Kieran’s post about his book on organ donation gives me a hook to write something about the other end of the system, about organ recipients and the institutions which are supposed to match them up with donated organs. More specifically, how one such institution, the Kaiser HMO of Northern California, quite spectacularly failed several thousand people who were depending on them, by not matching them up. The story has been around since early May, when it was broken by Charles Ornstein and Tracy Weber in the Los Angeles Times (cached here), since confirmed by an investigation by Medicare/Medicaid. It doesn’t seem to have gotten all that much attention among the blogs, but it’s outrageous, and deserves, for that reason alone, to be better known.

(I was hoping to end my guest-blogging here by kvetching about econophysics, which is merely trivial; but that will have to wait until next week, back at my own blog.)

Kaiser is a very large and old HMO, with a huge presence in the Bay Area and northern California. (In fact it was one of the very first HMOs, started by Kaiser Steel during WWII as a way of attracting workers to its foundries and shipyards when wages were frozen.) It actually consists of non-profit health plans and hospitals, and for-profit physicians’ partnerships, the Permanente Medical Groups; normally, patients in the health plans have to go to physicians in the groups to have their medical expenses covered. One notable exception, up until 2004, was the 1500—2000 Kaiser patients in northern California who needed kidney transplants because of renal failure: those procedures were sub-contracted to the hospitals at UCSF and UC Davis, which also managed the patients’ places on the waiting list.

That last bit requires some explanation. Once organs are donated, they need to be matched up to recipients. This is done by an organization called the United Network for Organ Sharing, which tries to trade off urgency, seniority (i.e., time spent waiting for an organ), proximity and compatibility (since the closer the match between the donor’s immune system and the recipient’s, the less problems from rejection). There is a heavy weight put on seniority, though especially close immunological matches can over-ride it. Each transplant center is responsible for keeping the network up-to-date about their patients who need organs, their immunological profiles, and their time spent on the waiting list.

What seems to have happened is that in 2002, a transplant surgeon named Arturo Martinez proposed to Kaiser that it could save money, and increase the utilization of its hospitals’ surgical capacity, by bringing the kidney transplant program in-house, and Kaiser agreed, with Martinez becoming head transplant surgeon. (It would be unfair, at this point, to say that Kaiser did this because it meant more business for the for-profit Permanente Medical Group, but it’s hard to imagine that counted against the proposal.) As of mid-2004, Kaiser patients on the waiting list were informed that they would no longer be covered for transplants at UCSF or UC Davis, though they were free to go ahead and have them if they could come up with the money (roughly $100,000).

So far, all this is maybe a little self-serving on Kaiser’s part, but not, in itself, appalling. (It’s certainly more than legitimate for health-care organizations to try to save money.) What happened, though, was that Kaiser completely screwed up the program. Remember that organs are allocated (basically) through the UNOS system. The patients were being removed from the listings under the university hospitals, and being added to the listings under the new Kaiser transplant program. Unless this was done correctly, this would mean that they’d look like new names on the list, and so all of their accumulated waiting time, one of the main determinants of priority, would vanish. This happened to a huge number of people on the list, basically reducing the chance that they’d get a kidney to next to nothing. This becomes less surprising when one learns that Kaiser never consulted UNOS about the massive transfer of patients it was planning, and “placed responsibility for submitting patient data … in the hands of a single clerk who had one hour of telephone training on UNOS’s database”, though not any more excusable. Needless to say, patients were not told that by staying with Kaiser, they were losing their place on the lists, and thereby reducing their odds of survival. Some of them, at least, seem to have been assured that they were keeping their places, when that wasn’t true, though this is less clear to me.

Losing seniority on the transplant lists wasn’t the only problem. Kaiser did very few transplants, compared to the number of organs which were available. This happened in part because they just didn’t have the capacity to keep up with their many patients (at one point they were down to a single nephrologist for the whole program, who was also supposed to be its medical overseer), and in part because of what seems to have been mis-placed perfectionism or caution. These combined to the point of repeatedly turning down “zero mismatch” kidneys, ones where the likely compatibility over-rode considerations of seniority. This happened several dozen times at least — twice for one patient alone. Again, needless to say, patients weren’t told about this. In a “it’s not a bug, it’s a feature” moment, Kaiser initially attempted to defend its program by pointing out how few patients had died after transplants — since they’d done so few.

