program. today, passions have cooled, and working mathematicians show little interest in foundational matters. the infinitary set theoretic methods that occasioned such controversy are casually absorbed in passing by the beginning graduate student and used unhesitatingly. like a military historian surveying the battlefield long after all the bodies have been cleared away, marcus giaquinto coolly revisits the controversies in the search for certainty. it all began with a necessary effort by mathematicians to put their house in order. although the methods of the calculus had proved highly successful, their underlying logic had been in grave need of clarification. calculus worked with numbers and functions, but no coherent theory of the so - called " real " numbers had been developed, and the notion of function had been stretched in the direction of a frightening arbitrariness. richard dedekind ' s elegant characterization of the real numbers in terms of " cuts " had a distinctly set - theoretic flavor, and georg cantor ' s new push into the " actual " infinite expanded the boundaries of the subject matter of mathematics into what hilbert later characterized as " cantor ' s paradise. " but cantor ' s infinite was plagued by paradox. the kernel of at least one of these paradoxes could manifest itself in what seemed like everyday reasoning, as bertrand russell showed in his famous paradox : if we consider the set s of all those sets that are not members of themselves, then s is a member of itself if and only if it is not a member of itself. this was particularly bad news for gottlob frege, whose ambitious logical system for the foundations of mathematics proved vulnerable to russell ' s paradox and was thus seen to be inconsistent. the highly influential but rather baroque three - volume principia mathematica was bertrand russell ' s effort ( with coauthor alfred north whitehead ) to revive frege ' s wrecked program. paradoxes such as russell ' s were to be avoided by slicing up the universe of mathematical discourse into discrete successive " types, " with set membership permitted only between adjacent types. meanwhile, ernst zermelo, who never accepted the stringent syntactic demands of formal logical systems, proposed a set of axioms for set theory. by the 1920s, it was realized that zermelo ' s axioms provided the basis of a formal system rivaling that of principia. in an important paper appearing in 1930, zermelo proposed what came to be called the iterative notion of set, in which a hierarchy of sets is built


axioms provided the basis of a formal system rivaling that of principia. in an important paper appearing in 1930, zermelo proposed what came to be called the iterative notion of set, in which a hierarchy of sets is built from some initial collection of things by iterating indefinitely the operation of forming the set of all subsets of a given set. he observed that his axioms could be construed as being about just this notion. a few years later, in an address on the foundations of mathematics, kurt godel emphasized that rather than being seen as a rival to principia, when viewed from the perspective of the iterative notion of set zermelo ' s system could be seen as the result of eliminating unnecessary complications and artificial restrictions from the whitehead - russell system. by the 1940s and ' 50s, set - theoretic methods had become a crucial part of the mathematician ' s toolbox. back in the 1920s, when passions were aflame, hilbert developed an ingenious strategy by which he intended to overcome his opponents. he would establish the legitimacy of methods that brouwer and weyl considered dubious by encapsulating those methods in formal systems whose consistency would then be proved using only methods of which they approved. in a revolutionary paper in 1931, the young godel demonstrated not only that consistency could not be proved using only these restrictive methods, but also that the same negative conclusion held even if the entire panoply of methods encapsulated in the systems in question was brought to bear. after godel, the foundations of mathematics were seen as inevitably open - ended, with more and more propositions becoming provable as ever more powerful methods were employed. godel liked to emphasize that these more powerful methods could be thought of as being essentially a matter of venturing sufficiently far out in the iterative hierarchy of sets. giaquinto has provided a careful and judicious discussion and analysis of these matters, supplying needed technical background for readers who are not mathematicians. although foundational questions have ceased to be of much importance to most mathematicians, controversies among specialists continue. readers of this book will be well prepared to follow the current literature on foundations of mathematics.


cerebral blood flow ( cbf ) the normal cerebral blood flow is approximately 50ml / 100g / min or 700 ml / min, which is roughly 14 % of the cardiac output. this ranges from 20ml / 100g / min in white matter to 70ml / 100g / min in grey matter. the kety - schmidt technique applies the fick principal using n2o to calculate whole brain cbf. cerebral blood flow = cerebral perfusion pressure / cerebrovascular resistance cerebral perfusion pressure cpp = cbf x cvr ( compare bp = co x svr ) cerebral perfusion pressure ( cpp ) is defined as the difference between mean arterial pressure ( map ) and intracranial ( icp ) or central venous pressures ( cvp ), whichever is the highest. map is the diastolic pressure plus one third of the pulse pressure ( difference between the systolic and diastolic ). cpp = map – icp ( or cvp, whichever is the highest ) a cpp less than 70 mmhg can lead to a rapid decrease in jugular venous bulb saturation ( normal range 65 % - 75 % ) because of increased oxygen extraction a number of studies on patients with severe head injuries have shown an increase in mortality and poor outcome when cpp falls to less than 70 mmhg for a sustained period. pressure autoregulation maintains cbf at a constant level in normal brain in the face of the usual fluctuations in blood pressure. it is a poorly understood local vascular mechanism. normally autoregulation maintains a constant blood flow between map 50 mmhg and 150 mmhg. however in traumatised or ischaemic brain, cbf may become blood pressure dependent. regional blood flow is tightly coupled to brain metabolism. energy metabolites cause local vasodilatation, assisting with rapid regional control of cbf. carbon dioxide can have a significant influence on cbf. as the arterial pco2 rises, vasodilatation increases cbf and when co2 is reduced vasoconstriction occurs. when paco2 is less than 3. 3kpa ( 25 mmhg ) there is no further reduction in cbf. therefore there is no advantage in inducing further hypocapnia as this will only shift the oxygen dissociation curve further to the left, making oxygen less available to the tissues. arterial po2 has a minimal effect until po2 drops below 6. 7 kpa ( 50 mmhg ), when cb


what makes some children more likely than others to dart across the street in traffic? according to a study in the december journal of experimental psychology : applied ( vol. 9, no. 4 ), it ' s whether they are risk - takers. in the study, lead author ulrich hoffrage, phd, a research scientist at the max planck institute for human development in berlin, and colleagues tested 22 boys and 22 girls who were 5 to 6 years old. the researchers first placed each child on the curb of a busy one - way street in munich where there was no traffic light or crosswalk. they then asked the children to indicate when they thought it was safe to cross the street. as the researchers expected, some children were more likely than others to say they ' d cross the street at potentially dangerous times. to find out why some children seem to be traffic daredevils, hoffrage and colleagues played a gambling game with the children. an experimenter presented each child with 10 wooden boxes, nine of which contained coveted stickers ; the tenth box was an empty " devil " box. the children were told to choose and open the boxes one - by - one. if they chose the devil box, the game ended and they lost their stickers ; but if they terminated the game before they found the devil, they were able to keep the stickers they ' d found. children who terminated the game early were classified as risk - avoiders, while those who pressed their luck were labeled risk - takers. overall, the researchers found that the children who were risk - takers in the gambling task were more likely to decide to cross the street, especially when the gaps between cars were midsized - - a time when it ' s often unclear whether it ' s safe to cross. the risk - takers also made their decisions to cross the street more quickly. moreover, while boys were more likely than girls to make risky decisions, whether a child was a risk - taker was a far better predictor of their street - crossing behavior than gender. the findings indicate that traffic - safety education should pay more attention to children ' s risk behavior and tailor their messages accordingly, says hoffrage. " if we succeed in identifying the mechanisms that make risk - takers accept higher levels of risk, " write the authors, " we can design and implement training programs tailored to those mechanisms. for instance, risk - takers may profit from training in visual timing skills. " - - d. smith bailey


this month in physics history november 1887 : michelson and morley report their failure to detect the luminiferous ether albert abraham michelson was born in strelno, germany in 1852. when he was two years old his family moved to the us, and he grew up in the rough mining towns of murphy ’ s camp, california and virginia city, nevada. as a youngster, he showed some aptitude for science, and at age 16 he obtained a special appointment to the u. s. naval academy from president u. s. grant. as a student at the naval academy, he excelled at optics and other sciences, and clearly had an aptitude for precision instruments and measurements. he graduated in 1873, and then became an instructor of physics and chemistry at the naval academy. in 1877, while conducting a classroom demonstration of foucault ’ s measurement of the speed of light, he realized he could make significant improvements on the method. within the next two years, michelson managed to measure the speed of light with much greater precision than ever before. the measurement brought him some recognition as a scientist, and settled him on pursuing a career in physics research. he then headed to europe to study for the next two years. working in berlin, he invented the device known as the michelson interferometer. he realized he could use the setup to detect the earth ’ s velocity through the ether. the basic design is simple and elegant. a beam of light is split and sent down two perpendicular paths. then, after bouncing off mirrors, the two beams are recombined, producing an interference pattern. if the earth was indeed traveling through the ether, the speed of light would differ depending on its direction with respect to the earth ’ s motion through the ether, and michelson ’ s interferometer would pick up a slight shift in the interference fringes. however, these early efforts found no evidence of the earth ’ s movement with respect to the ether. michelson was disappointed by the result and considered the experiment a failure. nonetheless, he continued his effort to detect the ether when he returned to the united states. in 1882 michelson took a position at the case school of applied science in cleveland, ohio. there he teamed up with chemist edward morley, who helped make some improvements in the experiments michelson had begun in berlin. the new apparatus was similar in basic design to his previous ones, but much more sensitive. it used extra mirrors to allow the light beams to bounce back and forth, creating a much longer path length.


