Daily Archives: January 7, 2016

Do not base a cryptosystem on the assumed hardness of discrete log in a Q-algebra

Alice Silverberg explaining the algorithm.

Alice Silverberg explaining the algorithm.

Alice Silverberg is a wonderful, formidable figure in Number Theory. Beyond her extensive research (look at her bibliography!), teaching, and professional service, she also worked as a mathematical consultant for the television show Numb3rs.  Her talk, based on joint work with Hendrik Lenstra, described their deterministic, polynomial-time algorithm to solve the discrete logarithm problem in Q-algebras.  This was the first talk in the AMS Special Session on Cryptography and Number Theory, happening today, tomorrow, and Saturday afternoon in room 606.

Kristin Lauter watching Alice Silverberg's talk.

Kristin Lauter watching Alice Silverberg’s talk.

 

Organized by Matilde Lalin, Michelle Manes, and Christelle Vincent in honor of Kristin Lauter’s AMS-MAA Invited Address, “How to Keep Your Genome Secret” (11:10 Friday in 6BC), the session features a really great slate of speakers.  I’m headed back there now for more math.

Paradise and Paradox

Yesterday morning I went to Xiao-Li Meng’s AMS-MAA invited address, entitled “Statistical Paradises and Paradoxes in Big Data.”  My stats background is not especially strong, but one of my favorite parts of the Joint Math Meetings is going to talks outside my area that I can actually love and understand.  This was one of those.  Professor Meng’s introduction set high expectations, and he really delivered in content and style.  He was incredibly energetic and funny.

One of Meng’s paradises of big data is “a larger general pipeline”–more people than ever before interested in statistics at all levels, and pursuing statistics academically.  Also, better airplane/taxi/party conversations for statisticians, and a current “golden era” for theoretical and methodological foundations.

However, one paradox is that big data may not be as big as it seems, when we consider quality.  Most “big data” is not randomly sampled and is correspondingly prone to bias.

Dr. Meng asked us to consider: When is a large non-random sample better than a small random sample, in measurable terms? To answer the question, he presented “A trio identity for Quality, Quantity, and Difficulty,” an simple statistical identity relating measures of the quality and quantity of data.

The gist: To minimize error, one can increase quantity (proportion of total population sampled) or increase quality (randomness of sample). To see the true value of a data set, it is possible to compute the effective sample size—the estimated size of a randomly sampled data set that would give the same error as the large, non-randomly sampled set. To illustrate, Meng considered a hypothetical survey of 160 million people (half of the US population), non-randomly sampled. For particular parameters, he computed an effective sample size of 400. Wow.

People use statistics to make decisions. We may want to answer the question “What choice is most likely to result in a good outcome for people like me?” Dr. Meng pointed out that the apparent answer may depend on what “like me” means. Reference population and level of resolution matter. Simpson’s paradox may even apply—what appears to be the best choice when we consider the entire population may appear to be the worse choice for both two partitioning subsets of the population. Meng used a 1986 study by C. R. Charig, D. R. Webb, S. R. Payne, J. E. Wickham on kidney stone pain treatments to illustrate. The following percentages of people found the given treatments effective:

Treatment A               Treatment B

273/350: 78%            289/350: 83%

Broken down by size of stone:

.                                 Treatment A              Treatment B

Large Stone            81/87: 93%                 234/270: 87%

Small Stone            192/263: 72%             55/80: 69%

Treatment B appears to be more effective for the population as a whole, but treatment A appears to be more effective for both people with large stones and people with small stones. Argh. Which one is more effective? How do we choose?

As always when I go to statistics talks, one of my major take-aways is that I need to think way more carefully about statistics.  And go to more statistics talks.

 

Also, Meng has an awesome section on rejection on his website, including a link to this interesting essay on rejection, a topic near to my heart.

Meetings survival tips: Knitting in committee meetings

My soon-to-be-scarf, courtesy of the AWM Executive Committee, the MAA FOCUS Editorial Board, and the AWM Business Meeting.

My soon-to-be-scarf, courtesy of the AWM Executive Committee, the MAA FOCUS Editorial Board, and the AWM Business Meeting.

I spent a large chunk of my day yesterday like many “grown-up” mathematicians do at the JMM: in committee/editorial board/business meetings. Don’t feel too bad for me though, I also went to a couple of receptions (mathematicians never outgrow the need for free food).  More importantly, though, I have found an excellent coping mechanism (and I know I’m not the only one): I bring my knitting.

You would think this might distract me from the content of the discussion (and you may even think that’s the reason I bring my knitting to meetings), but in fact it has the opposite effect: focusing on one thing actually helps me focus on the discussion. I am not good enough yet that I can read or make my own comments while knitting, though, so I tend to stop for those things. But it does make things in turns more interesting and easier to endure.

I mean, committee meetings are about approving motions, discussing future action, and in general deciding important things about the committee you’re in, so they need to happen. But more of these things are routine, we usually always agree, and they are by nature not super-exciting. So having my knitting makes it all seem more productive somehow: I helped make decisions AND in the end there is something pretty to show for it (meaning the thing I was knitting).

I’m sure people have other mechanisms for keeping themselves engaged and not too bored during a meeting, but this one is my favorite. It definitely is better than daydreaming (what I am prone to do when people are talking a lot) or looking at my phone (which people do way too much). How about you, any tips on how you deal with long business or committee meetings?

Addendum: If you’re interested in knitting and other crafty things, make sure you check out the Knitting Circle at 8:15pm tonight in the Sheraton Grand Ballroom D (on the 2nd floor).

Good Morning, JMM. It’s still dark outside.

Hello!  Just starting my shift here in the press room, quite proud that I made it by 7:30.  Luckily I had the east coast advantage.  Still, it’s dark outside and I’m drinking coffee, trying to stay upright.  I will be here in room 613 all morning, with all of the other glamorous members of the math press, like Barry Cipra and Samuel Hansen.

Barry Cipra and Samuel Hansen in the press room. Math journalism in action!

Barry Cipra and Samuel Hansen in the press room. Math journalism in action!

Samuel Hansen was busily hosting the first episode of the second season of his podcast.  Not sure what Barry Cipra was working on, but I’m sure it will be excellent.

Why did they leave me in charge of the pressroom?  Because everybody important is working on Who Wants to Be a Mathematician.  There are 10 really impressive contestants who will be competing in semifinal rounds at 9:30.  The finalists will compete at 10:25.  Mike Breen hosts the game, and Ken Ono will be hosting the awards ceremony at 10:45.  This is all followed by a public lecture by Simon Singh, entitled “Fermat’s Last Theorem versus The Simpsons“.  All the festivities are happening in room 6A here at the convention center.