On distinguishing trees by their chromatic symmetric functions

Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_T$, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$. The \emph{subtree polynomial} $S_T$, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of $T$ by their numbers of edges and leaves. We prove that $S_T =$, where $$ is the Hall inner product on symmetric functions and $\Phi$ is a certain symmetric function that does not depend on $T$. Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (\emph{spiders} and some \emph{caterpillars}), and one family of unicyclic graphs (\emph{squids}) whose members are determined completely by their chromatic symmetric functions.Comment: 16 pages, 3 figures. Added references [2], [13], and [15

Transferrin-polycation conjugates as carriers for DNA uptake into cells.

We have developed a high-efficiency nucleic acid delivery system that uses receptor-mediated endocytosis to carry DNA macromolecules into cells. We accomplished this by conjugating the iron-transport protein transferrin to polycations that bind nucleic acids. Human transferrin, as well as the chicken homologue conalbumin, has been covalently linked to the small DNA-binding protein protamine or to polylysines of various sizes through a disulfide linkage. These modified transferrin molecules maintain their ability to bind their cognate receptor and to mediate efficient iron transport into the cell. The transferrin-polycation molecules form electrophoretically stable complexes with double-stranded DNA, single-stranded DNA, and modified RNA molecules independent of nucleic acid size (from short oligonucleotides to DNA of 21 kilobase pairs). When complexes of transferrin-polycation and a bacterial plasmid DNA containing the gene for Photinus pyralis luciferase are supplied to eukaryotic cells, high-level expression of the luciferase gene occurs, demonstrating transferrin receptor-mediated endocytosis and expression of the imported DNA. We refer to this delivery system as "transferrinfection.

Was Hurricane Sandy the ‘Fat Tail’ of Climate Change?

Call them “black swans,” “unknown unknowns,” “fat tails,” or “10-foot women.” Whatever you call them, they’re bizarre events. They shouldn’t happen. Usually they don’t happen, but every once in a while they do happen, and then their impact makes daily events mere noise. This week, one did happen. Sandy and its aftermath have all the characteristics that make fat tails such unique and frightening events. Published in the Wall Street Journal Ideas Market on November 1, 2012

Why Environmental Action Is so Hard

Gambles may be appealing in a casino, but in the real world humans crave certainty. Essay adapted from Climate Shock (Princeton University Press, 2015)

What we know — and what we don’t — about global warming

We take out car, fire and property insurances for much lower probabilities. Here we are talking about the whole planet, and we haven’t shown willingness to insure ourselves. Meanwhile, we can, in fact, look at 11 degrees Fahrenheit and liken it to the planet ‘burning’. Think of it as your body temperature: 98.6 degrees Fahrenheit is normal. Anything above 99.5 degrees Fahrenheit is a fever. Above 104 degrees Fahrenheit is life-threatening. Above 109.4 degrees Fahrenheit and you are dead or at least unconscious. First published by PBS NewsHour’s Making Sen$e with Paul Solman. The accompanying NewsHour report aired on July 16, 2015

How does climate stack up against other worst-case scenarios?

Climate isn’t the only catastrophe threatening the planet, but it may be the one most in need of attention and resources. The following is excerpted from Climate Shock (2015) by Gernot Wagner and Martin L. Weitzman. Published here with permission from Princeton University Press. Published on Ensia.com on April 1st, 2015

Playing God

The climate problem, twice over: Seven billion "free riders," meet the "free drivers" of geoengineering. How serious is the threat of global warming? One way to figure out is to take your cues from some leading climate scientists: They have moved on. That doesn’t mean they’ve abandoned the issue, but they are looking beyond what all agree is the most obvious solution — decreasing the amount of carbon we spew into the atmosphere in the first place. These scientists are beginning to look for a Plan B. Published in Foreign Policy on October 24th, 2012

Bailing out the planet

Mount Pinatubo, a volcano in the Philippines that had been dormant for over 400 years, began to rumble on April 2, 1991. Two months later, volcanic activity went into overdrive, culminating in a final explosion on June 15. As a direct result of the volcanic eruption, global temperatures temporarily decreased by about 0.5°C (0.9°F), wiping out the entire temperature effects of human-caused global warming up to that point. Mount Pinatubo did all that by spewing some 20 million tons of sulfur dioxide into the stratosphere. That amount counteracted the global warming effect of around 585 billion tons of carbon dioxide that humans had managed to put into the atmosphere by then. Two years later, after most of the sulfur dioxide from Mount Pinatubo had washed out of the atmosphere, temperatures jumped back by the same 0.5°C and resumed growth where it left off. Excerpted from “Climate Shock: The Economic Consequences of a Hotter Planet” by Gernot Wagner and Martin L. Weitzman

Climate Change: Like an Asteroid

The threat of climate change must be taken far more seriously, before it is too late. If a civilization-as-we-know-it-altering asteroid were hurtling toward Earth, scheduled to hit a decade hence, and it had, say, a 5% chance of striking the planet, we would surely pull out all the stops to try to deflect its path. This essay is adapted from “Climate Shock: The Economic Consequences of a Hotter Planet” by Wagner and Weitzman (February 2015)

The planet won’t notice you recycle, and your vote doesn’t count

Put a group of economists in a room to debate the wisdom and virtue of individual action, and soon they’ll be debating the value of casting one’s vote: zero—in some strict, narrow, “economic” sense of the world. We can’t leave things there. It would be both rather depressing and also rather narrow-minded. Maybe statistics and economics alone aren’t the right tools with which to analyze one’s personal action. Ethics, for one, plays an important role. Excerpted from “Climate Shock: The Economic Consequences of a Hotter Planet” by Gernot Wagner and Martin L. Weitzman