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WormMathBook

This book aims to focus on the most important mathematical concepts and models of the OpenWorm project. The entire book is online and built using the Jupyter-book project.

  • Each part is dedicated to a major project
    • Each section of the chapter is a standalone Jupyter Notebook
      • Describing a concept, related videos/simulations/animations, examples, codes, and excercises
  • At the end of each section we have some mathematical problems to be solved
    • Concepts, questions and solutions first being proposed on the Discussions page
      • If approved, will be added to the book
  • Queries for each code come from the owmeta project
    • Using the rdf relations we try to connect a question to the related ontology in our knowledge-base
    • We try to have a parametric look into the code segments and questions
  • SymPy is being used to work with math and python
  • Related simulations are finally represtented through our simulation projects

Structure and Scenario

“Je me sers d'animaux pour instruire les hommes” - La Fontaine

The book is following a cycle of the C. ELegans' life. Each day some new capabilities are added and the worm becomes more complex. The questions regarding the new complexity, related math problems and solutions are discussed. Finally, an existing or a proposed model/simulation could be added in order to better demonstrate the process.

Part 1: Creation

  • Day 1 - Environment: The El's world is created and the El's egg is put into it
  • Day 2 - Gene Regulation: The cell's clock starts to work and gene regulations begin to happen
  • Day 3 - Cell Proliferation: The cell proliferates and different cells start functioning based on their fates
  • Day 4 - Worm Body: The El’s body comes to existence and interacts with the environment

Part 2: Networking

  • Day 5 - Circuit: A first circuit of cells start to interact
  • Day 6 - Neural Network: A neural network appears in the head and starts to interact with the body
  • Day 7 - Sleep and Noise: Behold; one shall not work on weekends. El stops working on this day, takes a nap, and tries to understand where all the noises and leaky currents come from
  • Day 8 - Neuromusclular System: El now has a full functioning network of neural and muscle cells

Part 3: Locomotion

  • Day 9 - Shake: The first command for a sinusoidal movement comes from El’s head
  • Day 10 - Swim: El tries to swim in the liquid environment
  • Day 11 - Crawl: El moves around and finds the beach, so, El tries to crawl on the soil
  • Day 12 - Hungriness: El goes back to the liquid world, moves and moves until feels tiredness and hungriness

Part 4: In Joy

  • Day 13 - Feeding: El senses a food source, goes toward the source and starts eating
  • Day 14 - Defecation: Behold; one shall not work on weekends. El tries to understand how to use the toilet instead.
  • Day 15 - Evolution: El feels loneliness, moves around, finds a club full of different types of nematodes and makes friends
  • Day 16 - Mating and Reproduction: El finds a mate, and falls in love, El’s wife starts lying eggs

Part 5: In Danger

  • Day 17 - Mechano-Sensation: El feels someone is touching El saying what are you doing here. El feels threatened starts to run as fast as possible
  • Day 18 - Toxicity: El finds out El is close to a toxic environment, so, tries to scape from there
  • Day 19 - Temperature: El feels a hot environment and tries to avoid entering the place
  • Day 20 - Dauer State: El feels hungry and can not find a food, so, decides to enter a dauer state in the hope of waking up in a food-rich plate

Part 6: Learning

  • Day 21 - Memory: Behold; one shall not work on weekends. El decides to continue sleeping. El’s head tries to make a map of where El has gone and what El has done
  • Day 22 - Recall: El wakes up and tries to remember where should El go now
  • Day 23 - Decision Making: El tries to make a decision to go toward the food source or the mate
  • Day 24 - Irrationality: El goes toward the food source, however, in the middle of the way some temptation says go find your mate. El changes the direction, uses up all the energy and becomes a dead El

Part 7: Aging

  • Day 25 - Resuscitation: The OpenWorm rescue team finds that El is dead. Revives El and looks for possible reasons.
  • Day 26 - Gene Therapy: The OpenWorm rescue team finds the genetic problem caused the irrational decision and treats the disease
  • Day 27 - Rehabilitation: El now suffers from the heart arrythmia and movement disability. The OpenWorm rescue team tries to rehabilitate El using drugs, artificial pacemaking, and rehabilitation techniques
  • Day 28 - Aging and Death: Behold; one shall not work on weekends. El suffers from different aging symptoms, goes to sleep. This time never awakes (maybe until the next cycle in a new world).

Worm Math Problems and Solutions

Every scenario in the book can contain different questions. Every question then comes with some math problems and solutions. Each question is going to be asked and discussed in the Discussions page. Selected questions become issues, and when the related math problem(s) are solved a pull request for an update to the book takes place.

Contribution

Every two contributors choose a math concept, read 2 * ~12 pages of related references and write a 2 * ~180 words abstract in a day. Then try to issue and solve at least one related problem.