the first mathematical model
play

The first mathematical model Modelling a rainbowfish population - PowerPoint PPT Presentation

Aug 25, 2022 •1.35k likes •1.72k views

The first mathematical model Modelling a rainbowfish population Dennis den Ouden-van der Horst Rainbowfish Predict the number of rainbowfish in our aquarium over time. Rainbowfish Predict the number of rainbowfish in our aquarium over time. :

  1. The first mathematical model Modelling a rainbowfish population Dennis den Ouden-van der Horst

  2. Rainbowfish Predict the number of rainbowfish in our aquarium over time.

  3. Rainbowfish Predict the number of rainbowfish in our aquarium over time. : time in days : Number of rainbowfish

  4. Rainbowfish Predict the number of rainbowfish in our aquarium over time. : time in days : Number of rainbowfish Initially : fish

  5. Rainbowfish Predict the number of rainbowfish in our aquarium over time. : time in days : Number of rainbowfish Initially : fish Birth rate : per day

  6. Rainbowfish Predict the number of rainbowfish in our aquarium over time. : time in days : Number of rainbowfish Initially : fish Birth rate : per day Death rate : per day

  7. The balance equation

  8. The balance equation : small time interval

  9. The balance equation : small time interval Change in during :

  10. The balance equation : small time interval Change in during :

  11. The balance equation : small time interval Change in during :

  12. The balance equation : small time interval Change in during :

  13. The balance equation : small time interval Change in during :

  14. The balance equation : small time interval Change in during :

  15. The balance equation : small time interval Change in during :

  16. The balance equation : small time interval Change in during :

  17. The balance equation : small time interval Change in during :

  18. The balance equation : small time interval Change in during :

  19. The balance equation : small time interval Change in during :

  20. The balance equation : small time interval Change in during :

  21. The balance equation : small time interval Change in during :

  22. The balance equation : small time interval Change in during :

  23. The differential equation A differential equation is an equation containing a derivative. Balance equation :

  24. The differential equation A differential equation is an equation containing a derivative. A derivative: Balance equation :

  25. The differential equation A differential equation is an equation containing a derivative. A derivative: Derivative of : Balance equation :

  26. The differential equation A differential equation is an equation containing a derivative. A derivative: Derivative of : Balance equation :

  27. The differential equation A differential equation is an equation containing a derivative. A derivative: Derivative of : Balance equation :

  28. The differential equation A differential equation is an equation containing a derivative. A derivative: Derivative of : Balance equation :

  29. The differential equation

  30. The differential equation

  31. The differential equation

  32. The differential equation

  33. The differential equation

  34. The differential equation

  35. Thank you for your attention!

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Mathematical Set Notation 8 February 2019 OSU CSE 1 Set Theory A mathematical model that

Mathematical Set Notation 8 February 2019 OSU CSE 1 Set Theory A mathematical model that

Mathematical Set Notation 8 February 2019 OSU CSE 1 Set Theory A mathematical model that we will use often is that of mathematical sets A (finite) set can be thought of as a collection of zero or more elements of any other mathematical

295 views • 25 slides
Mathematical analysis of three species model and introduction of the canonical model. Isao

Mathematical analysis of three species model and introduction of the canonical model. Isao

Mathematical analysis of three species model and introduction of the canonical model. Isao Kawaguchi NIRS, Japan Suggestions from Tatiana a) could you transform your experimental model into a generic model with competing preys and a

332 views • 20 slides
Mathematical String Notation 7 January 2019 OSU CSE 1 String Theory A mathematical model

Mathematical String Notation 7 January 2019 OSU CSE 1 String Theory A mathematical model

Mathematical String Notation 7 January 2019 OSU CSE 1 String Theory A mathematical model that we will use often is that of mathematical strings A string can be thought of as a series of zero of more entries of any other mathematical

401 views • 23 slides
A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation

A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation

Biological Preliminaries The Mathematical Model Discussion A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies Georgi Kapitanov Vanderbilt University Feb 17, 2012

337 views • 23 slides
First Order Circuits II: mathematical tools we use are a model intended to describe the observed

First Order Circuits II: mathematical tools we use are a model intended to describe the observed

3/4/20 Contemplating Mathematical Models One thing that we must remember is that all the First Order Circuits II: mathematical tools we use are a model intended to describe the observed characteristics of the real Step Response to world.

