April 18, 2014

10:00 PM | Peirce’s 1870 “Logic Of Relatives” • Comment 10.7
Here is what I get when I analyze Peirce’s “giver of a horse to a lover of a woman” example along the same lines as the dyadic compositions. We may begin with the mark-up shown in Figure 19. (19) If we … Continue reading →
3:25 PM | Announcements
Time for a short rundown of announcements. STOC will be held May 31-June 3 in New York City. Early registration and hotel deadline is April 30. Student travel support requests due by this Monday. The newly renamed ACM Conference on Economics and Computation (EC '14) will be held in Palo Alto June 8-12. Early registration deadline is May 15. Hotel deadline is May 19th but the organizers suggest booking early because Stanford graduation is June 13. The Conference on Computational […]
12:41 PM | Lecture 12 -- Privacy Yields an Anti-Folk Theorem in Repeated Games
Last week, Kobbi Nissim gave us an excellent guest lecture on differential privacy and machine learning. The semester has gone by fast -- this week is our last lecture in the privacy and mechanism design class. (But stop by next week to hear the students present their research projects!)Today we'll talk about infinitely repeated games. In an infinitely repeated game, n players repeatedly, in an infinite number of stages, play actions and obtain payoffs based on some commonly known stage game. […]
12:10 PM | More from xkcd.com
Here's another from xkcd.com, on our "good graphics" theme.
1:54 AM | Duality: Confidence intervals and the severity of tests
A question came up in our seminar today about how to understand the duality between a simple one-sided test and a lower limit (LL) of a corresponding 1-sided confidence interval estimate. This is also a good route to SEV (i.e., severity). Here’s a quick answer: Consider our favorite test of the mean of a Normal distribution with […]

April 17, 2014

5:14 PM | Talking quantum mechanics with second graders
“What’s the hardest problem you’ve ever solved?” Kids focus right in. Driven by a ruthless curiosity, they ask questions from which adults often shy away. Which is great, if you think you know the answer to everything a 7 year-old … Continue reading →
3:34 PM | On Forming an MAA Special Interest Group on Open Coursware
Last January in Baltimore, the question of how best to organize the open textbook community for our mutual benefit was raised. I suggested forming a special interest group through the Mathematics Association of America (MAA). At the time this was just an off-the-cuff remark. Since then I have discussed the idea with a couple of people and I believe there is sufficient potential in the idea to at least address how that might be done and to ask for comments.I have looked into the mechanics of […]
1:00 PM | RSRG does a triathlon
Our group has a history of doing athletic events during our outings over the years, hikes and even half-marathons.  But, this past weekend we tried something a little more involved, a triathlon!  Besides me, no one in the group had done a triathlon before (they hadn’t even done open water swimming before), but amazingly we […]
12:13 PM | Should you reveal a P = NP algorithm?
A reader asks What would you do if you could prove that P=NP with a time-complexity of n2 or better... moreover, would you publish it?   There are all these statements of the good that could come of it. But how would the government react in its present state? Would it ever see the light of day? How would a person be treated if they just gave it away on the internet? Could a person be labeled a threat to national security for giving it away?  I consider this a completely […]
5:21 AM | 403 – HW 3 – Computing eigenvalues
This set is due Thursday, May 8, at the beginning of lecture. (There will be another homework set, due the scheduled day of the final exam, Thursday May 15, at 11am, so I recommend you try to complete this set earlier than the scheduled deadline.) You can work on your own, or in groups of […]

April 16, 2014

7:30 PM | Peirce’s 1870 “Logic Of Relatives” • Comment 10.6
As Peirce observes, it is not possible to work with relations in general without eventually abandoning all of one’s algebraic principles, in due time the associative law and maybe even the distributive law, just as we have already given up … Continue reading →
5:50 PM | L'universo spiegato a mia sorella
Non voglio fare concorrenza alla splendida spiegazione di Amedeo o a quella tecnica di Corrado, ma mia sorella, leggendo il post di pancia scritto nella sera dell'annuncio di BICEP2, ha candidamente confessato di non aver capito cosa era accaduto quel giorno. E allora proviamoci, a raccontarlo. (da The Cartoon History of the Universe #1 di Larry Gonick)C'era una volta un'idea di universo, che era la Terra al centro, quindi il Sole, la Luna e gli altri pianeti e sullo sfondo le stelle fisse, […]

