I remember that especially russian scientists had traditionally kept an eye on the sun and likewise had partially different views on global climate developments so I also tried to find links to missions on the russian irradiance website but found no links.

As you know from the methane discussion I am especially interested in UV measurements. Unfortunately it seems first that sorce doesn't cover all ranges but secondly that it had a major breakdown lately especially in the higher UV range. (<100nm) This is somewhat disconcerting since it looks as if irradiation is on average on the rise since 2003 while there seem to be big differences between different spectral lines. Compare e.g. the time series (found no perma link) 1499.65nm and 115.5nm and 698.85nm.

]]>Dear Dr. Baez,

I am writing in reference to your "to-do list" as of July, 21, 2016 on the Azimuth Forum, in particular to your call for participation in the projects listed there.

I am a post-doctoral researcher in mathematics, currently based at the Università di Torino, Italy. My research interests have been gravitating towards (braided) monoidal categories for several years now and most of my research involved working with these structures and their associated graphical language at some point.

At the time of writing, I have a grant to continue carrying out research for two more years. I am involved in several mathematical divulgation projects for high school children in Belgium and more recently, I have been asking myself how I could spend my time left in research/academia in such a way as to give further shape to my social and ecologic engagement.

I came in touch with your work on (categorical aspects of) network theory through your Overview lecture given at University of Oxford (as available on YouTube), where you also invited new 'recruits' to join your research area.

I don't know if I could be of any use to one of your ongoing research projects that involve the use of (monoidal) category theory, but I would be most happy to give it a try. In case you agree, would you have a suggestion for a starting point for me in this?

(Disclaimer: Unfortunately, I have very little knowledge of physics, biology or ecology.)

Thanks in advance and best regards,

Isar Goyvaerts

I gave him a list of things to read and asked what topics he found most interesting.

]]>A friend of mine sent me an e-mail asking if I knew of any good resources for introducing undergraduate social scientists to the mathematics of networks.

In particular he said, "I want to give them a teaser on the math of networks, as applicable to social networks, life networks, etc.

Can your recommend any resources (books, video lectures, review articles, etc) that are are extremely accessible (i.e. easy)?"

Any of you folks have any recommendations?

Thanks, Blake

]]>If I do come up with any good dimensionaliy reduction techniques I'll put them here, but I also ought to check if this has been looked at before by others?

]]>If no-one happens to know this I'll look around and record any findings I make here on the forum.

]]>These models often have complex emergent behavior, and I am wondering what mathematical and computational tools exist to characterize their dynamics. This may intersect with the Azimuth Project's work on Petri nets. I'm toying with writing an internal grant proposal on "the complexity science of discrete event simulations" in the spring, if I can come up with some good ideas.

The example I'm focusing on right now is the SimX and SimCore frameworks developed by Los Alamos National Laboratory: *"SimX is a library for developing parallel, distributed-memory simulations in Python. SimX is written primarily in C++ and provides the simulation modeler with the core functionality needed in a parallel simulation library such as event queueing, time advancement, domain partitioning, synchronization and message passing. SimX APIs are exposed to Python, enabling rapid development and protyping of a parallel simulation entirely in Python. SimX is free software, available under the GNU LGPL license, and hosted on github."*

These frameworks have been used to implement transportation models (TRANSIM and FastTrans), epidemiological models (EpiSimS), telecommunications models (MIITS), etc. There are also people here who are interested in applying this to dynamic economic models, as opposed to the traditional computable general equilibrium models; I'm not sure how this would compare to the newer DSGE models. (And they probably won't get funded to do this anyway, given institutional politics ...)

Some questions that come to mind:

What is the appropriate mathematical structure to represent these models? Petri nets may be too specialized. Agent models can combine continuum state variables with discrete actors, or there can be hybrid discrete-continuous models. Many agent models can have their dynamics determined by an implicit optimization step, where each actor takes some utility-maximizing action (potentially with actor-specific utilities). This may be hard to describe using simple transition rules. Can anything useful be said about such complex dynamics?

