Articles from the Institute Letter

Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.

Gene regulatory networks are the source of many human diseases. How do we infer network structure from partial data? What is the network most likely to have produced the little bit that we can see?

From capturing interactions and inferring the structure of data to determining the infringement of freedom

In November, the Association of Members of the Institute for Advanced Study (AMIAS) sponsored two lectures by Jennifer Chayes, Member (1994–95, 97) in the School of Mathematics, and Quentin Skinner, Member in the Schools of Historical Studies (1974–75) and Social Science (1976–79). All current and former Institute Members and Visitors are members of AMIAS, which includes some 6,000 scholars in more than fifty countries. To learn more about the organization, upcoming events, and opportunities to support the mission of the Institute, please visit www.ias.edu/people/amias/. Following are brief summaries of the lectures by Chayes and Skinner; full videos are available at http://video.ias.edu/2013-amias-chayes and http://video.ias.edu/2013-amias-skinner/.

AGE OF NETWORKS

Jennifer Chayes, Distinguished Scientist and Managing Director of Microsoft Research New England and New York City:

Everywhere we turn, networks can be used to describe relevant interactions. In the high-tech world, we see the internet, the world wide web, mobile phone networks, and online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a globally networked economy. In epidemiology, we find disease spreading over ever-growing social networks, complicated by mutation of the disease agents. In problems of world health, distribution of limited resources, such as water resources, quickly becomes a problem of finding the optimal network for resource allocation. In biomedical research, we are beginning to understand the structure of gene-regulatory networks, with the prospect of using this knowledge to manage many human diseases.  

READ MORE>

By Hanno Rein

The customizable Comprehensive Exoplanetary Radial Chart illustrates the radii of planets according to colors that represent equilibrium temperatures, eccentricity, and other data relevant to assessing their potential habitability.

Pluto, the ninth planet in our solar system1 was discovered in 1930, the same year the Institute was founded. While the Institute hosted more than five thousand members in the following sixty-five years, not a single new planet was discovered during the same time.

Finally, in 1995, astronomers spotted an object they called 51 Pegasi b. It was the first discovery of a planet in over half a century. Not only that, it was also the first planet around a Sun-like star outside our own solar system. We now call these planets extrasolar planets, or in short, exoplanets.

As it turns out, 51 Pegasi b is a pretty weird object. It is almost as massive as Jupiter, but it orbits its host star in only four days. Jupiter, as a comparison, needs twelve years to go around the Sun once. Because 51 Pegasi b is very close to the star, its equilibrium temperature is very high. These types of planets are often referred to as “hot Jupiters.”

Since the first exoplanet was discovered, the technology has improved dramatically, and worldwide efforts by astronomers to detect exoplanets now yield a large number of planet detections each year. In 2011, 189 planets were discovered, approximately the number of visiting Members at the Institute every year. In 2012, 130 new planets were found. As of May 20 of this year, the total number of confirmed exoplanets was 892 in 691 different planetary systems.

READ MORE>

By Danielle S. Allen

Scholars of network theory have shown that increased social connectivity through bridging ties, in particular, brings improved social outcomes.

College campuses struggle with how to think and talk about diversity of all kinds, a struggle that has gone on for more than two decades now. Every year, there are stories from around the country about anonymous hate speech and offensive theme parties with equally offensive T-shirts as well as controversies about “political correctness.” Nor has there been a year in my roughly two decades in higher ed when I haven’t read or heard someone wondering, “Why do all the black kids sit together in the cafeteria?”

What are the stakes for how well we deal with diversity on college campuses? There are two answers to this question, one concerning the stakes for the campuses themselves, the other the broader social stakes.
First, for campuses. Social scientists have long distinguished between two kinds of social tie: “bonding ties” that connect people who share similar backgrounds and “bridging ties” that link people who come from different social spaces. Since the 1970s, scholars have been aware that “bridging ties” are especially powerful for generating knowledge transmission; more recently, scholars have argued convincingly that teams and communities that, first, emphasize bridging ties and, second, successfully learn how to communicate across their differences outperform more homogenous teams and communities with regard to the development and deployment of knowledge.

READ MORE>

by Steve Awodey and Thierry Coquand

Depicted here is a mathematical torus (a donut-shaped object that cannot be deformed into a sphere in a continuous way without tearing it) made of logical symbols. It represents homotopy type theory, a new branch of mathematics that connects homotopy theory (the study of continuous deformations) and type theory (a branch of mathematical logic).

In 2012–13, the Institute’s School of Mathematics hosted a special year devoted to the topic “Univalent Foundations of Mathematics,” organized by Steve Awodey, Professor at Carnegie Mellon University, Thierry Coquand, Professor at the University of Gothenburg, and Vladimir Voevodsky, Professor in the School of Mathematics. This research program was centered on developing new foundations of mathematics that are well suited to the use of computerized proof assistants as an aid in formalizing mathematics. Such proof systems can be used to verify the correctness of individual mathematical proofs and can also allow a community of mathematicians to build shared, searchable libraries of formalized definitions, theorems, and proofs, facilitating the large-scale formalization of mathematics.

The possibility of such computational tools is based ultimately on the idea of logical foundations of mathematics, a philosophically fascinating development that, since its beginnings in the nineteenth century, has, however, had little practical influence on everyday mathematics. But advances in computer formalizations in the last decade have increased the practical utility of logical foundations of mathematics. Univalent foundations is the next step in this development: a new foundation based on a logical system called type theory that is well suited both to human mathematical practice and to computer formalization. It draws moreover on new insights from homotopy theory—the branch of mathematics devoted to the study of continuous deformations in space. This is a particularly surprising source, since the field is generally seen as far distant from foundations.

READ MORE>

by Andrej Bauer

Recommended Viewing: An animated visualization of the GitHub collaborations of over two dozen mathematicians working on the HoTT book over a period of six months may be viewed at http://vimeo.com/68761218/.

Since spring, and even before that, I have participated in a great collaborative effort to write a book on homotopy type theory. It is finally finished and ready for pub­lic consumption. You can get the book freely at http://homotopytypetheory.org/book/. Mike Shulman has written about the contents of the book (http://​golem.ph.u­te­x­as.edu/category/2013/06/the_hott_book.html), so I am not going to repeat that here. Instead, I would like to comment on the socio-technological aspects of making the book and in particular about what we learned from the open-source community about collaborative research.

We are a group of two dozen mathematicians who wrote a six-hundred-page book in less than half a year. This is quite amazing since mathematicians do not normally work together in large groups. A small group can get away with using obsolete technology, such as sending each other source LaTeX files by email, but with two dozen people even Dropbox or any other file synchronization system would have failed miserably. Luckily, many of us are computer scientists disguised as mathematicians, so we knew how to tackle the logistics. We used Git and GitHub.com. In the beginning, it took some convincing and getting used to, al­though it was not too bad. In the end, the repository served not only as an archive for our files but also as a central hub for planning and discussions. For several months, I checked GitHub more often than email and Facebook.

READ MORE>

Pages