March 2011 - mathfun@mailman.xmission.com

[math-fun] Fw: Democrats attack Art Robinson's Children
by Eugene Salamin 25 Mar '11

25 Mar '11

I've been hesitant to forward to math-fun these emails concerning an academic political drama unfolding at Oregon State University. But it is far more of a threat than the pi redefinition proposal currently being discussed here. So far, there are six emails. I will post these one per day in order to avoid overload, unless the moderator declares this topic to be inappropriate, or people want it all right away. -- Gene ----- Forwarded Message ---- From: Art Robinson <art(a)rfc2010.com> To: Eugene <gene_salamin(a)yahoo.com> Sent: Mon, March 7, 2011 6:27:08 AM Subject: Democrats attack Art Robinson's Children Dear Friends, Since the November 2 election and our announcement that we would run again against Democrat Peter DeFazio in 2012, we have suffered some annoying personal and political attacks by the DeFazio political machine. While these attacks have cost us personally some time and money, they were the sort of thing that many political candidates endure behind the scenes. Unprecedented, however, has been an effort to arrange the expulsion of my three children, Joshua, Bethany, and Matthew, from their graduate studies in nuclear engineering at Oregon State University - a DeFazio political stronghold. This attack is, so far as I know, unprecedented in American politics. We need your help! For the past 4 months, our lives have been so disrupted by this attack at OSU that we have been distracted from our work, including work necessary to prepare for the 2012 elections. This is the reason that you have heard so little from us since the election. We have been working to further our scientific research and have made some preparations for 2012, but not as many as we would otherwise have done. Please read the following account. When we decided to run against DeFazio, I expected the unprincipled campaign for which he is well known. I never dreamed, however, that "political payback" would include a campaign to destroy the education, career, and future of three of my children who are outstanding graduate students in nuclear engineering at OSU. Now, the only thing that can save them and the embattled professor who risked his career to help them is a public outcry in their favor. Please read the following account and then, please help us with your letters, emails, phone calls, and faxes to OSU. Click here for more information and updates www.OregonStateOutrage.com. Please, also, accept our deepest thanks and gratitude for your support. Art Democrats Attack Republican Candidate’s Children By Art Robinson Published by WorldNetDaily http://www.wnd.com/index.php?fa=PAGE.view&pageId=271753 on March 7, 2011 The Democrat Political Machine is Attacking Republican Congressional Candidate Art Robinson’s Children and a Distinguished Nuclear Engineer at Oregon State University. Please help save these students and their courageous Professor. In an effort to do my part in rescuing our country from the out-of-control Obama administration, last year I ran for Congress in Oregon's 4th District against 12-term incumbent, far-left Democrat Peter DeFazio, co-founder of the House Progressive Caucus. Although I won the nominations of the Republican, Independent and Constitution Parties and the endorsement of the Libertarian Party, a massive media smear campaign by DeFazio, paid for with money raised by MoveOn.org and from special interests favored by DeFazio in Washington, resulted in a 54.5 percent to 43.6 percent victory for DeFazio in a race that was expected to be much closer. Although I had never run for public office before, I immediately announced my candidacy for Congress again in 2012. However, when you take a stand for what's right, sometimes there is retribution. On Nov. 4, 2010, as soon as the election results were in and they were sure their candidate had won, faculty administrators at Oregon State University gave new meaning to the term "political payback." They initiated an attack on my three children - Joshua, Bethany and Matthew - for the purpose of throwing them all out of the OSU graduate school, despite their outstanding academic and research accomplishments. OSU is a liberal socialist Democrat stronghold in Oregon that received a reported $27 million in earmark funding from my opponent, Peter DeFazio, and his Democrat colleagues during the last legislative session. Thus, Democrat activist David Hamby and militant feminist and chairman of the nuclear engineering department Kathryn Higley are expelling four-year Ph.D. student Joshua Robinson from OSU at the end of the current academic quarter and turning over the prompt neutron activation analysis facility Joshua built for his thesis work and all of his work in progress to Higley's husband, Steven Reese. Reese, an instructor in the department, has stated that he will use these things for his own professional gain. Joshua's apparatus, which