How can you characterize bifurcations, steady states, etc. in these models? Continuum dynamics approaches include center manifold reduction or numerical continuation methods. What can be done from a discrete event perspective?

What methods exist to construct reduced-order models from more complex discrete simulations? You could write an agent model with 300 million actors in it, but it could be beneficial to derive a simplified, more aggregate model that is faithful to the original dynamics. (This is different from building an aggregate model from the ground up, where premature averaging might lose some of the dynamics.) Reduced models can be more computationally efficient (permitting more uncertainty quantification and scenario exploration) and also easier to understand. There are a variety of methods to do this in continuum dynamics, such as Krylov subspace projection, balanced truncation, discrete empirical interpolation, etc. Can they be generalized? Ideally they'd preserve the

*stochastic*behavior of the system, not just its mean behavior (i.e., distributions).How can uncertainty be quantified in such models? Stochastic simulations often have intractable likelihood functions: you don't know how to write them down in closed form, and can only simulate from them. This requires methods like approximate Bayesian computation (ABC). A lot of the computer model calibration literature is devoted to developing Gaussian process emulators which construct simple statistical models of the output of numerical simulations, but these may be too smooth. Do we need "Markov process emulators" or "Petri net emulators" or other ways of building statistical approximations to large-scale discrete simulations? And how do we develop large scale MCMC for uncertainty quantification? Hamiltonian Monte Carlo is a method of choice for Bayesian computation in high-dimensional systems, but it requires continuous derivatives with respect to all the parameters, and also requires a likelihood to be available; can it work in discrete systems or in an ABC context?

More on uncertainty: how to characterize "predictability" within these models, and tie this to information theory? Can you see a tipping point coming (collapse of the power grid, global pandemic, ...)? What are the "signatures" of impending bifurcations? This has been studied in continuum dynamics, e.g. critical slowing-down; are there discrete analogues?

Still more on uncertainty: as mentioned earlier, agent models often have some individual utility-maximizing behavior. But this does not account for each agent's uncertainty about the system (Bayesian belief). Can these models be adapted to have agents making decisions under uncertainty, maximizing an

*expected*utility? And can they learn as they go, updating their beliefs and consequent actions (endogenous learning)? This probably intersects with approximate dynamic programming and optimal learning, as well as sequential Monte Carlo or ensemble Kalman filtering.How to characterize the high-risk tail-area behavior of these stochastic simulations? You can do it by brute-force Monte Carlo, but can theory help (e.g., suggest asymptotic distributional forms to fit to model output)? What about rare event simulation? Again, can theory help?

The most frustrating part of writing this paper was trying to explain the Markov Chain Monte Carlo method without becoming overly technical. If you look at most of the articles in this magazine, you'll see they have a light and breezy tone. Ours is verging on too heavy. The version on the blog ran into this problem:

We start by saying we want to compute P(S|M) - he probability that our model should have certain

**S**ettings, giving certain**M**easurements.Then we say we can't easily do that: we can only compute P(M|S).

Then Bayes' rule comes to our rescue by relating these two.

But then we say "Having glibly said that we can compute P(M|S), how do we actually do this?"

We describe an obvious way to do it.

But then we say this is inefficient.

Then we say Markov Chain Monte Carlo is better. We describe how that works, and we start by saying "compute the ratio P(S'|M)/P(S|M)"

At this point we've made a complete loop: we're back to acting like we can compute P(S|M)!

In a later draft we tried to quickly explain why we're not, in fact, being circular:

Note that this rule uses P(S|M) at each step, which we have to get from the P(M|S) value returned from our simulation by using Bayes' rule again. With some additional tricks, such as discarding the very beginning of the walk, this gives a set of samples which can be used to build an estimate of P(S|M).

Unfortunately, I think most readers will find this bewildering and disheartening.

So, in the new draft I've decided to gloss over all this stuff and give references for details.

