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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need equation to calculate similarity distance

Desperately need help, please. I need to write mathematically, separate equations for calculating distance so that a higher score means a and b are very similar, and a low score means not similar. I ...
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1answer
32 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
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17 views

Formula for sinusoidal-like graph

Come up with a formula using cosine that satisfies the points (0,347), (1, 76), (2,295), (3, 84), (4, 243), (5, 92). The problem I have with this question is that the amplitude and the midline do not ...
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48 views

Saying something about model parameters, knowing the half-life of total protein

I have the following model: $$ \frac{dP}{dt} = -{\color{blue}k} \frac{P}{{\color{blue}C} + P} + {\color{blue}r}P_u \\ \frac{dP_u}{dt} = {\color{blue}k} \frac{P}{{\color{blue}C}+P} - ...
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1answer
52 views

Number sequences in nature.

I'm getting ready to teach the second calculus course in the 4 course sequence at my school. One of the required topics is an introduction to number sequences. I want to motivate this section with ...
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15 views

Can multimodality exist in the absence of deterministic multistability?

I am not sure if this is the right SE to ask this question; it is about mathematical models for chemical reactions. I came across an article that says that multimodality of biochemical species can ...
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2answers
45 views

Which mathematical programming method is good for solving the described problem?

I need to solve the following problem. Let's say that there are 3 clients with different time windows. For simplicity let's say that travel distance is always 10 minutes and service time is 30 ...
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1answer
29 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
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91 views

What differential equation might model this almost-harmonic oscillator?

I need to precisely control the motion of a damped, driven (nearly) harmonic oscillator: $$ \ddot x(t) + \alpha\dot x(t) + \omega_0^2 x(t) \approx V(t) $$ I use the $\approx$ symbol because this is ...
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62 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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2answers
63 views

Locally small category whose collection of isomorphism classes cannot be a set

For natural examples of locally small categories like the category $\mathbf{Grp}$ of groups, the isomorphism classes themselves are normally not sets. In a set theory like ZFC, even the collection of ...
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19 views

Method for spacing tasks over 24 hour period

I have been asked to look into devising a quicker way to balance workload over a $24$ hour workday. The scenario: $24$ hour work day $8$ hours shifts $40$ minutes break time per shift Each shift ...
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1answer
87 views

Gompertz growth model problem

The growth of tumor cells is characterized with Gompertz model. $N'=-aNln(bN),$ where N(t) is proportional to the number of cells in the tumor, while a and b denote positive parameters. ...
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2answers
23 views

Modeling a greatest integer function

I'm trying to model a function that resembles a greatest integer function. The domain is from [0, $\infty$). The inputs from 0 to 1.5 (non-inclusive) need to be mapped to an output of 0, and 1.5 to ...
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30 views

square footage to non linear time [closed]

I'm a tarp maker and I'm trying to figure out how long it takes me to move the tarp around depending on the square footage of the tarp. For instance, it takes me 2 minutes to handle a 10sqft tarp, ...
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41 views

A good book on convolutional neural networks

Good evening! Don't you know a good book on convolutional neural networks, where the next questions are highlighted: 1) How are the backpropagations for convolutional and pooling layers are ...
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1answer
52 views

Modeling with Differential Equations - Help?!?!

So here's the problem that I'm working on at the moment: Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while Tank 2 initially contains 20 gals of water with 15 oz of salt in ...
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29 views

Matlab functions of variables

So I am writing a function to compute the following equations for an SIR model: So here's my code: ...
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29 views

Function that defines a skew bell shaped curve

The following formula describes a normal bell shaped curve: $$f(x,a,b,c) = \frac{1}{1+|\frac{x-c}{a}|^{2b}}$$ I am trying to model data that exhibits has skewed bell shaped behaviour (please see the ...
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1answer
54 views

ODE water drop modeling question

I have been working on a ODE homework which involves modeling the velocity of a drop of water falling from the sky. The ODE that models its velocity is given by: $$ mv'=kv^2-mg, \qquad ...
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11 views

looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
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2answers
62 views

How I can express this mathematically?

I'm working on a OR project. I have a code which fixes my problem which uses the constraint ((a =< b) or (c =< d) or (e =< f)) = True I need to rewrite this condition as mathematical ...
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39 views

Probabilistic model of parallel web servers

Note: The following probabilistic model of parallel web servers is abstracted from an engineering project. I am not good at probability theory and I am seeking some evaluations and suggestions. ...
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18 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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1answer
94 views

When graph theory cannot model the most basic problem in wireless networks. Why?

