Questions tagged [mathematical-modeling]

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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Why does this equation hold? This is a question about ddpm and nscn. [closed]

Can someone help me why this equation holds: $\nabla _{x_{t}}logq(x_{t})=E_{q(x_{0})}[\nabla _{x_{t}}q(x_{t}|x_{0})]$?This equation is about the connection between Denoising diffusion probabilistic ...
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Calculating confidence interval while fitting multiple datasets simultaneously.

I am dealing with six experimental datasets of two species interaction and I want to fit these six datasets to a coupled ode system simultaneously to get a set of estimated parameters and ...
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Isolating $z$ in the equation $x - 1 = - \frac{1-y^{z+1}-0.5(1-y^z)}{(1-y)y^z}$

I have a formula with multiple unknowns: $$x - 1 = - \frac{1-y^{z+1}-0.5(1-y^z)}{(1-y)y^z}$$ The way it is setup now allows to easily calculate $x$, but I would like to reformulate it to isolate $z$, ...
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Can a non-analytic function provide analytic solution (i.e., exact solution)? [closed]

What is an analytic function? What is an analytic solution? These two terms have the same meaning? If no, can a non-analytic function provide an analytic solution?
stranger's user avatar
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Stability of fixed points in a 2D discrete time dynamical system

I am studying the stability of fixed points in the Henon map for a project, and I have a question regarding it. The Henon map we are studying is given by: \begin{align*} x_{n+1}&=1+y_n-\alpha x_n^...
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Modeling scoring functions

I'm looking for general direction on topics to explore for this problem. I think I'm not searching for the right statistical concepts and therefore coming up empty handed. Also, I'm a computer ...
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What does it mean to use mathematical models to understand qualitative vs quantitative behavior? [closed]

I have been running into this recently, and I want to confirm I have the right idea. For example, Neff et al. (2023) state, "Although we study a mathematically very simple box model in order to ...
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prove existence, uniqueness and non-negativity of the system of ODE

I have an epidemic model with 9 compartments, where all epidemic parameters are non-negative. \begin{equation} \label{model} \begin{split} &\frac{dS}{dt} = \beta N -\delta S-\phi \frac {SI}{...
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For an epidemic model, I got a negative 'basic reproduction number' obtained by next-generation matrix method. How this can be corrected?

I have a system of 6 ODE representing infected subpopulations of a model of epidemic $$ \begin{cases} \dfrac{de}{dt} =\dfrac{dy_2}{dt} = \phi y_1(y_4+y_5)-p_2 y_2\\ \dfrac{dq^*}{dt} =\dfrac{dy_3}{dt} ...
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Latent Change Score Modelling

I am currently undertaking a research project that aims to assess the effectiveness of an intervention program. However, I am encountering difficulties in locating suitable resources for my study. ...
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Non-Dimensionalizing a Traffic Flow PDE for Physics Informed Neural Network Issue

I'm working on analyzing a traffic flow model described by the following partial differential equation (PDE): $V_{\max} \left(1 - \frac{2\rho}{\rho_{\max}}\right) \frac{\partial \rho}{\partial x} + \...
Proxy's user avatar
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Math-Bio: Reference/Example needed for a reaction-diffusion system coupled to a conservation law

DISCLAIMER: I also made a post about it in biology stack exchange but I'm not sure whether that forum is the most appropriate. Hence I thought to share my question here as well. While looking at this ...
kaithkolesidou's user avatar
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Find the best embeddding for this gene/lipid graph

I want to find a 'nice' drawing of the lipids and genes in my database. Lipids belong to one one of several classes, while genes belong to one of several regions. Each gene/lipid pair has an ...
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How to solve an ODE where the rate is directly proportional to two amounts?

Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
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Permutations of pairs with no pair ending up together.

I'm working on a general version of the problem linked here. To quote the original: Suppose 𝑛=10 married couples are invited to a bridge party. Bridge partners are chosen at random, without regard ...
ikeywikeywoo's user avatar
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ANFIS Model, tips about improving performance [closed]

I have a question regarding about improving the performance of an ANFIS (adaptive neuro Fuzzy inference system) model. In MATLAB, I have been training a model with 5 inputs, with 816 data point for ...
jocelyn matus ancavil's user avatar
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Cylindrical Water Reservoir Model and System Behavior [closed]

System Description We're looking for the mathematical model of a cylindrical water reservoir. The reservoir is characterized by three variables: The inlet flow, $Q_e(t)$, at time t The outlet flow, ...
Knowledge Seeker's user avatar
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In search of a model to describe worm behaviour

