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2013 April 25

Low heart rate, longer life

Filed under: Uncategorized — gasstationwithoutpumps @ 18:09
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The article  “Elevated resting heart rate, physical fitness and all-cause mortality: a 16-year follow-up in the Copenhagen Male Study”, in the journal Heart (doi:10.1136/heartjnl-2012-303375) says that a low resting heart rate is predictive of longevity, even after correcting for “physical fitness, leisure-time physical activity and other cardiovascular risk factors”, at least among healthy, middle-aged Caucasian men.

This is good news for me, as I have a low resting heart rate (around 52 bpm) and fit the other criteria.

I’m a little unclear on how they did the correction, as the fitness (measured with VO2max) was very highly negatively correlated with heart rate (R=–0.34). They say they used “Cox proportional hazards regression analysis”, which seems to me to suffer the problem of all regression methods when the input variables are highly correlated. They do claim “Assumptions regarding the use of Cox proportional hazards were met by inspection of the log minus log function at the covariate mean.”

The are showing a huge difference between resting rates under 50 bpm and over 50 bpm, then small differences up to 80 bpm, and big increases for over 80 bpm and even bigger for over 90bpm.  I wish that they had divided the group into equally populated classes, rather than every 10 bpm, as the 51–60bpm group has almost 36% of the subjects (1003/2978), and I’m pretty sure the low and high end of that group are different.  I also wish that they had used the median group (61–70 bpm) as their baseline, rather than the unusual group having heart rates under 50 bpm.  The 51–60bpm group has only a 5% lower risk than the 61–70 bpm group, while the under 50bpm group has about a 30% lower risk.  It would be interesting to have analyzed the data to try to get a smooth curve of risk vs. heart rate, though that would have required more sophisticated modeling and the data may not be sufficient to produce a reasonable curve.

2013 April 23

Chapter 22 homework

We finally finished off Chapter 21 of Matter and Interactions today, about 2 months behind my original schedule, having been repeatedly distracted.  We never did get around to measuring the magnetic field of a coil as a function of distance or current, either, though we’ll probably get back to trying that after the AP exams.

It looks like there is a chance my son will get to take the AP CS and AP Physics C: E&M exams this year, even though my first 5 attempts to find a place for him to take them failed. He needs to take the late exam for AP CS, since it conflicts with the Oregon Shakespeare Festival field trip and no one in the County offers Physics C—my attempts to get one of the high schools to offer the exam (which is at the same time as Physics B) all failed.  His consultant teacher is trying to arrange to be the proctor for him on the late AP CS and the late Physics C: E&M exams (it is now too late to register for the regular exams) through another high school in the same district.  I’m hopeful that she’ll be more successful in moving the bureaucracy than I was as an outsider.

Of course, he’ll probably never get any credit for taking the exams, since many of the schools he is applying to don’t do AP credit anyway, and he’ll have to retake physics at any of the schools he’s likely to choose.  But the exams will help validate that he has done rigorous work in physics, which should help him get into the colleges that would be a good fit for him. The AP CS exam is so low level that all it validates is that one has learned some Java syntax—but it might help with admissions offices also, as most will not be familiar with the new Art of Problem-Solving Java course.

In any case, we have to speed up a bit on the physics, despite the distractions, so here are the problems for Chapter 22 “Patterns of Fields in Space”: 22P15, 22p16, 22p18, 22P22, 22P23, 22P25, 22P29, 22P31, 22P33, 22P37.

statpics: Venn Disease

Filed under: Uncategorized — gasstationwithoutpumps @ 08:18
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One blog I follow is the statpics blog, in which Robert Jernigan posts pictures related to statistics (like wear patterns on doors showing the distribution of where people touch it, or examples of people abusing the notion of a bell curve).  Recently he posted the following Venn diagram from the NY Times as statpics: Venn Disease:

I was going to complain about the Venn diagram as being useless here, as it did not include the number who had none of the conditions, thus not allowing the viewer to determine the probability of each condition separately, which is essential to making any real sense of the figure (are the conditions correlated?).