he built and added to the OSU nuclear reactor with the guidance and ideas of his mentor, Michael Hartman, earned Joshua the award for best Masters of Nuclear Engineering thesis at OSU and has been widely complimented by scientists at prominent U.S. nuclear facilities. Meanwhile, faculty member Todd Palmer notified four-year Ph.D. student Bethany Robinson (OSU grade point average 3.89) that he was terminating her thesis work and taking all of her work in progress for himself. Some of Bethany's graduate work has already been used, without credit to Bethany, in the thesis of another favored student now recently hired on the department faculty. Palmer, until recently married to a member of the OSU psychology faculty, is now married to former OSU student Camille Lodwick. They are both faculty members in the nuclear engineering department. It is also rumored that Higley, a long-time associate of Palmer's and who is adamant that Bethany leave OSU, may dislike Bethany because of criticism Higley received when department students complained of sexual assault at wild drunken parties of OSU nuclear engineering students during taxpayer-financed trips to scientific meetings. These incidents may have been more likely because Higley had failed to report to OSU authorities an earlier instance of milder sexual harassment against Bethany, probably because Bethany - a brilliant but very mild-mannered, conservative, homeschooled Christian young lady - does not share Higley's views. My children and I attempted to counter all these actions against us as they unfolded, but were initially uncertain as to their ultimate intent. All became clear, however, when OSU faculty administrators abruptly took a further and very serious prejudicial action toward Joshua. At that point, OSU Professor of Nuclear Engineering Jack Higginbotham, who was privy to all of the meetings and actions, warned us and came to our defense. Professor Higginbotham, who also serves as president of the OSU Faculty Senate and director of the Oregon NASA Space Science Consortium, has been a member of the OSU faculty for 24 years. He has held many responsible positions in the university and has received numerous professional awards. Moreover, he is very widely admired for the many instances in which he has given special help to students at OSU. This is a man who thinks always of his students and never of himself. Professor Higginbotham warned us that faculty administrators at OSU were working to make certain that Joshua, his sister Bethany and, if possible, his brother Matthew never receive Ph.D. degrees in nuclear engineering from OSU, regardless of their examination, academic and research performance. Professor Higginbotham then reviewed with us the details of the plan to destroy the education of these students and advised me to do anything I could to protect my children. Since November, a remarkable battle has been raging within OSU. I considered an immediate public exposure of this plot and warned the faculty of this possibility, but instead my family and I decided to try to prevent a scandal at OSU and save the students within the confines of OSU. We fought these unprincipled academics on their own ground and held them off for four months. That effort is, however, now failing, and Joshua and Bethany are both slated for dismissal from the department of nuclear engineering very soon. Also, unless action is taken immediately, Professor Higginbotham's career will be completely destroyed. Indeed, in retribution for Professor Higginbotham's efforts to protect the Robinson students from these unprincipled attacks, he personally has become the target of a campaign of defamation, vilification, persecution, Star-Chamber humiliation and other career-destroying actions orchestrated by Higley and the other people who are attacking us. Now nearing success is a disgraceful effort to strip Professor Higginbotham of his faculty position and his research grants. His career now potentially in ruins, he is fighting back in hopes of saving himself and the positions of the students and staff who depend upon him at OSU and who may also lose their careers as collateral damage in these astonishing events. The attack on Professor Higginbotham, if not stopped, may also destroy the graduate work of his student, Matthew Robinson. Matthew (OSU grade point average 3.91) passed up a $57,000 per year offer from the MIT graduate school so he could join his brother and sister at OSU two years ago. Demonstrating unanimity with the DeFazio cause, both responsible OSU deans and the president of OSU, Edward Ray, have so far failed to halt these dishonorable and illegal actions. Ray, a supporter of DeFazio on the campus, has refused even to meet with me or my son Joshua concerning these events. Knowledgeable observers have concluded that orders for the attacks on the Robinson students are coming from sources far above Ray in the Democrat political machine. The department of nuclear engineering