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Michael Jennings

Publications and source records attributed to Michael Jennings.

4 recordsLinked to original sources

Resolving the Unresolved Galactic Winds in Multi-phase Models. I. Methodology and Application

Galactic winds shape galaxy evolution; however, the outflowing gas is complex: it consists of multiple ionization phases, and its properties vary spatially. Therefore, methods that combine high-fidelity observations with state-of-the-art galactic-wind models are limited. Here we investigate methods for fitting the column density profiles derived from high-quality outflow observations with the multiphase, multiscale wind model from Fielding & Bryan 2022. We identify three key outflow parameters: the initial hot-phase mass-loading factor ($\eta_\text{ M,hot,0}$), the initial cool-phase mass-loading factor ($\eta_\text{ M,cool,0}$), and the initial cool-cloud mass. We obtain good fits for most galaxies, with tight constraints on $\eta_\text{ M,cool,0}$ and moderate constraints on the other two parameters. We find the inferred $\eta_\text{ M,cool,0}$ and $\eta_\text{ M,hot,0}$ are mostly of order unity, with significant scatter. The constraints on $\eta_\text{ M,hot,0}$ suggest that the interaction between the cool and hot phases allows us to indirectly constrain the properties of the hot wind from cool-outflow observations. The model also predicts various radial trends. First, for all galaxies, the cool-phase outflow velocity increases between $1-2$ times of the half-light radius, then reaches a plateau. Second, most galaxies exhibit increasing $\eta_\text{ M,cool}$ and decreasing $\eta_\text{ M,hot}$ with radius, with a few showing the reverse trends. These results are effective, model-conditional constraints, and are consistent with other recent multiphase simulations and observations. This highlights that the velocity-radius mapping encoded in UV absorption profiles enables recovery of outflow spatial structures from spatially integrated spectra. Our method paves the way for future broad parameter studies and guides updates of outflow simulations in future work.

astro-ph.GA

PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition

We present PutnamBench, a new multi-language benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1692 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the problems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. PutnamBench requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

cs.AI

Zero-consistency root emulation for unprivileged container image build

Do Linux distribution package managers need the privileged operations they request to actually happen? Apparently not, at least for building container images for HPC applications. We use this observation to implement a root emulation mode using a Linux seccomp filter that intercepts some privileged system calls, does nothing, and returns success to the calling program. This approach provides no consistency whatsoever but appears sufficient to build all Dockerfiles we examined, simplifying fully-unprivileged workflows needed for HPC application containers.

cs.DC

Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II

We generalize the results of [AS], finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each the lift of a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.

math.GT