31
votes

### How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

You might explore the Institute of Geometry at Graz Tech Univ,
emphasizing free-form surfaces in architecture,
and the Industrial Geometry group
at Vienna Tech Univ.
Both rely heavily on deep ...

Community wiki

24
votes

### Applications of mathematics in clinical setting

Machine learning is on its way to provide the type of personalized health care referred to by the OP. In June of this year the FDA (US Food and Drug Administration) has proposed a regulatory framework ...

Community wiki

21
votes

### Unconventional examples of mathematical modelling

Economics offers many examples of simple models for various systems not based on physical principles. One nice example is Hotelling's line model, which gives rise to Hotelling's "law". It considers ...

Community wiki

20
votes

### How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

Some of the best numerical algorithms for solving partial differential equations are based on the de~Rham and the Koszul complex greatly generalising and stabilising finite element methods. This is ...

Community wiki

18
votes

### Unconventional examples of mathematical modelling

The book
Enns, Richard H., It’s a nonlinear world., Springer Undergraduate Texts in Mathematics and Technology. New York, NY: Springer (ISBN 978-0-387-75338-6/hbk; 978-0-387-75340-9/ebook). xii, 383&...

Community wiki

17
votes

Accepted

### Applications of mathematics in clinical setting

An example of a simple mathematical/evolutionary game theory model used to determine treatment scheduling in clinical treatment of metastic and castrate resistant prostate cancer can be found at https:...

Community wiki

14
votes

### How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

Of the several books of Pogorelov on the subject, one has been translated into English:
Pogorelov, A. V. Bendings of surfaces and stability of shells. Translated from the Russian by J. R. ...

Community wiki

14
votes

### Applications of mathematics in clinical setting

I'm going to conflate mathematics with statistics as Carlo Beenakker did. Then the earliest application that I know of is that Decision Trees were invented by Breiman et al. to analyze the issue of- ...

Community wiki

13
votes

Accepted

### Graphs resembling the math genealogy graph must have concentration in a small number of families?

Precisely this question was the starting point of the Galton - Watson theory of branching processes. To quote the opening paragraph of their 1875 paper On the Probability of the Extinction of Families:...

- 15.9k

11
votes

### Applications of mathematics in clinical setting

From the Automatic Control Laboratory at ETH Zürich, a project on automating anaesthesia:
The first steps to introduce feedback control in anesthesia were undertaken more than ten years ago. The ...

Community wiki

11
votes

### Virus community spread mathematical modeling

One of basic model is SIR model which has a good potential for describing epidemics. In this model $S$ denotes susceptible people, which are people that can be infected. The variable $I$ denotes the ...

Community wiki

10
votes

Differential geometry is important in "computerized vision" a central area of CS/applied mathematics. Steve Zucker's homepage give some information and further links. In particular, look at: ...

Community wiki

10
votes

### Applications of mathematics in clinical setting

I know of one mathematical system that was used before the widespread use of CT scans of brain in diagnosing stroke type. That of Scoring methods, which gave at those days a clinical decision that is ...

Community wiki

10
votes

Accepted

### Searching for an early, highly theoretical, even philosophical, math paper on models or small-world networks

Stanley Milgram, The Small World Problem, Psychology Today 2, 60 (1967)
seems to fit the bill: +50 years old, "kind of philosophical", and yes, iconic -- cited more than 9,000 times. There ...

- 159k

9
votes

### What's the name of this geometric mathematical modeling problem?

A supplement to Ian's answer: Here is the largest-area sofa known,
due to Gerver:
Gerver, Joseph L. (1992). "On Moving a Sofa Around a Corner". Geometriae Dedicata 42 (3): 267–283. (Springer link.)
...

- 146k

9
votes

### Unconventional examples of mathematical modelling

It appears that there are applications of dynamical systems to music. See, e.g., Rick Bidlack, Music from chaos: nonlinear dynamical systems as generators of musical materials or Boon and Decroly, ...

Community wiki

9
votes

### Unconventional examples of mathematical modelling

My favorite example is the use of hidden Markov models to analyze defensive strategies in basketball, as explained in Characterizing the spatial structure of defensive skill in professional basketball,...

Community wiki

8
votes

### Application for Differential Equation of higher order

The stationary / travelling wave / soliton regime of the KdV equation and its cousins give a lot of examples. For the original KdV, under the travelling wave ansatz we have the third order equation
$$ ...

- 32.9k

8
votes

Accepted

### What's the name of this geometric mathematical modeling problem?

The Moving sofa problem, I believe.

- 440

8
votes

Accepted

### Generalized linear models: What's the benefit of the underlying theory?

What are the benefits of a unified framework? You are right that we are rapidly going into some much used special cases line logistic regression or Poisson regression, but there is still benefit in ...

- 2,474

7
votes

### Unconventional examples of mathematical modelling

There are a lot of applications of ideas in dynamical systems to social media for things like event detection and forecasting. Some of the literature has to be taken with a grain of salt because of ...

Community wiki

7
votes

### Unconventional examples of mathematical modelling

Although it's presented as a game, the fox-and-duck problem may be cast as a control problem from the perspective of the fox. The aim of the fox is to catch the duck, while the duck conversely tries ...

Community wiki

7
votes

Accepted

### Examples of ODEs with complex constant coefficients and applications to physics?

A standard/classic example is a model for tippe top inversion. This model is a linear ODE with constant complex coefficients: $$
\ddot{z} + i \alpha \dot{z} + \beta \dot{z} + i \gamma z + \delta z = ...

- 5,700

6
votes

Accepted

### Curves similarity metric

If I may just expand upon Suvrit's suggestion, here is an image illustrating
the Fréchet distance,
the minimum length of a leash allowing a dog and its owner to walk
along the two curves without ...

- 146k

6
votes

Accepted

### Virus community spread mathematical modeling

this wikipedia article Mathematical modelling of infectious disease may be a good starting point; epidemiology mathematical models is a combination of terms that does the magic with e.g. google.
...

Community wiki

6
votes

### Suggestions for reducing the transmission rate?

This is just a slight expansion of my comment.
When the environment changes, behavioral parameters (that is, parameters like $M$ that describe people's behavior --- in this case the behavior of ...

Community wiki

6
votes

Accepted

### How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?

• Concerning the first of the two questions in the title, "How many persons pass your 1.5 meter neighbourhood during 1 week?"
Here is a graph from Mixing patterns between age groups in social networks,...

- 159k

6
votes

Accepted

### Current status on Richardson's model (growth model)

Minor remark: I have always known this model as the Eden model, it seems that most probabilists currently refer to it as such.
To answer your question, yes there are many interesting open questions, ...

- 8,114

5
votes

### How to study the global stability for this 3D system?

This is more a long comment than an answer, but I know that a similar problem, also originated from (macromolecular) biology, was studied and solved by Gaetano Fichera, Maria Adelaide Sneider and ...

- 4,931

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