For my bachelors thesis I am working with tubifex worms, and trying to develop a graph theoretical model that can help explain some mechanical and dynamical properties of the worms once they have ...
Rowan Potato's user avatar
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1 answer
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Stable coordinates in Indoor localization

I am implementing an Indoor localization demo for a project. In that i am using ultra wide band technology to calculate the distances from three different anchors to the moving object, then I use ...
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Derivation of an epitrochoid

I was working on an assignment and had a good idea to have a water jet model an epitrochoid to create a fountain. While the overall idea was approved by my teachers, I was told that I need to show a ...
TheShadowSider101's user avatar
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Navier Stokes Eqns: Boundary Conditions and Pressure Coupling

I have made it a personal long-term goal of mine to numerically solve the 1D transient Navier-Stokes equations for simple incompressible and compressible flow scenarios. I want to do it for a few ...
UserHandel's user avatar
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What is happening in this 'multi'-sinusoidal function?

Edit: Thanks to those commenting, I fixed my issue and now have reached the below function, as I had aimed. My remaining question would be how I might describe this function. I have taken the function ...
cadasc_56's user avatar
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Linear programming constraint involving maximum

I am trying to formulate a much bigger problem as an integer linear program, but I am stuck with one particular constraint and am not sure how to formulate it. To put it shortly, the problem deals ...
AlaskaYoung's user avatar
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Trying to find a solution to a problem related to the recursive sequence $S_{n}^{k}(a)$

I'm working on a problem related to a recursive sequence, and I'm having some trouble. The sequence $S_{n}^{k}(a)$ is defined as follows: $$S_{n}^{k}(a) = \begin{cases} \sqrt{a} & \text{if } n = ...
Apollisto's user avatar
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Closed-form solution for polynomial recurrence relation.

Is there a closed-form solution for the recurrence relation $x_{t+1} = x_{t}^\alpha + 1$, where $\alpha \in (0,1)$? If it were $x_{t+1} = x_{t}^\alpha$, then taking the Log of both sides would make it ...
Arseniy  Samsonov's user avatar
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Exploring Markov Models for Determining Car Insurance Costs

Question: I'm currently delving into the realm of Markov models to understand how they can be applied to determine the cost of car insurance. Thus far, I've come across the bonus-malus system and ...
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General state space form for ARIMA(p,d,q)(P,D,Q)

I cannot for the life of me find a resource which gives the general state space form for an ARIMA(p,d,q)(P,D,Q) model. I am reading Time Series Analysis by State Space Methods, by Durbin & Koopman,...
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3d fractal helix modeling

I'm trying to build a 3d visual to illustrate a concept. Imagine a circular helix. We could define a cylinder that contains that helix. But now imagine this cylinder takes the helicoïd shape too ! We ...
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Conversion of Abstract Units to Time in Polynomial Modeling of Snowboarder's Motion

I am currently working on a project where I model the motion of a snowboarder using a 4th-degree polynomial. The polynomial is currently defined in abstract units along the x-axis and y-axis. I have ...
Miles Jarra Gloekler's user avatar
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Problem in performing sensitivity analysis in prey-predator model

I tried to create a general prey predator model to simulate sensitivity analysis using PRCC and Latin hypercube sampling. But I can a bar plots which are empty. What is wrong in my approach? The code: ...
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How to use Euler-Lagrange equation to model a linear particle?

Suppose I have a particle with mass $m$ situated on a frictionless line which we can model using $\mathbb{R}$. Suppose that we supply/push the particle $m$ with a force $f(t)$. Let the position of ...
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Did R. Buckminster Fuller reference a corollary of a mathematical theorem in his book _Critical Path_?

From Critical Path (1981) , Part 2, Chapter 6 "The World Game" , Richard Buckminster Fuller & Kiyoshi Kuromiya make the Claim : It has been found that within a 100 mile radius a wind is ...
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How can I get the inverse of the transfer function $\Phi$? a question from Page 56 of Lemma 4.5 in the book "ESSENTIALS OF ROBUST CONTROL" [closed]

Let $\Phi(s) = = \gamma^2 I + B^*\left( (sI-A)(C^*C)^{-1}(sI+A^*) \right)^{-1}B + B^*(sI+A^*)^{-1}C^*D - D^*C(sI-A)^{-1}B - D^*D.$ How to compute the inverse of $\Phi$, in Page 56 of Zhou's book "...
MatrixWong's user avatar
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Flow Rate based on Pipe Combination without considering Hydraulic Effects