I did not complain on his blog for two reasons:

  • He requires commenters  to sign in with a Google account, and I prefer to leave blog comments using my WordPress account, so that people can find my blog from the comments.
  • I went back to the original source and found that the NY Times writer or artist had not been quite so cavalier with the data—there was another circle adjacent to the Venn diagram that included all those with none of the conditions.  (I was actually quite surprised to see that Jernigan had omitted an important part of the figure, as he is usually quite sensitive about probability distributions, so truncating a figure to omit one category seems out of character for him.)

I looked a bit at the pairwise comparisons on the last page of the NYTimes article, and decided that this way of presenting the data violated many of the principles of good data presentation.

First, it takes a huge amount of space to present just 3 numbers (the pairwise comparison shows percentages for conditions A&B, A&not B, B&not A).

Second, it is not possible to look at two different comparisons at the same time.

Third, the NYTimes Venn diagrams have rather distracting pointless animation, which is not visible in the static image I copied from Jernigan’s blog.

Fourth, the Venn diagram often implies a correlation (look how often these conditions co-occur!), when the probabilities of the conditions appear to be essentially independent in many cases.  For example, Alzheimer’s and high-blood pressure co-occur in 24% of the nursing home residents in the sample, but with probabilities of 46% for Alzheimer’s and 57% for high blood pressure, one would expect about 26% to have both if they were independent conditions.

The basic point of the original story is that people in assisted living facilities have very high probabilities of a debilitating medical condition (well, duh! that’s why they’re in assisted living, and not a lower-cost housing option) and that multiple conditions are common. One of their main points is that 9% of residents of assisted-living facilities have all three of dementia, heart disease, and high blood pressure, and that “treating these patients is extremely difficult because of complicated drug regimes and numerous side effects.”

Within the assisted living population the conditions seem to be nearly independent (though that is hard to tell from the Venn diagrams—they don’t give the sizes of all the parts in the 3-variable Venn diagram, and I did not click through all the pairs to check pairwise independence from the 2-variable Venn diagrams). But that near-independence may mean that multiple conditions are more common than a naive prediction based on independence in the overall population would suggest. To determine whether the conditions are correlated, one would have to look at the whole population at a given age, rather than just at the selected population in assisted living, since that selection probably under-represents those with no debilitating conditions. (I also wonder how “assisted-living facility” is defined, since I know that the definitions are quite different in California and Colorado, with a much looser definition in Colorado that would include many of the “independent-living” facilities in California.)

Doing a proper analysis of the data would require going back to the original study, which the byline-less NYTimes article only refers to vaguely as “the study, by the National Center for Health Statistics in 2010”.   I’m not interested enough to search for that study and see whether there is enough information to see whether any of the co-occurences are really surprising.

2013 April 21

Noise in nanopores

Filed under: Uncategorized — gasstationwithoutpumps @ 16:32
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I’ve been trying to understand the sources for noise in current measurements through nanopores, so that I can better understand the signals that are generated in the nanopore lab.  I’ve not studied noise in small signals before, so I’ve been having to rely on Wikipedia for information about sources of noise.  I’ve probably missed some important ones and would appreciate those more knowledgeable pointing out important noise sources that I missed.

I think that there are two main noise sources:  the nanopore itself and the resistors used in converting the nanopore current to a voltage in the first stage of amplification.  Each of these noise sources has two types of white noise: thermal noise (dependent on temperature) and shot noise (independent of temperature).

Thermal noise

The RMS current for thermal noise is i_{\mbox{\scriptsize thermal}} = \sqrt{\frac{4k_B T \Delta f}{R}} for a resistance of R at temperature T, with kB being Boltzmann’s constant, 1.3896593E-23 J/°K, and \Delta f being the bandwidth of the filter looking at the noise.  Normally, nanopore scientists don’t report the resistance of the nanopore, but the bias voltage and the DC current through the pore, but we can use Ohm’s law to rewrite the noise formula as i_{\mbox{\scriptsize thermal}} = \sqrt{\frac{4k_B T I \Delta f}{V}}.  A typical setup for a nanopore may have a voltage of 180mV and 60pA (for an open channel in 0.3M KCl), and a temperature of 25°C = 298.15°K, for 4 k_B T = \mbox{16.573E-21 J}, and noise of \mbox{2.35E-15} \sqrt{\Delta f} A/\sqrt{\mbox{Hz}}.

