Central limits from generating functions

Mitchell Lee

Let $(Y_n)_n$ be a sequence of $\mathbb{R}^d$-valued random variables. Suppose that the generating function \[f(x, z) = \sum_{n = 0}^\infty \varphi_{Y_n}(x) z^n,\] where $\varphi_{Y_n}$ is the characteristic function of $Y_n$, extends to a function on a neighborhood of $\{0\} \times \{z : |z| \leq 1\} \subset \mathbb{R}^d \times \mathbb{C}$ which is meromorphic in $z$ and has no zeroes. We prove that if $1 / f(x, z)$ is twice differentiable, then there exists a constant $μ$ such that the distribution of $(Y_n - μn) / \sqrt{n}$ converges weakly to a normal distribution as $n \to \infty$. If $Y_n = X_1 + \cdots + X_n$, where $(X_n)_n$ are i.i.d. random variables, then we recover the classical (Lindeberg$\unicode{x2013}$Lévy) central limit theorem. We also prove the 2020 conjecture of Defant that if $π_n \in \mathfrak{S}_n$ is a uniformly random permutation, then the distribution of $(\operatorname{des} (s(π_n)) + 1 - (3 - e) n) / \sqrt{n}$ converges, as $n \to \infty$, to a normal distribution with variance $2 + 2e - e^2$.

Restriction coefficients for partitions with at most three columns

Mitchell Lee

Let $r \geq 0$, and let $λ$ and $μ$ be partitions such that $λ_1 \leq r + 1$. We present a combinatorial interpretation of the plethysm coefficient $\langle s_λ, s_μ[s_r] \rangle$. As a consequence, we solve the restriction problem for partitions with at most three columns. That is, for all partitions $λ$ with $λ_1 \leq 3$, we find a combinatorial interpretation for the multiplicities of the irreducible $\mathfrak{S}_n$-submodules of the Schur module $\mathbb{S}^λ\mathbb{C}^n$, considered as an $\mathfrak{S}_n$-module.

The Frobenius transform of a symmetric function

Mitchell Lee

We define an abelian group homomorphism $\mathscr{F}$, which we call the Frobenius transform, from the ring of symmetric functions to the ring of the symmetric power series. The matrix entries of $\mathscr{F}$ in the Schur basis are the restriction coefficients $r_λ^μ= \dim \operatorname{Hom}_{\mathfrak{S}_n}(V_μ, \mathbb{S}^λ\mathbb{C}^n)$, which are known to be nonnegative integers but have no known combinatorial interpretation. The Frobenius transform satisfies the identity $\mathscr{F}\{fg\} = \mathscr{F}\{f\} \ast \mathscr{F}\{g\}$, where $\ast$ is the Kronecker product. We prove for all symmetric functions $f$ that $\mathscr{F}\{f\} = \mathscr{F}_{\mathrm{Sur}}\{f\} \cdot (1 + h_1 + h_2 + \cdots)$, where $\mathscr{F}_{\mathrm{Sur}}\{f\}$ is a symmetric function with the same degree and leading term as $f$. Then, we compute the matrix entries of $\mathscr{F}_{\mathrm{Sur}}\{f\}$ in the complete homogeneous, elementary, and power sum bases and of $\mathscr{F}^{-1}_{\mathrm{Sur}}\{f\}$ in the complete homogeneous and elementary bases, giving combinatorial interpretations of the coefficients where possible. In particular, the matrix entries of $\mathscr{F}^{-1}_{\mathrm{Sur}}\{f\}$ in the elementary basis count words with a constraint on their Lyndon factorization. As an example application of our main results, we prove that $r_λ^μ= 0$ if $|λ\cap \hatμ| < 2|\hatμ| - |λ|$, where $\hatμ$ is the partition formed by removing the first part of $μ$. We also prove that $r_λ^μ= 0$ if the Young diagram of $μ$ contains a square of side length greater than $2^{λ_1 - 1}$, and this inequality is tight.

