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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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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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
19 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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18 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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13 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
29 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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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
54 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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24 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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11 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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19 views

Formula for a Skewed Distribution

I'm trying to create a model of some data, using a skewed normal distribution. I have the following data: Mean Median Standard Deviation from the mean Standard Deviation from the median I've been ...
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1answer
79 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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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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25 views

Euler Bernoulli beam

A simple model of the beam subjected to bending stresses is given by Euler-Bernoulli differential equation. Finite element discretization leads to a system of liniar equations.As discretization size ...
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1answer
36 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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26 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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26 views

What statistical tests for headache journal? [migrated]

I track my pain levels in an online spreadsheet along with daily habits and trigger events. I want to test whether changes in my pain over time follow a trend (not concerned whether it is linear or ...
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1answer
29 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
17 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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30 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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61 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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29 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
25 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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37 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
14 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
133 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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22 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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28 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
51 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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15 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
71 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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36 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
42 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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64 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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32 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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53 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
90 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 , \ ...
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1answer
19 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 ...
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1answer
105 views

mathematical biology

Consider the single species population model defined by $$\frac{dR}{dt} = \frac{gR}{R+R_m} - dR,$$ for $t > 0$, where $g,R_m$, and $d$ are all positive parameters and $R(0) =R_0$. (a) Describe ...
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1answer
219 views

There are 5 servers. Each server has 1% downtime. What's the probability that at at least three servers are down?

There are 5 servers. Each server has $1$% downtime. What's the probability that at at least three servers are down? My reasoning is the following: A) There is $(1-0.01)^5$ probability that $5$ from ...
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19 views

Analyzing a recurrence model: equilibriums, stability and periodic behavior.

In orer to increase my knowledge in math I decided to analyze the following recurrence relation (logistic growth in ecology) $$N(t+1) = N(t) (1 + r(1-\frac{N(t)}{K}))$$ I found the equilibriums by ...
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2answers
63 views

A model for the spruce budworm population

A model for the spruce budworm population $u(t)$ is governed by $$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$ where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
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0answers
32 views

Mathematical interpretation of pressure (gradient)

I'm having some problem with the following. Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here ...
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Derivation of the Richards equation

I know the derivation of the Richards equation from two-phase flow equations and assuming that one pressure is constant (e.g. the books of Bear). However in the paper of Alt, Luckhaus and Visintin ...
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1answer
25 views

How to show the monotonicity of exponential growth?

I have a basic exponential growth model given by $N'(t)=N(t)\times r$ where $N(t)$ is the current population and $r>0$. My problem is to show if the initial population $N(0)=N_0>0$, then the ...
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Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
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15 views

relationship between two set of variable

i am trying to determine what kind of mathematical modeling could be applied following two variables,let us call them $x$ and $y$ ,namely change one variable has effect second on,i have several ...
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1answer
45 views

What is a good approximation of $(1-p)(1-q)$ as $(1-x)^2$, for $p,q \in (0,1)$?

I'm doing some scientific modeling, and I want to use $(1-x)^2$ to approximate $(1-p)(1-q)$, with $p, q \in (0,1)$. $p$ and $q$ are probabilities, and are not near zero. My intuition is that since ...
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27 views

Finding general solution to a non-linear discrete time recurrence relation

I am faced to a non-linear discrete time reccurence relation and I can't find the general solution. The first question is: Is there a general recipe for finding the general solution to non-linear ...