in the experiments michelson had begun in berlin. the new apparatus was similar in basic design to his previous ones, but much more sensitive. it used extra mirrors to allow the light beams to bounce back and forth, creating a much longer path length. michelson and morley conducted the experiments in a basement lab, and to minimize vibrations, the setup rested atop a huge stone block, which floated in a pool of mercury that allowed the entire apparatus to rotate. even with this exquisitely sensitive design, michelson and morley couldn ’ t detect evidence of motion through the ether. they reported their null result in november 1887 in the american journal of science, in a paper titled “ on the relative motion of the earth and the luminiferous ether. ” ( the paper is online at www. aip. org / history / gap / michelson / michelson. html. ) though disappointing to michelson and morley, the experiment revolutionized physics. some scientists initially tried to explain the results while keeping the ether concept. for instance, george fitzgerald and hendrik lorentz independently proposed that moving objects contract along their direction of motion, making the speed of light appear the same for all observers. then in 1905 albert einstein, with his groundbreaking theory of special relativity, abandoned the ether and explained the michelson - morley result, though it is uncertain whether einstein was actually influenced by their experiment. michelson and morley nonetheless both continued to believe that light must be a vibration in the ether, though michelson did acknowledge the importance of einstein ’ s work on relativity. although it couldn ’ t detect the non - existent ether, the michelson interferometer proved useful for other measurements. michelson used his interferometer to measure the length of the international standard meter in terms of wavelengths of cadmium light, and in 1920 he was the first to measure the angular diameter of a distant star, also using an interferometer. in 1901 michelson was the second president of the aps, and he became the first american to win the nobel prize in 1907, for his precision optical instruments and measurements made with them. in 1889 michelson moved to clark university in worcester, massachusetts, and then in 1892 to the university of chicago. he returned to his work refining measurements of the speed of light, and continued making more and more precise measurements right up to his death in 1931. ©1995 - 2013, american physical society aps encourages the redistribution of the materials included in this newspaper provided that attribution to the source is noted and the materials are not truncated


. ideally, contestants will use data visualization software such as microsoft research ’ s layerscape ( worldwide telescope ) to add visualization or maps to the learning unit. each entry should include a one - page description of subject, content matter, and how the arizona experience content was incorporated. lesson plans should strive to present an engaging and interactive learning experience that involves students in creative and analytical thinking through inquiry, investigation, and exploration of content. lesson plans must be classroom - tested prior to submission to the contest. only one entry per teacher is permitted, either individually or as a team. download entry form. each entry should include the following : - name of teacher ( s ) - project title - grade level ( s ) - statement of the objective, scope and strengths of the proposed lesson plan - statement of how and which arizona experience content is incorporated into the lesson plan - reflection paragraph about the effectiveness of the lesson in your classroom. - detailed description of the lesson plan - lesson description — describe the objective ( s ) and procedure to accomplish the objective ( s ) - content standards — note which of arizona state standards are addressed in the lesson plan - concepts — identify the concepts engaged by the lesson plan - objectives — student - oriented, observable, measurable and descriptive of a learning outcome - materials — worksheets, student activity forms, assignments, assessment tool ( s ), and other materials used in the lesson plan - time — in - class time required to complete the lesson nominations must be received by 5 : 00 pm on sunday, march 10, 2013. the entry must comply with the guidelines outlined on the application form. the imagine arizona selection committee reserves the right to disqualify entries that do not comply with the guidelines. winning curriculum will be publicized on the teachers ’ center at the arizona experience. entries will be judged by a selection committee including arizona experience team members and individuals from the education community. entries will be judged on the following criteria : - 25 points — incorporating the arizona experience materials ( e. g., publications, web site, multimedia resources, etc. ) - 15 points — arizona standard - based education approach - 15 points — evidence of exemplary teaching methods and effectiveness - 15 points — lesson originality and creativity - 15 points — ease of replication or adaptation ( across curriculum, age groups, and schools ) - all decisions of the selection committee are final and are not subject to appeal. cash prizes will be awarded for 1st, 2nd, and 3rd prize in both the individual and team category and for honorable mention ( s ). this


copyright © 2001 – 2008 jsd i set up some spreadsheets to solve laplace ’ s equation, with more - or - less any boundary conditions you want. the spreadsheet becomes, essentially, a 2d cellular automaton that directly emulates the physics. this version handles objects in a d = 2 universe in rectangular coordinates. in flatland, i. e. d = 2, the z direction simply does not exist. alas many people are unfamiliar with the laws of physics in flatland. therefore it might be better to think of this as a d = 3 universe in which all d = 3 objects are infinitely tall and translationally invariant along the z axis. in this case, the z direction exists, but is uninteresting, and the essential physics is the same as the d = 2 case. ( this is not the same as considering a thin flat “ d = 2 ” object embedded in the d = 3 universe! ) in any case, each cell represents an area dx∧dy in the xy plane. the spreadsheet to handle this case can be found in reference 1. occupying a large area near the upper left of the spreadsheet is a grid that i call the potential grid. you can set boundary conditions for the problem by choosing cells that you want to represent electrodes, and specifying the potential on these electrodes. for example, reference 1 contains three electrodes : within the universe, cells that are not electrodes are called vacuum cells. they contain a formula that will be used to calculate their potential, in accordance with laplace ’ s equation, subject to the specified boundary conditions. if you want to “ erase ” part of an electrode, you should use the copy - and - paste function to fill those cells with the vacuum formula. just to the right of the " potential " grid there is second grid that i call the | field | grid because it calculates and displays the magnitude of the electric field at each point. farther right is a third grid that calculates the charge density ( charge per unit volume ). if you add up all the cells in a given area, you get a charge per unit length. this means length in the z direction ; it is the charge per unit length of the object rooted in the given area and extending infinitely far perpendicular to the screen. principle of operation : consider a cross - shaped group of 5 elements somewhere on the spreadsheet, and label them as shown in figure 1. now the discrete approximation to the second derivative in


the given area and extending infinitely far perpendicular to the screen. principle of operation : consider a cross - shaped group of 5 elements somewhere on the spreadsheet, and label them as shown in figure 1. now the discrete approximation to the second derivative in the horizontal direction is b + c−2w, and in the vertical direction it is a + d−2w. the laplacian vanishes if w = ( a + b + c + d ) / 4, i. e. if the central element is equal to the average of its four neighbors. recall we are assuming ( d / dz ) is zero. this leads to an algorithm that says that for each cell in the vacuum, we want to equal the average of its four neighbors. so the basic step of the algorithm is to run through the grid and just set each cell to the average of the neighboring cells. that does not immediately solve the problem, because whenever we change a cell it requires us to change all the neighbors. however, each basic step brings us closer to a good solution, so we just repeat the basic step several times. this is called the relaxation algorithm. another way to motivate the same algorithm is to consider the electrostatic field energy. it depends on the square of the electric field, i. e. the square of the first derivatives of the potential. this energy is minimized when the central cell is equal to the average of its four neighbors. therefore each step of the update algorithm lowers the local energy. tangential remark : you can say that the field energy serves as a lyapunov function for the relaxation algorithm... but if this doesn ’ t mean anything to you, don ’ t worry about it. reference 1 has 841 cells arranged as a 29x29 grid. for a grid of this size, the relaxation algorithm converges in a few seconds. that ’ s fast enough that it ’ s not boring, but slow enough that you can observe the propagation of changes if you fiddle with the boundary conditions. there is a cell just above the top right of the potential grid, labeled object potential. if you change the value of this cell, you can watch how the charge distribution responds. while the algorithm is running, i. e. after you have changed something but before the algorithm has converged to a solution, the grid contains an approximate solution that doesn ’ t exactly satisfy laplace ’ s equation. that is, during this phase, there will be nonzero charge in the “ vacuum ”. this


but before the algorithm has converged to a solution, the grid contains an approximate solution that doesn ’ t exactly satisfy laplace ’ s equation. that is, during this phase, there will be nonzero charge in the “ vacuum ”. this is unavoidable ; because the spreadsheet strictly enforces local conservation of charge, as discussed in section 2. 2. that means there is no way for the objects to acquire the correct charge unless charge flows through the vacuum somehow. the algorithm gradually moves all this charge to the boundaries. the “ manual recalculation ” mode ( using the “ f9 ” key ) may help you observe this, as discussed in section 5. excel evaluates cells in a sequence that it chooses. the sequence defies simple description, and it has nothing to do with the physics. ( remember, this is an electrostatic problem ; there is no physically - significant timescale. ) unfortunately, this sequencing means charge propagates quickly in certain directions across the grid, and slowly in the opposite directions. if you were writing in a computer language that gave you more control than excel does, you could get rid of this unphysical asymmetry by evaluating things in checkerboard - sequence ( all the black squares, then all the white squares ) or in randomized order. as mentioned above, just outside the edge of the potential grid is a layer of cells that implement the boundary conditions. in this example, they implement born / von - karman periodic boundary conditions. that is, given a universe of n rows by m columns, row n + 1 is constrained to equal row 1, and column m + 1 is constrained to equal column 1. you can think of this as a torus, where the top edge of the n×m grid joins the bottom, and the left edge joins the right. equivalently, you can imagine tiling an infinite region with copies of the n×m grid, subject to the constraint that corresponding cells have the same value in every tile. below the potential grid is a graph with many traces ; each trace shows the potential as a function of x, while different traces show different y values ( rows ). clicking on one of the traces highlights the corresponding row. this may help you locate extremal values. below the field grid is a similar graph with many traces. you can make the universe bigger by adding more rows and columns if you like ; use the " fill across " and " fill down " features to propagate the vacuum formula into