Sets with few differences in abelian groups

Mitchell Lee

Let $(G, +)$ be an abelian group. In 2004, Eliahou and Kervaire found an explicit formula for the smallest possible cardinality of the sumset $A+A$, where $A \subseteq G$ has fixed cardinality $r$. We consider instead the smallest possible cardinality of the difference set $A-A$, which is always greater than or equal to the smallest possible cardinality of $A+A$ and can be strictly greater. We conjecture a formula for this quantity and prove the conjecture in the case that $G$ is a cyclic group or a vector space over a finite field. This resolves a conjecture of Bajnok and Matzke on signed sumsets.

Constraining Strong c-Wilf Equivalence Using Cluster Poset Asymptotics

Mitchell Lee, Ashwin Sah

Let $π\in \mathfrak{S}_m$ and $σ\in \mathfrak{S}_n$ be permutations. An occurrence of $π$ in $σ$ as a consecutive pattern is a subsequence $σ_i σ_{i+1} \cdots σ_{i+m-1}$ of $σ$ with the same order relations as $π$. We say that patterns $π, τ\in \mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in $\mathfrak{S}_n$ with exactly $k$ occurrences of $π$ as a consecutive pattern is the same as for $τ$. In 2018, Dwyer and Elizalde conjectured (generalizing a conjecture of Elizalde from 2012) that if $π, τ\in \mathfrak{S}_m$ are strongly c-Wilf equivalent, then $(τ_1, τ_m)$ is equal to one of $(π_1, π_m)$, $(π_m, π_1)$, $(m+1 - π_1, m+1-π_m)$, or $(m+1 - π_m, m+1 - π_1)$. We prove this conjecture using the cluster method introduced by Goulden and Jackson in 1979, which Dwyer and Elizalde previously applied to prove that $|π_1 - π_m| = |τ_1 - τ_m|$. A consequence of our result is the full classification of c-Wilf equivalence for a special class of permutations, the non-overlapping permutations. Our approach uses analytic methods to approximate the number of linear extensions of the "cluster posets" of Elizalde and Noy.

Reduced Random Walks in the Hyperbolic Plane$\hspace{1pt}!\hspace{-3.8pt}?$

Colin Defant, Mitchell Lee

We study Lam's reduced random walk in a hyperbolic triangle group, which we view as a random walk in the upper half-plane. We prove that this walk converges almost surely to a point on the extended real line. We devote special attention to the reduced random walk in $PGL_2(\mathbb{Z})$ (i.e., the $(2,3,\infty)$ triangle group). In this case, we provide an explicit formula for the cumulative distribution function of the limit. This formula is written in terms of the interrobang function, a new function $!\hspace{-3.8pt}?\colon[0,1]\to\mathbb{R}$ that shares several of the remarkable analytic and arithmetic properties of Minkowski's question-mark function.

Strontium Iodide Radiation Instrument (SIRI) -- Early On-Orbit Results

Lee J. Mitchell, Bernard F. Phlips, J. Eric Grove, Theodore Finne, Mary Johnson-Rambert, W. Neil Johnson

The Strontium Iodide Radiation Instrument (SIRI) is a single detector, gamma-ray spectrometer designed to space-qualify the new scintillation detector material europium-doped strontium iodide (SrI2:Eu) and new silicon photomultiplier (SiPM) technology. SIRI covers the energy range from 0.04-8 MeV and was launched into 600 km sun-synchronous orbit on Dec 3, 2018 onboard STPSat5 with a one-year mission to investigate the detector's response to on-orbit background radiation. The detector has an active volume of 11.6 cm3 and a photo fraction efficiency of 50% at 662 keV for gamma-rays parallel to the long axis of the crystal. Its spectroscopic resolution of 4.3% was measured by the FWHM of the characteristic Cs-137 gamma-ray line at 662 keV. Measured background rates external to the trapped particle regions are 40-50 counts per second for energies greater than 40 keV and are largely the result of short- and long-term activation products generated by transits of the SAA and the continual cosmic-ray bombardment. Rate maps determined from energy cuts of the collected spectral data show the expected contributions from the various trapped particle regions. Early spectra acquired by the instrument show the presence of at least 10 characteristic gamma-ray lines and a beta continuum generated by activation products within the detector and surrounding materials. As of April 2019, the instrument has acquired over 1000 hours of data and is expected to continue operations until the space vehicle is decommissioned in Dec. 2019. Results indicate SrI2:Eu provides a feasible alternative to traditional sodium iodide and cesium iodide scintillators, especially for missions where a factor-of-two improvement in energy resolution would represent a significant difference in scientific return. To the best of our knowledge, SIRI is the first on-orbit use of SrI2:Eu scintillator with SiPM readouts.