]]>http://www.skepticalscience.com/argument.php

Has anyone looked at these?

]]>The authors of the Wall Street Journal letter "No Need to Panic about Global Warming" have replied to a rebuttal of that letter, here:

http://online.wsj.com/article/SB10001424052970203646004577213244084429540.html

Scientifically the most interesting thing here is a graph that claims to compare predictions of global warming to the actual data. For a criticism of that graph, see below.

The WSJ rebuttal's reply ends with:

The computer-model predictions of alarming global warming have seriously exaggerated the warming by CO2 and have underestimated other causes. Since CO2 is not a pollutant but a substantial benefit to agriculture, and since its warming potential has been greatly exaggerated, it is time for the world to rethink its frenzied pursuit of decarbonization at any cost.

The way I personally perceive their final point is: "let's continue burning carbon (because that is what made us wealthy and happy) until it becomes too expensive to burn. Only the price of fossil fuels is the right measure to tell us when it's exactly the right moment for switching to other energy sources (or having to use less energy)."

Since CO2 is not a pollutant but a substantial benefit to agriculture

**Does anyone know of a study where it is exactly the lack of CO2 that prevents plants from achieving optimal growth? (instead of lack of soil water, nitrogen conversion, solar light, trace minerals...)**

I'm posting here because this is a more civilized place than Google plus.

]]>In doing numerical floating point work is full of pitfalls where you can lose almost all accuracy, one of which is when summing/sum-squaring/etc with a large set of small values (so that each individual value is likely to be small relative to the aggregate statistics). I'm thinking about how to compute a covariance matrix for a large set of items subject to the following requirements:

Anything other than a "look a each data item once" approach is unlikely to be viable (ie, not a two-pass algorithm).

There will be covariances for several different data streams being calculated interleaved (ie, it's not "here's a stream for one dataset, get it's covariance then move onto the next data stream").

However, I don't care about the covariance until everything has finished: it doesn't have to be in available form as the data is being processed.

This wikipedia page contains an algorithm, but it's maintaining a finished covariance matrix at all times. I'm just wondering if there's anything that gives higher accuracy through needing final post-processing at the end.

]]>]]>What do people think about the current state of play on the Azimuth Code Project? There are examples in Java, C++, R and Sage. A goal is to produce some interactive learning pages on the cloud. This either (non-exclusively) requires an ISP account with shell access eg from Linode, some rich academy, friendly online publisher or other where people can run multiple language compilers with some web service front end or port apps to a single language, e.g. Javascript or php (uggh) on a low-cost ISP without shell access.

I posted the FFT link as an example which would work on the low-cost solution and seems to fit the Azimuth spec for an educational web service. Perhaps there could be an Azimuth wiki page with useful software links? Incidentally, the Azimuth code project wiki page doesn't mention any of the interactive examples on the wiki or link the googlecode repo just coding standards which perhaps should be a different page.

A couple of environmentally-friendly C++ programmers and I have made some mods to David Tweed's excellent DSE code which he has kindly accepted. I'm just waiting for an account on google code to commit them. David's raised some interesting topics e.g. automatic differentiation on the Azimuth chat pages which I'm trying to get time to think about and reply to.

Suppose that we've got a stochastic dynamical system which is essentially only dependent on a finite "memory" of parameters (hence only influenced by "absolute time" in that certain system input variables might be dependent on absolute time, eg, that a catastrophic forest fire reducing food supplies happens in year 20 after the simulation starts). Then this for any set of data comprising a state (which may include historical datums or generalised velocities, etc) we can approximate the probability distribution of next states by running the simulation. If we do this for lots of states that we think are "likely states" then we've built up a lot of piecemeal information about the system, but is there any existing algorithms for calculating long-term probabilites of die-off, natural periods, etc? (For a discrete Markov chain you can look at things like power series in the transition matrix, but that assumes that you've got a finite set of states and have computed transition probs for all of them: is there a way more adapted to "sparsely sampled" transitions (since it's going to be computationally prohibitive to just approximate each transition by this method.)

