#### Filter Results:

#### Publication Year

2000

2015

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

#### Method

#### Organism

Learn More

We analyze the eigenvalue gap for the adjacency matrices of sparse random graphs. Let λ 1 ≥. .. ≥ λ n be the eigenvalues of an n-vertex graph, and let λ = max[λ 2 , |λ n |]. Let c be a large enough constant. For graphs of average degree d = c log n it is well known that λ 1 ≥ d, and we show that λ = O(√ d). For d = c it is no longer true that λ = O(√ d),… (More)

A simple nonconstructive argument shows that most ¿CNF formulas with Ò clauses (where is a large enough constant) are not satisfiable. It is an open question whether there is an efficient refutation algorithm that for most formulas with Ò clauses proves that they are not satisfiable. We present a polynomial time algorithm that for most ¿CNF formulas with Ò… (More)

We study the complexity of the following problem that we call Max edge t-coloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that has chromatic index at most t). We show that for every… (More)

We consider random 3CNF formulas with n variables and m clauses. It is well known that when m > cn (for a sufficiently large constant c), most formulas are not satisfi-able. However, it is not known whether such formulas are likely to have polynomial size witnesses that certify that they are not satisfiable. A value of m n 3/2 was the forefront of our… (More)

- William W. Craig, Finn E. Christensen, Charles J. Hailey, William W. Zhang, Steven E. Boggs, Daniel Stern +75 others
- 2013

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

Massive stars end their short lives in spectacular explosions--supernovae--that synthesize new elements and drive galaxy evolution. Historically, supernovae were discovered mainly through their 'delayed' optical light (some days after the burst of neutrinos that marks the actual event), preventing observations in the first moments following the explosion.… (More)

We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples. The observed sample consists of 10 X-ray selected clusters at redshifts z c ∼ 0.2 imaged with HST by Smith et al.. The simulated dataset is produced by lensing the Hubble Deep Field, which serves as a background source… (More)

- A M Soderberg, S R Kulkarni, E Nakar, E Berger, P B Cameron, D B Fox +19 others
- Nature
- 2006

Over the past decade, long-duration gamma-ray bursts (GRBs)--including the subclass of X-ray flashes (XRFs)--have been revealed to be a rare variety of type Ibc supernova. Although all these events result from the death of massive stars, the electromagnetic luminosities of GRBs and XRFs exceed those of ordinary type Ibc supernovae by many orders of… (More)

Let φ be a 3CNF formula with n variables and m clauses. A simple nonconstructive argument shows that when m is sufficiently large compared to n, most 3CNF formulas are not satisfiable. It is an open question whether there is an efficient refutation algorithm that for most such formulas proves that they are not satisfiable. A possible approach to refute a… (More)

- F Abe, D P Bennett, I A Bond, S Eguchi, Y Furuta, J B Hearnshaw +29 others
- Science
- 2004

Observations of the gravitational microlensing event MOA 2003-BLG-32/OGLE 2003-BLG-219 are presented, for which the peak magnification was over 500, the highest yet reported. Continuous observations around the peak enabled a sensitive search for planets orbiting the lens star. No planets were detected. Planets 1.3 times heavier than Earth were excluded from… (More)