Discovery of Comet Brooks, 1890

Discovery of Presolar Sic from Comet Wild-2

Introduction The preliminary examination of Stardust samples has yielded a number of surprising findings, such as the presence of large refractory mineral grains, including materials resembling CAIs, chondrules, and AOA fragments [1-3]. Furthermore, intact organics and fine grained materials are unexpectedly rare in Stardust tracks [4,5]. The fact that intact fine grained materials are uncommon...

Com2: Fast Automatic Discovery of Temporal ('Comet') Communities

Given a large network, changing over time, how can we find patterns and anomalies? We propose Com2, a novel and fast, incremental tensor analysis approach, which can discover both transient and periodic/repeating communities. The method is (a) scalable, being linear on the input size (b) general, (c) needs no user-defined parameters and (d) effective, returning results that agree with intuition...

Brooks' Theorem and Beyond

We collect some of our favorite proofs of Brooks’ Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques in graph coloring, such as greedy coloring, Kempe chains, hitting sets, and the Kernel Lemma. We also discuss standard strengthenings of vertex coloring, such as list coloring, online list coloring, and Alon–Tarsi orientations, since analo...

Books in Running Brooks

No Quantum Brooks' Theorem

First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as tropical, cyclical, and commutative. I also define a step logarithm function and express with it the bounds on quantum graph invariants in closed...