199 views • 9 slides
Construction of a Mathematical Model of a Cell as a Challenge for Science in the 21 Century and

Construction of a Mathematical Model of a Cell as a Challenge for Science in the 21 Century and

Enabling Grids for E-sciencE Construction of a Mathematical Model of a Cell as a Challenge for Science in the 21 Century and EGEE Project Victor Lakhno Institute of Mathematical Problems of Biology RAS EGEE User Forum CERN, 01-03.03.2006

440 views • 12 slides
Temporal Logic and Model Checking Model mathematical structure extracted from hardware or

Temporal Logic and Model Checking Model mathematical structure extracted from hardware or

Temporal Logic and Model Checking Model mathematical structure extracted from hardware or software Temporal logic provides a language for specifying functional properties Model checking checks whether a given property holds

1.56k views • 131 slides
Mathematical Strategies for Filtering Turbulent Systems: Sparse Observations, Model Errors, and

Mathematical Strategies for Filtering Turbulent Systems: Sparse Observations, Model Errors, and

Mathematical Strategies for Filtering Turbulent Systems: Sparse Observations, Model Errors, and Stochastic Parameter Estimation John Harlim Courant Institute of Mathematical Sciences, New York University July 1, 2009 What is filtering? 1.

1.2k views • 58 slides
Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model

Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model

Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model Checking and Systems Verification January - April 2015 1 / 25 What are we interested in? 2 / 25 What are we interested in? Software Controllers Code

1.05k views • 40 slides
Mathematical Logics 15. Elements of Model theory Luciano Serafini Fondazione Bruno Kessler,

Mathematical Logics 15. Elements of Model theory Luciano Serafini Fondazione Bruno Kessler,

Mathematical Logics 15. Elements of Model theory Luciano Serafini Fondazione Bruno Kessler, Trento, Italy November 19, 2014 Luciano Serafini Mathematical Logics What is model theory? First-order model theory. . . , . . . also known as

736 views • 73 slides
PERSPECTIVES IN MODEL THEORY OF FUZZY LOGIC PILAR DELLUNDE PRAGUE, THE FUTURE OF MATHEMATICAL

PERSPECTIVES IN MODEL THEORY OF FUZZY LOGIC PILAR DELLUNDE PRAGUE, THE FUTURE OF MATHEMATICAL

PERSPECTIVES IN MODEL THEORY OF FUZZY LOGIC PILAR DELLUNDE PRAGUE, THE FUTURE OF MATHEMATICAL FUZZY LOGIC, 16-18 JUNE 2016 LESSONS LEARNT FROM THE RECENT HISTORY OF CLASSICAL MODEL THEORY. 7 PROPOSALS IN MODEL THEORY OF MFL. WHAT IS MODEL

816 views • 32 slides
Mathematical modeling from ion channel to ECG h l t ECG an Introduction Mark Potse model

Mathematical modeling from ion channel to ECG h l t ECG an Introduction Mark Potse model

Mathematical modeling from ion channel to ECG h l t ECG an Introduction Mark Potse model Why a model? reality y A model is a theoretical construct that allows to translate theory into predictions allows to translate theory into

860 views • 37 slides
5G Positioning for connected cars (mmW) 5G introduction Mathematical model of 5G-mmW

5G Positioning for connected cars (mmW) 5G introduction Mathematical model of 5G-mmW

5G Positioning for connected cars (mmW) 5G introduction Mathematical model of 5G-mmW positioning Mutiple aspects of the achievable error Estimation principle Summer school on 5G V2X communications June 2018 Giuseppe Destino, CTR,

612 views • 28 slides
Lecture 3: Model-checker NuSMV B. Srivathsan Chennai Mathematical Institute NPTEL-course July -

Lecture 3: Model-checker NuSMV B. Srivathsan Chennai Mathematical Institute NPTEL-course July -

Lecture 3: Model-checker NuSMV B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 31 Model-checker Specify the model of the system Specify the requirements Model-checker will automatically check if system

1.72k views • 112 slides
Mathematical Models Pre-K through Grade 5 1. Array and Area Model (Grades 1-5) An array or area