Many thanks for any thoughts,

]]>I have a basic question about moments of time series (say, the average temperature at some place)

is there a mathematically rigorous way to define time-dependent moments of a time series? E.g. I've heard the claim that "since 1987 the average temperature of place X has become one degree higher" but I've got some problems with comparing the time average before the year $T$ to the time average after the year $T$, because I guess it depends on $T$. (in the case of the claim I suppose that $T=1987$ yields the maximal temperature difference)

I've read that for climate models one can use the ensemble mean. One can run an ensemble of models (and assume ergodicity to relate it to the time average) and take moments with respect to this ensemble. In this case one can notice that the ensemble moments exhibit time-dependent behaviour.

But I'm wondering if something similar is possible for just one time-series. Is there a mathematically rigorous and meaningful way to examine if some moments of a certain time series are time-dependent?

]]>Dear Prof. Baez,

Sorry for the unsolicited email, but I follow your blog and am hoping that you will be able to offer some guidance.

Within the next year I will finish my PhD on quark confinement/vortices, so it's time to think about what to do next. The usual HEP post-doc trail is not particularly appealing due to the lack of positions and overabundance of candidates. More importantly, I'm increasingly concerned with the global problems that we have and would like to use what talents I have help.

What chance do I have to transfer to the science of energy/resources or climate change? These are such important problems that I would be heart broken if the opportunities are as limited as in sciences that are more elective than necessary.

When I began my PhD in Adelaide I was the highest ranked applicant across all departments. I'm scared of ending my career in a high school instead of contributing scientifically to one of our urgent problems. I'd be extremely grateful if you are able to offer any advice.

Here is my answer, which doesn't seem as helpful as it should be:

Sorry to take so long to reply. I've been mulling over your question.

You write:

More importantly, I'm increasingly concerned with the global problems that we have and would like to use what talents I have help.

Great!

What chance do I have to transfer to the science of energy/resources or climate change?

It will take work, but the job opportunities in these areas are probably better than in more esoteric areas such as elementary particle physics.

Since I haven't tried getting a job in these areas, I'm probably not the best person to help you find one. However: did you read how Nathan Urban switched from quantum gravity to academic work on climate change? He describes it at the beginning here:

http://johncarlosbaez.wordpress.com/2010/09/09/this-weeks-finds-week-302/

As you can see, his skill at Monte Carlo computations were transferrable.

Also, read how Tim Palmer switched from quantum gravity to work on climate modelling, near the beginning here:

http://johncarlosbaez.wordpress.com/2010/12/07/this-weeks-finds-week-306-2/

Among other things:

JB: Thanks! I’ve been reading that book. I’ll talk about it next time on This Week’s Finds.

Suppose you were advising a college student who wanted to do something that would really make a difference when it comes to the world’s environmental problems. What would you tell them?

TP: Well although this sounds a bit of a cliché, it’s important first and foremost to enjoy and be excited by what you are doing. If you have a burning ambition to work on some area of science without apparent application or use, but feel guilty because it’s not helping to save the planet, then stop feeling guilty and get on with fulfilling your dreams. If you work in some difficult area of science and achieve something significant, then this will give you a feeling of confidence that is impossible to be taught. Feeling confident in one’s abilities will make any subsequent move into new areas of activity, perhaps related to the environment, that much easier. If you demonstrate that confidence at interview, moving fields, even late in life, won’t be so difficult.

In my own case, I did a PhD in general relativity theory, and having achieved this goal (after a bleak period in the middle where nothing much seemed to be working out), I did sort of think to myself: if I can add to the pool of knowledge in this, traditionally difficult area of theoretical physics, I can pretty much tackle anything in science. I realize that sounds rather arrogant, and of course life is never as easy as that in practice.

JB: What if you were advising a mathematician or physicist who was already well underway in their career? I know lots of such people who would like to do something "good for the planet", but feel that they’re already specialized in other areas, and find it hard to switch gears. In fact I might as well admit it — I’m such a person myself!

