The Azimuth Project
Blog articles in progress

There are usually several blog articles in various states of progress that need feedback and are being actively discussed in the forum before being posted to the blog. You can find them here. For an index of all blog articles that have been published, see Azimuth blog overview.

If you want to write a blog article on this wiki, go ahead! But there are some stylistic and formatting issues you need to think about. So, please start by reading How to blog.


Ville Bergholm

Noether’s theorem: quantum vs stochastic

Jacob Biamonte

Searching for the (im)perfect quantum diamond

Stochastic epidemic-type-1D-models

Quantum frontiers in network science

Lorenz Borsche

On peak oil

Frederik De Roo

Doubling CO2… then what?

  • Main author: Frederik De Roo

  • Wiki page: Blog - doubling CO2... then what??

  • Forum discussion group: Blog - doubling CO2… then what

  • Status: work in progress.

  • Summary: explains the logarithmic response of surface temperature to the rise in carbon dioxide

Background profiles in the atmosphere

  • Main author: Frederik De Roo

  • Status: planned, but doesn’t exist yet.

  • Summary: some background material necessary for the log forcing, but independent so better separately.

Curtis Faith

Curtis Faith on the Azimuth Project

Making decisions under uncertainty

Summary: Groups often want to make the right decisions. So they spend a lot of time in the decision process itself. A better approach is to acknowledge when perfect decisions don’t exist and to incorporate the uncertainty itself into your plans.

Brendan Fong

Cospans, wiring diagrams, and the behavioural approach

Categories in Control (Part 2)

Categories in Control (Part 3)

Categories in Control (Part 4)

Jan Galkowski

Warming slowdown? (part 1)

  • Main author: Jan Galkowski

  • Wiki page: Blog - warming slowdown? (part 1)

  • Status: published.

  • Summary: Is there something missing in the recent climate temperature record? Variability in the Earth climate observational record makes definitive determinations of warming difficult to establish, at least as determined by changes in mean global surface temperature. This recapitulates some of the history of the problem and its present status, focusing upon oceanic capture of heat, and addressing some of the technical discussion in the literature interpreting present trends. The problem is assessed from the perspective of the statistics of time series.

Manoj Gopalkrishnan

Lyapunov functions for complex-balanced systems

Marc Harper

Relative entropy minimization in evolutionary dynamics

Stationary stability in finite populations

Alastair Jamieson-Lane

Markov models of social change (part 1)

Tomi Johnson

Quantum network theory (part 1)

Quantum network theory (part 2)

Eugene Lerman

Networks of dynamical systems

Staffan Liljegren

Carbon cycle box models (part 1)

Carbon cycle box models (part 2)

Piotr Migdał

Quantum superposition

Vanessa Schweizer

Markov models of social change (part 2)

Matteo Smerlak

The mathematical origin of irreversibility

Statistical laws of Darwinian evolution

Cameron Smith

Hierarchical organization and biological evolution (part 1)

Hierarchical organization and biological evolution (part 2)

Hierarchical organization and biological evolution (part 3)

David Spivak

A networked world

Blake Stacey

Invasion fitness in moment-closure treatments

  • Main author: Blake Stacey

  • Wiki pages: introduction, logistic growth, epidemic in an adaptive network, evolution of altruism.

  • Forum discussion group: Invasion fitness in moment-closure treatments

  • Status: work in progress.

  • Summary: Moment closures are a way of forgetting information about a system in a controlled fashion, in the hope that an incomplete, fairly heavily “coarse-grained” picture of the system will still be useful in figuring out what will happen to it. Sometimes, this is a justifiable hope, but in other cases, we are right to wonder whether all the algebra it generates actually leads us to any insights. Here, we’ll be concerned with a particular application of this technology: studying the vulnerability of an ecosystem to invasion. We shall find expressions for invasion fitness, the expected relative growth rate of an initially-rare species or variety.

David Tanzer

Petri net programming (part 1) – Basic Petri nets, with simulator code

Petri net programming (part 2) – Introduction to stochastic Petri nets

  • Main author: David Tanzer

  • Wiki page: Blog - Petri net programming (part 2)

  • Forum discussion group: Blog - Petri net programming (part 2)

  • Status: published.

  • Summary: Introduces the concept of stochastic Petri nets. Starts with a general discussion of reaction network dynamics, followed by an exposition of the mass action kinetics (and its limitations). This is followed by an exploration of the continuous deterministic limit of the stochastic model. Finally, I calculate equilibrium solutions for simple reaction networks.