What strikes me as especially outrageous about all this is that the people being screwed over were people who needed new kidneys. To state the obvious, anyone who needs an organ transplant is very ill. It’s maybe less obvious that being that ill is a full-time job. One of the vital parts of the body is no longer working; to substitute for it requires extraordinarily complicated, time-consuming and generally unpleasant procedures. People who need new kidneys are people who are kept alive by dialysis, which is, indeed, complicated, time-consuming, often painful, almost always exhausting, and carries a non-trivial risk of infections, possibly fatal. People who need new kidneys are also often people who are very ill in other ways, since it’s not that common for both your kidneys to just stop working if nothing else is going on. (Kidney problems are, for instance, a not-uncommon complication of diabetes, and of high blood pressure. Dialysis, naturally, messes with blood pressure, adding yet another variable to monitor and regulate.) Simply staying alive, when you are multiply-sick person with organ failure, can pretty much demand all the time and attention you have to give, and a fair chunk of your loved ones’ as well. (There are good reasons why the families of people in situations like this tend to fall ill themselves.) You are certainly not in a position to check up on whether your medical organization has, through incompetence, messed up your position on the transplant lists. (Some Kaiser patients actually tried to keep up with their place on the lists, but were given the run-around.) And as for switching to another medical organization, do please show me the company which will extend coverage to someone who needs a new kidney, at a price which can be afforded by someone who needs a new kidney.

Since the Times broke the story, there’s been some improvement. The doctor who was medical head of the program, and apparently at least partly responsible for snafu of not transferring patients’ time, Sharon Inokuchi, has been relieved of her administrative duties. (In fact, if memory serves, she left Kaiser, but now I can’t find where I think i read that.) The program has been investigated by the Center for Medicare and Medicaid Services, which basically confirmed the newspaper reports, and forced it to promise major changes; it could still lose its eligibility for funding under those programs. The California state agency which regulates managed care is still, I believe, investigating. There’s talk of large fines, and there will certainly be lawsuits. All of this is to the good; it’s certainly better than nothing. But still, thinking about this makes me angry: Kaiser had a duty towards many very sick people, who were in a very poor position to look after themselves. It failed in that duty quite dramatically. In any organ transplant program, patients will die while waiting for a match. In most kidney transplant programs, though, about twice as many patients receive transplants as die while waiting; Kaiser managed to reverse that ratio. While it’s hard, in the nature of things, to identify any one patient who’s died and say “They would have lived, if only Kaiser hadn’t done this”, it’s almost certain that more of these people have died than would have otherwise. I don’t have a better remedy to propose than fines or lawsuits or institutional tinkering, but they all seem horribly inadequate.

(Via David R. in e-mail.)

Attention Conservation Notice: Over 1500 words on a wacky quasi-socialist economic scheme, from someone utterly lacking in credentials in economics. The scheme does not respect the sanctity of private enterprise, but at the same time would not reduce the alienation of labor one iota. Includes a lengthy quotation of a game-theoretic impossibility result.

In the previous installment in this series of modest proposals for the reform of corporate governance, I looked at ways of making the incentives of the managers of large, publicly-held corporations align more closely with those of their long-term shareholders. This left alone the question of the beneficiaries of corporate value; assuming that the managers are busily working to maximizing their revenue streams, who benefits from their industry and diligence? Having just read Mark Greif’s great essay on redistribution in n+1, I would like to make a suggestion. (Issue 4; long excerpt here, as pointed out by Matt in the comments.)

