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.
Main author: Ville Bergholm
Forum discussion page: Blog - Noether’s theorem: quantum vs stochastic
Status: published.
Summary: a discussion of how Noether’s theorem for Markov processes becomes stronger when the generator is a Dirichlet operator.
Main author: Jacob Biamonte
Wiki page: Blog - Searching for the (im)perfect quantum diamond
Forum discussion page: Blog - stochastic epidemic-type-1D-models
Status: working on it
Summary: fun article introducing some quantum technology.
Main author: Jacob Biamonte
Wiki page: Blog - stochastic epidemic-type-1D-models
Forum discussion page: Blog - stochastic epidemic-type-1D-models
Status: working on it
Summary: article about 1D epidemic models: later to be transformed into book chapter.
Main author: Jacob Biamonte
Wiki page: Blog - quantum frontiers in network science
Forum discussion page: Blog - quantum frontiers in network science
Status: published
Summary: announcement of the workshop on quantum networks at NetSci.
Main author: Lorenz Borsche
Wiki page: Blog - on peak oil
Forum discussion page:
Status: draft.
Summary: An introduction to the topic of peak oil.
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
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.
Main author: Curtis Faith
Wiki page: Blog - Curtis Faith on the Azimuth Project
Forum discussion group: Blog - Curtis Faith on the Azimuth Project
Status: published.
Summary: Curtis Faith introduces himself and talks about why he decided to help out on the Azimuth Project.
Main author: Curtis Faith
Wiki page: Blog - making decisions under uncertainty
Status: published.
Forum discussion group: Blog - 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.
Main authors: Brendan Fong and John Baez
Wiki page: Blog - cospans, wiring diagrams, and the behavioural approach
Status: draft.
Summary: We discuss some connections between the decorated cospan and operad of wiring diagram approaches to formalising composition of networks.
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.
Main author: Manoj Gopalkrishnan
Wiki page: Blog - Lyapunov functions for complex-balanced systems
Forum discussion group: Blog - Lyapunov functions for complex-balanced systems
Status: published
Summary: for a large class of chemical reaction networks, namely those with a complex balanced equilibrium, we can define a function called ‘free energy’ and prove it always decreases with the passage of time.
Main author: Marc Harper
Forum discussion group: Relative entropy minimization in evolutionary dynamics
Status: in progress
Summary: recent progress on how different kinds of relative entropy tend to decrease as evolution proceeds.
Main author: Marc Harper
Wiki page: Blog - stationary stability in finite populations
Status: in progress
Summary: The application of entropy minimization to finite populations.
Main author: Alastair Jamieson-Lane
Forum discussion group: Blog - Markov models of social change (part 2)
Summary: An introduction to cross-impact balance analysis and the new stochastic version, which are techniques for constructing self-consistent scenarios of complex situations.
Status: published
Main author: Tomi Johnson
Wiki page: Blog - quantum network theory (part 1)
Forum discussion group: Blog - quantum network theory
Status: published.
Summary: an introduction to quantum random walks, their relation to stochastic random walks, and their applications to the study of networks.
Main author: Tomi Johnson
Wiki page: Blog - quantum network theory (part 2)
Forum discussion group: Blog - quantum network theory
Status: published.
Summary: an introduction to quantum random walks, their relation to stochastic random walks, and their applications to the study of networks.
Main author: Eugene Lerman
Wiki page: Blog - networks of dynamical systems
Forum discussion group: Blog - networks of dynamical systems
Status: draft
Summary: how to use graphs to stitch together open systems into larger dynamical systems.
Main author: Staffan Liljegren
Wiki page: Blog - carbon cycle box models (part 1)
Forum discussion group: Blog - carbon cycle box models (part 1)
Status: almost done, needs some editing.
Main author: Staffan Liljegren
Wiki page: Blog - carbon cycle box models (part 2)
Forum discussion group: Blog - carbon cycle box models (part 2)
Status: draft
Main author: Piotr Migdał
Wiki page: Blog - Quantum superposition
Forum discussion group: Potential blog post series on quantum community detection
Status: published
Summary: This post introduces quantum superposition and role of its coherence (Quantum community detection part 1).
