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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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
40 views

Regression model for a shearing process

30 Widgets are randomly assigned to a shearing process. There are 3 such processes, each getting 10 widgets. The lengths of each widget are recorded before undergoing the shearing. The amount that ...
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0answers
102 views

How to model bending, folding of 2D figures?

2D shape can be folded in various ways. For example, trapezoid can have its sides (with the acute angles) folded, so that it will effectively become rectangle – with the difference, that part of the ...
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116 views

Best way to statistically compare two polynomial models?

I'm working on modeling and comparing data sets, and I need a good way to see if there is a significant difference between the data from the 2 models. An example of the models are here. I initially ...
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0answers
148 views

Considering the predator prey model to find the range of values to be a spiral

I have the following problem: Consider the predator-prey model: $$\frac{du}{dt}=u(1-\alpha(u)-v), \frac{dv}{dt}=\rho(-1-\alpha(v)+u),$$ where $\rho$ and $\alpha$ are positive parameters with ...
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16answers
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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. ...
3
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1answer
73 views

Inverse of itinerary function

Let $S^{-1}:\Sigma \to \Lambda$ be inverse of itinerary function. I showed that $S$ is continuous and bijective. How to show that $S^{-1}$ is continuous?
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1answer
396 views

Time-evolving probability distribution functions with an equation of motion

I came up with this question a while ago and haven't been able to gain any insight on it. You are playing baseball. As a batter with finite vision capabilities, the only information you have about ...
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1answer
270 views

a mathematical model for file system

We are supposed to come up with a mathematical model describing a file system and its operations. The file system stores metadata in a database, and retrieves it when necessary. How does one go about ...
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1answer
104 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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1answer
76 views

Which variable represents the predator and which the prey.

Just a quick question I have the following system: $$\frac{dx}{dt}=x\left(2-x-\frac{y}{1+x}\right),\qquad \frac{dy}{dt}=3y\left(\frac{x}{1+x}-4y\right)$$ It asks which variable represents the predator ...
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1answer
84 views

unit conversion doubt

Im a developer that likes maths, but dont have much experience, I had constructed a graphic that animates a bar that grows on the X axis according to a value. So, I have the values for the x ...
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1answer
13k views

How can I find the time constant of a first order system transfer function?

How can I obtain the time constant of the transfer function of a first order system, such as the example below? $$ \frac{C(s)}{R(s)} = \frac{2}{s + 3}$$ Where $C(s)$ is the output of the system and ...
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0answers
41 views

using a scientific paper to model the temperature of pools in an irrigation system

Quite a general question... I am referring to a scientific paper : http://www.springerlink.com/content/41p817v1584q1850/ I am trying to model water temperature over a year. I have the initial ...
3
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2answers
535 views

Recommended book on modeling/differential equations

I am soon attending a undergrad course named differential equations and modeling. I have dealt with differential equations before, but in that course just learned a bunch of methods for solving them. ...
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1answer
23 views

Smoother Generalized Mixed Linear Models

I wondered if anyone could help me figure out what a smoother was in regard to Generalized Mixed Linear Models or point me in direction of some relevant litterature. Regards!
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2answers
568 views

Binary Logistic Regression Model Processing

Thanks for showing interest and wanting to help out. My aim is to develop a model that - as accurately as possible - predicts how entities in a population will either cooperate or defect, as a % of ...
2
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0answers
77 views

Measuring Model Bias

If given the choice between two statistical models (for argument's sake, let's say Model 1 is $y = \beta_0 + \beta_1 x_1 + \epsilon$ and Model 2 is $y = \beta_0 + \beta_1 x^2_1 + \epsilon$), is there ...
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1answer
27 views

Is there a statistic model that selects attributes in each state?

Every state has its own sub-attributes, for example, state S{ATTR1, ATTR2, ATTR3}. We can train the model use data with states filled with all three attributes. When we want to predict, we just want ...
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2answers
2k views

Sound Triangulation

Hello guys I would appreciate it if someone could help me out here. I have been asked to create a simple visualization for an assignment. I am required to triangulate the source of a artillery cannon ...
3
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3answers
368 views

Predicting the next vector given a known sequence

I have a sequence of unit vectors $\vec{v}_0,\vec{v}_1,\ldots,\vec{v}_k,\ldots$ with the following property: $\lim_{i\rightarrow\infty}\vec{v}_{i} = \vec{\alpha}$, i.e. the sequence converges to a ...
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0answers
100 views

Modelling randomized cup stacking, animal behaviour

This question has no scientific relevance for me whatsoever, but is a real life question which left me puzzled for a while. Even though I am not going anywere with this, maybe there is still somebody ...
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1answer
64 views

64 possible values - continuous or discrete?

I have a response variable in a model that is calculated from binary values of an 8x8 grid of pixels, giving a proportion. Technically, there are only 64 possible values the result can take, so would ...
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2answers
337 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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2answers
2k views

How to derive and solve a difference equation.