The text for today is Gary Miller’s Managerial Dilemmas: The Political Economy of Hierarchy, an excellent book which I learned about from Henry Farrell. Ambitiously, Miller tries to explain why hierarchical corporations exist at all, why they take some of the forms they do, and how, in part, their form relates to their performance. Much of the book, especially the first part, is a partially-successful attempt to find good economic reasons for their features, i.e., efficiency-enhancing ones. (He does not seriously consider the option that enterprises are hierarchical for non-economic reasons, say that some people like bossing others around, which hierarchies let them do, and those people are able to select hierarchies over other, more efficient, forms. After all, it’s hardly historically unprecedented for powerful people to prefer institutions which lower aggregate output but give them a bigger share of the product. See, e.g., here.) He also tries to explain why theories of corporate organization that rely solely on economic “mechanism design”, i.e., structuring information and material incentives, will actually lead to sub-optimal results, for pretty basic game-theoretic reasons; getting beyond these impasses is fundamentally a political problem. This is potentially quite subversive in its own way, but it’s really the first part of the work, about the economic justification of the hierarchical enterprise, that I’m going to twist and abuse.

One of the features of the modern corporation that Miller attempts to rationalize is the existence of shareholders who are passive and, in the overwhelming majority, utterly disconnected from the day-to-day or even year-to-year operations of the company. He does so by means of the following impossibility theorem, attributed to Bengt Holmstrom. Having tried to summarize Holmstrom’s theorem better than Miller, and failed, I’ll just quote Miller.

Holmstrom assumes that there are n agents whose actions determine a level of revenue x. The actions taken are unobservable and are costly to each of the agents. In particular, we assume the production function is a team production in which the productivity of each individual’s action is determined by other individuals’ levels of effort.

Holmstrom points out the desirability of three characteristics of an incentive system — and then shows that they are logically inconsistent. First, Holmstrom examines the Nash equilibrium outcome of an incentive system. At such an equilibrium, each individual will find that he or she could not do better by choosing a different effort level, as long as all others do not change their effort levels. Simple marginal analysis tells us that, in such an equilibrium, each person will find that his or her marginal cost of effort is exactly equal to the marginal gain; otherwise, the individual could be better off by working harder or not as hard. Second, Holmstrom stipulates that the outcome be budget balancing — that is, the incentive system should exactly distribute the revenues generated by the actors among the actors. Third, Holmstrom examines Pareto efficiency. This means that the outcome should be such that the individuals in the organization could not find a different outcome that would make them all better off.

Holmstrom shows that no budget-balancing system can create a Nash equilibrium that is also Pareto efficient. In other words, every budget-balancing incentive system will induce a social dilemma among its participants. The reason is that individuals will bring their own marginal costs of effort into equality with their own marginal gain. This means that each individual will not undertake an additional unit of effort that will produce less individual gain than individual cost — even if that extra unit of effort produces more gain for other individuals on the team.

As an example, suppose there is some individual who has a marginal revenue productivity of $12: Each unit of her own effort generates an extra $12 for the team. According to Pareto optimality, she should exert additional effort as long as the cost to her of that effort is less than or equal to $12; each such unit of effort generates more revenue for the team that it costs her as an individual. The only way to motivate her is to make sure that she gets all of the marginal revenue of her last unit of effort. In a team, it is impossible for this to be the case for every individual, as long as the incentive system is budget balancing. If everyone gets all of the last dollar produced, the team will have to pay out more in incentives than it generates. But if the individual gets only one-third of the marginal revenue from her actions, she will work only as long as her effort costs her less than $4 per unit. [pp. 129—130]

This suggests a rather unusual role for shareholders: they provide a money-sink, someplace money can go other than those actually involved in production. This means that the economic mechanism no longer has to be budget-balancing, which actually makes efficiency possible. Miller suggests that this is one reason why the modern public corporation, with its separation between legal ownership (by stockholders) and day-to-day control (by managers) can work, to the extent that it does. It is precisely because the shareholders are passive, with very limited influence over the actual running of the corporation!

Today’s modest proposal — and I should make it very clear that Miller suggests nothing of the kind — is to take this separation of functions even further. Shareholders can use their legal ownership to intervene in the running of the company, though it is hard (and managers try to make it harder). By doing so, however, they become players in the team-production game, and lose their useful role as a money-sink. To limit this danger, while retaining the advantages of competitive markets for capital allocation and corporate control, I suggest the following. A substantial fraction — say three-quarters — of all profits of publicly-held corporations are to be paid to a new institution, which we might call the National Mutual Fund. (Close corporations and partnerships are exempt.) Once a year, the Fund would pay out its accumulated profits as dividend checks, giving an equal amount to every adult citizen. And that’s it.