Shot noise

The RMS current for shot noise is i_{\mbox{\scriptsize shot}} = \sqrt{2 q I \Delta f}, where q is the magnitude of the charge of the carriers (here 1.60217646E-19 C, since the charge carriers are K+ and Cl), and I is the DC current.  Again \Delta f is the bandwidth of the filter looking at the noise.  For a current of 60pA, the shot noise would be \mbox{3.259E-15} \sqrt{\Delta f} A/\sqrt{\mbox{Hz}}, slightly more than the thermal noise.

Combined noise in nanopore

The combined noise in the nanopore from both shot noise and thermal noise should then be i_{\mbox{\scriptsize pore}} = \sqrt{\left(2 q + \frac{4k_B T}{V}\right)I \Delta f}, which for 180mV and 60pA would be \mbox{4.02E-15} \sqrt{\Delta f} A/\sqrt{\mbox{Hz}}.  If a 1kHz low-pass filter is used, that makes an RMS noise level of 0.127pA, and with a 10kHz low-pass filter, 0.4pA.

Increasing the ionic concentration would provide a larger DC current (current proportional to concentration), and the noise current only grows with the square root of the DC current, so the signal to noise ratio also grows with the square root of the ionic concentration.

Amplifier noise

These noise levels are lower than what is actually observed, of course, because we haven’t taken into account noise generated in the first stage of amplification.

In the UCSC nanopore lab, they use an Axon Axopatch 200B Capacitor Feedback Patch Clamp Amplifier, which costs about $2000 used (if you have to ask the new price, you can’t afford it—you can get a quote, but there is no list price).  The web site claims “By introducing active cooling of components in the headstage to well below 0°C, the open-circuit noise in patch mode has been reduced to unprecedented levels, as low as <15 fA (RMS) at 0.1–1 kHz.”  But the lab uses a resistive headstage (so as to be able to make DC current measurements), with a 500MΩ feedback resistor in the current-to-voltage converter, which introduces thermal noise of about \mbox{5.76E-15} \sqrt{\Delta f} A/\sqrt{\mbox{Hz}}, larger than the nanopore noise. The shot noise for the resistor in the I-to-V converter should be the same as as the shot noise for the nanopore, since they have the same DC current. Combining the thermal and shot noises for both the nanopore and the resistor at 180mV and 60pA, I estimate \mbox{7.74E-15} \sqrt{\Delta f} A/\sqrt{\mbox{Hz}}, which would be 0.244pA at 1kHz, 0.547pA at 5kHz, and 0.774pA at 10KHz.  The noise levels observed in the signals are close to those levels, so there is not much that can be done to improve the amplifiers to get a better signal-to-noise ratio.

We could be interested in lower-cost amplifiers than the $2k lab instrument, but a very low noise off-the-shelf op amp (like the AD8432 ) has a noise level of about 2.0pA\sqrt{\Delta f}/\sqrt{\mbox{Hz}}, which is much larger than what is observed in the lab.  Designs have been done at UCSC for much lower noise amplifiers (Gang Wang; Dunbar, W.B., “An integrated, low noise patch-clamp amplifier for biological nanopore applications,” Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE , vol., no., pp.2718,2721, Aug. 31 2010-Sept. 4 2010 doi: 10.1109/IEMBS.2010.5626570) claiming “input referred noise of the amplifier is 0.49 pA RMS over a 5 kHz bandwidth”, from simulation (I don’t know whether they have fabricated and tested the amp yet).