I am having terrible trouble with the following question: Suppose that $x_n$ is the amount owed on a mortgage after n years, £$m$ is the monthly repayment and $r$ is the annual percentage interest ...
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2answers
85 views

Multiple regression with model $Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$

I'm currently working with data contained in $Y, X_1, X_2, \ldots, X_n$ and wish to fit it to the model: $Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$ where the $c_i$ are coefficients to be ...
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1answer
61 views

Reduce a range of values

I am using this weighted sum from the question How to build a function that gives recent years higher weight? To reduce the value I tried square root of $X,$ then tried the $8$th root, ...
2
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2answers
707 views

How to determine units in a partial differential equation

How do we determine the units used in a differential equation? Yes, in theory a PDE has nothing to do with units, but I'm interested in this question from a modeling point of view. By units, I mean ...
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0answers
316 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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2answers
535 views

How do I turn this piecewise function into a “normal” function?

I am a Java developer building a web app that I will be deploying "in the cloud" (I hate that expression) in a few months. I'm trying to develop a function that will let me spawn and kill the right ...
2
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0answers
139 views

Check my solution - Modelling of a spring with Differential Equation

I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
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2answers
369 views

What is the underlying function?

I have some value pairs. They are inversely proportional. I want to have a formula to get the second value from the first value. ...
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3answers
258 views

Mathematical (or physical) formulation of life

I recently started to have interest in the characteristics of life. Especially, I wonder if there are some kind of mathematical description of the true meaning of life and how it is emerged. Why does ...
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1answer
160 views

Mathematical idea behind tax bracket

This may be a lame question. The tax bracket is a way to calculate the tax based on the taxable income. For example Imagine that there are three tax brackets: 10%, 20%, and 30%. The 10% rate ...
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1answer
117 views

Good model to reward contributions

I hope you guys find this an interesting question. Imagine you want to implement a system that rewards people for their contributions (regardless of quality or any external assessment). What is a good ...
2
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1answer
267 views

Problem with ratios, dimensionless quantities

I've been trying to understand how a ratio of two of the same units gives a dimensionless quantity. It makes no sense to me. For example, density in terms of mass and volume: $$d = \frac{m}{V}$$ ...
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1answer
334 views

Classify the fixed points at the origin

Consider the linear system $$\frac{dx}{dt}= -3x+2y, \frac{dy}{dt}= ax+6y, a \neq -9$$ classify the fixed point at the origin? Is the correct approach to investigate the steady states and how these ...
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1answer
629 views

Stationary points of an ODE-system (again)

There is another exercise where I am given a non-linear system of ODEs and a question that confuses me: Consider $$x'=x(y+1)\\ \text{ and }\\ y'=xy+2.$$ "Determine stationary points of the ...
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1answer
320 views

System of ODEs and Lyapunov function

I've tried to solve a little problem that goes as follows: Consider a system of ODEs: $$x'=y-x^3\text{ and } y'=-x^3-y^3$$ And the function $$L(x,y)=\frac{1}{2}y^2+\frac{1}{4}x^4.$$ Now I shall show ...
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1answer
173 views

Describe the nature of the fixed points

I have the following system describing a free-market economy: $$\frac{dp}{dt}=\alpha r,\qquad \frac{dr}{dt}=-\beta r$$ Where $\alpha$ and $\beta$ are positive constants, $p$ is the price and $r$ the ...
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1answer
398 views

Why does this example of Hardy-Weinberg equilibrium not work?

Background Info Hardy-Weinberg equilibrium is a mathematical model of the frequencies of alleles (i.e., versions of a gene) in a population. The model states that the frequency of the 2 alleles in a ...
2
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1answer
61 views

Need some help on petri nets?

Here's the question: $\qquad$ How do we go about doing this ? I have very little knowledge on petri nets. Can someone answer it for me ? (And regarding the program part , just give me an idea on ...
6
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1answer
197 views

Sunk cost auction modeling.

Consider the following auction concept. I call it a "SUNK COST AUCTION" Each person bids, but you pay all of the money that you bid for every bid you make. So, if you bid \$1 that \$1 is gone, even if ...
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1answer
225 views

Problem with continuity of a piecewise function

I am stuck with a homework problem which is about the modelling of tumor growth by ODEs. The function $A(t)$ is the amount of drugs in the patients blood. During some intervals (namely, $(n,n+\tau)$, ...
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1answer
796 views

How to design a weighted formula with multiple inputs?

Apologies if this is the completely wrong verbiage for this sort of thing... kinda new to this. We're designing a social website, where users on the site have several statistics associated with them. ...
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1answer
53 views

Reduce the range of weighted sum

i am using this weighted sum How to build a function that gives recent years higher weight? but I am getting values in the range 1- 0.0000002 How can I reduce this range ? Make it something like ...
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0answers
59 views

How are these operations the same? How to convert a multiplication in a different form?

I am reading on a specific operation, how it should be done in order to avoid overflow during multiplication. The operation is: $$( A * \text{state} ) \% M;$$ This is susceptible to overflow. The ...
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1answer
213 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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1answer
76 views

Detecting lines and circles in x/y datasets

I'm trying to do some simple gesture recognition. Circles, I'm assuming, will simply be a set of points which are all within some specified distance range from center. Lines on the other hand, I'm not ...
3
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2answers
143 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 ...