values. below the field grid is a similar graph with many traces. you can make the universe bigger by adding more rows and columns if you like ; use the " fill across " and " fill down " features to propagate the vacuum formula into the new cells. beware : you must fill from a vacuum cell that is not adjacent to the newly - added cells or the results will be incorrect. you could extend this calculation to d = 3, removing any assumption of translational symmetry. one possible brute - force solution would be to make a spreadsheet with 29 different 29x29 grids and put the appropriately - generalized formula in them. on the other hand, when the problem gets this complicated, you ’ re probably better off using a more sophisticated programming language, such as c + +. reference 2 is similar to reference 1, but has several additional features. for one thing, it uses a fancier formula in the vacuum cells. it uses a technique called “ over - relaxation ” to improve the speed of convergence. this is described at e. g. reference 3. basically the idea is to figure out how big a step the simple relaxation algorithm would have ‘ taken, and take a step larger than that by a factor of gamma, in hopes of moving more quickly towards the final result. gamma = 1 corresponds to the plain old relaxation algorithm, with no over - relaxation. values between 1 and 2 make sense. ( if gamma were set greater than 2, the electrostatic energy would increase at every step, so the algorithm would not converge. ) the value of gamma is controlled by a cell near the top right of the potential grid. more generally, reference 4 describes a fancy fortran program for doing calculations of this sort. if you ’ re interested in such things, take a look there. reference 2 has another cute little feature, the “ gate ” cell at the lower right of the potential grid. setting it to zero sets the vacuum potential to zero everywhere. setting it back to a nonzero value allows the potentials to be recalculated. this is convenient if you just want to watch how the solution propagates. it is also invaluable for recovering from the following situation : if you enter an invalid expression into a cell in or near the vacuum, the spreadsheet will be unable to calculate the neighboring cell values, and the problem will spread from cell to cell like a disease. as mentioned above, all the potential grids in reference 1 and reference 2 implement periodic boundary conditions – also


vacuum, the spreadsheet will be unable to calculate the neighboring cell values, and the problem will spread from cell to cell like a disease. as mentioned above, all the potential grids in reference 1 and reference 2 implement periodic boundary conditions – also known as born / von - karman boundary conditions. periodic boundary conditions are not the only possible choice. another option to have a hall of mirrors. that is, imagine that just to the left of the model universe there is a mirror - image copy of itself. then impose periodic boundary conditions on the pair ( with the appropriate double - length period ). do the same in the vertical direction. you can turn on this feature in the advanced spreadsheet by putting a nonzero value in the cell labeled “ hall of mirrors ” near the lower - right corner of the potential grid. the hall - of - mirrors condition has an interesting property : it causes the directional derivative of the potential, in the direction perpendicular to the edge, to be zero at the edge of the universe. for some applications, for instance if you are trying to model the “ self - capacitance ” of some object, the hall - of - mirrors boundary condition may approximate the desired physics better than periodic boundary conditions would. in reference 2, over on the lower right below the main charge - density grid, there is a pair of smallish grids labeled “ charge conservation ”. they serve to illustrate the principle of global charge neutrality and local charge conservation. the pair consists of a potential grid and the corresponding charge - density grid. in this potential grid, you can put an arbitrary arrangement of values in the cells. no matter what you do, no matter how weird the potential - arrangement is, the total charge ( i. e. the sum over the charge - density grid ) comes out zero, provided you don ’ t mess with the periodic boundary conditions. it is easy to see why this must be so : we calculate the charge by convolving the operator ( a + b + c + d−4w ) with the potential grid. every nonzero potential cell contributes to the convolution grid five times : once as a, once as b, once as c, once as d, and once ( weighted by - 4 ) as w. if you add those five contributions, you get zero every time. ( there may be small discrepancies due to roundoff errors, which we ignore. ) the cells in this little grid are just numbers. we do not run the relaxation algorithm


if you add those five contributions, you get zero every time. ( there may be small discrepancies due to roundoff errors, which we ignore. ) the cells in this little grid are just numbers. we do not run the relaxation algorithm on them. this should make it clear that the global charge neutrality, in this model system, has nothing to do with the relaxation algorithm. you could use potential values from the relaxation algorithm, or from some other algorithm, or from a random - number generator, and the total charge in the universe would still be zero. no algorithm can change this zero. this zero can be seen as a manifestation of gauss ’ s law. we can consider the edge of the universe to be a gaussian pillbox. the periodic boundary condition ensures that whatever field lines leave the top of the universe re - enter the bottom of the universe. therefore there is no net flux flowing into the universe. ( in the example, the field happens to be zero at the edge, making it extra - obvious that there is no net flux. ) since there is no net flux, the net charge on the interior must be zero. the validity of gauss ’ s law depends on the structure of the operator ( a + b + c + d−4w ) and not much else. its applicability depends on the boundary condition for the universe itself. global charge neutrality automatically implies global conservation of charge. global conservation is vaguely interesting, but it is important in physics, however, to have a local conservation law. here ’ s why : suppose some charge unaccountably disappeared from my lab. it would give me little comfort to be told that it reappeared in some unknowable distant part of the universe ; i would be unable to distinguish non - local conservation from from non - conservation. fortunately, our model system does have a local conservation law. if you increase the potential in any one cell, it causes an increase in the charge - density in the corresponding cell — but this increase is exactly counterbalanced by a decrease in the four neighboring cells ( not in some goofy distant cells ). again, this depends on the structure of the laplacian, not on the update algorithm. just below the aforementioned pair of grids is yet another pair of smallish grids, labeled “ gauge invariance ”. as in most of the other grids, i have imposed born / von - karman periodic boundary conditions. as before, this exhibits global charge neutrality and local charge conservation. this grid is


. the grounded enclosure option does not generally converge to the same limit, as is obvious from the following : using any of the aforementioned spreadsheets, if you have just one object and nothing else, the capacitance of the object is always zero. gauge invariance guarantees it. that is, you can put any potential you like on the singleton object, and it won ’ t develop any charge. the only way to produce a charge is to have two ( or more ) objects with different potentials. ( the enclosure, if present, counts as an object like any other. there is nothing special about the enclosure. ) i created another very - similar spreadsheet that solves laplace ’ s equation in d = 3 for objects with rotational symmetry about the z axis. it can be found in reference 5. unlike the previous versions, it does not assume translational invariance along the z axis, so you can calculate the behavior of objects shaped like pears, or bowls, et cetera. each cell represents an area dr∧dz in polar coordinates. note that i am avoiding the word “ cylindrical ” because mathematicians use the word to describe anything with translational invariance, while physicists use the same word to describe anything with rotational invariance. sigh. this is the same as the previous spreadsheet, but it uses the formula for the laplacian in polar coordinates as discussed at e. g. reference 6. the potential grid represents a slice through the axis of symmetry. rotational symmetry implies that any such slice has reflection symmetry. if you fill in the left half - plane of the potential grid ( with your chosen objects and other boundary conditions ), the spreadsheet formulas will mirror it in the right half - plane. it is not necessary or desirable for you to manually change anything in the right half - plane. similar remarks apply to the symmetry of the charge - density grid ; it represents a slice through the axis of symmetry. in d = 3 with rotational symmetry about the z axis, the laplacian is ( d / dr ) 2 + ( 1 / r ) ( d / dr ) + ( d / dz ) 2 ; we know the phi - derivative is zero. ( you can contrast this with the previous cases, namely d = 3 with translational symmetry in the z direction, where the laplacian was ( d / dx ) 2 + ( d / dyf ) 2 ; we knew the z - derivative was zero. ) in the cells of


namely d = 3 with translational symmetry in the z direction, where the laplacian was ( d / dx ) 2 + ( d / dyf ) 2 ; we knew the z - derivative was zero. ) in the cells of the spreadsheet, i have simplified the formula by observing that ( 1 / r ) ( d / dr ) is equal to ( 1 / x ) ( d / dx ) on the slice of interest, by cancellation of a factor of sign ( x ). in this spreadsheet there is a fourth grid, just to the right of the grid that shows the charge per unit volume. it shows the charge per unit area ( dr∧dz ) in a ring. you can find the total charge on an object by summing the numbers in this grid. there is no point in summing the numbers in the charge - per - unit - volume grid ; that doesn ’ t make sense for several reasons, including dimensional analysis. to improve the accuracy, i use a smart estimate of the quantity ( 1 / r ) ( d / dr ). in particular, i take the arithmetic mean of the left - hand difference ( w−b ) / x1 and the right - hand difference ( c−w ) / x2 ; this accounts for an important nonlinearity because the radius is different in the two denominators. validity checks : i verified that a region with a log ( r ) potential produces zero charge density, with high accuracy. i also checked that the field calculation and charge calculation are automatically gauge invariant, because of the structure of the lapacian operator. i implemented periodic boundary conditions in the z direction, and this is the default behavior. i also implemented hall - of - mirrors boundary conditions, which you can optionally use instead. in the r direction, there is only one choice : the perpendicular component of the electric field vanishes on this boundary. this is reminiscent of the hall - of - mirrors boundary condition, but there is no physical interpretation in terms of tiling the universe. instead, this can be viewed as surrounding the region of interest, at each z level, with an annulus extending to infinity. the potential on this annulus depends on z but is independent of r. this means that outside the region of interest, there will be zero charge, although there will be nonzero fields. these fields seem a bit unphysical. to make these fields go away, you can arrange that the potential at the large - r boundary is independent of


