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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Mathematical calculation

I encountered during my reading to ridge regression that $$(X^TX+\lambda I)^{-1}X^TX = I-\lambda(X^TX+\lambda I)^{-1}$$ What mathematical manipulation has been done here? Thanks in advance
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60 views

Proportionally Distributing $N$ items across $B$ bins.

My question is similar to this: Proportional Distribution My problem follows: I have $N$ items that cannot be broken up into fractional components, but should be distributed across $B$ bins where ...
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1answer
23 views

Why is there a division by $z$ in this mathematical model of a camera?

I'm reading the OpenCV documentation on what mathematical model they use for a camera. The below quoted text can be found on this website, scrolling down to the section "Detailed Description". I do ...
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1answer
18 views

Multi Valued Model

Suppose we have a set of observations $\{(x_1,y_1),...,(x_n,y_n)\}$ and a function $f$ that provides an optimal (in some sense) prediction of an output given an input. Also suppose that for some $i$ ...
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23 views

intuition about system of coupled differential equations

I have a system with two components A and B where A is being depleted at a constant rate, and A activates B. Activation of B by A follows the Hill equation: $dA/dt = -r_{A}$ $dB/dt = V_m\...
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20 views

How do I model the optimization of haircuts (price vs. frequency vs. satisfaction)?

My goal is to use a simple, real world situation to apply optimization algorithms to and find optimal choices based on computation. What information do I need to gather and what questions do I need to ...
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1answer
66 views

How to adjust the parameters of Lotka-Volterra equations to fit the extremal values of each population

I found a graph that represents predator and prey populations over time, and I was hoping that someone could explain how I could generate two Lotka-Volterra equations that would give a good ...
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12 views

Express a prefix tree mathematically

(I am not a math wiz, btw.) Imagine you have a tree (or a trie), where the root node has M amount of children and each child then has M - k children, where k can but does not have to reach zero, what ...
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71 views

explain why accounting data follows Benford's law

I've spent a lot of time recently investigating on Benford's law. Many sources state that Benford's law can be useful when auditing accounting data. Non-fraudulent accounting data (under "good" terms) ...
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1answer
18 views

Can anyone specify what kind of function can be used in this case?

I have some data as shown in the figure, and I just want to collapse all the 4 curves into a single curve. The 4 curves correspond to 4 different values $a$ mentioned in the legend. I think the best ...
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1answer
25 views

Modeling - First Order vs Higher Order Differential Equations

Throughout my engineering education, I've only witnessed modeling using First Order differential equations. Almost all of my Higher Order knowledge was given either via a spring or heat equation or ...
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1answer
40 views

Interest rate, probability of tuition

A new government introduces tuition of 10.000 Euro/year, increasing yearly with the inflation rate of 2%. At the same time, a prospective 'perpetual student' enrolls at the university. She expects ...
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1answer
74 views

Modeling particles moving through a chamber

Consider the following phenomenon. Particles each traveling with speed $v_i$ metres per second enter a chamber at a rate of $r$ particles per second. Upon entering the chamber, each particle begins ...
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35 views

Applied Rational Choice Theory

I am a programmer researching the application of Rational Choice Theory. I have found many links to the philosophical nature of it. And fewer documents formalizing it's mathematical principles. ( ...
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0answers
19 views

Regarding pedigrees

Here's a errrhmm.... a modelling problem. Applied math. Or something. We're given pair of sets $X,Y$ (for notational simplicity, assumed disjoint). Let $T_{X,Y}$ denote the following disjoint union:...
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0answers
56 views

Future Space Opportunities for a Mathematician [closed]

I don't know if this question should be asked here or on "Mathematics Educators", however I'll post it here for the moment. I've just finished my first year of Mathematics and I do really like maths. ...
2
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3answers
61 views

Problem of Linear Programming, Scilab or Octave

I have to solve this with Octave or Scilab. There's an airplane company with airplanes flying to 3 different destinations (London, Paris, Rome). Schedule of flights ...
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0answers
35 views

Model for headphone quality as a function of price

I've looked for any mathematical model that shows headphone quality as a function of the price of the headphones, but have not found anything yet. Of course, "quality" is quite subjective, which could ...
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29 views

Prediction for time series

Suppose we have several weeks (say, 30) in a row and number of advertisements sent on e-mails on each week and number of the following orders of the product. How can I estimate the necessary number ...
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33 views

tangent space in a moving coordinate frame

I've got a problem in some geometry of flow. For the sake of completeness I will give the complete derivation of the equation of interest, but I will seperate it into derivation part and question ...
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1answer
200 views

Is there any probability model for multi-stage motion of an object such as this.

I have this following case (please refer to attached pic below) where a particle is resting on the ground and it needs a minimum amount of force (Fmin) to reach from one level to the next level. But ...
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3answers
859 views

Probability sum of 5 before sum of 7

Pair of fair die are rolled (independently I hope) infinitely. Find probability sum of 5 appears before sum of 7. 2 approaches: $$P(\text{sum of 5 appears before sum of 7})$$ $$= P(\text{roll 1 ...
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0answers
39 views

What constitutes sensitivity to initial conditions for a system of continuous ODEs?

