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.

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Probability in single-lane traffic flow: What are the odds of “choke points” being encountered?

Let's say you have a single-lane road (single in this case meaning single lane in each direction, or what you could also call two-lane). Let's say you have a random number of vehicles on a given ...
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1answer
365 views

exact solution to lotka-volterra equations [closed]

I am looking for exact or perturbative solution realistic lotka-volterra (the one with logistic term in one of the equations) equations in population dynamics. Any reference where they have done it ...
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276 views

Summation notation problem

Any help is greatly appreciated! Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. ...
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159 views

How to model multi-step cell differentiation

Can I better explain cell lineages using PDEs or stochastic?
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595 views

Automation of 3D Paper Modeling

I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
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2answers
151 views

How to build a function that gives recent years higher weight?

I want to have a value for users between 0-1 , that shows how much they like movies of specific type depending on how many movies they have watched and movie type ( comedy , etc ). I have a data of ...
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112 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
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106 views

Including non-markovian processes in a birth-death process

Current model I want to model a stochastic system with a birth-death (Markovian) model. I therefore have this kind of $n$ times $n$ (where $n$ is the number of possible states) transition matrix: ...
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318 views

Cubic population model question

Have the following population model, $$ \frac {dN}{dt}= cN(N-k)(1-N)$$ The first stage of the question is to investigate the steady states, however im a little stuck on finding the solution to the ...
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162 views

How would I rearrange this equation to make the subject $t$?

$$s(t) = 4t + \frac2{t-3} + \frac23$$ where $s$ represents the position of either particle in the tubular cloud-chamber measured in centimetres, while $t$ represents the time in nano-seconds. It's ...
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890 views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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How to start creating Mathematical models?

I know this is a quite general question , but I've always heard about creating mathematical models in economics, social sciences, engineering,... And I would want to know what are the starting points ...
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3answers
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Good book for mathematical modeling

Could you recommend/suggest a good book about mathematical modeling (Not advanced) with examples about classical mechanics, dynamics, aerodynamics, chemistry, electronics and etc?
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457 views

Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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Cleaning up the Great Lakes - Differential equation systems

Problem Details The idea of the problem is to find out how long it would take to flush the Great Lakes of pollution. They're set up as a series of five tanks and you are given inflow rates of clean ...
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4answers
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Cat Dog problem using integration

Consider this equation : $$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$ where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$. Now how to proceed ? This equation ...
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1answer
302 views

Combining probabilities from different sample spaces

I'm working on a project whereby I'm supposed to determine whether two objects (parts of moving machinery) will be in physical contact with one another given the uncertainty in their positions. I know ...
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Is there a general solution for the “Spider and the Fly Problem”?

(I would be appreciative if somebody could give a more formal formulation of this problem.) The Spider and the Fly Problem is a problem in which the objective is to minimize the distance the spider ...
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1answer
515 views

Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
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388 views

Population Dynamics model

I am currently searching for population dynamics models. Concerning animal population growth, I have found the following so far : Growth models for fish Predator-prey : Lotka-Voltera and ...
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235 views

Four Color Theorems: Graphs vs. Maps [closed]

This question has changed dramatically from its original form. Please See the improved question. ORIGINAL QUESTION: There are two variants of the four color theorem that are commonly cited: (4CTG): ...
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864 views

Why the $Vega$ of the Black Scholes Model is at its maximum for at-the-money options?

In my course script, it is said that the Vega of the Black Scholes Model is at its maximum for at-the-money options. In order to verify this, I did the following calculations: In the Black Scholes ...
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1answer
203 views

General solution to Wright-Fisher model - Diploid selection

Wright-Fisher models are classical theoretical results in evolutionary biology. There are two discrete time models, one for haploid selection and one for diploid selection (the meaning of these models ...
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100 views

Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...
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1answer
75 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
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107 views

Finding a logical expression (under some constrains) s.t. it is equivalent to another one

In this question, it was made clear, when $\bullet$ some statement $A$ is stronger than another statement $B$, namely if $A\Rightarrow B$ holds; and when the statement $A$ is weaker than another ...
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361 views

Finding a model for multiple non-linear regression

I want to implement a regression analysis, but I have problems with finding a model for the given data. There are $149$ $(x,y,z)$-values. $y$ values are all positive, $x$ is between $[-10, 10]$ and ...
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How to calculate perceived value?

