Questions tagged [mathematical-modeling]

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

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Optimizing response times of an ambulance corp: short-term versus average

Background: I work for an Ambulance service. We are one of the largest ambulance services in the world. We have a dispatch system that will always send the closest ambulance to any emergency call. There is a belief that this results in the fastest…
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How to create new mathematics?

How do scientists and mathematicians create new mathematics for describing concepts? What is new mathematics? Is it necessarily in format of previous mathematics? Can one person make (invent or discover) a mathematics such that it isn't in format of…
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Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping?

So we have a differential equation to model an oscillator: $$5f''(t)+10f(t)=0$$ Where the initial conditions are $f(0)=0$ and $f'(0)=4$. It is given that $f(t) = \frac{2\sqrt 2}{5}\sin\sqrt2 t$. Now, if we make make a slight change to the original…
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What are the best books to study Neural Networks from a purely mathematical perspective?

I am looking for a book that goes through the mathematical aspects of neural networks, from simple forward passage of multilayer perceptron in matrix form or differentiation of activation functions, to back propagation in CNN or RNN (to mention some…
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Is there a simple-ish function for modeling seasonal changes to day/night duration and height of the sun?

I'm a hobbyist programmer, and not much of a mathematician. I'm trying to model something like the seasonal change in day length. There are two other questions here that are very similar to mine, and I posted a bounty for one of them, but the…
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Coronavirus growth rate and its (possibly spurious) resemblance to the vapor pressure model

The objective is the model the growth rate of the Coronavirus using avaibale data. As opposed to the standard epidemiology models such as SIR and SEIR, I tried to model a direct relation between the number of infected or deaths as a function of time…
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Geometrical construction for Snell's law?

Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the indices of refraction $n_1$ and $n_2$.…
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Why is there a unique solution to the frog puzzle?

I'm pretty sure this is a trivial question but eh... The Frog Puzzle is a famous 8th-grade problem (playable here): $3$ red frogs and $3$ blue frogs are sitting on lily pads, with a spare lily pad in between them. Frogs can slide onto adjacent…
krirkrirk
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Taxicab metric *with stoplights*; does it ever give the Euclidean metric?

This question is not terribly formal in nature, but please bear with me: what I’m looking for is a model of traveling via taxi on a grid of streets where the “metric” in some sense becomes the standard Euclidean metric in a limit, for non-trivial…
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Chance versus Skill

Question. How does one mathematically analyze situations that involve chance and skill? Let's take the coin flip as a simple example. Assume that it possible to skillfully flip a coin to get the landing you want. Also assume zero cheating. FIRST…
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How does Elo rating scale with games played?

I only take two players starting out at 0 Elo and have them play against each other with one player winning all games. Also I consider a pure version of the Elo system without artificially introduced cut-offs (like FIDE's 400 point rule). The winner…
user1583209
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When modelling a real world event by assuming it has probability p, what are we saying/assuming about how that event behaves?

There are countless books on statistics, and how to apply probability-theory to the real world. But I have never really understood what we are actually doing when we model a real world phenomenon with probability theory. If you have real world…
user119615
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What is Nassim Taleb's criticism of 538's election model?

Nassim Taleb has tweeted criticism about 538's political predictions that I don't follow. He seems to be making a theoretical argument. I am very weak on stochastic modeling (though I know basic PDEs). Can someone help me understand at least the…
abnry
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Can we abuse traffic patterns to get home earlier?

I had a heated discussion with my co-worker today, and was wondering if someone here could shed some light on this situation. The post is a bit lengthy, but I wanted to put all my intuition down in writing so you all only need to help as minimally…
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Random walk on a cube

Start a random walk on a vertex of a cube, with equal probability going along the three edges that you can see (to another vertex). what is the expected number of steps to reach the opposite vertex that you start with?
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