attracted the Robinson students to OSU during a better day when it was directed by distinguished nuclear engineer José Reyes, who has now moved to NuScale Power. The department was in the hands of a group of very outstanding nuclear engineers. The ranks of these engineers have unfortunately been thinned by retirements and departure to other universities, including Michael Hartman now at the University of Michigan, but still mentoring Joshua. The engineers no longer control the department. The department is now controlled by ideologues, most of whom do not have Ph.D.s in nuclear engineering. Nepotistic husband-and-wife combinations and new hires of their own graduate students have brought the department under the control of unprincipled people who have enthusiastically participated in the attacks on the Robinson students and Professor Higginbotham - attacks that have violated numerous OSU academic rules, several laws and the most basic professional ethics. Professor Higginbotham, Joshua, Bethany and Matthew Robinson can still be rescued - but only by immediate, intense public pressure. OSU administrators think they can violate ethical academic standards of professional conduct, break formal OSU rules and regulations, and even violate U.S. laws with impunity because, in any resulting litigation, they would be defended by lawyers from the Oregon Department of Justice, assuring that only students with huge sums of money and many years to invest in litigation can oppose them. The Robinsons do not have those huge sums of money, and, moreover, they want to complete their education - not receive money in exchange for the destruction of their education and opportunities. If these people succeed, a delighted Peter DeFazio will be able to brag to the voters that the Robinson children were thrown out of Oregon State University. Why else but to favor DeFazio would the OSU administration condone seemingly irrational actions that are potentially so damaging to the reputation of the university? OSU dances to the tune of the Democrat machine, and DeFazio controls that machine. As things stand today, Jack Higginbotham and his students and staff, along with Joshua Robinson are in immediate danger. Bethany Robinson is slated for dismissal soon after and without the Ph.D. that she has nearly completed. The dismissal of Matthew Robinson may not be far behind. And the danger to Professor Higginbotham's other students is likewise very high. Please don't let this happen! Please notify OSU of your interest in this matter and urge the university to stop its destructive actions against Joshua, Bethany and Matthew Robinson and against Professor Jack Higginbotham, the remarkable president of the OSU faculty senate who has risked his career to help them! Contact information for the OSU nuclear engineering department is: Phone: 541-737-2343. Fax: 541-737-4678. E-mail: joan.stueve(a)oregonstate.edu. Mailing address: 116 Radiation Center, Corvallis, OR 97331-5902. Please also contact the President of OSU, Edward Ray. Phone: 541-737-4133. Fax: 541-737-3033. E-mail: pres.office(a)oregonstate.edu. Mailing address: 600 Kerr Administration Building, Corvallis, OR 97331-2128. The email address of the OSU Vice-President for University Relations and Marketing, Todd Simmons, is todd.simmons(a)oregonstate.edu For more information or to take further action, please visit: www.OregonStateOutrage.com. Please ask these people why the destruction of the academic work and careers of these students and Professor Higginbotham is so important that they are willing to sacrifice the good name of Oregon State University. Please ask them to stop the attacks on the Robinson students and Professor Higginbotham. Further details and regular updates regarding this issue will be posted by Art Robinson at www.OregonStateOutrage.com. Arthur Robinson, Ph.D., the 2010 Republican candidate for U.S. Congress in Oregon's 4th congressional district, is a research professor of chemistry and co-founder of the Oregon Institute of Science and Medicine. After graduating from the California Institute of Technology in 1963 and earning his Ph.D. from the University of California at San Diego, he served as a UCSD faculty member until co-founding the Linus Pauling Institute of Science and Medicine with Linus Pauling in 1973. In 1981, Dr. Robinson, his wife, chemist Laurelee Robinson, physicist Martin Kamen, and later joined by Nobel-winning biochemist R. Bruce Merrifield, cofounded the Oregon Institute of Science and Medicine. In recent years, Dr. Robinson has also directed the Petition Project, which has obtained the support and signatures of more than 31,000 American scientists for a petition opposed - entirely on scientific grounds published in peer reviewed journals - to the hypothesis of "human-caused global warming." ============================================== Our mailing address is: Art Robinson for Congress P.O. Box 1250 Cave Junction, OR 97523 Our telephone: 1-541-255-2785

