Blockchain Papers

Peter R. Killeen

You need to transfer heat from one fluid at 100°C to another at 0°C without mixing them. Given some tubing, you could wrap one length around another. Then, with enough wound tubing, pumping both in at one end, at the nether end you would find that both fluids came out at about 50°C. Good.Can you do better? Can Nature? This is the nut of one (and thereafter many) of the problems Knut Schmidt-Nielsen (of Norwegian lineage, if you wondered; with a statue of him gazing at a camel on the Duke campus, if you wanted to wonder) was driven to by a sojourn in Arizona Sonoran desert half a century ago. There his naturalist's eyes found surprisingly abundant wildlife given the rigor of the environment. Consider the lowly kangaroo rat. It never drinks water and has no appetite for moisture-rich greens. But like all of us, the rat must breathe, and that means exhaling air saturated with moisture that he can scarce afford to lose. Warm air carries more water than does cool. Perhaps those clever little rodents used your tubing architecture to pass incoming and outgoing air by each other, so the outgoing air wasn't so warm, and with a few sniffles of the condensing cooler air the rat could regain some drops of what would be lost. That would be good. But Nature invented a way, and reinvented it dozens of times, that does better.Switch the input of one of your tubes to the nether end. Hot air coming in would then meet outgoing air just a little less hot than it and raise temperature a bit more, and so on down the tubes, until at the end, the now relatively cold incoming air would meet the almost equally cold outgoing, and the transfer of heat would be almost perfect. 100° is squandered on heating 0° but is well spent on 90°. This is called countercurrent exchange (CCE), here countercurrent heat exchange. I shall be mentioning a number of neat ideas that have some generality in this review. I call them cachets.1 They are terms of art that compress an intriguing idea into a simple expression. Words that you can drop at a party.2 You can think with them. Knut plots the temperature of exhalation from a dozen species of birds, and it is a linear function of ambient temperature—but always significantly below body temperature. Those little kangaroo rats do it even better than the birds, and he shows why with cross-sections of their sinuses. Knut is smarter than I, as he can generate a mathematical model of the process, which performs quite well. He is also wiser than I, as he does not write the equations of the model, just describes how it works.What these littlest of nature's mammals do, the biggest can too. How do whales not lose all their core heat through those fins and flukes, which are perfect radiators fanning frigid waters? CCE: They warm the incoming blood with the outgoing, so when the blood gets to the fins it is near their chilly temperature, and the blood returning from the fins is warmed to about core temperature. This clever design is no fluke; evolution works miracles!The brain needs stable temperatures. How do you keep a cool head in hot times? You've already guessed it: CCE, as the carotids spread out in a mesh (called a rete) passing its blood against the flow of venous blood coming in from the nasal sinuses, which cools it as necessary, before sending it on to the brain. Farther down a man's body another organ needs to be kept cool despite how hot he is; CCE to the rescue!Fireplaces are romantic, but most of the heat that is not made on the couch goes up the chimney. The Franklin stove is more efficient, as the stove box and chimney pipe radiate heat into the room. But while heating your front, it chills your back, because it must draw in cold air to feed the flames, and that comes from outside your house. A psychology graduate student improved the situation with countercurrent heat exchange. Close your eyes now before reading on, and see if you can figure out how. Now open them.3CCE works great to preserve the milieu intérieur. But what if you want to move some of that milieu extérieur? Suppose that, unlike the whales, you need to lose heat? Breathing in and out through the nose would tend to conserve your body heat. If you were a dog, what would you do? Perhaps find a way for the hot air to exit other than the one used by the cooler air coming in. In my Sonoran desert my Lucy spends a lot of her time panting. The nose is the primary cooler, inhaling; that long dripping tongue is merely a secondary heat exchange, designed primarily to amuse and bemuse you as it exhales through the mouth.You may have watched your dog pant, but have you noticed that