Main author: Vanessa Schweizer
Forum discussion group: Blog - Markov models of social change
Summary: An introduction to applications of stochastic cross-impact balance analysis.
Status: published
Main author: Matteo Smerlak.
Wiki page: Blog - the mathematical origin of irreversibility
Status: published
Summary: An introduction to the mathematical origin of irreversibility in nonequilibrium thermodynamics, including results such as the detailed fluctuation theorem and the integral fluctuation theorem.
Main author: Cameron Smith
Wiki page: Blog - hierarchical organization and biological evolution (part 1)
Forum discussion group: Blog - hierarchical organization and biological evolution (part 1)
Status: published
Summary: An introduction to hierarchical systems, which asks why evolution favors the development of such systems. See also the old Wiki page: [[Blog - evolution and categories]. This is part of a larger attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.
Main author: Cameron Smith
Wiki page: Blog - hierarchical organization and biological evolution (part 2)
Forum discussion group: Blog - hierarchical organization and biological evolution (part 2)
Status: in progress
Summary: An attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.
Main author: Cameron Smith
Wiki page: Blog - hierarchical organization and biological evolution (part 3)
Forum discussion group: Blog - hierarchical organization and biological evolution (part 3)
Status: in progress
Summary: An attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.
Main author: David Spivak
Wiki page: Blog - a networked world
Status: draft
Summary: A three-part introduction to the motivations behind David Spivak’s work on network theory.
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.
Main author: David Tanzer
Wiki page: Blog - Petri net programming (part 1)
Forum discussion group: Blog - Petri net programming (part 1)
Status: published.
Summary* Introduction to Petri nets, taking a hands-on approach. Contains a brief tutorial, then discussion of the programming approach, and ends with a small program to simulate a Petri net.
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.
Main author: David Tanzer
Wiki page: Blog - Petri net programming (part 3)
Forum discussion group: To be created
Status: draft – not ready for review.
Main author: David Tanzer
Wiki page: Blog - Petri net programming (part 4)
Forum discussion group: To be created
Status: draft – not ready for review.
Main author: David Tanzer
Wiki page: Blog - Petri net programming (part 5)
Forum discussion group: To be created
Status: draft – not ready for review.
Main author: David Tanzer
Wiki page: Blog - Petri net programming (part 6)
Forum discussion group: To be created
Status: draft – not ready for review.
Main author: David Tweed
Wiki page: Blog - Science, models and machine learning
Status: Main content finished, text needs final polish.
Summary: A collection of definitions about machine learning in one place that will be useful to refer to in future articles.
Main author: David Tweed
Wiki page: Blog - Worried about the environment You're seeing things
Status: text, a few supporting links.
Summary: Thoughts about the disproportionate impact of pictures on human psychology.
Main author: Tim van Beek
Wiki page: Blog - your model is verified, but not valid! Huh?
Forum discussion group: Blog - your model is verified, but not valid! Huh?
Status: published.
Summary: Critics of climate science in general, and sceptics of the statement that anthropogenic (man-made) global warming is real, often claim that climate models are wrong and cannot be trusted. But what does “wrong” mean here and what can and should be done to make models more trustworthy, from a software engineering viewpoint? In a first step, we’ll introduce some relevant technobabble.
Main author: Tim van Beek
Wiki page: Blog - putting the Earth in a box
Forum discussion group: Blog - putting the Earth in a box
Status: published.
Summary: An introduction to energy balance models.
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.
Main author: Tim van Beek
Wiki page: Blog - eddy who?
Forum discussion group: Blog - eddy who?
Status: published.
Summary: A short introduction to turbulence: It is all about eddies.
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.
Main author: Tim van Beek
Wiki page: Blog - fluid flows and infinite dimensional manifolds (part 1)
Forum discussion group: Blog - Fluid flows and infinite dimensional manifolds (part 1)
Status: published.
Summary: Fluid flows can be modelled by one parameter subgroups of diffeomorphism groups. How diffeomorphism groups can be seen as infinite dimensional Riemannian manifolds, and how certain nonlinear partial differential arise as geodesic equations.