I am currently working on a disease model (5 dimensions) which seems to exhibit sensitivity to initial conditions. I have used numerical analysis following the method described in Wolf's paper (link ...
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1answer
46 views

Books on mathematical biology

Can someone recommend good books on mathematical biology for self study. Especially to understand SIR models and stochastic models such as branching process. For SIR models I want more of beginner ...
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19 views

SIR model parameter notation

I am reading on SIR models and I found this article In the article it has three groups as one without vaccination, one with only whole cell(wP) vaccination, and one with only acelluar(aP) vaccination....
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1answer
16 views

Poisson Mean Term reduce with time

I've had a search for the answer to this problem but I can't find a solution anywhere. I am using a Poisson model and estimating the average time of a potential insurance claim arising in the future. ...
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1answer
19 views

Finding equation of a bent sufficiently flexible cardboard of length $l$ fitting into a gap of width $m<l$

I was thinking about how the walls of a barrel is made then I realized it is someone like fitting a piece of wood of length $l$ in between some "gap" of length $m<l$. This would cause the piece of ...
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1answer
28 views

Increase Profit sale car with respect to rebate

Tesla makes $ 1,500 $ dollars on sale of model 3. It is estimated for every $100$ dollars of rebate, sales increase by $15$%. Use one variable optimization to maximize profits. I did pass my calc ...
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1answer
19 views

How to denote the aggregation of values into a vector?

How do I denote that I am aggregating values into a vector? For example, I have a set of values $F$ in which a function $fun$ will be applied. Finally, a vector is build with the results. For ...
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0answers
23 views

Do you know an operation in which the order of elements does not matter but repetitions is allowed?

In order to present a concept in an article, I need an operation in which the order of elements does not matter but repetitions is allowed. For example, if a have some vectors [1 2 3], [2 3 1], [1 2 ...
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2answers
51 views

How do I develop a formula to find the height of a male using his femur? [closed]

I'm a grade eleven math student and I need a formula to find the height of a 15/16 year old male subject using only the length of his femur. I'm very confused on how to do this, please help, it's for ...
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0answers
13 views

What is the mathematical model for a Parallel Machine Scheduling with multi-processes?

Parallel machine scheduling is a problem contains $i$ jobs and each job have $j$ processes and each processes can be processed on $k$ different machine. Processes can not be interrupt and have to be ...
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0answers
12 views

Bounds on the divisor of Webster's apportionment method

I am currently in the process of studying various apportionment methods in a summer class, and while learning about Webster's apportionment method (also known as Webster-Willcox or method of major ...
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1answer
29 views

Solving functional equation $\frac{f(s, t)}{f(s, m)} = \frac{1}{1+s(m-t)}$

I want to find a functional equation $f(s,x)$ such that $$\frac{f(s, t)}{f(s, m)} = \frac{1}{1+s(m-t)}$$ If it helps the context I need this in is where $t$ is a member of a set of real number and $m$...
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1answer
27 views

What model should I use for judging a dimension given only composed data with another?

I am attempting to upgrade a modeling system using a limited type of statistical information, but with the sample covering the entire system. The problem is how to use the additional information in ...
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0answers
14 views

Analysis of incomplete system of diferential equations

I need to find information about the kinetics of a reaction. I tried to solve this problem first generalizing the equations for the different kind of reactions yielding an equation like: $$ \dot{x} =...
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0answers
23 views

Simple example of “Spike-and-Slab Prior” for Bayesian Inference

I would really like to understand how Spike-and-Slab Priors work in relation to Linearized Models. Can somebody provide a toy example of a Spike-and-Slab Prior with a Bernoulli spike and a Gaussian ...
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0answers
11 views

How to model a point force with uncertain concentration point?

I consider a beam which is bent under influence of a point force concentrated at some point $\xi$ of the beam. The exact co-ordinate of $\xi$ is not known, but it is known a neighbourhood $(l_0,l_1)\...
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1answer
38 views

Can anyone answer this equation or tell me what it is? [closed]

I have been sent an image, and have no idea what it means. Think this is the best site to try. The image is of the equation $$W_T=\sum_{i=1}^nW_i\;.$$
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Which of the following is more efficient?

In an auditorium where 100 people are sitting, with 10 people in each of the 10 rows. What will be the most efficient way of increasing the distance between the first row and the stage: by making the ...
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2answers
68 views

asymmetrical sine wave

How do you model a sine wave that begins to shift over asymmetrically (like a ocean swell approaching a beach)? Is sine even the right function for this model, or is some other type of function better?...
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0answers
13 views

Match harmonics while decoding the speech signal

There is a matlab's program. In the input parameters is a wav file. After executing a program there are appearing an array of frames. Frames partially recover each other. In each frame there are ...
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0answers
18 views

function to model breaking wave

What is a good parametric function to model a breaking wave (im ok with something complicated)? More specifically, I am looking for a general form, such that it looks like a normal swell and then as a ...
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0answers
14 views

Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
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1answer
41 views

Conditioning Poisson on Poisson [closed]

There is a bus, whose departure at a stop is distributed as poisson(mu). People arriving to the same stop is distributed as poisson(lambda). Find the PMF of the number, N, of people on any given bus. ...
2
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2answers
108 views

Model for spread of infection, with vaccination

I'm trying to solve following problem: $N = 10^6$ ... number of people $ir = 8\% $ ... infection rate time unit - 1 day And when there are 3% of population infected, vaccination begins. Its effect ...
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1answer
17 views

Using a continuous function to describe discrete data

I've always been told to use discrete functions with discrete data and continuous functions with continuous data. This especially comes to light when talking stats and people emphasize the difference ...
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21 views

Modeling simple linear equations

This should be pretty simple but I'm blanking on this. I need to model (graph) how path 1 becomes equally as efficient as path 2 as the distance of path 2 increases. distance of path 1 (from A to B) =...
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how do I resolve equations that are both dependant on each other

I'm working on a project concerning the ideal power equation of aerodynamic bodies seen here: $$P = \frac{1}{2}C A D v^3 + \frac{W^2}{Db^2v}$$ where $P$ = power, $C$ = coefficient of drag, $A$ = ...
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1answer
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How can I adduce the mathematical model in my master thesis?

Please explain how to adduce and describe the mathematical model obtained by neural network modeling, if the model contains 50 inputs and five neurons in the hidden layer. How to show values of ...