UPDATE 2013 Nov 13:  A student showed me a data sheet for an off-the-shelf ($3–$4) op amp that has low enough noise for this purpose: the AD8625 (or AD8626 or AD8627).  They have only a 0.25pA bias current and a current noise density of 0.4 fA\sqrt{\Delta}/\sqrt{\mbox{Hz}}. That’s actually better than the AxoPatch 200B, whose manual reports about 0.1 pA at 10kHz, which is 1fA \sqrt{\Delta}/\sqrt{\mbox{Hz}}.   Even better specs are available for  the AD549L (about $40) with a 60fA bias current and a current noise density of 0.11 fA\sqrt{\Delta}/\sqrt{\mbox{Hz}}.   Of course, once the amplifiers are this good, most of the noise is coming from thermal noise in the feedback resistor (about 6 fA\sqrt{\Delta}/\sqrt{\mbox{Hz}}), unless one uses capacitive feedback (which precludes measuring DC currents).

I don’t know why I missed these op amp before, as they have been around since 2002 or 2003.

2013 April 20

College tours around LA

Sorry I’ve not been posting this week, but I’ve been on the road with my 11th-grade son around Los Angeles for science fair and college campus tours.

On Monday and Tuesday, we had the California State Science Fair, where he had a project in the math and software high school division, and I was judging in the math and software middle-school division.  He did not expect to win anything this year, as he had a fairly straightforward engineering project—the Arduino data logger that he wrote for my circuits class to use.  The project was well done for a high school student (comparable to some senior projects I’ve seen by college students), but not flashy in the way that science fair judges like. Indeed he did not win anything at state this year, but he was one of only 11 students who had been to state science fair 6 or more times—so he shows consistent quality and perseverance, even if he never wins the lottery that science fair judging often is.  The top math and software award at the high-school level this year went to a math project (not a software project), which is a bit unusual.  I did not read the poster for it in any detail, which I now regret, as it must have been pretty good to overcome the usual judging bias in favor of software.

The middle-school math and software category had a unanimous vote for the first-place project: an ambitious image-processing project with an interesting application and pretty good code (properly commented—a rarity at the middle-school level or even the high-school level).   The order of the next few projects was more strongly debated, but all of them were very good projects, and the order ended up depending more on the tastes and persuasive abilities of the judges than on the inherent merits of the projects.

Since we were down in Los Angeles for the science fair, we decided to extend the trip by 3 days to visit three colleges in the area: Caltech, UCLA, and Harvey Mudd.  [The science fair is right by USC, but that was not our list of colleges to visit—we’ve seen the campus often enough, and the academic program did not appeal.] Originally we had planned a west-to-east sweep (UCLA, Caltech, Harvey Mudd) to minimize the transit time, but Caltech was not doing tours on Thursday and Friday (preparing for their admitted-students yield event this weekend), so we changed the order to Caltech, UCLA, Harvey Mudd. To get from the science fair to Pasadena, we took a DASH bus, the red line (subway), and the gold line (light rail).  That used 2 different transit systems (LA DOT runs the DASH buses, and Metro runs the subway, the light rail, and all the other buses that we took on this trip).

I couldn’t find any reasonably priced motels or hotels near UCLA in my on-line searches, so we stayed one night in Pasadena and two nights in Claremont, with the UCLA tour sandwiched in between the 2-hour, 2-bus Pasadena-Westwood and 3-hour (bus, subway, train) Westwood-Claremont transits.  I had originally planned to take a taxi from UCLA to Claremont (a pretty expensive ride across Los Angeles), but my son wanted to include a Metrolink commuter rail link in the trip somewhere in our trip, so we ended up taking the Metro number 2 bus from UCLA to the red line, the red line to Union Station, and Metrolink to Claremont.  The subway and commuter rail portions were fairly pleasant, but the number 2 bus was so full that we felt guilty for having luggage—Metro probably needs to run more buses on that route during rush hour.

The LA transit system is usually maligned by the locals, who claim that it is so bad that they have to drive everywhere, but it seemed pretty reasonable to us—under-utilized, perhaps, but reasonably quick and with decent connections.  Of course, just about any local bus system will only provide about 10-mile-per-hour transportation, so bicycling is almost always faster, but that is an option that is seems very , very few people choose in Los Angeles.

OK, enough on transit, what about the 3 colleges?