models of deliberation. they have all brought commissioners from different perspectives together to talk and argue with an idea of coming up with some action - guiding recommendation. let me give you the most obvious example from recent history : the commission that president clinton put together. shortly after it was formed, dolly was cloned, and president clinton charged the commission with coming up with recommendations on how the government should approach the issue of cloning. the commission deliberated and came up with a report that the president recommended. similarly, on a different issue, shortly after our commission was created, craig venter announced that he had synthesized a genome in a cell that was self - replicating. and president obama has asked our commission to deliberate on that issue and come up with a report in six months that recommends to the federal government policies that the government should undertake, both in reaction to this development and other developments in the field. why did you decide to take on this challenge? my scholarly expertise is political philosophy and ethics of public policy. i spent my entire professional career writing and speaking about ethics of public policy and in particular about the advantages of making democracy more deliberative. i founded an ethics center at princeton - - the university center for human values. i ' ve written books on deliberation and democracy and articles on bioethics. so when the president asked me, it seemed, first, " how could i not accept a call to serve from the president? " and, second, it was a sweet spot of mine to be able to bring a group of experts together to deliberate about important issues in bioethics. you are known for this idea of deliberative democracy. could you explain it? the easiest way of understanding it is what it isn ' t : it ' s the opposite of sound - bite democracy. the idea is quite simple, which is : democracies do better to the extent that they allow people to discuss, including robustly argue about, their differences to try to find common ground where possible - - and, where common ground isn ' t possible, to come to the greatest respect possible for reasonable differences of perspective on controversial issues. so it ' s the give - and - take of viewpoints with an aim of finding common ground and reaching mutual respect where common ground isn ' t possible. can you give an example of how this might work? friday, june 18, 2010 according to a new pew global survey, views of the united states remain more favorable than they were a few years ago : the positive views are not unanimous


t possible. can you give an example of how this might work? friday, june 18, 2010 according to a new pew global survey, views of the united states remain more favorable than they were a few years ago : the positive views are not unanimous. see muslim views of the united states : the survey finds a fair amount of cross - national agreement regarding one aspect of america ’ s image : its religiosity. when asked whether the u. s. is too religious or not religious enough, majorities or pluralities in 18 of 22 countries say it is not religious enough. this is especially true in all three arab nations surveyed – jordan ( 89 % ), egypt ( 81 % ), and lebanon ( 64 % ) – as well as in indonesia ( 67 % ) and pakistan ( 55 % ). majorities also hold this view in india ( 57 % ), brazil ( 55 % ), mexico ( 56 % ), kenya ( 53 % ) and nigeria ( 57 % ). the exceptions on this question are the economically advanced nations of western europe and japan. in particular, the french are considerably more likely than others to see the u. s. as too religious ( 71 % ). more than four - in - ten feel this way in britain ( 47 % ), germany ( 46 % ) and japan ( 42 % ). the spanish are divided : 38 % think the u. s. is too religious and 40 % believe it is not religious enough. thursday, june 17, 2010 but now all is bright for minor parties. california voters just passed a " top - two " primary in which candidates from all parties run in one big mid - year primary and the top two finishers - - regardless of party - - end up on the november ballot. george will writes : it ’ s becoming a more familiar story : voters, frustrated by the anti - incumbent malaise sweeping the political landscape, turn on incumbents and put their weight behind underdogs. although good management and fundraising certainly play a role in party growth, today ’ s zeitgeist could help make a libertarian boom out of the two - party bust. for the 2010 election, 171 candidates for u. s. congress are running with an “ l ” beside their names, up from 127 in 2008 and 114 in 2006. at all levels of public office, the party counts 716 candidates running as libertarians this year, compared to 593 in 2008, and 596 in 2006. wes benedict, executive director of the libertarian national committee, said


long terminal repeat ( ltr ) retrotransposons are a widespread kind of transposable element present in eukaryotic genomes. they are a major factor in genome evolution due to their ability to create large scale mutations and genome rearrangements. compared to other transposable elements, little attention has been paid to elements belonging to the metazoan bel / pao subclass of ltr retrotransposons. no comprehensive characterization of these elements is available so far. the aim of this study was to describe all bel / pao elements in a set of 62 sequenced metazoan genomes, and to analyze their phylogenetic relationship. we identified a total of 7, 861 bel / pao elements in 53 of our 62 study genomes. we identified bel / pao elements in 20 genomes where such elements had not been found so far. our analysis shows that bel / pao elements are the second - most abundant class of ltr retrotransposons in the genomes we study, more abundant than ty1 / copia elements, and second only to ty3 / gypsy elements. they occur in multiple phyla, including basal metazoan phyla, suggesting that bel / pao elements arose early in animal evolution. we confirm findings from previous studies that bel / pao elements do not occur in mammals. the elements we found can be grouped into more than 1725 families, 1623 of which are new, previously unknown families. these families fall into seven superfamilies, only five of which have been characterized so far. one new superfamily is a major subdivision of the pao superfamily which we propose to call dan, because it is restricted to the genome of the zebrafish danio rerio. the other new superfamily comprises 83 elements and is restricted to lower aquatic eumetazoans. we propose to call this superfamily flow. bel / pao elements do not show any signs of recent horizontal gene transfer between distantly related species. in sum, our analysis identifies thousands of new bel / pao elements and provides new insights into their distribution, abundance, and evolution. transposable elements ( tes ) are dna sequences that have the ability to replicate within a genome using a variety of mechanisms. they are present in almost all eukaryotic genomes, and they play an important role in genome evolution by creating genetic variation through their mobility. although most new te insertions have a negative effect on the host ' s fitness, they significantly contribute to genome evolution. tes can


namely tas, bel, pao, sinbad, and suzu, no exhaustive analysis of the bel / pao subclass of ltr elements is available. here, we search for bel / pao elements in 62 non - mammalian metazoan and in 11 mammalian genomes. we use a de novo search approach to identify all bel / pao elements in this set of genomes. after separating the elements into families, we study the phylogenetic relationship between these families, and extend the current classification of bel / pao elements. an origin in very early metazoan evolution is often assumed for bel / pao elements, but no conclusive evidence exists. alternatively, bel / pao elements might have evolved later, only in a subset of metazoan genomes, and were then transmitted to other metazoan phyla by horizontal transfer. this might explain why, for example, no bel / pao elements are present in mammalian genomes. our sequence data allows us to address this possibility in a preliminary fashion. figure 1 shows the species in whose genomes we searched for bel / pao elements. species in which our approach did identify bel / pao elements are highlighted in green. species without bel / pao elements are shown in red. the taxonomic range of the species we analyzed is broad. it includes both eumetazoa and parazoa, bilateria and radiata, protostomes and deuterostomes, and comprises species from 11 different phyla. of the 62 genomes we analyzed 27 ( 44 percent ) are from arthropods, reflecting a bias in currently available genome sequences. figure 1. overview over analyzed genome sequences and their taxonomic classification. the names of 62 non - mammalian species whose genomes we analyzed are grouped by phylum. 11 additional mammalian genomes we analyzed are summarized as " 11 mammals ". next to each species, the number of bel / pao elements we identified is shown. if we were not able to identify any element in one genome, the genome name is shown in red. genome sequences where bel / pao elements had been already identified previously are marked with an asterix ( * ). for completeness we list seven additional species where no complete genome sequence was available but where bel / pao elements had been identified previously ( shown in parentheses ). a : abe et al. ( 2001 ), c1 : cook et al. ( 2000 ), c2 : copeland et al. ( 2005 ), j : jurka and


bel / pao elements had been identified previously ( shown in parentheses ). a : abe et al. ( 2001 ), c1 : cook et al. ( 2000 ), c2 : copeland et al. ( 2005 ), j : jurka and kohany ( 2010 ), l : llorens et al. ( 2008 ), s : steinemann and steinemann ( 1997 ). the majority of species whose genomes we analyzed belong to one of the three eumetazoan phyla nematoda, arthropoda and chordata. in all of these three phyla bel / pao elements had been identified previously. in contrast to previous work, we also had access to species from new superphyla and from the subkingdom parazoa. this allowed us to identify elements in these new metazoan clades as well. for example, no bel / pao element has been identified thus far in the subkingdom parazoa. we identified 24 bel / pao elements in the sponge amphimedon queenslandica, a member of this subkingdom. in addition, we identified new bel / pao elements in the cnidarian, echinoderm, and hemichordate phyla. in total, we identified 7, 861 bel / pao elements in 53 of our 62 genomes, including 20 species where no bel / pao elements have been identified before. these elements include full length elements and fragments with a minimum length of 2, 000 base pairs. previous studies reported around 160 bel / pao families, but in most genomes the copy number of these families has not been reported [ 6, 11, 14, 16, 18, 25 ]. our analysis thus is the first to determine the abundance of bel / pao elements in multiple genomes. the nucleotide sequences of all bel / pao elements are listed in additional file 1. additional file 1. nucleotide sequence of all identified bel / pao elements. nucleotide sequence of all bel / pao elements that we identified de novo in fasta format. each record ( element ) has a unique fasta identifier consisting of three parts : ( i ) element identifier, ( ii ) internal family identifier as listed in additional file 4, and ( iii ) species identifier as listed in additional file 2. all identifier are joined by the underscore symbol ' _ '. for example, the identifier 5 _ nc - 3