Main author: Tim van Beek
Wiki page: Blog - fluid flows and infinite dimensional manifolds (part 2)
Forum discussion group: Blog - fluid flows and infinite dimensional manifolds (part 2)
Status: published.
Summary: Explaining Euler’s equation as a geodesic equation of ideal incompressible fluids.
Main author: Tim van Beek
Wiki page: Blog - fluid flows and infinite dimensional manifolds (part 3)
Forum discussion group: Blog - fluid flows and infinite dimensional manifolds (part 3)
Status: stub.
Summary: Comparing the Euler equation with the Navier-Stokes equation for incompressible fluids.
Main author: Tim van Beek
Wiki page: Blog - fluid flows and infinite dimensional manifolds (part 3)
Forum discussion group: Fluid flows and infinite dimensional manifolds III
Status: stub.
Summary: Explaining the Jacobi equation and how this can be used to put a bound on weather predictions.
Main author: Tim van Beek
Wiki page: Blog - fluid flows and infinite dimensional manifolds (part 5)
Forum discussion group: Fluid flows and infinite dimensional manifolds part 5
Status: stub.
Summary: Revisiting the Burgers equation as the simplest example of a nonlinear partial differential equation
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.
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?
Main author: Tim van Beek and Glyn Adgie.
Wiki page: Blog - increasing the signal-to-noise ratio with more noise
Status: published
Summary: An introduction to stochastic resonance.
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.
Main author: John Baez
Wiki page: Blog - El Nino project (part 1)
Forum discussion group: Blog - El Nino project (part 1)
Status: published.
Summary: an introduction to Azimuth Code Project’s work on Experiments in El Nino prediction and detection.
Main author: John Baez
Wiki page: Blog - El Nino project (part 2)
Forum discussion group: Blog - El Nino project (part 2)
Status: published.
Summary: a basic introduction to the physics of El Niño.
Main author: John Baez
Wiki page: Blog - El Nino project (part 3)
Forum discussion group: Blog - El Nino project (part 3)
Status: published.
Summary: A summary of Ludescher et al’s work on El Niño prediction.
Main author: John Baez
Wiki page: Blog - El Nino project (part 4)
Forum discussion group: Blog - El Nino project (part 4)
Status: published.
Summary: an overview of Graham Jones’ work on replicating the paper by Ludescher et al.
Main author: John Baez
Wiki page: Blog - El Nino project (part 5)
Forum discussion group: Blog - El Nino project (part 5)
Status: published.
Summary: a comical tale of how John Baez, pure mathematician, starts struggling to to use R to analyze climate data.
Main author: Steve Wenner
Wiki page: Blog - El Nino project (part 6)
Forum discussion group: Blog - El Nino project (part 6)
Status: published.
Summary: Steve Wenner’s critique of Ludescher et al’s methodology.
Main author: John Baez
Wiki page: Blog - El Nino project (part 7)
Forum discussion group: Blog - El Nino project (part 7)
Status: published.
Summary: on the definition of El Niño.
Main author: John Baez
Wiki page: Blog - El Nino project (part 8)
Forum discussion group: Blog - El Nino project (part 8)
Status: published.
Summary: on Y. Berezin, A. Gozolchiani, O. Guez and S. Havlin’s paper “Stability of climate networks with time”.
Wiki page: Blog - El Nino project (part 9)
Forum discussion group: Blog - El Nino project (part 9)
Status: draft.
Summary: a study of covariances and correlations in Pacific sea surface air temperatures.
Main author: Dara O Shayda
Wiki page: Blog - Exploring climate data (part 1)
Forum discussion group: Blog - Exploring climate data (part 1)
Status: published.
Summary: wavelet transforms of air pressure anomalies at Darwin and Tahiti.
Main author: Blake Pollard
Wiki page: Blog - Exploring climate data (part 2)
Forum discussion group: Blog - Exploring climate data (part 2)
Status: published.
Summary: Visualizing the sea surface air temperatures on a line along the equator in the El Niño basin.