Radiation damage assessment of SensL SiPMs

Lee J. Mitchell, Bernard Phlips, W. Neil Johnson, Mary Johnson-Rambert, Anika N. Kansky, Richard Woolf

Silicon Photomultipliers (SiPMs) are quickly replacing traditional photomultiplier tubes (PMTs) as the readout of choice for gamma-ray scintillation detectors in space. While they offer substantial size, weight and power saving, they have shown to be susceptible to radiation damage. SensL SiPMs with different cell sizes were irradiated with 64 MeV protons and 8 MeV electrons. In general, results show larger cell sizes are more susceptible to radiation damage with the largest 50 um SiPMs showing the greatest increase in current as a function of dose. Current increases were observed for doses as low at ~2 rad(Si) for protons and ~20 rad(Si) for electrons. The U.S. Naval Research Laboratory's (NRL) Strontium Iodide Radiation Instrument (SIRI-1) experienced a 528 uA increase in the bias current of the on-board 2x2 SensL J-series 60035 SiPM over its one-year mission in sun-synchronous orbit. The work here focuses on the increase in bulk current observed with increasing radiation damage and was performed to better quantify this effect as a function of dose for future mission. These include the future NRL mission SIRI-2, the follow on to SIRI-1, Glowbug and the GAGG Radiation Instrument (GARI).

The Compton Spectrometer and Imager Project for MeV Astronomy

John A. Tomsick, Steven E. Boggs, Andreas Zoglauer, Eric Wulf, Lee Mitchell, Bernard Phlips, Clio Sleator, Terri Brandt, Albert Shih, Jarred Roberts, Pierre Jean, Peter von Ballmoos, Juan Martinez Oliveros, Alan Smale, Carolyn Kierans, Dieter Hartmann, Mark Leising, Marco Ajello, Eric Burns, Chris Fryer, Pascal Saint-Hilaire, Julien Malzac, Fabrizio Tavecchio, Valentina Fioretti, Andrea Bulgarelli, Giancarlo Ghirlanda, Hsiang-Kuang Chang, Tadayuki Takahashi, Kazuhiro Nakazawa, Shigeki Matsumoto, Tom Melia, Thomas Siegert, Alexander Lowell, Hadar Lazar, Jacqueline Beechert, Hannah Gulick

The Compton Spectrometer and Imager (COSI) is a 0.2-5 MeV Compton telescope capable of imaging, spectroscopy, and polarimetry of astrophysical sources. Such capabilities are made possible by COSI's germanium cross-strip detectors, which provide high efficiency, high resolution spectroscopy and precise 3D positioning of photon interactions. Science goals for COSI include studies of 0.511 MeV emission from antimatter annihilation in the Galaxy, mapping radioactive elements from nucleosynthesis, determining emission mechanisms and source geometries with polarization, and detecting and localizing multimessenger sources. The instantaneous field of view (FOV) for the germanium detectors is >25% of the sky, and they are surrounded on the sides and bottom by active shields, providing background rejection as well as allowing for detection of gamma-ray bursts or other gamma-ray flares over >50% of the sky. We have completed a Phase A concept study to consider COSI as a Small Explorer (SMEX) satellite mission, and here we discuss the advances COSI-SMEX provides for astrophysics in the MeV bandpass.

BurstCube: A CubeSat for Gravitational Wave Counterparts

Judith Racusin, Jeremy S. Perkins, Michael S. Briggs, Georgia de Nolfo, John Krizmanic, Regina Caputo, Julie E. McEnery, Peter Shawhan, David Morris, Valerie Connaughton, Dan Kocevski, Colleen Wilson-Hodge, Michelle Hui, Lee Mitchell, Sheila McBreen

