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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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
127 views

Creating a model

Here's a seemingly simple pondering. If one item is more valuable the higher it is (i.e., $a=5$ is worth more than $a=2$) and another item is more valuable the lower it is (i.e., $b=2$ is worth more ...
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0answers
55 views

Transport problem wth time management

Are there general methods for solving the transportation problem with additional conditions: Time management (transportation from point A to point B is so much) Transportation of more than one ...
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0answers
196 views

How to parametrize a function such that it approaches $f(0)=0$ and $f(1)=1$ with different speed

I need a function (polynome) that values $0$ at $0$ and $1$ at $1$ and has these values as local maxima and minima. So far so easy the straight solution is: $$f(x) = -x^4+2x^2$$ Now I want to ...
2
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1answer
140 views

Could you help me to find a model for this curve?

I am very bad in mathematics and I'm not able to find by myself the model corresponding to this kind of curve. I wish to have a quick growth at the beginning, then it should increase slowly for a ...
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1answer
45 views

How to solve these simultaneous equations:

$1 = 1/2y - bx,$ $1 = 1/2x - ay$ I need x,y it in terms of constants, but I can't figure it out!
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1answer
135 views

Iterative model fitting

I have a sequence of points $\{(x_k,y_k,z_k)\}$ and I need to fit some $2D$ model $P(x,y)$ that approximates $z$ in some sense. The $z_k$$'s$ are noisy samples of some $2D$ function $z_k = f(x,y) + ...
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1answer
157 views

Actuarial / Modelling question - difference between RUN date and VAL date

My understanding is that RUN date is the date you do the RUN (eg in prophet / moses / igloo / whatever, the date on which you performed the calculations) Whereas VALuation date is the initial 'as at' ...
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0answers
145 views

Should I get the absolute value of the result of the inverse discrete fourier transform?

The result of equation 36 can be positive and negative.And if I don't get the absolute value of it,the ocean surface tend to be very regular.But according to the paper,the author never get the ...
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1answer
446 views

Complex results in inverse Fourier transform for simulating ocean water

I don't understand the equation37 in simulate ocean water by Jerry Tessendorf.The result is all complex number, how to be the slope.Even if I compute the magnitude of it,the result is just positive ...
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0answers
25 views

Model to reward adaptative communication

I'm currently working in different simulations focused on the study of artificial evolution of communications in robots, and I have stumbled against the problem of its mathematic formulation. The ...
2
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3answers
2k views

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 ...
3
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0answers
105 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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0answers
118 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 ...
2
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0answers
151 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 ...
187
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16answers
7k views

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
75 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
418 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
281 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 ...
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2answers
551 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
579 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 ...
2
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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
101 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 ...
2
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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
345 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
86 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
727 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 ...
2
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0answers
320 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
548 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
143 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
378 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. ...
4
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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 ...
2
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1answer
168 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
271 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
345 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
667 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
328 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 ...