Hubble E. (1929). A relation between distance and radial velocity among extra-galactic nebulae, Proceedings of the National Academy of Sciences, 15 (3) 168-173. DOI:

Gamow G. (1948). The Evolution of the Universe, Nature, 162 (4122) 680-682. DOI:

Alpher R.A. & Herman R. (1948). Evolution of the Universe, Nature, 162 (4124) 774-775. DOI:

Alpher R., Bethe H. & Gamow G. (1948). The Origin of Chemical Elements, Physical Review, 73 (7) 803-804. DOI:

Peebles P.J.E., Schramm D.N., Turner E.L. & Kron R.G. (1994). The Evolution of the Universe, Scientific American, 271 (4) 52-57. DOI:

McLeish T.C.B., Bower R.G., Tanner B.K., Smithson H.E., Panti C., Lewis N. & Gasper G.E.M. (2014). History: A medieval multiverse, Nature, 507 (7491) 161-163. DOI:

5:04 PM | Magical modular furniture
#MIT #design #furniture #technology #Milano Transform is a magical, modular furniture developed by MIT: The work is comprised of three dynamic shape displays that move more than one thousand pins up and down in realtime to transform the tabletop into a dynamic tangible display. The kinetic energy of the viewers, captured by a sensor, drives the wave motion represented by the dynamic pins.The motion design is inspired by the dynamic interactions among wind, water and sand in nature, Escher’s […]
12:11 PM | Errors on percentage errors
The MAPE (mean absolute percentage error) is a popular measure for forecast accuracy and is defined as     where denotes an observation and denotes its forecast, and the mean is taken over . Armstrong (1985, p.348) was the first (to my knowledge) to point out the asymmetry of the MAPE saying that “it has a bias favoring estimates that are below the actual values”. A few years later, Armstrong and Collopy (1992) argued that the MAPE “puts a heavier penalty on forecasts that exceed the […]
5:49 AM | AERA Philadelphia and NCTM New Orleans: Forty Sessions
Forty sessions. Forty. You see, I'm one of those people who really try to get my money's worth out of a conference, and when it's somebody else's money (thanks, National Science Foundation!) I try even harder. My 10-day conference marathon started with a rough day of travel, but in the remaining nine days I went to just about everything I could. I just made the conference my one and only priority — I didn't go sighseeing on "company time," I ate only when necessary (I lost 7 pounds in 10 […]
5:14 AM | A. Spanos: Jerzy Neyman and his Enduring Legacy
A Statistical Model as a Chance Mechanism Aris Spanos  Jerzy Neyman (April 16, 1894 – August 5, 1981), was a Polish/American statistician[i] who spent most of his professional career at the University of California, Berkeley. Neyman is best known in statistics for his pioneering contributions in framing the Neyman-Pearson (N-P) optimal theory of hypothesis testing […]

April 15, 2014

4:17 PM | Markov Chain Monte Carlo Example
Let’s look at a problem called parameter estimation. As usual, we have a bunch of coin flips. What we’ve learned to do with Bayesian statistics is calculate some posterior distribution that tells me how likely the bias is. I ask … Continue reading →
2:23 PM | Restricted Invertiblity by Interlacing Polynomials
In this post, I am going to give you a simple, self-contained, and fruitful demonstration of a recently introduced proof technique called the method of interlacing families of polynomials, which was also mentioned in an earlier post. This method, which may be seen as an incarnation of the probabilistic method, is relevant in situations when […]