Is there a known formula to calculate perceived value? If I am auctioning some popular product that is worth $100 (shelf price), how much would people bid if they: Have a 1 in ...
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42 views

$4$ or more type $2$ implies $3$ or less type $1$

I'm having difficulties with the logic with the last part of the reformulation part of the problem below. Let $x_i$ be the the number of ships of type $i$ to purchase. For $4a:$ (the ...
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1answer
40 views

Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ...
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1answer
128 views

Interperate Jacobian Determinant - Stability of Equilibriums

In my SIR model, I have the following Jacobian Matrix \begin{align*} J =\begin{bmatrix} -\alpha I & -\alpha S & \zeta & 0 \\ \alpha I & \alpha S - \beta - \rho & 0 & 0 \\ 0 ...
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174 views

How to plot a phase potrait of a system of ODEs (in Mathematica)

I am asked to use mathematica to plot the fixed-points of the following system $$ \frac{dN}{dt} = -\gamma N \left( 1 - \left( \beta M + N\right) \right) $$ $$\frac{dM}{dt} = M \left( 1 - \left( ...
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1answer
66 views

Finding a value that makes an expression negative

Background: I am working on the mathematical modeling of infectious diseases, namely HIV and TB. In the process of proving global asymptotic stability of the Disease-Free Equilibrium, I must ...
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1answer
2k views

Simple math formula to calculate average

I am making a software that deals with employee trust. I am trying to make a math formula (no need to tell that I am bad in math :) ). Here is the scenario: ...
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88 views

Maximise population coverage subject to budget constraint

Let $t_i =$ $1$ if transmitter i is to be constructed and $0$ otherwise, $c_j =$ $1$ if community j is covered and $0$ otherwise. Obj func: Max $$z = [10, 15, ..., 10] \cdot c$$ s.t. ...
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1answer
24 views

Definition of a function whose codomain is set of probability measure over cartesian product with dependency between sets in the product

I am thinking about the following function: $$ p : A \to \Delta \big( F(x, y(t) ) \times T \big) ,$$ where $t \in T$ denotes continuous time, and $\Delta (X)$ denotes the set of all probability ...
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69 views

Are my results realistic or is there an error somewhere?

The background is that I'm solving a problem in Numerical Analysis which I asked about here: Is my derivate correctly programmed? Now if I use the new code, then I get a result that is along the ...
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1answer
68 views

How do I determine the critical number that would the eradicate pests and that it is less than a quarter of the environment carrying capacity

The sterile insect release method for pest control releases a number of sterile insects into a population. If a population n of sterile insects is maintained in a population, a possible simple model ...
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1answer
72 views

Understanding mathematical syntax in SO(3)

In this paper, pp. 2, I found the following differential equation system and a statement: There are two things not clear to me: the hat map symbol seems to make mathematical symbolics shorter and ...
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1answer
54 views

Establishing a inequality

I need to establish an inequality containing $19$ terms in $7$ variables. My problem arises in the context of proving that the HIV-only Quasi Disease-Free Equilibrium of a HIV-TB co-epidemic model ...
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3answers
66 views

Linear nonhomogenous ODE

Solve: $$y''(t)=-y(t)-\cos(t),\ \ \ \ \ \ y(0)=y'(0)=0$$ I'm sorry that I have no approach to solve it. In my solution I have the hint to solve it with resonance but I don't know anything ...
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60 views

Finding the largest eigenvalue of a sparse matrix

I would like to find the largest eigenvalue of a sparse matrix by hand- this is part of analyzing a mathematical model for infectious diseases. The nonzero entries are very complicated - hence Maple ...
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1answer
261 views

nullclines with variables

I know how to solve nullclines, the following link is very helpful http://mcb.berkeley.edu/courses/mcb137/exercises/Nullclines.pdf However I don't understand how to solve equations that have only ...
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1answer
169 views

General solution to Wright-Fisher model - Haploid selection

Wright-Fisher models are classical theoretical results in evolutionary biology. There are two models, one for haploid selection and one for diploid selection (the meaning of these models does not ...
0
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1answer
427 views

Edge weight function for graph instance of scheduling and allocation problem

I have difficulties developing a proper (non-scalar) edge cost function $c_e$ for my resource scheduling problem, which I mapped into a graph problem. Processes $P_i$ need resources $R_i \in ...
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1answer
157 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...