Substantially reducing the flow of dividends associated with stock ownership should cause a large one-time shock to the level of the stock market. (Roughly speaking, shares should drop by about 3/4.) However, because the Fund collects uniformly, it should not distort relative prices, which are what matter for purposes of capital allocation. The net worth of stock-holders, likewise, will suffer a one-time drop, but this will be partially compensated for by their receiving payments from the Fund in the future. Anyway, lots of things affect the value of stock holdings; it’s not like someone purchased their labor with a promise of future benefits, and then tried to back out of a freely-entered contract when it came time to pay up.

A further wrinkle would be to curb the practice of retained earnings. These account for a huge fraction of corporate capital formation, but they are also one of the ways in which managements escape market discipline. (For some figures on this, see Henwood’s Wall Street, pp. 72—76.) I suppose one could make a Hayekian argument in favor of the practice, but, really, if management can make a good case that a pet project will earn at least a normal rate of return, it shouldn’t be hard for them to raise funds on the open capital market, and if they can’t make such a case, it’s hard to see how they’d be discharging their fiduciary duties to shareholders by pursuing it anyway. This reform, I should add, is logically separate from that of instituting the National Mutual Fund. However, since corporations would pay more out in dividends, it would tend to increase the value of shares, reducing the shock to the level of the stock market.

It is hard to see why the actions of the National Mutual Fund could not be at least as rule-bound and de-politicized as those of a central bank run by skilled technocrats. Indeed, it would seem easier to reduce the discretion of the Fund’s officials to the vanishing point, and to strictly keep it from meddling with the affairs of any corporation, which would be deeply counter-productive. For their part, the citizens receiving the dividends would get the benefits of “portfolio diversification in their income“, but their incentives to meddle politically with individual firms, even quite large firms, would be quite muted. Moreover, they would have a direct and tangible incentive in the health of the corporate sector as a whole, making them less likely to support market-distorting measures to benefit particular firms, geographical regions or industrial sectors. We would move, in short, towards a true ownership society.

*: Actually, there’s a very substantial excerpt ; thanks to Matt in the comments for pointing it out.

It’s a hot, lazy Sunday, which seems like a good time for browsing through livejournal communities dedicated to photos of peacefully rusting machines, quietly crumbling buildings, and similar modern ruins:

Abandoned Places [via David Chess]

Decayed Machinery [via I forget who, years ago]

The photographers are all amateurs, so the quality (to the slight extent I can judge) is quite variable, but many manage to capture the suggestion of sunset and sadness, of unhappy stories brought to a close, which fascinates me about such scenes. Some of these photos, in fact, seem as good as, say, those in Terry Evans’s book on the former Joliet Arsenal, Disarming the Prairie, bringing to mind the words of the poet:

These are the halls of the dead, where the spiders spin and the great circuits fall quiet, one by one.

— But I see I’m getting melodramatic, and it’s just too hot and sticky and still to sustain that.

Would making Berkeley’s first-year economics Ph.D. graduate students this fall read short biographies of William Gates and William Marshall as a way of getting at the idea that there are non-market societies that work very differently from our own today—would that be a teaching idea of extraordinary brilliance or of total insane lunacy?

And: those of us who teach things other than economics, what books do or should we hand out as ice-axes for our students’ frozen seas? ( This one is mine.)

You, the author of the paper, have a responsibility to make your ideas comprehensible. If the first method you choose to explain them fails, then you listen to what people say about where they lost all track of understanding and write a new paper—- with NEW explanations, not the same explanations that failed last time only renumbered. … [This is] not something that is drilled into young scientists; that it is YOUR responsibility to make your ideas clear to others, not their responsibility to try to figure out what you are talking about. As science grows ever larger and ever more complex, I think it is time for all scientists to be much more explicit and much more ruthless on this point.