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[math-fun] math-fun & politics
by Schroeppel, Richard 25 Mar '11

25 Mar '11

Note for newcomers -- the Math-Fun list discourages most political discussion: It's inflammatory, and I want to maintain a place to talk about math. Rich rcs(a)xmission.com

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[math-fun] Redefiining Pi again
by Stephen B. Gray 25 Mar '11

25 Mar '11

http://www.huffingtonpost.com/ian-squires/republicans-introduce-leg_b_83782… This Republican legislator has an excellent idea, to simplify math by officially setting Pi=3. But she stopped short of a much better simplification, which would be to make Pi=0. That eases geometry, addition, and mutiplication. Our kids would leap to the top of international math ratings. It would also make round structures much cheaper because they would have no circumference. If God had meant us to do math, he would already have set Pi=0. Steve Gray

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Re: [math-fun] Redefiining Pi again
by Dan Asimov 25 Mar '11

25 Mar '11

As believable as this article is, April 1 seems to have arrived early this year. The Huffington Post article is a hoax. --Dan << http://www.huffingtonpost.com/ian-squires/republicans-introduce-leg_b_83782… This Republican legislator has an excellent idea, to simplify math by officially setting Pi=3. But she stopped short of a much better simplification, which would be to make Pi=0. That eases geometry, addition, and mutiplication. Our kids would leap to the top of international math ratings. It would also make round structures much cheaper because they would have no circumference. If God had meant us to do math, he would already have set Pi=0. >> ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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Re: [math-fun] Integral of Gaussian over sphere
by Eugene Salamin 25 Mar '11

25 Mar '11

From: Eugene Salamin <gene_salamin(a)yahoo.com> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Wed, March 23, 2011 6:03:33 PM Subject: [math-fun] Integral of Gaussian over sphere Can anyone find a closed form expression for the integral of exp[(-1/2) (a[1] x[1]^2 + a[2] x[2]^2 + ... + a[n] x[n]^2)] over the unit (n-1)-sphere? In the n=2 case, we have a x^2 + b y^2 = a cos(t)^2 + b sin(t)^2 = (1/2) ((a+b) + (a-b) cos(2t)), and integrating over t in [0, 2 pi] gives 2 pi exp((-1/4) (a+b)) BesselI(0, (1/4) (a-b)). -- Gene ______________________________________________ I can express this as a single integral along a contour. I will slightly change the problem. Let I be the integral of exp(-(a[1] x[1]^2 + a[2] x[2]^2 + ... + a[n] x[n]^2)) over the (n-1)sphere of radius r. Since the integration is over a compact region, the integral is well defined for all complex a[k]. I will assume a[k] > 0, allowing analytic continuation to do the rest. Let ρ be the radial coordinate. Introducing the delta function δ(ρ-r) into the integrand, we can then integrate over all n-space. We have δ(ρ^2-r^2) = δ(ρ-r)/(2r) + δ(ρ+r)/(2r) = δ(ρ-r)/(2r), since ρ+r > 0. It is well-known, at least to physicists, that one can represent the delta function as δ(t) = (1/(2π)) int(exp(iωt), ω=-inf..inf). Then δ(ρ-r) = 2r δ(ρ^2-r^2) = 2r δ(sum(x[k]^2, k=1..n)-r^2). Then I is r/π times the integral of exp(-(sum((a[k]-iω) x[k]^2, k=1..n)) exp(-iωr^2) over all x[1], ..., x[n], ω from -infinity to +infinity. First integrate over the x[k] the first exponential expression above. This step requires positive a[k], or at least Re a[k] > 0. This integral is sqrt(π^n / prod((a[k]-iω), k=1..n)), and we have I = (r/π) π^(n/2) int(exp(-iωr^2)/sqrt(prod((a[k]-iω), k=1..n)), ω=inf..inf). The integrand has poles or branch points at ω = -i a[k], which lie on the negative imaginary axis. Also, exp(-iωr^2) is analytic in the lower ω half-plane, and --> 0 for Im ω --> -inf. Hence the contour can be deformed to go up from -i inf on the left side of the negative imaginary axis, clockwise around the -i a[k] closest to the origin, and down to -i inf on the right side of the imaginary axis. If two of the a[k] are equal, they contribute a pole to the integrand, and their contribution to I can be evaluated by residues. A pair of unequal a[k] can be joined by a branch cut, with the contour going around the cut. If n is odd, at least one branch cut necessarily extends to (-i inf). Note that poles are contoured clockwise, so they contribute -2πi times the residue. When n=2, a[1]=a[2]=a, we get I = 2πr exp(-a r^2), as expected. But for n>2, it looks wrong; r should appear to the n-1 power. But consider n=4, a[1]=a[2]=a, a[3]=a[4]=b. Working out the residues, we get I = 2π^2 r (exp(-ar^2) - exp(-br^2))/(b-a). As b-->a, this becomes 2π^2 r^3 exp(-ar^2), as it should. The double pole at ω=-ia differentiates the exp(-iωr^2), providing the extra two powers of r. More generally, suppose we scale r-->sr, a[k]-->a[k]/s^2, ω-->ω/s^2, dω-->dω/s^2. Then exp(-iωr^2) is unchanged, 1/sqrt(prod((a[k]-iω), k=1..n)) is multiplied by s^n, the integral is multiplied by s^(n-2), and finally I is multiplied by s^(n-1), displaying the r^(n-1) dependence. When n=2, a[1] /= a[2], there is a pair of branch points joined by a cut. Its Fourier transform integrated along the cut is a Bessel function, but I'm too lazy to work it out to verify its correctness. When n=4 with no two a[k] equal, the formula asks us to take the Fourier transform along the cuts of the function, which if integrated just by itself, gives an elliptic integral. This, and for larger n, quickly exceeds my skill with special functions. Perhaps the reader is curious as to my interest in this problem. I've been working on the problem of fitting a line y = ax + b to data (x[i], y[i]) when both x[i] and y[i] are subject to error. The usual least squares solution assumes that the x[i] are free of error. A proper Bayesian solution must provide, not just a single "best fit", but rather a probability distribution p(a,b|x[i],y[i],σx,σy). The proposed problem, with n=2, arises in normalizing this probability to unit total integral. So this can be done with nothing worse than BesselI. More generally, fitting a plane y = sum(a[k] x[k], k=1..n) + b yields a probability distribution p(a[k],b) whose normalization requires the integral of an (n+1)-dimensional Gaussian over the n-sphere. -- Gene