April 14, 2014

11:36 PM | The rank recovery problem
Yuehaw Khoo, Amit Singer, and myself just uploaded an open problem note to the arxiv entitled “Open problem: Tightness of maximum likelihood semidefinite relaxations”. This note is about a problem/conjecture that I think is really interesting and would love to hear your thoughts on. The note is already rather short (3 pages) but I will […]
11:23 PM | Generating tables in LaTeX
Typing tables in LaTeX can get messy, but there are some good tools to simplify the process. One I discovered this week is tablesgenerator.com, a web-based tool for generating LaTeX tables. It also allows the table to saved in other formats including HTML and Markdown. The interface is simple, but it does most things. For complicated tables, some additional formatting may be necessary.     Similar functionality is available via plugins in Excel, OpenOffice and Libreoffice — useful if the […]
9:55 PM | Polymath8b, X: writing the paper, and chasing down loose ends
This is the tenth thread for the Polymath8b project to obtain new bounds for the quantity ; the previous thread may be found here. Numerical progress on these bounds have slowed in recent months, although we have very recently lowered the unconditional bound on from 252 to 246 (see the wiki page for more detailed results).  While there may […]
9:47 PM | [기노사키 온천여행 03] 아침 식사를 하는 이유 – 료칸 미키야(三木屋)
기노사키 온천역에서 무료 셔틀 버스를 타고 도착한 료칸 미키야! 버스를 타고 한 10분 정도 걸렸던 것 같다(물론 걸어서 15분 거리지만 이곳저곳 료칸에 정차하느라 많은 시간을 소진했기 때문). 오오.. 역시 뭔가 고급스러운 로비의 모습. 이 료칸은 무려 100년이 넘은 목조 건물이라고 … Continue reading →Related Posts ?[교토 쿠라마 여행 05] 쿠라마 온천 노천탕을 즐기다 […]
3:48 PM | Tsar Nikita and His Scientists
Once upon a time, a Russian tsar named Nikita had forty daughters:                 Every one from top to toe                 Was a captivating creature,     … Continue reading →
3:30 PM | Can 19th-century technology solve the energy storage dilemma?
Energy storage is basically a holy grail for the power system community these days.  If we had cost-effective, large-scale energy storage, many of the challenges that go along with incorporating renewable energy into the grid would disappear.  But, we don’t, and the basic feeling is that we need some sort of new idea to get […]
2:53 PM | Phil 6334: Notes on Bayesian Inference: Day #11 Slides
  A. Spanos Probability/Statistics Lecture Notes 7: An Introduction to Bayesian Inference (4/10/14) Spanos lecture 7: An Introduction to Bayesian Inference from jemille6 Filed under: Bayesian/frequentist, Phil 6334 class material
1:32 PM | Graph: Class Numbers of Imaginary Quadratic Fields
Here’s a cool picture I made with Sage and R of class numbers of where is squarefree. It consists of the first five thousand such (click image to enlarge): The even class numbers are shown in red +-signs and the odd class numbers are shown as blue disks. If you look carefully at the bottom […]
10:48 AM | Frequentists vs. Bayesians on the Exploding Sun, and Much More...
Time for something light.  Check out xkcd.com, "A webcomic of romance, sarcasm, math, and language," written by a literate former NASA engineer.  Really fine stuff.  Thanks to my student M.D. for introducing me to it.  Here's one on Fisher vs. Bayes:
6:50 AM | From when even the cars had moustaches
Every year about this time, my campus holds a spring celebration, with all the student organizations setting up pavilions in the park to sell food and advertise for new members, with the creative anachronists bashing each other with padded swords, and with a car show. Why a car show? I don't know, but I always enjoy seeing the variety of shapes and colors compared to today's mostly-the-same boxes. My favorite this year was a 1950 Chevy Fleetline, found rusting in a swamp in Tenessee; after a […]
3:45 AM | Big data, prediction, and scientism in the social sciences
Much of my undergrad was spent studying physics, and although I still think that a physics background is great for a theorists in any field, there are some downsides. For example, I used to make jokes like: “soft isn’t the opposite of hard sciences, easy is.” Thankfully, over the years I have started to slowly […]

Lazer, D., Kennedy, R., King, G. & Vespignani, A. (2014). Big data. The parable of Google Flu: traps in big data analysis., Science, 343 (6176) 1203-1205. PMID:

2:40 AM | Factorization in coNP- in other domains?
I had on an exam in my grad complexity course to show that the following set is in coNP FACT = { (n,m) : there is a factor y of n with 2 \le y \le m } The answer I was looking for was to write FACTbar (the complement) as { (n,m) | (\exists p_1,...,p_L) L \le log n for all i \le L,  p_i \le n and p_i is prime, not necc distinct. n =p_1 p_2 ... p_L } To prove this work you seem to need to use the Unique Factorization theorem and you need that PRIMES is in NP (the fact that its in P does […]
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