TP: Talk to the experts in the field. Face to face. As many as possible. Ask them how your expertise can be put to use. Get them to advise you on key meetings you should try to attend.

JB: Okay. You’re an expert in the field, so I’ll start with you. How can my expertise be put to use? What are some meetings that I should try to attend?

TP: The American Geophysical Union and the European Geophysical Union have big multi-session conferences each year which include mathematicians with an interest in climate. On top of this, mathematical science institutes are increasingly holding meetings to engage mathematicians and climate scientists. For example, the Isaac Newton Institute at Cambridge University is holding a six-month programme on climate and mathematics. I will be there for part of this programme. There have been similar programmes in the US and in Germany very recently.

Of course, as well as going to meetings, or perhaps before going to them, there is the small matter of some reading material. Can I strongly recommend the Working Group One report of the latest IPCC climate change assessments?

What else should I have told this person?

]]>Now, I'm right in saying that if I'm estimating the distributions of $x$ for each set of parameters in $\theta_0, \dots, \theta_m$, it doesn't matter (statistics-wise) if I reuse the same "set of independent pseudo-random sequences" for the distribution estimation of $x$ for each $\theta_i$?

]]>This is my first post at this forum. I come as someone who does not know much about the issues of concern to Azimuth, but in principle I am interested to learn more and help out if I can.

I'm not a vegetarian myself, so I do not mean for this discussion to be carry political or moral overtones, but I am curious about getting some good information on the impact of meat and dairy production on AGW, e.g., estimates of an individual's carbon footprint due to meat and dairy consumption. Possibly this would make a good article for Azimuth. Can anyone point me to decent studies on this general sort of thing? (And please excuse any naivete inherent to the question. Have I chosen the right category for this discussion?)]]>

There's some known way of trying to sample a random distribution which is a bit like Markov chain Monte Carlo, but instead of a single point (or "particle") walking around randomly, you have a bunch of particles, which can split at various times, and/or die out. Or something like that. Do you remember what I'm talking about? What was it?

All of a sudden this seems exactly like the "phylogenetic trees" discussed on the blog. In these trees we have a Markov chain of random DNA evolution along each edge, but sometimes species split (or die out, but people don't talk about that as much).

I may be modifying my memory of our old conversation to make it seem more similar to the new stuff.

]]>Googling turned up these first two hits:

It might make sense to decide on a CAD format now so that we can load in a model of the earth later. In the meantime, we can start playing around with something simple like a single tetrahedron.

]]>I'm probably about a week away from having my minuscule C++ library in a state where I'd like to put it onto the Code Project. At that stage I'll have written some documentation and done some commenting, but since it's a new approach still under development I don't plan to do detailed comments on things that might well change. If it survives for a couple of months without major changes I'll add more comprehensive commentary.

So I guess the way is to add a new implementation language for C++, with this as a subproject? I can provide a unixy makefile to build a sample project, unless something else is required? Finally, I guess I ought to get added to the commiters list please Tim. My email is David period Tweed sign-of-the-at gmail period com.

]]>do u know if we can use any server on any of your institutions/organizations ?

]]>Please, everyone: don't hesitate to create new pages on organizations that seem interesting and relevant. The main thing to avoid is organizations with strongly 'political' goals - e.g. political parties. Most interesting for us are organizations that provide accurate information or are focused on solving ecological or energy problems.

does this include organisations like Greenpeace and WWF or not? Ok, these are well-known, so it doesn't matter so much whether we include them or not. More specifically, yesterday I heard about a (rather local) organisation, the Sea First Foundation. They provide references.

Btw, right now our [[Organisations]] page is mixed, for example, [[DESERTEC]] and [[SeaRISE]] are projects, many others are purely insitutes (but maybe it's difficult to draw a line)

]]>http://www.indriid.com/military-cclimate.png

(The image is extracted from this PDF presentation.)