Petri net programming (part 3) – The rate equation

Petri net programming (part 4) – Limits of the deterministic model

Petri net programming (part 5) – Markovian dynamics

Petri net programming (part 6) – Stochastic simulation algorithms

David Tweed

Science, models and machine learning

Linear maps that fill pigeon-holes

Worried about the environment? You’re seeing things!

Tim van Beek

Your model is verified, but not valid! Huh?

Putting the Earth in a box

A quantum of warmth

  • Main author: Tim van Beek

  • Wiki page: Blog - a quantum of warmth

  • Status: published.

  • Forum discussion group: Blog - a quantum of warmth

  • Summary: A closer look at the heat balance of the Earth and its atmosphere. An explanation of downward longwave radiation (DLR), generated by the atmosphere of the earth and why it does not violate the second law of thermodynamics.

Eddy who?

Category theory, databases, and rhizomes.

  • Main authors: William Zeng and Brendan Fong

  • Wiki page: Blog - Category theory, databases, and rhizomes?

  • Status: outline

  • Summary: Category theory helps us understand the structure of information. We will introduce some recent work on applications of category theory to databases and discuss some implications of this work. There may even be some real world demos, and there will certainly be many examples.

Fluid flows and infinite dimensional manifolds (part 1)

Fluid flows and infinite dimensional manifolds (part 2)

Fluid flows and infinite dimensional manifolds (part 3)

Fluid flows and infinite dimensional manifolds (part 4)

Fluid flows and infinite dimensional manifolds (part 5)

Good vibrations

  • Main author: Tim van Beek

  • Wiki page: Blog - good vibrations

  • Forum discussion group: Blog - good vibrations

  • Status: stub.

  • Summary: Recapitulation of previous blog posts and short tour to molecular quantum mechanics necessary to understand that radiation equations of the atmosphere of the earth.

The color of night

  • Main author: Tim van Beek

  • Wiki page: Blog - the color of night

  • Forum discussion group: Blog - The color of night

  • Status: partially done.

  • Summary: How big is the effect of downward longwave radiation (DLR) really? What do measurements say? What instruments are used? Are there alternative explanations of the 33 Kelvin gap of the zero dimensional energy balance model?

Increasing the signal-to-noise ratio with more noise

Ken Webb

Connections: Petri nets, systems biology, and beyond

  • Main author: Ken Webb

  • Wiki page: Blog - connections: Petri nets and beyond (part 1)

  • Wiki page (series outline): Connections: Petri nets, systems biology, and beyond

  • Forum discussion group: Connections: Petri nets, systems biology, and beyond

  • Status: work in progress.

  • Summary: A brief but systematic exploration of various types of networks, and how they’re really all the same. Starting with a simple reaction network and corresponding Petri net, I demonstrate how to transform these into systems biology networks, systems of differential equations, Unified Modeling Language (UML) diagrams, mind maps, agent based models, and more. Along the way I introduce third-party tools that are able to process each of the resulting formats. This first part restricts itself to the transformation to differential equations.

El Niño project

El Niño project (part 1)

El Niño project (part 2)

El Niño project (part 3)

El Niño project (part 4)

El Niño project (part 5)

El Niño project (part 6)

El Niño project (part 7)

El Niño project (part 8)

El Niño project (part 9)

Exploring climate data

Exploring climate data (part 1)

Exploring climate data (part 2)

Exploring climate data (part 3)

This Week’s Finds

Week 309

Week 314

Week 317

Week 318

Interview with Didier Paillard


Azimuth Project news

Stabilization wedges (part 5)

Mathematics of the Environment (part 3)

Network theory

Network theory (part 1)

Network theory (part 2)

Network theory (part 3)

Network theory (part 4)

Network theory (part 5)

Network theory (part 6)

Network theory (part 7)

Network theory (part 8)

Network theory (part 9)

Network theory (part 10)

Network theory (part 11)

Network theory (part 12)

Network theory (part 13)

Network theory (part 14)

Network theory (part 15)

Network theory (part 16)

Network theory (part 17)

Network theory (part 18)

Network theory (part 19)

Network theory (part 20)

Network theory (part 21)

Network theory (part 22)

Network theory (part 23)

Network theory (part 24)

Network theory (posts not in the main series)

Network theory (Biamonte guest posts)

Network theory (Fong guest posts)

Petri net software

  • Main author: John Baez

  • Wiki page: Blog - Petri net software

  • Forum discussion group:

  • Status: draft

  • Summary: an overview of software for simulating Petri nets, especially the rate equation and master equation for stochastic Petri nets, based on material collected by Jim Stuttard at Petri net.

Contributions to external blogs

Prospects for a green mathematics

category: blog, meta