BurstCube will detect long GRBs, attributed to the collapse of massive stars, short GRBs (sGRBs), resulting from binary neutron star mergers, as well as other gamma-ray transients in the energy range 10-1000 keV. sGRBs are of particular interest because they are predicted to be the counterparts of gravitational wave (GW) sources soon to be detectable by LIGO/Virgo. BurstCube contains 4 CsI scintillators coupled with arrays of compact low-power Silicon photomultipliers (SiPMs) on a 6U Dellingr bus, a flagship modular platform that is easily modifiable for a variety of 6U CubeSat architectures. BurstCube will complement existing facilities such as Swift and Fermi in the short term, and provide a means for GRB detection, localization, and characterization in the interim time before the next generation future gamma-ray mission flies, as well as space-qualify SiPMs and test technologies for future use on larger gamma-ray missions. The ultimate configuration of BurstCube is to have a set of $\sim10$ BurstCubes to provide all-sky coverage to GRBs for substantially lower cost than a full-scale mission.

Bender--Knuth Billiards in Coxeter Groups

Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, Mitchell Lee

Let $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$, where $I$ is a finite index set. Fix a nonempty convex subset $\mathscr{L}$ of $W$. If $W$ is of type $A$, then $\mathscr{L}$ is the set of linear extensions of a poset, and there are important Bender--Knuth involutions $\mathrm{BK}_i\colon\mathscr{L}\to\mathscr{L}$ indexed by elements of $I$. For arbitrary $W$ and for each $i\in I$, we introduce an operator $τ_i\colon W\to W$ (depending on $\mathscr{L}$) that we call a noninvertible Bender--Knuth toggle; this operator restricts to an involution on $\mathscr{L}$ that coincides with $\mathrm{BK}_i$ in type $A$. Given a Coxeter element $c=s_{i_n}\cdots s_{i_1}$, we consider the operator $\mathrm{Pro}_c=τ_{i_n}\cdotsτ_{i_1}$. We say $W$ is futuristic if for every nonempty finite convex set $\mathscr{L}$, every Coxeter element $c$, and every $u\in W$, there exists an integer $K\geq 0$ such that $\mathrm{Pro}_c^K(u)\in\mathscr{L}$. We prove that finite Coxeter groups, right-angled Coxeter groups, rank-3 Coxeter groups, affine Coxeter groups of types $\widetilde A$ and $\widetilde C$, and Coxeter groups whose Coxeter graphs are complete are all futuristic. When $W$ is finite, we actually prove that if $s_{i_N}\cdots s_{i_1}$ is a reduced expression for the long element of $W$, then $τ_{i_N}\cdotsτ_{i_1}(W)=\mathscr{L}$; this allows us to determine the smallest integer $\mathrm{M}(c)$ such that $\mathrm{Pro}_c^{\mathrm{M}(c)}(W)=\mathscr{L}$ for all $\mathscr{L}$. We also exhibit infinitely many non-futuristic Coxeter groups, including all irreducible affine Coxeter groups that are not of type $\widetilde A$, $\widetilde C$, or $\widetilde G_2$.

Radiation Damage of $2 \times 2 \times 1 \ \mathrm{cm}^3$ Pixelated CdZnTe Due to High-Energy Protons

Daniel Shy, David Goodman, Ryan Parsons, Michael Streicher, Willy Kaye, Lee Mitchell, Zhong He, Bernard Phlips

Pixelated CdZnTe detectors are a promising imaging-spectrometer for gamma-ray astrophysics due to their combination of relatively high energy resolution with room temperature operation negating the need for cryogenic cooling. This reduces the size, weight, and power requirements for telescope-based radiation detectors. Nevertheless, operating CdZnTe in orbit will expose it to the harsh radiation environment of space. This work, therefore, studies the effects of $61 \ \mathrm{MeV}$ protons on $2 \times 2 \times 1 \ \mathrm{cm}^3$ pixelated CdZnTe and quantifies proton-induced radiation damage of fluences up to $2.6 \times 10^8 \ \mathrm{p/cm^2}$. In addition, we studied the effects of irradiation on two separate instruments: one was biased and operational during irradiation while the other remained unbiased. Following final irradiation, the $662 \ \mathrm{keV}$ centroid and nominal $1\%$ resolution of the detectors were degraded to $642.7 \ \mathrm{keV}, 4.9 \% \ ( \mathrm{FWHM})$ and $653.8 \ \mathrm{keV}, 1.75 \% \ (\mathrm{FWHM})$ for the biased and unbiased systems respectively. We therefore observe a possible bias dependency on proton-induced radiation damage in CdZnTe. This work also reports on the resulting activation and recovery of the instrument following room temperature and $60^{\circ}\mathrm{C}$ annealing.