I would really appreciate help on the following: Let us assume that we have n pumps pumping water through n pipes. The pumps are running at a constant power. It doesn't change. The flow rates in the ...
user22644's user avatar
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Logistic growth decreasing

In a city, the initial population is $$P(0)=70281$$ and 10 years after, $$P(10)=66277$$ I have to find $P(t)$ using the logistic model with max value equal to 80000, which gives the following equation ...
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Reparametrization of rational Bézier curve

I am trying to solve the following task Using rational Bézier curve find the control points and weights of one sixth of a circle $c_1$, such that $$c_1(0)=\{3,0\},c_1(1)=\{\frac{3}{2},\frac{3\sqrt{3}}{...
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Is it possible to integrate real numbers into my custom vocabulary within the framework of model theory?

So, I want to use model theory to approach an applied task. Developing the corresponding vocabulary, I realized I needed real numbers within my formulas and, thus, real numbers within the language. I ...
Seeker's user avatar
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Degrees of Freedom in PCA

Suppose we are doing PCA over a historic time series of temperatures. The feature for the PCA to be explained is the time when the temperature was observed every hour. Let’s say for the sake of ...
Identicon's user avatar
2 votes
1 answer
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Pseudo if statements in LP programming

When designing LPs for exams I often run across problems where I would like to input an "if-statement". For example: $5\leq x_b$ if $p_a\geq 10$ I've tried dividing by itself and using floor ...
Aron Fredriksson's user avatar
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1 answer
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How do I describe a Quarter Car Suspension with differential equations?

So I've been struggling with describing this Quarter Car Suspension with a differential equation: The main point of difficulty for me is the fact that there are two x variables (x1 and x2) and I'm ...
Dimitris02's user avatar
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1 answer
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Examples of PDEs that found application after discovery

I am a 2nd year mathematics undergraduate in the UK and recently took an introductory elective in partial differential equations. The focus was on solving some classical examples, all arising from an ...
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Optimization Models and the chicken-and-egg problem

I have started working with optimization models to minimize the total generation costs of electricity in a system. The basic idea in this model is to minimize the overall system cost given a certain ...
Eve Chanatasig's user avatar
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Finding the optimal policy of an MDP just solving the primal problem associated

I need to find a method that allows me to determine the optimal policy of a finite-horizon Markov Decision Process with a discount factor without solving the dual problem of the linear programming ...
chitranjan_iyengar_01's user avatar
1 vote
2 answers
128 views

Finding the area by Green's Theorem

If I have $\ x=\sin^3t$ and $\ y = \cos^3t$ I'm using Green's theorem to calculate the area enclosed by the curve via integration, but at the end I'm getting negative area $-3\pi/8$, which is wrong. ...
Mohaboko's user avatar
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Advice on explaining this system observation analytically

I am playing around with an disturbance observer to estimate disturbance in a nonlinear system. (I had to screen snip the equations because the equation editor doesn't seem to work for me) System ...
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2 votes
1 answer
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How to force my differential equations give a bounded solution?

I have modeled the interaction of two physical quantities, $S$ and $B$, by the following differential equations (the second one is a delay differential equation): $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(...
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Penalty function $f(a, b)$ for $a, b \in \mathbb{R}^+$ which adds a high positive penalty only when both $a, b$ are very small

I'm doing Bayesian recruitment curve fitting where my curve has two parameters $a$ and $b$. Both $a, b \in \mathbb{R}^+$. I have put a Truncated Normal prior on $a$ and a Half Normal prior on $b$. I'm ...
chesslad's user avatar
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Two CSTR in series (glucose to acetate)

Problem Hello, I am studying modeling and control course and I'm struggling with drawing neat figure describing the reactor system and to write the differential equations in detail describing the ...
태주강's user avatar
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Programming C# Navier Stokes Modeling

I just started C# programming Navier Stokes model for 3D visualized compressible fluid liquid/gas properties management of gasket-plate heat exchanger models of my company. In reality, I can't even ...
11thG's user avatar
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1 vote
1 answer
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Determining the average rate of change of a product's price over time

I'm currently studying a model that describes the cost of 1 kg of a product $p$ in dollars over time, given by the equation $$\frac{d^3p}{dt^3} + a\frac{dp}{dt} = b,$$ where $a = 9[year^{ - 2}], b = ...
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