Science is a social, collaborative process, so part of being a good scientist is effective communication. Scientific communication is overwhelmingly written communication (scientific disciplines are, in a sense, literary communities), so part of being a good scientist is being a good writer. Unfortunately, scientists get little training in writing, and much of that consists of being advised to follow the rules found in horrid little compendia. Fortunately, there is some actual research on effective written communication, that is, on how to arrange your words so that their readers tend to acquire clear notions of your ideas. The best practical guide here, I’ve found, is Joseph William’s Style: Towards Clarity and Grace. However, I have just discovered (via Paradise Blogged) a fine essay by George Gopen and Judith Swan, “The Science of Scientific Writing“, which gives a clear yet concise presentation of the work. (Gopen and Williams are collaborators.) Here is their own summary of how to be clear:

1. Follow a grammatical subject as soon as possible with its verb.
   
2. Place in the stress position the “new information” you want the reader to emphasize.
   
3. Place the person or thing whose “story” a sentence is telling at the beginning of the sentence, in the topic position.
   
4. Place appropriate “old information” (material already stated in the discourse) in the topic position for linkage backward and contextualization forward.
   
5. Articulate the action of every clause or sentence in its verb.
   
6. In general, provide context for your reader before asking that reader to consider anything new.
   
7. In general, try to ensure that the relative emphases of the substance coincide with the relative expectations for emphasis raised by the structure.
   

If these rules, and the notions behind them, are valid, they should apply to more than just
scientific writing; in particular, they should hold for other kinds of academic prose. Looking at their examples of revising scientific writing, expressing the same complicated and precise ideas in more easily grasped ways, I couldn’t help but be reminded of the humanistic “bad writing” controversy, where the case for the defense often seems to rest on complexity, and the example of scientific jargon. The examples of Gopen and Swan, Williams, etc., show that those defenses do not hold. Scholars of the humanities may have reasons for being unclear which don’t apply to scientists, but I can’t think of any good ones.

A staple of bad movies and trashy novels about scientists (i.e., the kind I read) is the neglected genius whose ideas are rejected with incomprehension by the scientific establishment during his life, because they are simply Too Far Ahead Of His Time to be grasped by lesser mortals, only for the scientific community to rediscover these insights decades later. This sort of thing can make for entertaining fiction (if dreary self-mythologization), but it simply doesn’t happen all that often in real life, especially not when the hero is a part of the establishment, and indeed a much-honored one. It certainly doesn’t show up, with documentary evidence, in the staid, reliable pages of Reviews of Modern Physics. Nonetheless:

Gregory L. Eyink and Katepalli R. Sreenivasan, “Onsager and the theory of hydrodynamic turbulence”, Reviews of Modern Physics 78 (2006): 87—135; no free copy

Abstract: Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less well known is his ground-breaking work and lifelong interest in the subject of hydrodynamic turbulence. He wrote two papers on the subject in the 1940s, one of them just a short abstract. Unbeknownst to Onsager, one of his major results was derived a few years earlier by A. N. Kolmogorov, but Onsager’s work contains many gems and shows characteristic originality and deep understanding. His only full-length article on the subject in 1949 introduced two novel ideas — negative-temperature equilibria for two-dimensional ideal fluids and an energy-dissipation anomaly for singular Euler solutions — that stimulated much later work. However, a study of Onsager’s letters to his peers around that time, as well as his private papers of that period and the early 1970s, shows that he had much more to say about the problem than he published. Remarkably, his private notes of the 1940s contain the essential elements of at least four major results that appeared decades later in the literature: (1) a mean-field Poisson-Boltzmann equation and other thermodynamic relations for point vortices; (2) a relation similar to Kolmogorov’s 4/5 law connecting singularities and dissipation; (3) the modern physical picture of spatial intermittency of velocity increments, explaining anomalous scaling of the spectrum; and (4) a spectral turbulence closure quite similar to the modern eddy-damped quasinormal Markovian equations. This paper is a summary of Onsager’s published and unpublished contributions to hydrodynamic turbulence and an account of their place in the field as the subject has evolved through the years. A discussion is also given of the historical context of the work, especially of Onsager’s interactions with his contemporaries who were acknowledged experts in the subject at the time. Finally, a brief speculation is offered as to why Onsager may have chosen not to publish several of his significant results. [My links.]