The space "just above" BQP

Scott Aaronson, Adam Bouland, Joseph Fitzsimons, Mitchell Lee

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform measurements that do not collapse the wavefunction. This (non-physical) model of computation can efficiently solve problems such as Graph Isomorphism and Approximate Shortest Vector which are believed to be intractable for quantum computers. Furthermore, it can search an unstructured N-element list in $\tilde O$(N^{1/3}) time, but no faster than Ω(N^{1/4}), and hence cannot solve NP-hard problems in a black box manner. In short, this model of computation is more powerful than standard quantum computation, but only slightly so. Our work is inspired by previous work of Aaronson on the power of sampling the histories of hidden variables. However Aaronson's work contains an error in its proof of the lower bound for search, and hence it is unclear whether or not his model allows for search in logarithmic time. Our work can be viewed as a conceptual simplification of Aaronson's approach, with a provable polynomial lower bound for search.

Orbits in $(\mathbb{P}^r)^n$ and equivariant quantum cohomology

Mitchell Lee, Anand Patel, Hunter Spink, Dennis Tseng

We compute the $GL_{r+1}$-equivariant Chow class of the $GL_{r+1}$-orbit closure of any point $(x_1, \ldots, x_n) \in (\mathbb{P}^r)^n$ in terms of the rank polytope of the matroid represented by $x_1, \ldots, x_n \in \mathbb{P}^r$. Using these classes and generalizations involving point configurations in higher dimensional projective spaces, we define for each $d\times n$ matrix $M$ an $n$-ary operation $[M]_\hbar$ on the small equivariant quantum cohomology ring of $\mathbb{P}^r$, which is the $n$-ary quantum product when $M$ is an invertible matrix. We prove that $M \mapsto [M]_\hbar$ is a valuative matroid polytope association. Like the quantum product, these operations satisfy recursive properties encoding solutions to enumerative problems involving point configurations of given moduli in a relative setting. As an application, we compute the number of line sections with given moduli of a general degree $2r+1$ hypersurface in $\mathbb{P}^r$, generalizing the known case of quintic plane curves.

Benchmarking of Geant4 simulations for the COSI Anticoincidence System

Alex Ciabattoni, Valentina Fioretti, John A. Tomsick, Andreas Zoglauer, Parshad Patel, Lee Mitchell, Andrea Bulgarelli, Pierre Jean, Gabriele Panebianco, Nicolò Parmiggiani, Cristian Vignali, Peter von Ballmoos, Eric Wulf

The Compton Spectrometer and Imager (COSI) is an upcoming NASA Small Explorer satellite mission, designed for all-sky observations in the soft gamma-ray domain with the use of germanium detectors (GeDs). An active Anticoincidence System (ACS) of BGO scintillators surrounds the GeDs to reduce the background and contribute to the detection of transient events. Accurately modeling the ACS performance requires simulating the intricate scintillation processes within the shields, which significantly increases the computational cost. We have encoded these effects into a correction matrix derived from dedicated Geant4 simulations with the inclusion of the optical physics. For this purpose, we use laboratory measurements for the energy and spatial response of the ACS lateral wall to benchmark the simulation and define instrument parameters, including the BGO absorption length and the electronic noise. We demonstrate that the simulations replicate the experimental energy resolution and light collection uniformity along the BGO crystal, with maximum discrepancies of 20% and 10%, respectively. The validated simulations are then used to develop the correction matrix for the lateral wall, accounting for the light collection efficiency and energy resolution based on the position within the crystal. The gamma-ray quantum detection efficiency is also position-dependent via the inclusion of the optical physics. It is enhanced by $\sim$8% close to the SiPMs and suppressed by $\sim$2% in the adjacent corners with respect to the average value. Finally, we explore the energy threshold and resolution of the bottom ACS, considering the impact of its smaller crystals compared with the lateral walls.