I have a set of wireless links. These links are denoted by $\mathcal{L}=\{\ell_1, \dotsc, \ell_n\}$. Every link $\ell_i$ is composed of one transmitter $s_i$ and one receiver $r_i$. Initially, all ...
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33 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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1answer
39 views

How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
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46 views

Predictor-Corrector for Adams-Moulton

What is the order of the corrector of Adams-Moulton type required in order to apply Milne's method for estimating the error in PECE mode? Find the coefficient of the leading term in the truncation ...
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1answer
33 views

What are the Routh Hurwtiz Criteria for 3$\times$3 Matrices?

The Criteria I know (for dynamical systems) is... The eigenvalues of a matrix are guaranteed to be negative if Tr($J$)<0 and det($J$)>0, where $J$ is the Jacobian of some 2 dimensional dynamical ...
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1answer
30 views

Conceptual Car Density

This is more a conceptual question that requires a physical answer rather than a mathematical one. The question is Explain why a density wave moves forward for light traffic. Consider both cases in ...
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49 views

Stationary distribution of a “birth-death model” that does not have Markov property

A typical birth-death process is defined such as the probability of going from any state $j$ to any state $i$ is given by: $$ p_{ij}= \begin{cases} b_i & \text {if $j = i+1$} \\ ...
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2answers
67 views

mathematical biology1

Consider the infectious disease model defined by \begin{equation} \frac{dS_3}{dt}= -\rho I_3S_3+\gamma I_3+\mu-\mu S_3\tag 1 \end{equation} \begin{equation} \frac{dI_3}{dt}=\rho I_3S_3-\gamma ...
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37 views

Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
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1answer
41 views

Continuous superposition of bump functions

I am trying to "model" Fig 2 with a superposition of a bump function. I understand that bump functions are bounded and can be often differentiated. The bump function I have used is shown in Fig 1. My ...
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3answers
93 views

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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1answer
27 views

Finding maximum displacement from a BVP

I have solved the following BVP (Border Value Problem): $$y'''' = -P, y(0) = y(L) = 0, y'(0) = y'(L) = 0$$ Where $L=4 , P=24$ The DE describing it is: $y(x) = -x^2(x-4)^2$ This apparently is ...
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Difficult transition between homogenous and heterogeneous paramaters

I'll start with an example in queueing theory. Lets assume a M/D/k queue, i.e. a queue with $k$ servers where arrival rate is determined by a Poisson process. We try to find the mean waiting time. ...
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2answers
137 views

Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
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25 views

is following model stationary?

I am interested if following model is stationary,model is represented by following formula $$ x(n) = \sum_{p=1}^{P} a_p \cos(2\pi f_pn + \phi_p) + \epsilon(n) $$ $n$ is changing from $1$ to $N$, I ...
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0answers
33 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
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1answer
62 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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20 views

Derivation of the advection equation

Is there a good derivation of the advection equation available online? By that I mean the equation $\partial_t u = -\nabla( \vec{v} u)$ I know a good explanation for the one-dimensional case ...
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1answer
124 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
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38 views

Sensitivity of coefficients in ODE

I am trying to formulate a mathematical model as part of an op-research problem, and I'm running into a roadblock concerning differential equations of a certain kind; I was hoping to understand if ...
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1answer
61 views

Maths concept for salient point in graph data

I have collected data concerning the total post counts of users in an online forum (see graphic). What I am hoping to do is compare the language of 'first posts' with the language of 'later posts'. ...
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73 views

mathematical biology (steady-states)

non-dimensionalisation equation: \begin{equation} \frac {du}{d\tau}=\frac{\overline{\lambda}_{1} u}{u+1} -\overline{r}_{ab}uv -\overline{d}u \end{equation} where $\overline{\lambda}_{1}= \frac ...
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41 views

Eloquent method to analyse a four dimensional system ODEs qualitatively

Given a nonlinear four dimensional system of ODEs, I have found the fixed point and linearized to acquire the Jacobian. I am beginning to calculate the eigenvalues of the Jacobian from the quartic ...
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1answer
86 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
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1answer
106 views

Mathematicals biology

Consider the two species competition model given by $$ \frac{da}{dt }= [λ_1 a /(a+K1)] - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= [λ_2 b *(1-b/K2)] - r_{ba}\cdot ab , \ ...
2
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1answer
28 views

Trouble finding equilibrium points

I'm working on a nonlinear predator prey model and am struggling finding my equilibrium points. I've done this three times and gotten three different answers. I'd appreciate if someone could check ...