]]>It isn't obvious to me that problems of this sort benefit from that level of sophistication or detail when the general assumptions may not hold. Nevertheless, sophisticated models seem to be more and more common. My question is what additional predictive benefit do we gain from these sophisticated models? I suppose that when they don't hold up we know we are missing something in the model but I'm skeptical of our ability to incorporate sophistication when we don't comprehend the basics.

We can't predict a hurricane track out more than a few days in most cases. Yet it seems to me that the GCMs are far more complicated and make far more assumptions than hurricane models.

For example, in Pacala's comments in the video linked to at the end of [[Stabilization wedges]] he indicates that if CO_{2} fertilization doesn't hold up as a sink process, then the problem of global warming may be more than four times worse than we assumed (i.e. we'll need 34 wedges instead of 8). Yet, we run multi-decadal simulations of weather models that incorporate assumptions like the one for CO_{2} fertilization.

Another sample problem listed on Wikipedia (paper here):

In 2000, a comparison between measurements and dozens of GCM simulations of ENSO-driven tropical precipitation, water vapor, temperature, and outgoing longwave radiation found similarity between measurements and simulation of most factors. However the simulated change in precipitation was about one-fourth less than what was observed. Errors in simulated precipitation imply errors in other processes, such as errors in the evaporation rate that provides moisture to create precipitation. The other possibility is that the satellite-based measurements are in error. Either indicates progress is required in order to monitor and predict such changes.

So what am I missing here? How useful is it to model at increasing levels of sophistication when we're not sure of some of the more important basics? Or more importantly, how important it is to make public the predictions of these models when it seems to me they are not yet ready to predict anything other than broad ranges of variability.

I am worried that all this sophistication makes it seem like we know more than we really do while at the same time it obscures and makes seem less certain what we are pretty confident in.

**The biggest problem** with these sophisticated simulations is that they are very opaque to anyone but the scientists who work on them. The general public cannot understand them so they have to "trust" the scientists. The scientists themselves may make programming errors that they are not even aware of. Yet the core problem is fairly easy to understand and not disputed. So science ends up creating a PR problem that is easily exploited by those who benefit from the status quo.

It seems to me that this may be one area where we can help the larger communications effort in a concrete way. If we can lay out simply and in an easy-to-understand manner the basics, and what those basics indicate, that should be more convincing.

]]>Traditional texts and articles have a list of references at the end of the article, with small indications such as references numbers in the text. The need for full references is clearly to provide enough detail to find the exact source listed, but presumably its done this way for the following reasons:

Paper is a static medium (a full reference can't appear in a mouse-over). Putting all very long lines inline in the text would break up normal reading, so putting them at the end moves them out of the way.

It's easy for authors and readers to scan through an alphabetical ref list and look somehting up, spot something that they think ought to be there isn't, etc.

To what extent do these apply to the wiki (in principle, ignoring for the moment Instiki limitations)? It's possible to "hide" the full reference details as referring to them comes up in the main text, and have means of making them visible, eg, mouseover. It's also possible to automatically compile a secondary list of references (either at the end or on a separate page) from the text, so it doesn't sacrifice the utility of point (2). So the traditional reasons for reference structuring don't apply. Why might we want to keep things that way:

Tradition/familiarity ourselves or judgement by readers who use those criteria.

Similarly, if wiki material is intended to migrate to a traditional format, eg, a printed version or submitted as a journal article.

It provides somewhere to stick references that aren't explicitly mentioned in the text.

I certainly find the current layout difficult at times, since it's often time consuming to find the reference a mention in the main text refers to. (Mea culpa in that I haven't bothered to learn how to do markdown reference-links. However no-one else seems to have done it either.) Certainly on a page which has multiple "orthogonal" sections, it'd be nice if it was acceptable to put references only of relevance to that section at the end of a section. Being more radical, it might be interesting to come up with some guidelines for when it's appropriate to put references in as they come up in a text block, and if so how.

Any responses/ideas?

]]>