Hermite--Hadamard inequalities for nearly-spherical domains

Noah Kravitz, Mitchell Lee

A conjecture of Pasteczka, generalizing the classical Hermite--Hadamard Inequality, states that if $Ω\subseteq \mathbb{R}^d$ is a compact convex domain such that $Ω$ and $\partial Ω$ have the same center of mass, then for every convex function $f: Ω\to \mathbb{R}^d$, the average value of $f$ on $Ω$ is less than or equal to the average value of $f$ on $\partial Ω$. Pasteczka proved this conjecture for the case where $Ω$ is a polytope with an inscribed ball. We generalize this result by proving Pasteczka's conjecture in the case where some point lies at most $(d+1)|Ω|/|\partial Ω|$ away from all hyperplanes tangent to $\partial Ω$.

BurstCube: Concept, Performance, and Status

Jacob R. Smith, Michael S. Briggs, Alessandro Bruno, Eric Burns, Regina Caputo, Brad Cenko, Antonino Cucchiara, Georgia de Nolfo, Sean Griffin, Lorraine Hanlon, Dieter H. Hartmann, Michelle Hui, Alyson Joens, Carolyn Kierans, Dan Kocevski, John Krizmanic, Amy Lien, Sheila McBreen, Julie E. McEnery, Lee Mitchell, David Morris, David Murphy, Jeremy S. Perkins, Judy Racusin, Peter Shawhan, Teresa Tatoli, Alexey Uliyanov, Sarah Walsh, Colleen Wilson-Hodge

The first simultaneous detection of a short gamma-ray burst (SGRB) with a gravitational-wave (GW) signal ushered in a new era of multi-messenger astronomy. In order to increase the number of SGRB-GW simultaneous detections, we need full sky coverage in the gamma-ray regime. BurstCube, a CubeSat for Gravitational Wave Counterparts, aims to expand sky coverage in order to detect and localize gamma-ray bursts (GRBs). BurstCube will be comprised of 4 Cesium Iodide scintillators coupled to arrays of Silicon photo-multipliers on a 6U CubeSat bus (a single U corresponds to cubic unit $\sim$10 cm $\times$ 10 cm $\times$ 10 cm) and will be sensitive to gamma-rays between 50 keV and 1 MeV, the ideal energy range for GRB prompt emission. BurstCube will assist current observatories, such as $Swift$ and $Fermi$, in the detection of GRBs as well as provide astronomical context to gravitational wave events detected by Advanced LIGO, Advanced Virgo, and KAGRA. BurstCube is currently in its development and testing phase to prepare for launch readiness in the fall of 2021. We present the mission concept, preliminary performance, and status.

Graham's Number is Less Than 2^^^6

Mikhail Lavrov, Mitchell Lee, John Mackey

In [5] Graham and Rothschild consider a geometric Ramsey problem: finding the least n such that if all edges of the complete graph on the points {+1,-1}^n are 2-colored, there exist 4 coplanar points such that the 6 edges between them are monochromatic. They give an explicit upper bound: F(F(F(F(F(F(F(12))))))), where F(m) = 2^^(m)^^3, an extremely fast-growing function. By reducing the problem to a variant of the Hales-Jewett problem, we find an upper bound which is between F(4) and F(5).

Boolean, Free, and Classical Cumulants as Tree Enumerations

Colin Defant, Mitchell Lee

Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called troupes. Using a generalization of troupes that we call weighted troupes, we generalize this result to allow for multivariate cumulants. Our result also gives a combinatorial description of the corresponding Boolean cumulants. This allows us to answer a question of Defant regarding his troupe transform. We also provide explicit distributions whose cumulants correspond to some specific weighted troupes.