as listed in additional file 4, and ( iii ) species identifier as listed in additional file 2. all identifier are joined by the underscore symbol ' _ '. for example, the identifier 5 _ nc - 3 _ 1 represents element 5 belonging to family nc - 3 and is present in species 1 ( drosophila melanogaster ). format : zip size : 17. 7mb download file variable abundance of elements the abundance of bel / pao elements is highly variable between different species. nine of our 62 studied genomes do not contain any bel / pao elements, and 14 further species contain no more than ten elements. the relative majority of species ( 22 in total ) contain between eleven and 100 elements, and 16 species contain between 101 and 1000 elements. only one species, the yellow fever mosquito aedes aegypti, harbors more than 1000 elements ( a total of 2524 elements ). the number of bel / pao elements in each species ' genome is listed in additional file 2 and in figure 1. previous results reported that no bel / pao elements are present in mammalian genomes. we could confirm this finding using eleven mammalian genomes which we analyzed in addition to the 62 genomes we just discussed ( see methods for list of genome names ). additional file 2. list of used genomes, repbase update, and gypsy database elements. all used metazoan genomes are listed together with an internal identifier. additionally we give the current url from which the genome sequence can be accessed, the accession numbers, number of sequences of the genome included in our analysis, overall number of nucleotides, the number of bel / pao elements we identified in that genome, the number of different bel / pao families we identified in that genome, and to which subkingdom / superphylum / phylum the species belong. additionally we list all mammalian genomes we used and all genomes we excluded from our analysis. furthermore, we give the name of all bel / pao elements from repbase update and from the gypsy database, together with the species name they occur in, and an internal identifier. the internal identifiers are also used for the nucleotide sequences in additional file 1 and in the sequence alignment of additional file 7. format : xls size : 181kb download file this file can be viewed with : microsoft excel viewer because genome size can influence the abundance of elements in a species, we compared the number


file 1 and in the sequence alignment of additional file 7. format : xls size : 181kb download file this file can be viewed with : microsoft excel viewer because genome size can influence the abundance of elements in a species, we compared the number of bel / pao elements per mega base pair ( mbp ) between species. additional file 3 shows a histogram of this ltr element density for the species we studied. the number of bel / pao copies ranges from less than 0. 01 copies per mbp in 17 species to 3. 55 copies per mbp in the fruit fly drosophila ananassae. most genomes contain fewer than one bel / pao element per mbp. only the mosquito and fruit fly genomes contain more. five species have between one to two copies per mbp. these are ( in ascending order of element density ) the mosquito anopheles gambiae ( mean copy number per mbp 1. 14 ), the fruit flies drosophila virilis ( 1. 34 ), drosophila melanogaster ( 1. 37 ), the mosquito aedes aegypti ( 1. 85 ), and the fruit fly drosophila yakuba ( 1. 96 ). two fruit fly species have between two and three copies per mbps ( d. willistoni ( 2. 14 ) and d. persimilis ( 2. 9 ) ). the species with the highest overall copy number ( a. aegypti ) is not the species with the highest density of bel / pao elements. this observation can be explained by the fact that a. aegypti has, with 1. 3 gb, a more than 6 times larger genome than the mosquito and fruit fly genomes. additional file 3 shows that the total copy number per species and the number of copies per mbps show a statistically significant association for the genomes we analyzed ( spearman ' s rank correlation coefficient 0. 78, p = 5 × 10 - 12, n = 53 ). additional file 3. bel / pao copy number per mbps. a ) the histogram shows the number of genomes containing a given copy number of bel / pao elements per mbps. the inset shows the number of genomes containing between zero and one bel / pao elements per mbps. the eight genomes containing more than one bel / pao element per mbps come from either fruit fly or mosquito species. b ) relationship


inset shows the number of genomes containing between zero and one bel / pao elements per mbps. the eight genomes containing more than one bel / pao element per mbps come from either fruit fly or mosquito species. b ) relationship between total copy number and copy number per mb for each genome. each point in the graph represents one genome and shows the total bel / pao copy number and the copy number per mbps. note the logarithmic scale on both axes. format : pdf size : 245kb download file this file can be viewed with : adobe acrobat reader bel / pao elements are the second most abundant subclass of ltr retrotransposons to evaluate how important bel / pao elements are as a genome constituent, we compared their abundance to that of the other three ltr element subclasses. figure 2 shows for each genome containing bel / pao elements the fraction of ltr elements that our de novo search identified, and that we were able to classify into one of the four ltr classes. bel / pao, ty1 / copia, ty3 / gypsy and dirs elements are represented by different shades of grey in the figure. ty1 / copia and ty3 / gypsy are commonly considered the most abundant ltr elements, but our analysis invalidates that pattern. although ty3 / gypsy elements still are the most abundant class of ltr elements, they are followed by bel / pao elements, with ty1 / copia a distant third. specifically, while ty3 / gypsy elements constitute an average of 68. 9 percent of classifiable elements in a genome, bel / pao comprise 21. 6 percent, and ty1 / copia elements contribute an average of 6. 7 percent. dirs elements are a distant fourth with 2. 8 percent, and they occur only in 19 genomes. in terms of absolute numbers, we identified 25, 024 ty3 / gypsy elements, 7861 bel / pao elements, 2445 ty1 / copia elements and 1009 dirs elements. the roundworm brugia malayi is the only organism in which we only identified bel / pao elements ( 29 elements ) and no elements belonging to the other three classes. because our identification procedure of transposable elements purposedly excludes small element fragments, we cannot exclude that this organism may have contained elements from other families in the past. we also note that b. malayi is not the sole species containing only elements from


our identification procedure of transposable elements purposedly excludes small element fragments, we cannot exclude that this organism may have contained elements from other families in the past. we also note that b. malayi is not the sole species containing only elements from one ltr subclass. for example, there are also 11 species which do not contain any bel / pao elements ( figure 2 ). figure 2. separation of ltr elements in different classes for each genome. for each genome that contains bel / pao elements, we show the abundance of bel / pao, ty1 / copia, ty3 / gypsy and dirs elements, based on our classification. the horizontal axis indicates the relative abundance of each element class in each genome, normalized to the interval ( 0, 1 ). the difference in the length of each bar to the frequency of one reflects unclassified transposable elements. their frequency is quite large in some genomes. the three most abundant phyla in our data set ( arthropods, nematodes, chordates ) are labeled. many different families we next wished to group our identified bel elements into families based on their sequence similarity on the nucleotide level. to this end, we pursued a graph - based approach. the nodes in the graph we studied are bel / pao elements. edges represent sequence similarity between elements. the approach we pursued clusters the elements in the graph into families, using a fast and scalable unsupervised markov cluster algorithm ( mcl ) for graphs, which is based on the simulation of stochastic flow on graphs [ 27, 28 ] ( see methods for details ). to validate the accuracy of our clustering approach, we first clustered only the bel / pao elements from the especially well - studied genome of d. melanogaster. we then compared our classification of the 178 d. melanogaster elements with ( i ) the annotation of elements in the genome sequence of d. melanogaster, and ( ii ) the d. melanogaster elements in repbase update. our approach resulted in the family classification shown in figure 3, where the 178 bel / pao elements we identified form ten families labeled from a ) to j ). in this figure, each node represents an element and different node colors indicate different families. in the figure, we labeled elements in each family with the established names from the genome sequence ( left name in each panel ), and with the name of the most similar


this figure, each node represents an element and different node colors indicate different families. in the figure, we labeled elements in each family with the established names from the genome sequence ( left name in each panel ), and with the name of the most similar repbase update element ( right name ). our classification is identical to the previous classification of these elements, with the exception of one family. this family ( d ) ) contains two elements belonging to the previously described ninja - dsim - like family, and one belonging to the aurora family. the other three elements in this family were not previously annotated. additionally, we find three more ninja - dsim - like elements that belong to the family in panel h ) in our classification. in sum, the method we use classifies only one out of 178 ( 0. 6 percent ) d. melanogaster bel / pao elements in a different family than previous annotations and divides one family. this low incidence of misclassification motivated us to apply the method to larger sets of elements. figure 3. markov clustering of d. melanogaster bel / pao elements. we clustered all 178 bel / pao elements from d. melanogaster into ten families based on their sequence similarity using the mcl algorithm from within biolayout. we refer to these families as mcl families. a node in the graph represents one element. edges represent nucleotide sequence similarity between two elements ( see methods for details ). elements clustered into the same family are shown in the same color. the absence of an edge between two elements, indicates that the elements do not share sufficiently high sequence similarity over at least 500 bp ( see methods ). we compared the elements of the mcl families to previous annotation of these elements in the d. melanogaster genome and in repbase update. each mcl family is labeled with two names separated by a slash. the left name is from the drosophila genome annotation, the right name is from repbase update. dashes ' - ' indicate that a family has not been previously annotated. note that one family has two names : 3s18 in the genome annotation and bel in repbase update. elements from family d ) were previously annotated as belonging to two different families. we next applied our method to all 7, 861 bel / pao elements we had identified. this resulted in 817 families with at least two elements and 908 singletons. we assigned