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[math-fun] NYTimes: Where Has All the Nitrogen Gone?
by Henry Baker 25 Mar '11

25 Mar '11

FYI -- I guess I'm not the only one wondering where the nitrogen went! (See previous posting on the possibility of the Earth losing a significant portion of its atmosphere in the "k-T event" ~60 million years ago.) http://scientistatwork.blogs.nytimes.com/2011/03/23/where-has-all-the-nitro… Scientist at Work - Notes From the Field March 23, 2011, 2:06 pm Where Has All the Nitrogen Gone? By ALYSON SANTORO Alyson Santoro, a postdoctoral researcher at Woods Hole Oceanographic Institution, writes from off the coast of Chile, where she is studying microbes in the nitrogen cycle. The federal government isnÂt the only group with a problem balancing its budget these days. Oceanographers have a budget problem too. Nitrogen Â an essential nutrient for all life on the planet Â is at the heart of this budget crisis. Some estimates of the amount of nitrogen leaving the ocean exceed estimates of the amount of nitrogen coming in by several hundred teragrams (thatÂs one billion kilograms) per year. Does this mean that the ocean is actually losing nitrogen? Probably not, but it does mean that we donÂt have a good understanding of where in the ocean nitrogen is coming and going. Over the next five weeks, I will be joining a team of researchers from around the world on a research cruise to the eastern tropical South Pacific off the coast of Chile to see if this could be one area where the ÂmissingÂ nitrogen could be entering the ocean. ...

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Re: [math-fun] Model of road network development.
by Henry Baker 25 Mar '11