At Caltech we had a very small tour group (just 3 prospective students) and a friendly, barefoot tour guide.  We were shown the Caltech “houses” and the guide talked a lot about Caltech traditions.  Some of the traditions (like the honor code) seem great, but a lot of the other traditions seemed to be based mainly on rivalry, competition, and mean-spirited pranks. The social activities mentioned (like the interhouse parties) seemed to be mainly competitive events also (which house could build the most elaborate set for their party).  We saw almost no students while on the tour, no classrooms, no professors—very little other than the houses and the outsides of buildings.  The campus seemed strangely deserted for a Wednesday afternoon in the middle of the term.

The Caltech campus does have some nice-looking buildings, and there are supposedly a lot of Nobel prize winners around, but we didn’t hear much about students actually interacting with the professors—the impression was that the professors mainly kept their heads down and did research with their postdocs and grad students. My son had tried to arrange meetings with a computer science faculty member by e-mail, but the first one he contacted suggested he talk to someone else, and that person said he was too busy, but that my son should just wander down the hall and stick his head in an open door.  We ended up not talking to any Caltech faculty or even seeing any from a distance.

The one academic message that we got from Caltech was “physics”.  They teach physics at Caltech—occasionally they give it a different name (math, chemistry, computer science, engineering, … ), but when you look at the research interests of the faculty, it is almost all physics in different flavors.  My son likes physics, and would probably do ok at Caltech, but he has other interests as well, and Caltech does not seem to provide instruction or opportunities in them.  He also likes doing applied work more than theory, and Caltech (according to the student tour guide and what we could glean from the web) is very theory-oriented.  Caltech does have some theater that he could participate in, but their entire “theater and visual arts” program apparently fits in a small 2-story house and a shed at the corner of campus, and there was no one around on a Wednesday afternoon to get any information from.

UCLA was in many ways the opposite of Caltech.  It is a large, bustling campus, crowded with students the whole time we were there. Students walked or hung out in groups (very little wheeled transportation, because of the number of hills and stairs).  There did not seem to be many quiet places on campus (unlike Caltech, where the entire campus seemed to be silent).

The tour group we were with for a 2-hour walking tour was large—probably 15 students plus accompanying family members.  The tour guide showed us many buildings (including the insides of a nice library), but no residences (which are a 20-minute walk away from the academic buildings), and she told us about admissions and other generic information.  The campus tours seem to be entirely student run (the campus tours office is in the student government building and staffed entirely by students), rather than part of the admissions office.  The tour was pretty good, for a large, generic tour, and UCLA does have some nice-looking buildings (and nice-looking students, but I’m not supposed to notice that).

We had arranged a meeting with a CS faculty member, who told us about his classes and research. Undergrad computer science at UCLA has huge classes (60–80 in upper-division courses, and three times that in lower-division courses). The faculty member told us that he does not allow undergrads into his grad courses and that few undergrads get research opportunities.  He did not have numbers, but estimating from what he said, it sounds like only about 5% of CS majors at UCLA get involved in faculty research—an appallingly small number.  It sounds like it is hard for an undergrad at UCLA to get a first-rate computer science education, because they are so focused on pumping through huge numbers of OK students.

UCLA does have a great reputation in theater, so we went over to the opposite side of campus to find out whether a non-theater major could ever get roles.  We did not talk to a theater faculty member nor an administrator, but to a friendly group of theater majors.  They basically said that non-majors had essentially no chance of getting a role (or even tech work) in any theater department production—even the theater minors only got theater-appreciation classes, not acting classes.  They did say that there were some non-departmental theater productions, but that they knew almost nothing about them.  In short, it sounded like what my son wants (a really advanced computer science education with the ability to do a fair amount of acting on the side) is not available at UCLA.

