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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What is connexity (in simple language)? [on hold]

Please explain the meaning of connexity, connex elements in simple language
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43 views

How do impulsive differential equations work? Can you provide an example?

I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they ...
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538 views

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 ...
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19 views

How to model function with unknown exponents?

I know the Cobb-Douglass function which describes the production quantity: $$Q(K, L) = A \cdot K^\alpha \cdot L^\beta$$ Also I do know multiple assignments of K ...
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3answers
43 views

Smooth function to model a well or pit

In order to solve a Physics problem, I have to model an axisymmetric well or pit on a plane. I am looking for a function $f(x)$ that is smooth and monotonic in the domain $(0,1)$, where the origin ...
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1answer
41 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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41 views

Rayleigh-Bénard convection

I have a nondimensionalized linear perturbation system relevant to the appropriate pure conduction solution for Rayleigh-Bénard convection in upper planetary atmospheres under the compressible gas ...
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1answer
314 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
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1answer
46 views

Assistance with Bayesian Random Effects and Mixed Effects Models

I am looking to build either a random effects or mixed effects model for a project I am working on, but have had trouble finding good sources and understanding the general structure of the model. ...
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9 views

Has anyone come across a non-constant population SIR model with infected birth?

I've come up with a seemingly new type of SIR model for one of my classes which allows for non-constant population and infected members to birth more infected members (such as is the case for many ...
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1answer
29 views

Estimating number of slaves imported before 1790

I have a statistics problem I am having a hard time figuring out how to model mathematically. The 1790 US Census counted 697,681 slaves and 59,196 free Africans in the United States. (A) assume ...
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1answer
537 views

How did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
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1answer
27 views

Establishing a stable state withing a discrete dynamic model

Given the following discrete dynamic model: $P_0=360$ and $R_0=80$ and $t[0,200]$ $P_t=1,18*P_{t-1}-0,002*R_{t-1}*P_{t-1}$and $R_t=0,86*R_{t-1}+0,0004*P_{t-1}*R_{t-1}$ One can rewrite the ...
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1answer
313 views

Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
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14 views

Mathematical model for MILP optimisation problem- power scheduling

I am having trouble trying to formulate a mathematical model for the problem below to solve later as an MILP problem using different optimization software. I want to formulate the model so as to ...
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1answer
48 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...
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1answer
31 views

What does this determinant mean?

I have the following Jacobian matrix for an equilibrium of an SIR model $$J=\left( \begin{array}{cccc} -\text{$\alpha $N} & 0 & \zeta & 0 \\ \text{$\alpha $N} & -\beta -\rho & ...
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1k views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
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25 views

How to find the basic reproductive number of a discrete SIS epidemic model

I have been following a textbook called Mathematical Models in Population Biology and Epidemiology. The SIS model is given by the system \begin{aligned} S_{n+1} &= \Lambda + S_n e^{-\mu} ...
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775 views

Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and ...
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1answer
81 views

Is this probabilistic balls-and-bins problem well-defined and is my solution correct?

Problem definition: There are $n$ bins, labeled with $1, 2, \ldots, n$. Let $X_i$ be a random variable denoting the number of balls contained in the $i$-th bin. The collection of random variables ...
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2answers
30 views

Split cab fare proportional to saving made across the board

Interesting dilemma. I've figured out how to split a cab fare 3 ways (proportional to time, mileage and equally) but I've found that when the cab fare is split proportional to time and mileage, the ...
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1answer
25 views

Split a cab fare proportional to the time everyone has spent in taxi

How would you split a cab fare proportional to the time everyone has spent in the taxi? Total journey time = 19 min Fare = $17.25 ...
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23 views

mathematical model of an assignment/scheduling problem

I am solving a scheduling problem and I am able to abstract it into an assignment problem of assigning 45 machines to 42 jobs. the assignment problem was given as having 14 jobs, each with 3 tasks and ...
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18 views

For a given data set formulate the mathematical model that minimizes the largest deviation between the data and the line y = ax + b

X Y 1.00 3.60 2.30 3.00 3.70 3.20 4.20 5.10 6.10 5.30 7.00 6.80 I am looking to find min r, a an b using Chebyshev approximation criterion. Using Least Squares I calculated y = ...
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45 views

Anyone know about definition of weak dictator?

I am trying to prove arrow's impossibility theorem in case which ties are allowed in individual preference lists and so is social preference list. It says that if $p$ is a weak dictator, then we can ...
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19 views

Determining a function from a graph

I have the following graph created in Excel based on 10 data points. Does anyone here know of a good continuous function that could be constructed from the data? What methods are typically used for ...
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17 views

Questions about arrow's impossibility theorem.