she does not increase the frequency of panting as she gets hotter? This is what the engineers call bang-bang control4: It is either on or off. Why is frequency not a smooth function of temperature? Think about it for a moment before reading the answer suggested by a student of Knut's.5 Mammals cannot use CCE to increase the oxygenation of their blood from the air they breathe, but birds can, and fish breathing through gills use CCE to extract 80–90% of the oxygen that flows over them. “It was during the work with the ostrich that the need for further understanding of bird respiration became acute” is the type of sentence that regularly charms you in How Animals Work. Dogs pant at resonant frequencies; do large birds tune their breathing tracts and wingbeat so that breathing and flying are synchronized?A colleague designed a charter school decades ago in which he used CCE for knowledge exchange, having more advanced students tutor the less advanced throughout the grades. It is still in operation. To what novel uses might you put CCE?There is a mechanism similar to CCE, called countercurrent multipliers (CCMs), where a solution is concentrated “uphill,” as the kidneys concentrate urine. I shall let you turn to Knut for explication of this and other questions. But before you turn, ponder how you might design a CCM and for what else it might be a cachet.In looking through the book you will come across many straight lines, often in double-log coordinates. These are scaling laws. The cost of running in animals ranging from the white mouse to a horse is a near perfect power function (slope −0.40) of their body weight. There are many such scaling laws in biology, typically power functions, and often their observed slope can be derived rationally (West, Brown, & Enquist, 1997) or readily interpreted. A fascinating recent book about such laws is Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies (West, 2017). He delivers on the promise of the subtitle. Question: Do psychologists’ favorite power functions, the psychophysicist's sensory scaling laws, and the behaviorist's generalized matching law fit into any of these schemes?An early observation of scaling laws at work was given by biologist J. B. S. Haldane: “You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.” As the length of an animal doubles, its surface is squared and its mass is cubed. Your cachet: “the square–cube law.” The mass, and thus the kinetic energy that must be dissipated by the animal, increases as the cube of its length, but its landing or impact surface increases only as its square. The strength of bones increases with their cross-sectional area, whereas the mass they must support increases with the volume of the animal. Thus, ants can have very skinny legs, but elephants must have huge columns of legs. Gullivers just can't travel. HO-scale model trains are 1/87 the length of a real train. Their mass is thus 87–3 that of the real train. Less weight to hold them on the track, so they more readily flip at just a few feet per second, with linearly proportional wheel flanges of little help.Gas exchange is a surface phenomenon and so varies as the square of the length of an animal, but the mass it needs to service grows as the cube of the length. What are the design features of our lungs that help deal with his disparity? Drugs are absorbed as a function of the area they come in contact with, about the square of body length, but the mass that they must serve increases as its cube; good dosing requires knowledge of the square–cube law. But metabolic rate is another factor, and that decreases uniformly with body weight; drugs are slower to clear in a large animal, as Knut's story about dosing an elephant6 revealed. Because of this metabolic scaling, all species live for the same number of heartbeats.7 In prescribing a novel drug, my physician looked it up in the pharmacopeia, looked at me up and down, and asked, “I need to dose this in proportion to your skin area. Do you know what that is, Peter?” I just grinned and shook my head, and “No” was all I said.Someone challenges you to draw a curve from point A to point B below it and to its right, so that a frictionless ball rolling from A to B would get there faster than along any other curve. (Hint: This is a situation where CCE won't help.) What would you draw? A straight ramp? A semicircle? A catenary? This optimization problem had bemused good mathematicians for several years. Galileo thought, but couldn't prove (because the calculus was not yet invented), that it was a parabola (close but wrong). In 1696 Johann Bernoulli, one of a clan of gifted Swiss mathematicians, posed