Main author: Nadja Kutz
Wiki page: Blog - Exploring climate data (part 3)
Forum discussion group: Blog - Exploring climate data (part 4)
Status: draft.
Summary: Visualizing the missing CRUTEM data.
Main author: John Baez
Wiki page: Blog - week 309
Forum discussion group: This Week’s Finds - Week 309
Status: published.
Summary: Another application of Hopf bifurcations with noise, this time to predator-prey systems.
Main author: John Baez
Wiki page: Blog - week 314
Forum discussion group: Blog - week 314
Status: published.
Summary: The first part of an interview with Thomas Fischbacher.
Main author: John Baez
Wiki page: Blog - week 317
Forum discussion group: Blog - week 317
Status: published
Summary: A sketchy introduction to glacial cycles and Milankovich cycles.
Main author: John Baez
Wiki page: Blog - week 318
Forum discussion group: Blog - week318
Status: published
Summary: A bit more detail on Milankovitch cycles.
Main author: John Baez
Wiki page: Blog - interview with Didier Paillard
Forum discussion group: Blog - interview with Didier Paillard
Status: work in progress.
Summary: John Baez interviewing Didier Paillard about his work on the glacial cycles.
Main author: John Baez
Wiki page: Blog - Azimuth Project news
Forum discussion group: Blog - Azimuth Project news
Status: published.
Summary: What’s new on the Azimuth Project?
Main author: John Baez
Wiki page: Blog - stabilization wedges (part 5)
Forum discussion group: Blog - stabilization wedges (part 5)
Status: published.
Summary: Pacala’s 2008 followup on the original Pacala-Socolow Stabilization wedges paper.
Main author: John Baez
Forum discussion group: Blog - mathematics of the environment (part 3)
Status: published.
Summary: a discussion of the greenhouse effect, including the Schwarzschild equation and Beer-Lambert law.
Main author: John Baez
Wiki page: Blog - network theory (part 1)
Forum discussion group: Blog - network theory (part 1)
Status: published.
Summary: Networks, and diagrams of networks, show up in many branches of science. It would be nice to find a unified framework for these ideas.
Main author: John Baez
Wiki page: Blog - network theory (part 2)
Forum discussion group: Blog - network theory (part 2)
Status: published.
Summary: One can adapt ideas from quantum field theory to describe the theory of stochastic Petri nets. The master equation versus the rate equation.
Main author: John Baez
Wiki page: Blog - network theory (part 3)
Forum discussion group: Blog - network theory (part 3)
Status: published.
Summary: The rate equation of a stochastic Petri net, and applications to chemistry and infectious disease.
Main author: John Baez
Wiki page: Blog - network theory (part 4)
Forum discussion group: Blog - network theory (part 4)
Status: published.
Summary: The master equation of a stochastic Petri net, and analogies to quantum field theory.
Main author: John Baez
Wiki page: Blog - network theory (part 5)
Forum discussion group: Blog - network theory (part 5)
Status: published.
Summary: Analogies between quantum theory and probability theory.
Main author: John Baez
Wiki page: Blog - network theory (part 6)
Forum discussion group: Blog - network theory (part 6)
Status: published.
Summary: Writing the master equation using annihilation and creation operators.
Main author: Jacob Biamonte
Wiki page: Blog - network theory (part 7)
Forum discussion group: Blog - network theory (part 7)
Status: published.
Summary: An example: the stochastic version of the logistic equation in terms of annihilation and creation operators, and how to obtain an equilibrium Poisson distribution.
Main author: John Baez
Wiki page: Blog - network theory (part 8)
Forum discussion group: Blog - network theory (part 8)
Status: published.
Summary: A review of our work so far: how to get the rate equation and the master equation from a stochastic Petri net. A bit about Feynman diagrams.
Main author: Brendan Fong and John Baez
Wiki page: Blog - network theory (part 9)
Forum discussion group: Blog - network theory (part 9)
Status: published.