Mathematical Models Pre-K through Grade 5 1. Array and Area Model (Grades 1-5) An array or area

Mathematical Models Pre-K through Grade 5 1. Array and Area Model (Grades 1-5) An array or area model is an arrangement of a set of objects organized into equal groups in rows and columns. Arrays or area models help make counting easy in the

283 views • 11 slides
Mathematical Analysis of Epidemiological Models II Jan Medlock Clemson University Department of

Mathematical Analysis of Epidemiological Models II Jan Medlock Clemson University Department of

Endemic Model Vaccination Tomorrow Mathematical Analysis of Epidemiological Models II Jan Medlock Clemson University Department of Mathematical Sciences 22 July 2009 Endemic Model Vaccination Tomorrow Endemic Model d t = N I (

325 views • 13 slides
Managing Audit Risks For the year ended 30 June, 2018 Presented by Belinda Aisbett CA. BAcc. SSA

Managing Audit Risks For the year ended 30 June, 2018 Presented by Belinda Aisbett CA. BAcc. SSA

Managing Audit Risks For the year ended 30 June, 2018 Presented by Belinda Aisbett CA. BAcc. SSA SSAud Director Super Sphere Pty. Ltd. Slide No: 1 Introduction o Asset valuation risks o Cost base relief hangover risks o

185 views • 17 slides
Efficiency/Effectiveness Trade-offs in Learning to Rank Tutorial @ ECML PKDD 2018

Efficiency/Effectiveness Trade-offs in Learning to Rank Tutorial @ ECML PKDD 2018

Efficiency/Effectiveness Trade-offs in Learning to Rank Tutorial @ ECML PKDD 2018 http://learningtorank.isti.cnr.it/ Claudio Lucchese Franco Maria Nardini Ca Foscari University of Venice HPC Lab, ISTI-CNR Venice, Italy Pisa, Italy l a

936 views • 39 slides
Image sharpening exercise Running a simple parallel program 1 Reusing this material This work

Image sharpening exercise Running a simple parallel program 1 Reusing this material This work

Image sharpening exercise Running a simple parallel program 1 Reusing this material This work is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License.

378 views • 16 slides
2.13 Point Kinematics Having introduced in the previous Sections the different representations of

2.13 Point Kinematics Having introduced in the previous Sections the different representations of

71 Basilio Bona - Dynamic Modelling If we use the quaternions, the Euler parameters, the Cayley-Klein parameters or the Rodrigues vectors, it in unclear what are the parameters that take the place of the i in (2.65). Using these alternative

222 views • 11 slides
10-601B Recitation 2 Calvin McCarter September 10, 2015 1 Least squares problem In this

10-601B Recitation 2 Calvin McCarter September 10, 2015 1 Least squares problem In this

10-601B Recitation 2 Calvin McCarter September 10, 2015 1 Least squares problem In this problem we illustrate how gradients can be used to solve the least squares problem. Suppose we have input data matrix X R n p , output data y R

95 views • 5 slides
Class = functions + data (variables) in one unit INF1100 Lectures, Chapter 7: A class packs

Class = functions + data (variables) in one unit INF1100 Lectures, Chapter 7: A class packs

Class = functions + data (variables) in one unit INF1100 Lectures, Chapter 7: A class packs together data (a collection of variables) and functions as one single unit Introduction to Classes As a programmer you can create a new class and thereby

287 views • 11 slides
AM 205: lecture 19 Last time: Conditions for optimality, Newtons method for optimization

AM 205: lecture 19 Last time: Conditions for optimality, Newtons method for optimization

AM 205: lecture 19 Last time: Conditions for optimality, Newtons method for optimization Today: survey of optimization methods Newtons Method: Robustness Newtons method generally converges much faster than steepest descent

307 views • 10 slides
Direct multisearch for multiobjective optimization A. Ismael F. Vaz University of Minho -

Direct multisearch for multiobjective optimization A. Ismael F. Vaz University of Minho -

Direct multisearch for multiobjective optimization A. Ismael F. Vaz University of Minho - Portugal aivaz@dps.uminho.pt Joint work with A. L. Custdio, J. F. A. Madeira, and L. N. Vicente Southampton October 21, 2010 A.I.F. Vaz (UMinho) DMS

1.75k views • 147 slides

More recommend