previously annotated as belonging to two different families. we next applied our method to all 7, 861 bel / pao elements we had identified. this resulted in 817 families with at least two elements and 908 singletons. we assigned a unique identifier to each family, which we report in additional file 4. most ( 696 ) families have ten or fewer member elements. only three families have more than 100 copies. one of these families is present in the fruit flies of the melanogaster subgroup ( 143 copies ). this family corresponds to the roo family which has been described earlier to have a high copy number in d. melanogaster. the family with the second highest copy number ( 207 copies ) is present in the fruit fly d. ananassae, and that with the highest copy number ( 397 copies ) in the carolina anole anolis carolinensis, an arboreal lizard. these two families, however, do not share any similarity to families of known elements. table 1 shows the ten families with the highest copy number. additional file 4. bel / pao families and their copy numbers. for each bel / pao family we list the copy number, species, and the superfamily in which they are present. families that we did not use in the phylogenetic tree construction are not assigned to a superfamily. format : xls size : 183kb download file this file can be viewed with : microsoft excel viewer table 1. top ten families with highest copy number only 42 of the families ( 2. 4 percent ) we identified are not restricted to one genome, but contain elements from different genomes. most ( 35 ) of these families occur in the drosophila melanogaster and obscura groups. four families have elements in two mosquito genomes and three families are distributed in the three nasonia wasps. all these families are therefore restricted to closely related species. in addition to the family classification we just described, which clusters elements regardless of which genome they occur in, we carried out an analogous classification, but separately for elements within each genome. the two classifications do not differ dramatically. additional file 5 describes the results of the species - specific classification. additional file 5. species specific family classification. we describe the differences and agreements between the among - species family classification as used in the main text and the within - species family classification. format : pdf size : 16. 4mb download file this file can be viewed with : adobe acrobat reader phylogenetic relationship among bel / pao


the among - species family classification as used in the main text and the within - species family classification. format : pdf size : 16. 4mb download file this file can be viewed with : adobe acrobat reader phylogenetic relationship among bel / pao families we next wanted to use our large data set to validate the existing classification of bel / pao elements into the previously identified superfamilies bel, tas, suzu, sinbad and pao. to this end, we used the protease, reverse transcriptase and integrase domains of each element. we constructed a consensus sequence for each domain in each of our element families or used the domain sequences themselves for elements that were singletons ( see methods for details ). we then used these ( consensus ) sequences to construct a multiple alignment of each of the domains using mafft ( three alignments in total ). subsequently, we concatenated these alignments and constructed a phylogenetic tree from them using phyml _ alrt, a version of phyml that incorporates an approximate likelihood ratio test to estimate the statistical support of the tree topology. in this tree reconstruction, we included as outgroups the domains of the canonical sequence from the gypsy and copia elements from d. melanogaster, as given by repbase update. the consensus sequences for each of the families and domains we identified are listed in additional file 6. additionally, we provide the relevant alignments in additional file 7. we defined superfamilies in this tree as major, deep - branching clades, which are easily identifiable based on the tree structure, and further discussed below. the complete phylogenetic tree is shown in figure 4a, and in additional file 8 with partly collapsed clades, and representative species names assigned to branches. figure 4b shows an additional version of the tree with collapsed major clades. in figure 4b the triangles represent the divergence between the elements within each major clade, with long triangles indicating great divergence. numbers next to tree branches indicate the statistical support for a clade ranging from 0 ( least significant ) to 1 ( highly significant ). figure 4c shows the same tree for the purpose of comparing it to previously proposed phylogenetic trees of bel / pao elements. for clarity, this panel does not show the divergence within each major clade, and the order of the branches is reorganized to ease the comparison to these previous phylogenetic trees ( shown in figure 4d and 4e ) [ 16, 23 ]. to avoid confusion, we note that if we refer


divergence within each major clade, and the order of the branches is reorganized to ease the comparison to these previous phylogenetic trees ( shown in figure 4d and 4e ) [ 16, 23 ]. to avoid confusion, we note that if we refer to bel / pao elements below, we mean the entire subclass of ltr elements we studied. if we refer to only bel or pao elements, we mean the bel and pao superfamilies, respectively. additional file 6. amino acid sequences of consensus domains. a fasta file with all amino acid sequences for the domain consensus files we used for the phylogenetic tree reconstruction. the identifier consists of the family identifier ( see additional file 4 ) and the domain name, for example nc - 1 _ integrase represents the consensus sequence of the integrase domain of family nc - 1. format : txt size : 548kb download file format : txt size : 1. 3mb download file figure 4. phylogenetic tree of bel / pao families. the phylogenetic tree is based on the concatenated amino acid sequence of the three protein domains protease, reverse transcriptase, and integrase. the tree is based on 893 transposable element families for which we could construct a consensus sequence for all three domains. in addition to data from these families, we used in this analysis all bel / pao elements from repbase update where we could identify all three domains ( total of 92 elements ). some of these repbase update elements are from species whose genomes we did not analyze here. furthermore, we included 16 elements from the gypsy element database gydb, in order to associate clades in the tree to previously described subclades of the bel / pao element class. a list of these elements is found in additional file 2. different colors indicate major clades. a ) same phylogenetic tree as in a ) but with major clades collapsed into triangles indicating superfamily divergence and statistical support values for the branches. we constructed the tree using phyml with an approximate likelihood ratio test to estimate the statistical support of the tree topology. this statistical support is indicated by the numbers at the branches which range from 0 ( least significant ) to 1 ( highly significant ). all branches leading to the major clades have very high support. c ) same phylogenetic tree as in a ) but without divergence triangles, and branches are reorganized to facilitate comparison with trees in d ) and e ). d ) and e ) phylogenetic relationship


branches leading to the major clades have very high support. c ) same phylogenetic tree as in a ) but without divergence triangles, and branches are reorganized to facilitate comparison with trees in d ) and e ). d ) and e ) phylogenetic relationship of bel / pao clades as described by copeland et al. and llorens et al, respectively. high resolution tree and graphic files are available from the authors upon request. additional file 8. phylogenetic tree of bel / pao elements with species names. the figure shows the same tree as in figure 4 in the main text but with the species names shown in which the elements occur. if a clade of elements contained only element families from the same species or from very closely related species ( e. g. mosquito species ), the clade was collapsed to reduce the size of the tree. all species names are shown at the leaves of the tree. if all species in one clade of the tree belonged to the same genus, such as the genus drosophila, only the genus name is shown, with the number of species in brackets. major clades are highlighted in different colors. format : pdf size : 414kb download file this file can be viewed with : adobe acrobat reader previous studies identified five different superfamilies of bel / pao elements which are named after the first identified element in the subclade : bel, tas, suzu, sinbad and pao. two previous phylogenetic studies both found that bel and tas elements formed one clade and sinbad and pao another one. in both studies, suzu elements alone formed a third clade [ 16, 23 ]. however, the trees that emerged from these two studies differ in one major way. copeland et al. identified elements belonging to the suzu superfamily as more distantly related to the other four clades than these clades are to each other ( figure 4d ). in contrast, the study by llorens et al. grouped the suzu superfamily with the pao / sinbad clade ( see figure 4e ). two new superfamilies of bel / pao elements our phylogenetic analysis shows some similarities to the previous studies. for example, we find that pao and sinbad form part of the same clade as do bel and tas. similar to what copeland et al. ( 2005 ) reported, the elements from the suzu family are more distantly related to the other clades than these clades to each other. however, there are two major differences


do bel and tas. similar to what copeland et al. ( 2005 ) reported, the elements from the suzu family are more distantly related to the other clades than these clades to each other. however, there are two major differences. first, we found that the pao superfamily groups into two separate clades ( green clades in figure 4a and 4b ). we kept the name pao for the larger of these clades, because it contains the original pao element identified in bombyx mori. we propose the new name dan for the second, smaller clade, because we have identified it in the zebrafish danio rerio, and it currently only contains elements from this organism. second, we identified a new superfamily ( discussed below ), for which we propose the name flow. table 2 shows the number of families and elements per superfamily and additional file 9 the minimal, maximal, and median element and ltr sequence lengths for each superfamily. we note that we could have classified our data into many more superfamilies, but our aim was not to proliferate the number of superfamilies unnecessarily, while preserving previous classifications as much as possible. fortunately, the clear partitioning of our family tree into few major clades made this task easy and unambiguous. we also note that our phylogenetic analysis is based on more than 40 times more sequence data than previous analyses. table 2. number of elements, families, species and phyla for every superfamily additional file 9. structural information of superfamilies. the table shows the minimal, maximal, and median element lengths ( in basepairs ) and the minimal, maximal and median ltr length for the major superfamilies we identified. format : pdf size : 10kb download file this file can be viewed with : adobe acrobat reader table 3 shows the average amino acid similarity in percent between the consensus sequences within a superfamily and among different superfamilies. not unexpectedly, the average similarity of elements within one superfamily ( diagonal in table 3 ) is generally higher than the average similarity of elements in different superfamilies ( off - diagonal in table 3 ). the only exception are elements belonging to the tas superfamily. they are on average slightly less similar to each other than elements in some different families, e. g., elements in the dan and sinbad superfamily. the average similarity within one superfamily varies between 37. 4 percent for the sequences belonging to the tas superfamily, to 63. 53