Catching Element Formation In The Act

Chris L. Fryer, Frank Timmes, Aimee L. Hungerford, Aaron Couture, Fred Adams, Wako Aoki, Almudena Arcones, David Arnett, Katie Auchettl, Melina Avila, Carles Badenes, Eddie Baron, Andreas Bauswein, John Beacom, Jeff Blackmon, Stephane Blondin, Peter Bloser, Steve Boggs, Alan Boss, Terri Brandt, Eduardo Bravo, Ed Brown, Peter Brown, Steve Bruenn. Carl Budtz-Jorgensen, Eric Burns, Alan Calder, Regina Caputo, Art Champagne, Roger Chevalier, Alessandro Chieffi, Kelly Chipps, David Cinabro, Ondrea Clarkson, Don Clayton, Alain Coc, Devin Connolly, Charlie Conroy, Benoit Cote, Sean Couch, Nicolas Dauphas, Richard James deBoer, Catherine Deibel, Pavel Denisenkov, Steve Desch, Luc Dessart, Roland Diehl, Carolyn Doherty, Inma Dominguez, Subo Dong, Vikram Dwarkadas, Doreen Fan, Brian Fields, Carl Fields, Alex Filippenko, Robert Fisher, Francois Foucart, Claes Fransson, Carla Frohlich, George Fuller, Brad Gibson, Viktoriya Giryanskaya, Joachim Gorres, Stephane Goriely, Sergei Grebenev, Brian Grefenstette, Evan Grohs, James Guillochon, Alice Harpole, Chelsea Harris, J. Austin Harris, Fiona Harrison, Dieter Hartmann, Masa-aki Hashimoto, Alexander Heger, Margarita Hernanz, Falk Herwig, Raphael Hirschi, Raphael William Hix, Peter Hoflich, Robert Hoffman, Cole Holcomb, Eric Hsiao, Christian Iliadis, Agnieszka Janiuk, Thomas Janka, Anders Jerkstrand, Lucas Johns, Samuel Jones, Jordi Jose, Toshitaka Kajino, Amanda Karakas, Platon Karpov, Dan Kasen, Carolyn Kierans, Marc Kippen, Oleg Korobkin, Chiaki Kobayashi, Cecilia Kozma, Saha Krot, Pawan Kumar, Irfan Kuvvetli, Alison Laird, Martin Laming, Josefin Larsson, John Lattanzio, James Lattimer, Mark Leising, Annika Lennarz, Eric Lentz, Marco Limongi, Jonas Lippuner, Eli Livne, Nicole Lloyd-Ronning, Richard Longland, Laura A. Lopez, Maria Lugaro, Alexander Lutovinov, Kristin Madsen, Chris Malone, Francesca Matteucci, Julie McEnery, Zach Meisel, Bronson Messer, Brian Metzger, Bradley Meyer, Georges Meynet, Anthony Mezzacappa, Jonah Miller, Richard Miller, Peter Milne, Wendell Misch, Lee Mitchell, Philipp Mosta, Yuko Motizuki, Bernhard Muller, Matthew Mumpower, Jeremiah Murphy, Shigehiro Nagataki, Ehud Nakar, Ken'ichi Nomoto, Peter Nugent, Filomena Nunes, Brian O'Shea, Uwe Oberlack, Steven Pain, Lucas Parker, Albino Perego, Marco Pignatari, Gabriel Martinez Pinedo, Tomasz Plewa, Dovi Poznanski, William Priedhorsky, Boris Pritychenko, David Radice, Enrico Ramirez-Ruiz, Thomas Rauscher, Sanjay Reddy, Ernst Rehm, Rene Reifarth, Debra Richman, Paul Ricker, Nabin Rijal, Luke Roberts, Friedrich Ropke, Stephan Rosswog, Ashley J. Ruiter, Chris Ruiz, Daniel Wolf Savin, Hendrik Schatz, Dieter Schneider, Josiah Schwab, Ivo Seitenzahl, Ken Shen, Thomas Siegert, Stuart Sim, David Smith, Karl Smith, Michael Smith, Jesper Sollerman, Trevor Sprouse, Artemis Spyrou, Sumner Starrfield, Andrew Steiner, Andrew W. Strong, Tuguldur Sukhbold, Nick Suntzeff, Rebecca Surman, Toru Tanimori, Lih-Sin The, Friedrich-Karl Thielemann, Alexey Tolstov, Nozomu Tominaga, John Tomsick, Dean Townsley, Pelagia Tsintari, Sergey Tsygankov, David Vartanyan, Tonia Venters, Tom Vestrand, Jacco Vink, Roni Waldman, Lifang Wang, Xilu Wang, MacKenzie Warren, Christopher West, J. Craig Wheeler, Michael Wiescher, Christoph Winkler, Lisa Winter, Bill Wolf, Richard Woolf, Stan Woosley, Jin Wu, Chris Wrede, Shoichi Yamada, Patrick Young, Remco Zegers, Michael Zingale, Simon Portegies Zwart