it as a challenge to the world (the small world of 17th-century mathematicians). Johann had the correct answer (but with a flawed derivation), which took him weeks to arrive at, in his back pocket, yet he had to extend the deadline because of the paucity of returns. In the end, six great mathematicians provided answers: Johann Bernoulli, Newton, Jakob8 Bernoulli, Leibniz, Tschirnhauß, and l'Hôpital. When Newton eventually found the problem in his post, he completed his proof overnight (taking longer than he would have in his prime) and submitted it anonymously.9 When Bernoulli saw it, he said he knew it surely to be Newton's solution, just “as one knows the lion by its claw.” The correct answer was a segment of a cycloid, the curve traced by a point on a circle rolling along a line. One of the solutions evolved into the calculus of variations, which tells us what kinds of functions, or curves, satisfy a minimum or maximum—a big brother to the simple calculus you may have met in high school.Alexander uses the calculus of variations to prove that the shortest distance between two points is a straight line. Why prove the obvious? To sharpen our pencils. But he starts simpler, first reviewing high school calculus by using homely examples, such as the optimal shape for a can to minimize the metal used to contain a particular volume. Any guesses?10 He wryly notes that most of the cans in his grocery store do not satisfy this solution: “They may have been applying some other optimization criterion.” This, the “optimal for what?” question, is a recurrent issue in optimality theory. What is the optimal speed for an airplane? Given the relation between power used and air resistance and lift, Alexander provides a solution for minimal power between two airports. Then he derives another for minimal fuel: If you fly a bit faster, using more power, you get there sooner, using less fuel. What is optimal depends on what variables you are talking about. What is the optimal lifestyle: fast and furious and everything goes, or calm, centered, and academic? Husband the candle or burn it at both ends? “Optimal for what?” is the question that you are starting to learn to ask.As Alexander explains, calculus is the tool of choice for optimization, and it typically involves some variant of taking the derivative of a function and setting it to zero. However, that gives you an extremum, which could be either a maximum or a minimum. You need to check which, and there are several straightforward techniques to do so (e.g., take the second derivative at that point. If it is positive, the curve is going up from there, and you are at a minimum; negative, at a maximum). If you are sometimes embarrassed by your mathematical mistakes, join the crowd. Some designers of an early flying wing aircraft, precursor to the B2, concluded that you maximized range if all the weight of the craft was in the wings. Eventually the contract was canceled because of inadequate range (“insufficient funds” is what the press release originally said after 15 aircraft were built). A subsequent investigator found that the extremum in this case was a minimum, not a maximum; the designers had apparently failed to check the second derivative and designed the worst, not best, possible configuration! They were “embarrassed” by their mistake but refused to step back from the design, on which the B2 was based (Biddle, 1989). They redesigned their claim instead, arguing that it optimized other objectives. (It didn't.) The B2 incurred billions of dollars in redesign. Clearly those designers were optimizing their claims over objectives other than the best aircraft design to maximize range.11After analyzing optimized structures such as bones and eggshells, Alexander turns to motion: walking, running, flying, and leaping. He shows the utility of catastrophe theory, at least qualitatively, in the analysis of gaits. He slowly ponders the order in which tortoises should move their feet. Of most interest to this audience is his review of optimal foraging: In selecting prey, should a bird eat only the biggest worms or anything it comes to? How long should a carnivore pick over a carcass before moving on? When should a challenged stag fight and when should it run? You have already mused over the relevant variables, I'm sure. 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Hans‐Jürgen Bandelt