Nobody outside of statistical physics (and maybe physical chemistry) has heard of Onsager, but he was indeed a great physicist, albeit in a very technical, non-flashy way. By the time he did this work on turbulence, he was already well-known in statistical mechanics for the analytical solution of the Ising model, his theory of phase transitions in liquid crystals, and, perhaps most importantly, a pair of classic papers from 1931 which basically founded modern irreversible thermodynamics, for which he would eventually win the Nobel Prize. (Eyink and Sreenivasan give a fuller discussion of his accomplishments, including the Onsager-Machlup theory of non-equilibrium processes, on which Eyink himself has done important work.) We’re definitely not talking about some marginal figure cut off from the scientific community.

Nonetheless, his attempts to get people to pay attention to these ideas on turbulence were singularly unsuccessful. The reaction of Theodore von Kármán, a deservedly great name in fluid mechanics, was to describe it (in a letter to his student C. C. Lin) as “somewhat ‘screwy’ “; Onsager also corresponded with Lin, who replied in the classic manner of someone wanting to put an end to a conversation (quoted on p. 117): “I am sorry to say that I have not made much progress, except that I desire still more to see something done in this line to bring your ideas down to my level of understanding.” As for the statistical physicists, Eyink and Sreenivasan describe their reaction as one of “polite incomprehension” (except on the part of von Neumann — in an unpublished report). The fact that one of Onsager’s letters describing his ideas (reproduced as Appendix A in this paper) is headed “The little vortices who wanted to play”, and begins “Once upon a time there were n vortices of strengths K1, … , Kn in a two-dimensional frictionless incompressible fluid” probably didn’t help, either. Most of all, a combination of discouragement over this reception, a tendency to be a slow and perfectionist author, and having scads of major research projects going simultaneously kept Onsager from even trying to publish any of this material.

The moral, I hope, is clear: statistical physicists who wander into other areas of science, and find their ideas dismissed by the best experts on those subjects, should nonetheless publish in Physical Review, in a “Fools! I’ll show them all!” spirit, provided they are Lars Onsager.

(It’s interesting that this paper was written by two physicists active in this area, rather than by a historian of science. It seems doubtful to me that a historian, reading the relevant materials in the Onsager archives, would have realized that there was a story here, unless they were familiar with modern work on turbulence at a deeply technical level — unless they had “contributory” as well as “interactional” expertise. And if anyone had gone over those archives around 1990, before these ideas were re-discovered, what would they have made of it?)

Two of my more public-spirited fellow citizens have recently identified looming threats to our own Commonwealth of Pennsylvania.

1. Our beloved junior senator, Rick Santorum (via Pharyngula):
   

   Most scientists unfortunately, those that certainly are advocating for this [embryonic stem cell research], and many others feel very little moral compulsion. It’s a utilitarian, materialistic view of doing whatever they can do to pursue their desired goals.

   
   I, for one, will be happier voting on Mr. Santorum’s re-election in November, knowing that my ballot will play a part in the age-old struggle between utilitarian materialism and deontological idealism, as well as the sagas of human-canine relations and Old Corruption.


2. Our beloved linguistics professor, Mark Liberman:
   

   More than a third of all Pennsylvanians are native speakers of a language other than English — and many of them have not even tried to learn English since immigrating, or at least prefer to carry out their daily lives in another language, living together in neighborhoods where their native language dominates. Some people worry that the majority status of English is critically endangered. 25 years ago, a major political figure warned that these “aliens … will never adopt our language or customs, any more than they can acquire our complexion”, and so far, his prediction seems to be right on the money.

   
   And let’s not forget what they’ve done to our cooking!