to each other than elements in some different families, e. g., elements in the dan and sinbad superfamily. the average similarity within one superfamily varies between 37. 4 percent for the sequences belonging to the tas superfamily, to 63. 53 percent between sequences belonging to the dan superfamily. the average similarity between different superfamilies ranges from 26. 51 percent between elements from the tas superfamily and the suzu superfamily, to 39. 07 percent between elements from the dan and sinbad superfamilies. table 3. average amino acid similarity between bel / pao superfamilies distribution of superfamilies the number of species and phyla covered by each superfamily is shown in table 2 and a list of phyla covered by each superfamily can be seen in additional file 10. some superfamilies are restricted to one phylum. the dan and pao superfamilies have the most restricted host range and occur only in the fish danio rerio and in arthropods, respectively. pao elements occur mainly in the different drosophila and mosquito genomes, with the exception of a few elements that are present in the parasitoid wasp nasonia vitripennis. other superfamilies are present in different phyla and in a wider range of host organisms. an example is the tas superfamily, which is present in cnidaria, nematoda, arthropoda, hemichordata, and porifera. it also occurs in different host organisms within all phyla, e. g., in almost all our nematode genomes ( 11 genomes ). some superfamilies are present in a wide range of phyla but all species are restricted to a certain habitat type, such as aquatic habitats for the suzu superfamily. we note that our study is the first to identify elements of the bel / pao subclass in the subkingdom parazoa. these elements fall into the bel and tas superfamilies. elements of the flow superfamily the five families belonging to the new superfamily we discovered are all present in lower animals that live in aquatic habitats, hence the name flow. one of flow ' s families occurs in the starlet sea anemone nematostella vectensis ( 7 copies ), and two families occur in the fresh water hydra hydra magnipapillata ( 55 copies ). both species belong to the phylum cnidaria. we found the other two families in the plan


vectensis ( 7 copies ), and two families occur in the fresh water hydra hydra magnipapillata ( 55 copies ). both species belong to the phylum cnidaria. we found the other two families in the planarian schmidtea mediterranea ( 21 copies ), phylum platyhelminthes. the elements are between 3303 to 16272 base pairs long with an average of 7452 base pairs. the five families of the flow superfamily are not highly similar to one another. specifically, the amino acid similarity ranges from 33. 89 percent between the consensus sequence of n. vectensis and one of the consensus sequences from s. mediterranea, to 53. 95 percent between the two consensus sequences from s. mediterranea. the average similarity is with 45. 48 the second lowest similarity within a superfamily. the average similarity to the other bel / pao superfamilies varies from 29. 96 percent ( suzu superfamily ) to 37. 42 percent ( pao superfamily ). highly similar elements in closely related species we used blastn to compare each bel / pao element against all other 7, 860 elements to search for possible signs of horizontal transfer of bel / pao elements between our studied species. if an element is only transferred vertically from parent to offspring, we expect to find no high similarity between elements from distantly related species. in contrast, highly similar elements occurring in very distantly related species might indicate horizontal transfer of an element between these species. in this analysis, we required an identity of at least 80 percent over at least 20 percent of the length of an element, but at least over 300 bp. this criterion is a liberal threshold for recent transfer events and allows for some divergence of sequence since the transfer. using this criterion, we found no signs of similar sequences in very different species. the only similar sequences in different species occurred in closely related species within the same genus, i. e., in fruit flies of the genus drosophila, in parasitoid wasps of the genus nasonia, and in roundworms of the genus meloidogyne. previous work had identified a horizontal transfer of a bel element between the fly drosophila ananassae and the endosymbiont wolbachia. motivated by this observation, we attempted to identify further possible horizontal transfers to endosymbiont genomes and viruses through a blast search of our consensus sequences for the concatenated protease, reverse


site lists 88 non - mammalian metazoan genomes as " in progress " http : / / www. ncbi. nlm. nih. gov / genomes / leuks. cgi webcite. some of these species cover phyla which have not been studied so far with respect to bel / pao elements. therefore, the results of our study will likely be extended with every new genome release. a ten - fold increase in family number we clustered our bel / pao elements into 1, 725 families ( 817 multi - element families and 908 singletons ) which is more than a ten - fold increase in family number compared to the approximately 160 bel / pao families known so far. part of this increase can be explained by the 251 families identified in the 20 previously not analyzed genomes. however, the bulk of this increase in family number comes from newly identified families in previously studied species. for example, we identified two previously unknown families with a copy number of more than 200 elements. one potential explanation for the high family number might be that our clustering approach divided the elements from one species into too many small families. however, our analysis of the well - studied and well - annotated fruit fly d. melanogaster genome argues against this possibility. this analysis finds that the ten families we identify are largely congruent with previous annotation. the only exception are elements belonging to the ninja - dsim - like family ( nine elements ). our clustering approach divided this family into two families. additionally in one of the two ninja - dsim - like families, we find an element from the aurora family. however, this change in annotation affects only one in 178 elements ( 0. 6 percent ). the aurora element is the only element of that family in d. melanogaster, raising the possibility that one of the ninja - dsim - like elements was falsely annotated as an aurora element. indeed, the alignment of all annotated ninja - dsim - like elements in d. melanogaster shows a high average sequence divergence ( in both ninja - dsim - like families the elements have an average similarity of 64 percent ) and the aurora element is very similar to large parts of some of the ninja - dsim - like elements. overall, the comparison of our families to the previously annotated tes in d. melanogaster shows that our clustering does not separate the elements into too many small families. our approach correctly


the ninja - dsim - like elements. overall, the comparison of our families to the previously annotated tes in d. melanogaster shows that our clustering does not separate the elements into too many small families. our approach correctly classified 177 out of 178 elements. we therefore believe that the high number of bel / pao families we identified is a faithful reflection of actual bel / pao element diversity. major subclades separated early previous studies, which were based on fewer than 25 bel / pao elements, identified five superfamilies of bel / pao elements : pao, sinbad, bel, tas and suzu [ 16, 23 ], named after the first element identified in each superfamily. our phylogenetic tree is based on 893 bel / pao families and it also identified these five known superfamilies. additionally we found one completely new superfamily ( flow ), and a deep separation of the pao superfamily into the two highly divergent superfamilies pao and dan. we separated the dan superfamily from the sinbad superfamily for two reasons. first, one element from the dan clade was previously annotated to belong to the pao superfamily. in contrast, we find that the dan clade is more closely related to the sinbad superfamily. the best way to resolve this conflict, in our view, is to propose dan as a second superfamily. second, because the sinbad superfamily also contains elements from danio rerio, the dan clade is not simply a subbranch of the sinbad superfamily that contains all elements from danio rerio. in sum, we think that the dan clade should be viewed as a separate superfamily. it is very likely that new elements of this superfamily will be identied in genomes that we did not study. the superfamily tree topology we find differs somewhat from previously reported topologies [ 16, 23 ]. we find a very high statistical support for our tree topology ( see figure 4b ). this high support makes it unlikely that our tree topology is not correct, especially as it is also supported by many more sequences than any of the previous studies. additionally the average sequence similarity of elements within one superfamily almost always shows greater amino acid sequence similarity than elements in different superfamilies, which supports our classification into superfamilies. most ( 656 of 893 ) of our families belong to the pao or bel superfamily. this is not surprising because these superfamilies are mainly restricted to arthropod genomes and


supports our classification into superfamilies. most ( 656 of 893 ) of our families belong to the pao or bel superfamily. this is not surprising because these superfamilies are mainly restricted to arthropod genomes and 27 of our genome sequences ( 44 percent ) belong to this phylum. the other five superfamilies show a more diverse distribution of host genomes. here, the host genomes come from more than one phylum and, for the tas and bel superfamily, even from both metazoan subkingdoms. the variation in the host species range that we observe has several candidate explanations that our data cannot resolve. on the one hand, bel / pao superfamilies might have been lost in some phyla. on the other hand, horizontal transfer of bel / pao elements between species belonging to different phyla might be at work. for example, if bel / pao elements originated in the eumetazoa, a horizontal transfer event to amphimedon queenslandica might explain the presence of bel / pao elements in the parazoa. we did not find any evidence of recent horizontal transfer between distantly related species, because no such species contain highly similar bel / pao elements. this, however, does not exclude the possibility of ancient horizontal transfer events. to identify such transfer events is beyond the scope of our study. but regardless of whether element loss or horizontal transfer explains the current bel / pao element distribution, bel / pao elements probably originated early in metazoan evolution. this is because bel / pao elements occur in both metazoan subkingdoms, and in a wide range of host species from different phyla. flow, a new superfamily of bel / pao elements we found a new bel / pao superfamily ( flow ) which consists of five families and a total of 83 elements present in lower animals. we identified three of these families in two species belonging to the phylum cnidaria ( hydra magnipapillata, nematostella vectensis ), and the other two families in a species belonging to the phylum platyhelminthes ( schmidtea mediterranea ). in both phyla, cnidaria and platyhelminthes, only eleven and two bel / pao elements, respectively, had been identified before [ 16, 23, 38 ]. the five flow families are quite diverse ( average similarity 45. 48 percent ). this