Summary: A quantum field theory proof of the most exciting theorem in D. F. Anderson, G. Craciun and T. G. Kurtz’s paper Product-form stationary distributions for deficiency zero chemical reaction networks.
Main author: John Baez
Wiki page: Blog - network theory (part 10)
Forum discussion group: Blog - network theory (part 10)
Status: published.
Summary: An example of a simple reversible reaction.
Main author: Brendan Fong and John Baez
Wiki page: Blog - network theory (part 11)
Forum discussion group: Blog - network theory (part 11)
Status: published
Summary: Brendan Fong proves a version of Noether’s theorem for Markov processes.
Main author: John Baez
Wiki page: Blog - network theory (part 12)
Forum discussion group: Blog - network theory (part 12)
Status: published
Summary: A comparison of quantum mechanics and stochastic mechanics.
Main author: John Baez
Wiki page: Blog - network theory (part 13)
Forum discussion group: Blog - network theory (part 13)
Status: published
Summary: A comparison of the quantum and stochastic versions of Noether’s theorem.
Main author: John Baez
Wiki page: Blog - network theory (part 14)
Forum discussion group: Blog - network theory (part 14)
Status: published
Summary: The Desargues graph and its role in chemistry.
Main author: John Baez
Wiki page: Blog - network theory (part 15)
Forum discussion group: Blog - network theory (part 15)
Status: published
Summary: More on the Desargues graph; graph Laplacians and how they generate Markov processes and also quantum processes.
Main author: John Baez
Wiki page: Blog - network theory (part 16)
Forum discussion group: Blog - network theory (part 16)
Status: published
Main author: John Baez
Wiki page: Blog - network theory (part 17)
Forum discussion group: Blog - network theory (part 17)
Status: published
Main author: John Baez
Wiki page: Blog - network theory (part 18)
Forum discussion group: Blog - network theory (part 18)
Status: published
Summary: The rate equation for a diatomic gas: an example of many of the concepts we’ve seen.
Main author: John Baez
Wiki page: Blog - network theory (part 19)
Forum discussion group: Blog - network theory (part 19)
Status: published
Summary: The master equation for a diatomic gas: an example of many of the concepts we’ve seen.
Main author: Jacob Biamonte
Wiki page: Blog - network theory (part 20)
Forum discussion group: Blog - network theory (part 20)
Status: published
Summary: A discussion of the Perron-Frobenius theorem and its role in understanding Dirichlet operators.
Main author: John Baez
Wiki page: Blog - network theory (part 21)
Forum discussion group: Blog - network theory (part 21)
Status: published
Summary: A deeper look at the concept of ‘deficiency’, in preparation for proving the deficiency zero theorem.
Main author: John Baez
Wiki page: Blog - network theory (part 22)
Forum discussion group: Blog - network theory (part 22)
Status: published
Summary: A reformulation of the rate equation, in preparation for proving the deficiency zero theorem.
Main author: John Baez
Wiki page: Blog - network theory (part 23)
Forum discussion group: Blog - network theory (part 23)
Status: published
Summary: A study of Markov processes, in preparation for proving the deficiency zero theorem.
Main author: John Baez
Wiki page: Blog - network theory (part 24)
Forum discussion group: Blog - network theory (part 24)
Status: published
Summary: Proof of the deficiency zero theorem.
Main author: Jacob Biamonte
Wiki page: Blog - network theory (Biamonte guest posts)
Forum discussion group: Blog - network theory (Biamonte guest posts)
Status: no longer needed; most of this material has by now appeared in the Network Theory series.
Summary: Jacob Biamonte on stochastic Petri nets and chemical reaction networks.
Main author: Brendan Fong
Wiki page: Blog - network theory (Fong guest posts)
Forum discussion group: Blog - network theory (guest posts)
Status: work in progress.
Summary: Brendan Fong on stochastic Petri nets and chemical reaction networks: material that might go into posts on the Azimuth blog.
Main author: John Baez
Wiki page: Blog - Petri net software
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.
Authors: John Baez and David Tanzer
Wiki page: Blog - prospects for a green mathematics
Forum discussion group: Blog - prospects for a green mathematics
Status: published