Under the rubric “Can Blogging Derail Your Career?”, the Chronicle of Higher Education has seven bloggers discussing Yale’s decision to not hire Juan Cole as a professor of history, and the role, if any, played by his blog in that decision: Siva Vaidhyanathan, Dan Drezner, Brad DeLong, Michael Bérubé (all: yay!), Glenn Reynolds and Ann Althouse (both: hiss), and Erin O’Connor (null result), with a “response” by Cole, which doesn’t actually address the others’ posts specifically, and reads like a separate essay on the same subject as the others. (Via DeLong.)

(Some of the things which were written about Cole as part of the controversy (e.g.,) give the impression of a professor who attains incomprehensibility not through obscurity but through foaming at the mouth. As it happens, though, I sat in on his seminar on millenarian movements when I was a post-doc at Michigan, and nothing could be further from the truth. I suppose I could have missed all the sessions which degenerated into hours-long rants about Zionist Entities… Of course, I don’t know why Yale didn’t give him the job, but if it was because they thought he was too spittle-flecked to be presentable to parents and alumni, they were misinformed.)

The fact that this post is not filed under “Middle East Politics” isn’t going to stop anyone in the comments, is it?

First off, I should thank Henry and the rest of the Timberites for the kind invitation to guest-post, and that very warm introduction. In exchange, I’m going to blog more or less as I usually would, only here. This means some big bricks of posts about “complex systems”, so called, which is or was my scientific field, more or less; and also any miscellaneous outrages which catch my eye this week. Mounting my usual hobby-horses on this stage is a poor exchange for their generosity, but mounting hobby-horses is why I started blogging in the first place, and anyway I’m big on conscienceless nomothetic exploitation of cooperators.

Today I want to talk (below the fold) about some recent work in the statistical mechanics of disordered systems, which might help explain how our sense organs work, and actually involves some good uses of the self-organized criticality and power laws; tomorrow or the day after I’ll get to the smoldering question of “Why Oh Why Can’t We Have Better Econophysics?”

Folklore says that the dark-adapted human eye can detect a single photon; this isn’t quite true, but we can consciously detect a few tens of photons, and some species are that sensitive. Of course, we can see not only in the dark but also during broad daylight, but then the number of photons falling on every part of the retina is huge; the eye isn’t overwhelmed and saturated, though now one or ten photons more or less makes no discernible difference. In the jargon, the eye, and the other sensory organs, have both a large “dynamic range” (we can see in the dark and in the daylight), and “nonlinear response” (changes which are noticeable in the dark aren’t against a high-intensity background). Some version of these facts, including the basic (power-law) form of the relationship between physical stimulus intensity and perceived sensory magnitude, have been known since the nineteenth century. This makes it all the more puzzling that sensory neurons show a linear response over a narrow dynamic range, beyond which they saturate.

You could evade this difficulty by having lots of neurons with different operating ranges, so that raising stimulus intensity saturated some but activated others. The problem is that there don’t seem be that wide a spectrum of operating ranges for individual neurons. In a recent paper, Osame Kinouchi and Mauro Copelli (who blog together at Semciência) offer another way, which has to do with the way sensory neurons interact with each other in a network.

Osame Kinouchi and Mauro Copelli, “Optimal dynamical range of excitable networks at
criticality”, Nature Physics 2 (2006): 348—351; free preprint version at q-bio.NC/0601037 *

Abstract: A recurrent idea in the study of complex systems is that optimal information processing is to be found near phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard and biologically relevant quantity is optimized at criticality. Here we give a clear example of such a phenomenon: a network of excitable elements has its sensitivity and dynamic range maximized at the critical point of a non-equilibrium phase transition. Our results are compatible with the essential role of gap junctions in olfactory glomeruli and retinal ganglionar cell output. Synchronization and global oscillations also emerge from the network dynamics. We propose that the main functional role of electrical coupling is to provide an enhancement of dynamic range, therefore allowing the coding of information spanning several orders of magnitude. The mechanism could provide a microscopic neural basis for psychophysical laws.

