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Quantitative Formal Modeling and Worst-Case Performance Analysis

Approx. 17 hours to complete

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Course Summary

This course is an introduction to the mathematical modeling of biological phenomena. It covers topics such as differential equations, probability theory, and graph theory.

Key Learning Points

Learn to create mathematical models to describe biological phenomena
Understand the importance of probability theory in modeling
Apply graph theory to model complex systems

Job Positions & Salaries of people who have taken this course might have

- USA: $72,000 - $137,000
- India: ₹400,000 - ₹1,600,000
- Spain: €21,000 - €44,000
- USA: $72,000 - $137,000
- India: ₹400,000 - ₹1,600,000
- Spain: €21,000 - €44,000
- USA: $60,000 - $120,000
- India: ₹300,000 - ₹1,500,000
- Spain: €17,000 - €35,000
- USA: $72,000 - $137,000
- India: ₹400,000 - ₹1,600,000
- Spain: €21,000 - €44,000
- USA: $60,000 - $120,000
- India: ₹300,000 - ₹1,500,000
- Spain: €17,000 - €35,000
- USA: $85,000 - $170,000
- India: ₹500,000 - ₹2,000,000
- Spain: €25,000 - €50,000

Learning Outcomes

Create mathematical models to describe biological phenomena
Apply probability theory to model biological systems
Use graph theory to model complex biological systems

Prerequisites or good to have knowledge before taking this course

Basic knowledge of calculus and linear algebra
Familiarity with programming in Python

Course Difficulty Level

Intermediate

Course Format

Online
Self-paced
Video lectures
Assignments
Quizzes

Similar Courses

Systems Biology and Biotechnology
Biostatistics in Public Health

Related Education Paths

Notable People in This Field

Uri Alon
Albert-László Barabási

Related Books

Description

Welcome to Quantitative Formal Modeling and Worst-Case Performance Analysis. In this course, you will learn about modeling and solving performance problems in a fashion popular in theoretical computer science, and generally train your abstract thinking skills.

After finishing this course, you have learned to think about the behavior of systems in terms of token production and consumption, and you are able to formalize this thinking mathematically in terms of prefix orders and counting functions. You have learned about Petri-nets, about timing, and about scheduling of token consumption/production systems, and for the special class of Petri-nets known as single-rate dataflow graphs, you will know how to perform a worst-case analysis of basic performance metrics, like throughput, latency and buffering. Disclaimer: As you will notice, there is an abundance of small examples in this course, but at first sight there are not many industrial size systems being discussed. The reason for this is two-fold. Firstly, it is not my intention to teach you performance analysis skills up to the level of what you will need in industry. Rather, I would like to teach you to think about modeling and performance analysis in general and abstract terms, because that is what you will need to do whenever you encounter any performance analysis problem in the future. After all, abstract thinking is the most revered skill required for any academic-level job in any engineering discipline, and if you are able to phrase your problems mathematically, it will become easier for you to spot mistakes, to communicate your ideas with others, and you have already made a big step towards actually solving the problem. Secondly, although dataflow techniques are applicable and being used in industry, the subclass of single-rate dataflow is too restrictive to be of practical use in large modeling examples. The analysis principles of other dataflow techniques, however, are all based on single-rate dataflow. So this course is a good primer for any more advanced course on the topic. This course is part of the university course on Quantitative Evaluation of Embedded Systems (QEES) as given in the Embedded Systems master curriculum of the EIT-Digital university, and of the Dutch 3TU consortium consisting of TU/e (Eindhoven), TUD (Delft) and UT (Twente). The course material is exactly the same as the first three weeks of QEES, but the examination of QEES is at a slightly higher level of difficulty, which cannot (yet) be obtained in an online course.

Outline

Introduction
Introduction
Some suggested reading material

Modeling systems as token consumption/production systems
A single picture tells more than a thousand words
Consumption and production of tokens
Modeling an intensive care unit
Modeling a wireless LAN radio
Modeling and refining an industrial robot
Pick your own system
Classes of Petri-nets
Causality, choice and concurrency (modeling patterns)
Refinement of consumption/production systems
Interpreting pictures for performance analysis
Draw your own model
Always ask yourself...
The refinement of the robot.
Tooling
Basic modeling ideas
Modeling Warehouse 13
Modeling features
Definition of refinement
Which is a refinement of which?

Syntax and semantics
Warning: prepare for some set theory!
Syntax and semantics
The basics
Extensions
Prefix orders
Exercise on prefix orders
Proof that flows form a prefix order
Formalizing interpretations as functions
Counting is order preserving
Formalizing the Petri-net interpretation
Proof that the number of tokens in a single-rate dataflow cycle is constant
Formalizing timing
Formalizing eager scheduling
Formalizing periodic scheduling
Flags and Fitch style proofs
Slides of the proof
Slides of the proof
Exercise: Formalize best-case response times
About the next quiz.
Bipartite graphs
Thinking about observation functions
Isomorphism
Summarize!
Formalizing performance properties

Performance analysis
Running example
Throughput is bounded by 1/MCM
Proof - a
Proof - b
Proof - c
Proof - d
Proof - e
Proof - f
Proof - g
Proof - h
Proof - i
Proof - j
The throughput bound is tight
Periodic scheduling of a dataflow graph
Latency analysis of a periodic schedule
Latency analysis of an eager schedule
The formal definition of latency
The boot-up time of a dataflow graph
Optimizing latency estimates w.r.t. boot-up time
Buffering and backpressure
Slides of the proof
Alternative proof in synchronization and linearity
Summarize!
Calculating the MCM and worst-case throughput
Calculate some periodic schedules
Calculating optimal periodic schedules and their latencies
Calculating suitable buffer sizes

One final example
One final example
2015 Assignment on dataflow modeling.
Additional dataflow exercises
Example of an exam at masters level (without solutions)
Another example of an exam (with solutions)
Material created by fellow students

Summary of User Reviews

Discover the art of quantitative formal modeling with this course. Students rave about the quality of the content and the engaging teaching style. One key aspect is the course's ability to teach complex concepts in a simple way.

Pros from User Reviews

High-quality content
Engaging teaching style
Simple explanations for complex concepts
Interactive exercises
Practical applications

Cons from User Reviews

Lengthy lectures
Requires prior knowledge of calculus
Limited peer interaction
Not suitable for beginners
Requires a significant amount of time commitment

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Quantitative Formal Modeling and Worst-Case Performance Analysis

Welcome to Quantitative Formal Modeling and Worst-Case Performance Analysis. The reason for this is two-fold. The analysis principles of other dataflow techniques, however, are all based on single-rate dataflow....

Save Course