complete list of all genomes we analyzed is present in additional file 2. although previous studies did not identify any bel / pao elements in mammalian genomes, we downloaded eleven mammalian genome sequences from the ncbi ' s eukaryotic genome sequencing project site to validate this observation : bos taurus, canis lupus familiaris, equus caballus, monodelphis domestica, mus musculus, ornithorhynchus anatinus, rattus norvegicus, ailuropoda melanoleuca, cavia porcellus, lama pacos, pteropus vampyrus. we used a combination of two de novo identification algorithms to identify all ltr elements in our set of genomes. specifically, we applied the two de novo ltr identification algorithms ltrharvest and find _ ltr to identify all possible ltr elements in our genomes. subsequently, we separated our de novo identified elements into the four ltr classes ty1 / copia, ty3 / gypsy, bel / pao and dirs, merged the two sets of bel / pao elements from each algorithm into one set, and assigned an identifier to each element. we now explain important details of this procedure. ltrharvest and find _ ltr both search for structural features, such as ltr sequences, to identify full length ltr elements in a genome sequence. among all de novo ltr identification programs ltrharvest and find _ ltr give the best results with regard to the number of true ltr elements detected. however, the number of false positives can also be high for both programs. therefore we accepted only candidate elements for further analysis that contained at least one functional domain known to be present in ltr retrotransposons and at least one open reading frame longer than 300 bp. to identify these domains we used hidden markov models obtained from pfam ( asp _ protease, peptidase _ a17, rvt _ 1, rvt _ 2, rve, integrase _ zn, gp36, retrotrans gag, integrase, integrase _ zn, tlv _ coat ) and used hmmer http : / / hmmer. janelia. org webcite to compare these pfam domains to our de novo candidate elements. only if hmmer had found at least one domain with an e - value smaller than 0. 01 in


hmmer http : / / hmmer. janelia. org webcite to compare these pfam domains to our de novo candidate elements. only if hmmer had found at least one domain with an e - value smaller than 0. 01 in an element, we kept the element for further analysis. we used ltrharvest with the minimum distance between two ltr sequences ( option - mindistltr ) set to 2000 base pairs and allowed overlapping hits ( option - overlaps ). we used find _ ltr with default values. both programs, but especially ltrharvest, return overlapping and nested elements. where several elements were nested, we only took the innermost element, because it probably represents the younger element. where elements overlapped, we randomly chose one of the elements for further analysis. to divide our elements from both de novo sets into ty1 / copia, ty3 / gypsy, bel / pao and dirs classes, we constructed specific hidden markov models for each class. to this end, we downloaded all canonical ltr sequences, prototypic sequences that either represent consensus sequences or a sequence example for a te family, for each of the four classes from repbase update, a database containing repetitive dna elements in eukaryotes ( 478, 941, 106 and 68 sequences for ty1 / copia, ty3 / gypsy, bel / pao and dirs, respectively ). we then used the pfam hidden markov models for the domains listed in the previous paragraph, and identified these domains in all sequences from a given class using hmmer ( http : / / hmmer. janelia. org webcite ; e - value < 0. 0001 ). for each ltr class we took all identified domain sequences and aligned the sequences belonging to the same domain using mafft, checked the alignments manually for obvious errors, and constructed a new hidden markov model using hmmer. we next used hmmer to compare each of the new candidate elements that we had identified against these class - specific hidden markov models. for each candidate element and each element class we obtained in this way an e - value that reflects how well the element matches the class. we assigned the candidate element to an element class if it matched this class with the smallest ( most significant ) e - value among all four classes we matched it with. if we did not find a model with an e - value below 10 - 20, we did not classify the element. by the


if it matched this class with the smallest ( most significant ) e - value among all four classes we matched it with. if we did not find a model with an e - value below 10 - 20, we did not classify the element. by the time we had finished this ( time - consuming ) analysis, a larger set of specific hidden markov models for each of the four element classes than our set became freely available. we tested if this new set improved the classification substantially, which was not the case ( results not shown ). at this stage, our analysis had created two sets of elements classified as bel / pao elements, one set from each of our de novo searches. for each species, we then merged these two bel / pao sets into one set of elements according to the following rules : if only one of the search algorithms had identified an element at a given genome position, this element was used for the final set. if both algorithms had identified an element at the same position, we took the element identified by find _ ltr, because in our experience find _ ltr identified the ltr start and end positions more accurately. if both algorithm had identified an element within 20 bp of each other, we took the element identified by find _ ltr. otherwise, if both algorithms had identified an element, and if these elements were overlapping but their start and end positions differed by more than 20 bp, we took the element which had a length between 2, 000 to 15, 000 bp. we chose these length thresholds, because based on known elements they are lower and upper bounds for full length elements. if both elements were within this length range, we randomly chose one element. if neither element fulfilled this length criterion, we eliminated the element from further analysis. this occurred only for 0. 7 percent ( 53 out of 7914 ) of elements we analyzed. the next stage of our analysis began with the bel / pao elements we had identified, and grouped them into different families. to this end, we used the markov cluster ( mcl ) algorithm, a fast and scalable unsupervised markov clustering algorithm for graphs based on simulation of stochastic flow in graphs [ 27, 28 ]. this algorithm subdivides a graph whose nodes are transposable elements, and whose weighted edges reflect sequence similarity among elements, into subgraphs. the algorithm defines a family based on the higher connectivity between elements of one family than to elements of a different family. it can therefore overcome the limitations of a fixed


the graph - based grouping procedure we used, our elements correspond to nodes and the similarity score between two elements correspond to the edge weight between the two nodes. we loaded the scores into biolayout, a 3d graph visualization tool, and started mcl from within this tool. the inflation option of the mcl algorithm affects the cluster granularity. we tested different inflation values on our set of 178 bel / pao elements from the well studied drosophila melanogaster genome, and compared the resulting clustering to the genome annotation. we found that an inflation value of 4. 0 and a pre - inflation value of 3. 0 best reproduced the known d. melanogaster families. we also used these values for our clustering analysis among genomes. additionally, we set the smallest detectable cluster size to one. biolayout assigns an arbitrary color to each element family, and paints the nodes belonging to a family in that color. changing the length threshold for our blast matches above would influence the number of element pairs we find, and therefore the number of edges in our graph. a lower length threshold would increase the edge number, whereas a higher threshold would decrease it. we explored different length thresholds and did not find qualitative differences between the clustering of the elements. also, the number of families with multiple elements did not vary much. by decreasing the length threshold progressively, however, our approach identified fewer singletons ( families with only one member ), because increasing numbers of singletons got added to existing multi - element families. conversely, increasing the length threshold, results in more singletons, as families become more and more fragmented. these new singletons typically are the most diverged elements in a family. sequence alignment and phylogenetic reconstruction we next describe how we constructed the phylogenetic tree that helped us classify elements into superfamilies. our procedure had three steps. in the first, we defined, separately for each family, a consensus sequence for each of the protease, reverse transcriptase and integrase domains ( three consensus sequences per family ). second, we used these consensus sequences to produce a multiple sequence alignment of elements in all families. third, we constructed a phylogenetic tree from this alignment. we now describe important details of each step. in the first step, we constructed for each of the families we had identified multiple alignments of the protease, reverse transcriptase and integrase domains using mafft version 5. to this end, we used the amino acid sequences of the


of the tree topology. this approach is superior to a bootstrap calculation with respect to accuracy and power, and it is computationally much more efficient. the method assigns to each branch a statistical significance ranging from 0 ( least significant ) to 1 ( highly significant ). we used the default options of phyml _ alrt with the jtt matrix for amino acid substitutions, the proportion of invariable sites set to zero, and with only one category of substitution rate. we chose the χ2 - based parametric branch support for approximate likelihood ratio tests. as outgroups we used the domain sequences from the copia and gypsy element in drosophila melanogaster, as given by repbase update [ 47, 48 ]. we then separated our bel / pao families into superfamilies based on the major clades in the phylogenetic tree. using the protdist program from the phylip package we calculated the average percent similarity of sequence pairs within a superfamily, as well as for sequence pairs whose members belonged to different superfamilies. nc carried out the research. nc and aw designed the study and wrote the manuscript. all authors read and approved the final manuscript. we would like to acknowledge support from swiss national science foundation grants 315200 - 116814, 315200 - 119697, and 315230 - 129708. xiong y, eickbush th : origin and evolution of retroelements based upon their reverse transcriptase sequences. [ http : / / www. ncbi. nlm. nih. gov / pubmed / 1698615? dopt = abstract ] webcite malik hs, henikoff s, eickbush th : poised for contagion : evolutionary origins of the infectious abilities of invertebrate retroviruses. [ http : / / genome. cshlp. org / cgi / content / abstract / 10 / 9 / 1307 ] webcite song su, gerasimova t, kurkulos m, boeke jd, corces vg : an env - like protein encoded by a drosophila retroelement : evidence that gypsy is an infectious retrovirus. [ http : / / genesdev. cshlp. org / cgi / content / abstract / 8 / 17 / 2046 ] webcite miguel c, simoes m, oliveira mm, rocheta m : envelope - like retrotransposons in the plant kingdom : evidence of their presence in gym


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