25 Mar '11

It's interesting that you mention arteries & capillaries. There has been some work on how arteries & capillaries develop in animals and humans. Sportspersons are particularly interested in the development of capillaries, as a higher % of capillaries in the muscles lead to greater performance and endurance. So-called "red" muscle fibers have better blood supplies than "white" muscle fibers. It is conjectured that the build-up of "waste" products like lactic acid encourages the development of more capillaries. Arteries can also increase in size with exercise -- at least in the young. It is conjectured that the eddies & vortices that form in smaller vessels somehow encourage the artery to grow -- perhaps from the vibration? The drug industry has investigated vascularization because one way to kill a cancer is to keep it from developing a good blood supply. So scholor.google.com may be able to help you find those who might have written similar simulation models. At 07:27 AM 3/24/2011, Allan Wechsler wrote: >I have been mulling over a possible simulation of the development of road >systems, and for some reason I can't force myself to actually start writing >code. I'm hoping that some math-funster will kick me out of my rut. My >hope is that the model will generate realistic-looking road networks from >scratch. I'm curious to see if it will capture some of the features we are >used to in road networks: a preference for right-angled intersections, a >fractal-ish vascularization of the area with major and minor arteries giving >way to capillaries, and so on. And if it doesn't, I'm even more curious to >know what kinds of networks it will generate instead. > >We begin with a plane region, possible a square or a disk. At the beginning >of the simulation, travel speed is a fixed constant, say 1 meter per second. > >We select two points at random from the region, with a uniform distribution, >and imagine that somebody needs to travel from one point to the other. The >traveler selects the fastest possible route, and goes. > >The act of traveling over a route increases the speed limit along that route >by one centimeter per second. After that first journey, the travel speed is >1 meter per second everywhere, except along the line between those first two >points; along that line, the speed is 1.01 meters per second. > >We now select a new two points at random, find the shortest path by the >modified metric, and perform the journey; again, the speed limit is >increased by 0.01 meters per second along the chosen route. If the new >endpoints lie near the original line, there will be an advantage in sidling >toward that line, and scooting along it until the destination nears. (My >algebra indicates that there is a critical angle at which it is most >advantageous to join an existing route.) > >After repeating this process thousands of times, what sort of road network >will have developed?

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[math-fun] Integral of Gaussian over sphere
by Eugene Salamin 24 Mar '11

24 Mar '11

Can anyone find a closed form expression for the integral of exp[(-1/2) (a[1] x[1]^2 + a[2] x[2]^2 + ... + a[n] x[n]^2)] over the unit (n-1)-sphere? In the n=2 case, we have a x^2 + b y^2 = a cos(t)^2 + b sin(t)^2 = (1/2) ((a+b) + (a-b) cos(2t)), and integrating over t in [0, 2 pi] gives 2 pi exp((-1/4) (a+b)) BesselI(0, (1/4) (a-b)). -- Gene

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[math-fun] Model of road network development.
by Allan Wechsler 24 Mar '11

24 Mar '11

I have been mulling over a possible simulation of the development of road systems, and for some reason I can't force myself to actually start writing code. I'm hoping that some math-funster will kick me out of my rut. My hope is that the model will generate realistic-looking road networks from scratch. I'm curious to see if it will capture some of the features we are used to in road networks: a preference for right-angled intersections, a fractal-ish vascularization of the area with major and minor arteries giving way to capillaries, and so on. And if it doesn't, I'm even more curious to know what kinds of networks it will generate instead. We begin with a plane region, possible a square or a disk. At the beginning of the simulation, travel speed is a fixed constant, say 1 meter per second. We select two points at random from the region, with a uniform distribution, and imagine that somebody needs to travel from one point to the other. The traveler selects the fastest possible route, and goes. The act of traveling over a route increases the speed limit along that route by one centimeter per second. After that first journey, the travel speed is 1 meter per second everywhere, except along the line between those first two points; along that line, the speed is 1.01 meters per second. We now select a new two points at random, find the shortest path by the modified metric, and perform the journey; again, the speed limit is increased by 0.01 meters per second along the chosen route. If the new endpoints lie near the original line, there will be an advantage in sidling toward that line, and scooting along it until the destination nears. (My algebra indicates that there is a critical angle at which it is most advantageous to join an existing route.) After repeating this process thousands of times, what sort of road network will have developed?

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[math-fun] Puzzle: Skew planes in 4-space?
by Dan Asimov 23 Mar '11

23 Mar '11

Fred's query reminds me of the time in 1994 that I gave a lecture -- about 4-dimensional space -- to the Hampshire College summer math program for mathematically talented high school students. Some brilliant youngster asked me whether there could be skew (2D) planes in 4-space. (Skew meaning neither parallel nor intersecting.) I thought about it for a few seconds . . . and then a few more seconds . . . and had to admit I didn't know. But I went home and soon figured it out. Can you? --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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