Neurons, like muscle cells, are “excitable”, in that the right stimulus will get them to suddenly expend a lot of energy in a characteristic way — muscle cells twitch, and neurons produce an electrical current called an action potential or spike. Kinouchi and Copelli use a standard sort of model of an excitable medium of such cells, which distinguish between the excited state, a sequence of “refractory” states where the neuron can’t spike again after it’s been excited, and a resting or quiescent state when the right input could get it to fire. (These models have a long history in neurodynamics, the study of heart failure, cellular slime molds, etc.) Normally, in these models the cells are arrayed in some regular grid, and the probability that a resting cell becomes excited goes up as it has more excited neighbors. This is still true in Kinouchi and Copelli’s model, only the arrangement of cells is now a simple random graph. Resting cells also get excited at a steady random rate, representing the physical stimulus.

Kinouchi and Copelli argue that the key quantity in their model is how many cells are stimulated into firing, on average, by a single excited cell. If this “branching ratio” is less than one, an external stimulus will tend to produce a small, short-lived burst of excitation, and there will be no spontaneous activity; the system is sub-critical. If the branching ratio is greater than one, outside stimuli produce very large, saturating waves of excitation, and there’s a lot of self-sustained activity, making it hard to use a super-critical network as a detector. At the critical point, however, where each excited cell produces, on average, exactly one more excited cell, waves of excitation eventually die out, but they tend to be very long-lived, and in fact their distribution follows a power law.

(People who teach courses on random processes are very fond of branching processes, because the basic model can be solved exactly with hundred-year-old math, but there are endless ramifications, and some of the applications are very technically sweet. Like most mathematical scientists, Kinouchi has certain tools he tends to return to, and critical branching processes are one of them.)

As Kinouchi and Copelli say in their abstract, the idea that the critical point, where things are just about to go unstable, is a useful place for processing or transmitting information is a persistent theme of complex systems. (You could, arguably, even trace a version of the idea back to William James’s Principles of Psychology.) It has also, before this, been one of the weakest of our ideas. The original work from the 1980s on “evolving to the edge of chaos” has proved impossible to replicate, I would even say experimentally refuted. (Why the phrase and idea continue to propagate is another question for another time.) Stu Kauffman’s studies of models of gene regulatory networks certainly suggests that information moved through these most easily near their critical point, but I don’t think anyone has done a careful information-theoretic analysis of that. In any case, E. coli doesn’t care about the bandwidth of its regulatory network: it cares about reliably making lactase when it only has lactose to eat, i.e., specific adaptive functions. Prior to this, I can only think of one situation where the idea has been made precise and has strong evidence to back it up (namely, this paper), but that’s a purely mathematical exercise of no biological relevance.

What Kinouchi and Copelli have done is very different: they’ve actually identified something biologically important which is maximized at the critical branching ratio, namely the dynamic range. The network as a whole responds to the stimulus, and its dynamic range can be many orders of magnitude wider than that of its component cells. It is this enhancement which is maximized at the critical branching ratio, and falls off sharply for networks which are even a little sub- or super- critical. As a bonus, the shape of the response function is of the correct power-law form, though, in their model, the exact exponent isn’t right. Modifying the network structure, or some model details, changes the exponent, but the dynamic range is still sharply peaked at the critical branching ratio.

There are a lot of other nice things about this paper, which I won’t get in to least I repeat it all, but I will point out one thing: while their central qualitative results are pretty robust to small tweaks, there are some details of their model which make it a fair caricature of some excitable media, but not all. These are quite deliberately matched to properties of the olfactory system and the retina, but wouldn’t work in, say, the cortex, where the dynamics of excitation are different. So this isn’t an “over-universal” model, but one of particular phenomena produced by particular mechanisms. In fact, looking at olfaction, they are able to make a prediction about the effects of knocking out specific genes which are involved in the fast, symmetrical electric couplings they assume. Nobody seems to have done those experiments yet, but, at least to this non-biologist, it seems feasible, and, now, very interesting.

*: Here’s an anecdote illustrating how broken academic publishing is. Kinouchi and Copelli work at the University of Saõ Paulo, which doesn’t, for reasons of economy, subscribe to Nature Physics. To get an electronic copy of their own published paper, they were forced to write correspondents at other universities. I couldn’t help them, because my school doesn’t feel like it can afford to subscribe to Nature Physics either.