Dear Sir, In science, it is not surprising to have exciting claims later refuted by hard evidence – although it may even be harder to have them corrected in the same journal where they originally appeared (Don't challenge a winning paper: Bär, 2006). One of the main reasons why false claims could pass through peer reviewing and eventually appear in print is (i) limited knowledge about certain genetic markers in a newly emerging field at the time of submission or (ii) insufficient screening of the published data for comparison and (iii) inadvertent documentation and analysis of the novel data underlying such claims. It may then take some years before the true causes for a particular finding would come to light. This apparently applies to the remarkable claim made by Holyoake et al. (2001) that the mitochondrial DNA (mtDNA) mutations G9055A and G11719A would compromise the semen quality of those men who possess any of these mutations in their mtDNAs (leading to reduced sperm motility and/or low sperm count). This study won the 2nd Prize of the European Academy of Andrology in 2001 – a winning paper, thus. The results of this study were aptly challenged by Montiel-Sosa et al. (2002), who (i) pointed to the fact that site 11719 determines a basal European mtDNA haplogroup (nowadays referred to R0), (ii) hinted at the peculiar frequency of the 11719 polymorphism as reported by Holyoake et al. (2001), and (iii) argued that ethnic origins of samples in a mixed population would matter and that 'the control and low sperm motility group could be non-homogenous'. Indeed, no reference to haplogroups, constituting the major branches of the mtDNA phylogeny, was made in the study by Holyoake et al. (2001), although it was submitted at a time (September 2000) where the role of the two particular (G9055A and G11719A) and other mutations was already quite well understood. Holyoake et al. (2002) in their reply to Montiel-Sosa et al. (2002) emphasized that they were only 'interested in single nucleotide substitutions in relationship to poor semen quality'. This popular 'allelic' approach gleaned from the analysis of the nuclear genome, however, is patently unsuitable for a deeply hierarchical genetic system such as mtDNA. First, the allelic view ignores the tight link between different mutations in the mtDNA phylogeny (as between G9055A and G11719A). Clusters of mutations would show up together and could then not serve as independent indicators of a disease phenotype. Second, disregard for the mtDNA phylogeny leaves out the option of phylogenetic proof-reading of obtained mtDNA results in regard to potential errors (Bandelt et al., 2005a). Not unexpectedly, the detailed haplogroup analysis of Pereira et al. (2005) for a large Portuguese sample did not support the notion that men carrying an mtDNA from a specific haplogroup overall had an increased or a reduced risk of infertility. These authors also warned that the observation by Ruiz-Pesini et al. (2000) that 'haplogroups H and K are significantly more abundant in nonasthenozoospermic and asthenozoospermic populations, respectively' may have been caused by population stratification. As long as patients and controls are not controlled for ethnic background, geographical matrilineal ancestry and social stratum (which certainly matters in countries with a considerable record of recent immigration), mere correlation of a mutation/haplogroup with a disease phenotype may be spurious and thus cannot provide sufficient evidence for an association. The complete mtDNA data of Ingman et al. (2000) as well as the RFLP-based analysis of West Eurasian mtDNAs of Macaulay et al. (1999) would have provided the necessary background information for the SSCP analysis aimed at by Holyoake et al. (2001). Curiously, the Ingman et al. (2000) study was referred to in a later article (Gemmell & Sin, 2002) by the same senior author (F. Y. T. Sin), but apparently without reappraising the findings of his former paper. If the data by Ingman et al. (2000) had been inspected at the time, then it would have become clear that the frequencies of the mutations observed by Holyoake et al. (2001) are mutually inconsistent and thus cannot realistically correspond to real-world data. To see this, take a preview of the worldwide mtDNA phylogeny as seen from the early Ingman et al. (2000) data, but now enriched with the up-to-date information about the nesting of the corresponding haplogroups, as displayed in Figure 1 of Bandelt et al. (2006). Nucleotide A at site 8860 is shared by virtually all mtDNAs worldwide that are not closest relatives of the revised Cambridge reference sequence (rCRS; Andrews et al., 1999). In Table 3 of Holyoake et al. (2001) the frequencies are recorded as 2/102 and 1/59 instead of the expected frequency of (nearly) 100%! The other frequencies in that table do not fare much better. Virtually all mtDNAs not belonging to