If we had chosen to work in a context where ties are allowed in the individual preference lists, then Arrow’s Theorem no longer holds with the conclusion that there is a person whose list is always ...
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18 views

Analyzing/Modeling DynamoDB Usage

I'm seeking the correct mathematical tools to analyze/model a real world process for the purpose of optimizing resource allocation. I want to analyze consumed throughput of a AWS DynamoDB table and ...
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1answer
37 views

How to connect the deterministic and probabilistic descriptions of the SIR model

I am a 17 year old student and I was reading up on epidemic modelling for a math project, specifically the SIR model and I came across this: "This" refers to the assumptions to which the Markov Chain ...
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31 views

Which Probabilistic model to apply for this problem

I am a little confused about which probabilistic model to apply to this. Say I have an intern who is entering data on a daily basis. I have a clerk who at the end of the week pulls out a random ...
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17 views

Oversampling and trees

I want to create a model to predict the propensity to buy a certain product. As my proportion of 1's is very low, I decided to apply oversampling (to get a 10% of 1's and a 90% of 0's). Now, I want to ...
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24 views

Classifying growth as percent increase.

So I have been thinking about resource consumption a lot after watching the most important video you will ever see. It is pretty long so I will summarize it as follows, the professor makes a strong ...
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41 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
14 views

How do you scale a set of number such that they sum to 0.5 after scaling

Suppose I have a set of numbers of various different values (>0.0). I want to scale these numbers so that they all sum to 0.5. The scaling is required so that the relative strength of the numbers with ...
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12 views

Good similarity metric of models

I have a bunch of models that are being produced by some code I have. Many of them are different types but let's say for the simple case that all models can be represented by $\beta_0...\beta_n$. I ...
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34 views

Modelling a transfer function for plant/system empirically

In an attempt to learn about PID controllers, I'm designing a small desktop thermal control system. I have a power resistor mounted to a heatsink, with a thermister placed nearby to measure ...
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2answers
31 views

Stochastic Calculus For Finance: Conditional Expectation of Binomial Tree Model

I'm reading through Stochastic Calculus For Finance Volume 1, page 32. The conditional expectation of $S_2$ knowing $1=H$ is $p*S_2(HH) + q*S_2(HT) = 0.5*16 + 0.5*4 = 10$ But how do I calculate ...
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50 views

Applied mathematics commonly needed in the following industries

I was just wondering if anyone could shed more light on specific topics in applied mathematics or other skills (programming, etc) commonly used in the following industries: oil and gas, ...
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290 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
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3k views

Examples of types of mathematical models

I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic ...
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1answer
34 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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2answers
57 views

Swimming Problem - How can I do this?

I have a problem with the following diagram. The triangle is just a possible path and may not be the shortest. If the boy has to get to the destination in the fastest way possible: What ...
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1answer
25 views

How to get the chemical form of the the lotka-volterra ODEs

I know how to work from a chemical equation to an ODE, as described here: http://brunel.ac.uk/~cspgoop/uploads/ode_chemical_network.pdf How do I go the other way? I want to convert the ...
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2answers
29 views

Unusual Probability Question

Wheel of fortune: Assume that the probability for an angle φ is P(φ) = λ$φ^2$. The game pays $1000 times the angle. a) What is λ? b) Find the expectation and the variance of the game. Comments: ...
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1answer
28 views

Generalize discrete Lyapunov equation for n-th order linear dynamics system

My specific application is analysis of dynamic textures using linear dynamics systems of the form $$ I(t) = Cz(t) + w(t) \\ z(t + 1) = Az(t) + Bv(t), $$ where $I(t)$ is the original signal, $z(t)$ ...
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34 views

Looking for advice on a math project

I had an idea of modeling the evolution of population in the dining hall (just the section where people get their food, not where people eat their food) and discussing the properties of this Dynamical ...
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22 views

How to form an equation from given graph

Hello, How can I form the mathematical equation from the given characteristics? I have attached here the excel file data of X andY axis along with the formed graph. I want to form the mathematical ...
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26 views

Check if intervals overlap

I have a set of activities $A$, where each activity $i \in A$ has a starting date $s_i$ and an end date $e_i$ (or equivalently a starting date and a duration $d_i$). Therefore, each activity can be ...
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32 views

Predicting profit with price variation

I am currently working on a high school project that aims to predict profit from X amount of items to Y amount of profit based off a deviated sale price. For instance: I sale 10 cookies for 10 ...