All Questions
Tagged with applied-mathematics reference-request
23 questions
95
votes
14
answers
14k
views
Deep learning / Deep neural nets for mathematician
I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".
Most of the papers/books that are often quoted in papers/...
37
votes
3
answers
3k
views
On Mathematical Analysis of MathSciNet & MathOverflow
This question has two original motivations: mathematical and social.
The mathematical motivation is mainly based on what I have seen about Zipf's law here and there. The Zipf's law simply states ...
17
votes
4
answers
2k
views
Differential geometry applied to biology
This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers.
I'm looking for current areas of research which apply techniques from ...
- 171
14
votes
8
answers
3k
views
Relevant mathematics to the recent coronavirus outbreak
I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
11
votes
2
answers
588
views
Orthogonal polynomial under linear transformation
Let $M_n(x) = x^n$ be the standard monomials. The binomial formula allows one to expand $M_n(ax+b)$ as a linear combination of $M_k(x)$, for $k \leq n$, giving
$$
M_n(ax+b) = (ax+b)^n = \sum_{k=0}^n \...
- 141
7
votes
1
answer
500
views
Further Developments of Lieb-Schultz-Mattis theorem in Mathematics
The Lieb-Schultz-Mattis theorem [1] and its higher-dimensional generalizations [2] says that a translation-invariant lattice model of spin-1/2's cannot allow a non-degenerate ground state preserving ...
- 10.5k
6
votes
2
answers
935
views
Human brains considered as directed graphs
I assume that human brains can be considered as directed graphs with neurons as nodes and synapses as edges. I explicitly don't want to consider the weights, the dynamics of neural activity (based on ...
- 9,720
5
votes
1
answer
436
views
Book about the history of mathematics for weather prediction
Can someone recommend a book about the history of mathematics being used for weather prediction, preferable one which covers recent developments?
- 1,181
5
votes
1
answer
5k
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Kalman filters and stock price prediction
Could someone be so kind as to direct me to a good source that would explain time series (more specifically) stock price prediction using Kalman filters, Extended kalman filters or particle filters. ...
- 51
4
votes
2
answers
2k
views
On Mathematical Foundations of Football
Football (soccer) is arguably one of the most unpredictable sports. Countless variables play a role in determining the outcome of a certain football match. Due to the high complexity of the entire set ...
3
votes
2
answers
348
views
Request for some references exploring the connections of Riemann surfaces with medical imaging
I'd like to know some references for a beginner who has basic background in Riemann surfaces and differential geometry, and would like to start learning/working on more applied areas, medical imaging/...
- 1,467
3
votes
0
answers
50
views
How to construct lattice points in bounded symmetric domain?
Consider the Hermitian bounded symmetric domain for $k \leq m$:
$$
C_{k, m} = \{ Z \in \mathbb{C}^{m\times k} \,|\, Z^*Z < I_k \}
$$
where $I_k$ is the $k\times k$ unit matrix. If I am not mistaken,...
- 8,597
2
votes
1
answer
138
views
Reference request: probabilistic models on climate (change)
I am looking for probabilistic models to address climate change. Are they known in the existing literature?
I have found the post Math behind climate modeling. concerning PDE models.
Many thanks for ...
user128095
2
votes
1
answer
539
views
What is the sum capacity of a scalar gaussian broadcast channel?
"On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel" by Giuseppe Carie and Shlomo Shamai talks, in part, about the following type of link (paraphrasing):
A transmitter with $...
2
votes
1
answer
101
views
What are partial differential equations with fast reaction terms?
I know $u_t(t,x)=\Delta u^m(t,x),\;\; (t,x)\in (0,\infty)\times \mathbb{R}$ is the fast-diffusion equation when $m\in (0,1).$
But how are PDEs with fast reaction terms defined in general? I also wish ...
2
votes
0
answers
133
views
Reference book for stochastic processes
I am looking for a good reference book for properties of stochastic processes for applied research. What I would like the reference to have is a collection of results on a large list of stochastic ...
- 121
2
votes
0
answers
209
views
Literature on Lyndon words and the Lie commutator
Since I lost my paper notes in a domestic conflagration in Japan some ten years ago, I've occasionally tried to recall one particular author who wrote in the 1900s about Lyndon words / strings, or ...
- 10.5k
2
votes
0
answers
47
views
Where to read about this kind of "measure of irredundancy" of a set from a family of sets?
Studying a very practical problem from psychometrics, I encountered the following construction.
Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...
- 18.4k
1
vote
1
answer
280
views
Application of Yamabe and Liouville type equation
Let $\Omega$ be a domain in $\mathbb{R}^n$. I am interested in the following critical elliptic partial differential equations (PDEs):
The Yamabe Type Equation (for $n>2$):
\begin{equation}
-\...
- 914
1
vote
0
answers
107
views
Plethora of variant neural networks?
Since a decade ago when new life was breathed in to neural networks in the form of deep learning a plethora of different architectures have come about. Is there a reference that gives compendium of ...
- 13.9k
1
vote
0
answers
202
views
Doubts related Shifting from Pure to Applied math [closed]
I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months.
I have ...
- 127
0
votes
0
answers
49
views
Gaussian white noise model in application
I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by,
$$
X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d ...
- 73
0
votes
0
answers
2k
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The collected works of John von Neumann
Might there be an online collection of John von Neumann's collected works in pdf format? I'm particularly interested in his approach to applied mathematics(ex. shockwaves, hydrodynamics).
Note: I ...
- 3,871