I had expected Harvey Mudd to be similar to Caltech.  They both have reputations for being very techie schools with impossibly high workloads, and Harvey Mudd was started by someone with close ties to Caltech.  They both have a similar-sounding common core requirement and both have a very pure form of honor code (tests are unproctored take-home exams, with students responsible for timing themselves as well as following directions about whether notes and books are permitted).  There were a number of observable differences, though, even on a one-day visit:

  • Harvey Mudd has some of the ugliest buildings I’ve seen on any college campus.  The concrete block buildings with “warts” make UCSC’s cast concrete bunkers look stylish in contrast.  It is clear that Mudd has not been investing in the amenities wars—there is no luxury here.  The interior of the dorms look a lot like the concrete-block dorms I lived in back in the early 70s at Michigan State, but perhaps even more crowded.
  • The campus is small.  Our walking tour showed us every building on campus, including a walk through the main academic building, showing us classrooms, faculty offices, and even the wood shop and machine shop (which Mudders can use 24/7 once they have passed the safety training). The class in which students have to make a hammer to specifications from a chunk of wood and a chunk of metal seems like a good, practical course.
  • The campus is flat, so wheeled transportation is common (bikes, unicycles, skateboards, long boards, and freeline skates seemed the most popular).
  • The density of students was between that of Caltech and UCLA.  There were plenty of students around, but it was never so crowded or so loud as to be claustrophobic. A lot of the students were wearing geek T-shirts and seemed likely to be the sorts of kids my son would get along well with.
  • Faculty were clearly visible—one physics professor even kibbitzed the tour guide as he was giving the explanation of the physics core courses.
  • The admissions office gave my son a ticket for a free meal at the dining hall (and a reduced-price ticket for me).  We had lunch there, and the food was pretty good for a dining hall—more important it included several things that my son would eat on a regular basis.  We also noticed that several of the faculty ate there.  I don’t know if Harvey Mudd encourages the faculty to eat with the students (free lunch might do the trick, or the unavailability of other options), but it was good to see faculty and students in the same hall, even if at different tables.  I also noticed that none of the students were eating alone—almost everyone was in a group of 2 to 10 students. For a group of geeks, that is a rather astonishing bit of social engineering—I wonder how they accomplished it.
  • My son was also given a list of all the classes meeting at Harvey Mudd this semester and invited to sit in on any of them.  Unfortunately, we were there on a Friday, so few classes were meeting (mostly long labs).  We sat in on one of the “choice” labs for a while, and saw mainly one-on-one mentoring by the faculty member, which was good to know about, but not very exciting to watch.
  • Harvey Mudd does have an 11-course humanities, social science, and arts (HSA) requirement, about half of which has to be done at Harvey Mudd, with the rest usually being done at the other Claremont colleges.  It would be possible for him to do a theater concentration (5 theater-related courses), by taking the one Harvey Mudd theater course (simply titled “Shakespeare”) and 4 courses at Pomona.  Most of the Mudders take a fair number of courses at the other Claremont colleges—usually PE courses and courses in their HSA concentration, and cross-registration seems to be fairly straight-forward, since the Claremont colleges share a common registration system.
  • There is an aikido course at Scripps that my son could take for PE—he’s not done aikido since he was quite young, but thinks that he would enjoy picking it up again more than most PE options.
  • My son had made an appointment with a computer science faculty member and we had a good conversation with him about the Harvey Mudd requirements and opportunities in computer science.  All the computer science students have to do research or development projects and most do more than one (the senior clinic plus one or more summer research projects).  There seems to be enough depth in courses and research in the fields my son is interested in that the lack of grad courses is not really important.  Even the required common-core first course in computer science has an option for students sufficiently advanced in CS, so that he would not have to repeat stuff he’s already done.
  • The tour guide talked a lot about coöperation, mentoring, and group projects—concepts that were independently brought up by the admissions officer and by the CS faculty member.  The group projects don’t seem to be the one-person project forced on a group that most middle-school and high-school projects are, but projects big enough to benefit from multiple people working on them.  They do practice pair programming in most CS classes, which will be a new experience for my son.

Although I had expected Caltech and Harvey Mudd to be very similar schools from what I knew before the visits, I ended up with very different impressions of them.  Caltech seems to be a competitive school with a physics-centric, theoretical focus, while Harvey Mudd is a cooperative school with an applied engineering focus.  My son will probably apply to both, since getting in is largely a lottery (they both have about a 10% acceptance rate and his test scores are only average for either school), but I think that he’d end up much happier at Harvey Mudd.  UCLA looks much less attractive (other than financially), but he’ll probably apply to several of the UC schools as he is much more likely to get into them.

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