the basal West Eurasian haplogroup R0 (which encompasses the sister haplogroups R0a and HV) bear the characteristic mutation G11719A. Assuming the frequency for this mutation in 'normozoospermic' men reported by Holyoake et al. (2001), one would be forced to conclude that all 80 control mtDNAs are members of haplogroup R0 (Table 1). Such a population sample has never been observed anywhere in the world. Moreover, this zero frequency is at odds with the other mutation frequencies recorded, as there is evidence that the other two basal West Eurasian haplogroups, JT and U (including K), were observed in both, the 'normozoospermic' and the 'subnormozoospermic' men (Table 1). The two frequencies of G11719A, on their own, are thus far apart from any realistic value, indicating that the recognition of G11719A via SSCP analysis must have been strongly hampered by technical problems. There is, by the way, little evidence that Polynesian mtDNAs played a noticeable role, because the vast majority of them would fall into a specific branch of haplogroup B. This haplogroup would be pinpointed by the 9 base-pair (bp) deletion, which, however, was found at a meagre 2.8% in the total sample. Note that the 9-bp deletion is also seen sporadically on many haplogroup backgrounds other than B. Furthermore, potential Sub-Saharan African mtDNA mutations (possibly C7789A) or (South-)East Asian mtDNA mutations (possibly G7853A) are present (if at all) at similarly minor frequencies; thus, in particular, the suggestion of considerable African mtDNA ancestry (Montiel-Sosa et al., 2002) receives no support from the data. Therefore, the vast majority (perhaps >95%) of mtDNAs analysed by Holyoake et al. (2001) must have been of European descent. Table 4 of Holyoake et al. (2001), which provides the full haplotype information, indicates further problems. Mutations that would be expected to be linked with other mutations in view of the above inequalities are not just absent but show up in unexpected combinations, almost random-like, which would rather suggest sample mix-up. Moreover, the haplogroup K mutation G9055A should always entail the mutation G11719A specific to non-R0 lineages, but according to that table, both mutations are rather unlinked. In the present Table 2, some haplotypes from Table 4 of Holyoake et al. (2001) are listed that combine at least two mutations. In three cases, all from the 'subnormozoospermic' group, one observes potentially mosaic patterns (Table 2). The best explanation for the odd frequency spectrum as well as the incomplete and mosaic haplotypes is, in the first place, massive failure of the SSCP analysis carried out by Holyoake et al. (2001). Such a mis-analysis is not an infrequent phenomenon in medical genetics (see e.g. Bandelt et al., 2005b). But why would have 'subnormozoospermia' triumphed over 'normozoospermia' e.g. in the screening of G11719A? And why would the 11719 polymorphism, if deemed crucial for 'subnormozoospermia', have only been analysed in a meagre 33 instead of, say, 131 patients? And what about G9055A? A normal mtDNA sample of predominantly mixed European descent would hardly show so few (<1%) haplogroup K members (Behar et al., 2006). The consistent trend in identifying mutations at frequencies that are far too low, especially for the 'normozoospermic' group, could suggest that the SSCP analysis was biased and effectively carried out only for a minority of the samples. It then seems that the number of fully screened mtDNAs was smaller for the 'normozoospermic' group than for the 'subnormozoospermic' group. In summary, there is no solid evidence that primary mtDNA substitutions other than recognized pathogenic mutations, mainly in heteroplasmic state, which usually cause complex disease phenotypes, influence sperm motility in any way. Therefore, it would be premature to accept all hypotheses and interpretations put forward by Gemmell & Sin (2002) and St. John et al. (2005), who took the results of Ruiz-Pesini et al. (2000) and Holyoake et al. (2001) at face value. Before far-reaching implications are discussed, the underlying data should come under scrutiny first. It would certainly be desirable to re-study the mtDNA samples employed by Holyoake et al. (2001) by performing highest quality sequencing. In any case, there is an urgent need for a new start of mtDNA analysis of samples from men with idiopathic infertility (or subfertility) by complete mtDNA sequencing in order to provide a solid database to which any subsequent case studies could get compared and evaluated. The most recent work of Pereira et al. (2007) is a promising first step in this direction.