation/model can be thought of as a ...
- 1,611
0
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1
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Equivalence of Wind Forces: Intensity vs. Duration [closed]
The strongest tornado in the world happened recently in Greenfield Iowa with winds over 318 mph: https://www.facebook.com/watch/?v=2176728102678237&vanity=reedtimmer2.0
I am curious, are less ...
user531026
3
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1
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80
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On the relationship between graph isomorphism and equivalence in ETL workflow dependency graphs
$\newcommand{\inn}{\mathrm{in}}\newcommand{\out}{\mathrm{out}}$Let $G = (V, E)$ and $G' = (V', E')$ be two DAGs representing dependency graphs of ETL workflows. Each node $v \in V$ (or $v' \in V'$) ...
user530362
4
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1
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510
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Domino equation derivation
Can the functional form of $G$ in the expression $\frac{V}{\sqrt{gH}} = G\left(\frac{d}{H}\right)$ be rigorously derived from first principles, where $V$ is the limiting wave speed of a line of ...
- 59
0
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Practical applications of dandelin spheres
I know that dandelin spheres can be used to prove the focal properties of conic sections, but I heard that they can be used to help track the orbits of planets. All the sources I looked up only said ...
0
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36
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Conjugate gradient-like algorithm with multiple search directions
I am solving an $n*n$ system $Ax=b$ in CUDA where $A$ is a sparse matrix. Currently I am solving it using the conjugate gradient algorithm.
I have noticed that $Ax$ where $x$ is $n*1$ has roughly the ...
- 71
0
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1
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106
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Spectral theory: a key to unlocking efficient insights in network datasets
In the context of directed or undirected graphs, matrices such as adjacency and Laplacian matrices are commonly used. The eigenbasis of these matrices addresses some practical implications, such as ...
- 4,058
1
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Maximizing the integral of a transformation that depends on a neighborhood of values of the original function
I'm not an expert in analysis whatsoever, so I might be posing a well-established question, or even an unanswerable one. Also, any suggestion on changes that might make the problem better are welcome.
...
- 11
0
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98
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Interpolation polynomials with constraints
Lets consider a collection of $n$ points $\{Z_i\}_{i=1}^n\subseteq \mathbb{D}^k(1)=\{(z_1,\ldots,z_k)\in\mathbb{C}^k:\forall j\leq k, |z_j|\leq 1\}$. Let $h: \{Z_i\}_{i=1}^n \to \mathbb{D}^1(1)$ be a ...
- 502
4
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0
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Non-Noetherian (classical) algebraic geometry
My starting point for this question is that, in a very classical sense, algebraic geometry is the study of solution spaces of systems of polynomial equations over an algebraically closed field. It is ...
- 365