Irreducibility and Galois Groups of Random Polynomials

In 2015, I. Rivin introduced an effective method to bound the number of irreducible integral polynomials with fixed degree d and height at most N. In this paper, we give a brief summary of this result and discuss the precision of Rivin\u27s arguments for special classes of polynomials. We also give elementary proofs of classic results on Galois groups of cubic trinomials

Improving Continuous-time Conflict Based Search

Conflict-Based Search (CBS) is a powerful algorithmic framework for optimally solving classical multi-agent path finding (MAPF) problems, where time is discretized into the time steps. Continuous-time CBS (CCBS) is a recently proposed version of CBS that guarantees optimal solutions without the need to discretize time. However, the scalability of CCBS is limited because it does not include any known improvements of CBS. In this paper, we begin to close this gap and explore how to adapt successful CBS improvements, namely, prioritizing conflicts (PC), disjoint splitting (DS), and high-level heuristics, to the continuous time setting of CCBS. These adaptions are not trivial, and require careful handling of different types of constraints, applying a generalized version of the Safe interval path planning (SIPP) algorithm, and extending the notion of cardinal conflicts. We evaluate the effect of the suggested enhancements by running experiments both on general graphs and $2^k$-neighborhood grids. CCBS with these improvements significantly outperforms vanilla CCBS, solving problems with almost twice as many agents in some cases and pushing the limits of multiagent path finding in continuous-time domains.Comment: This is a pre-print of the paper accepted to AAAI 202

Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

Recent theories suggest that the excitations of certain quantum Hall states may have exotic braiding statistics which could be used to build topological quantum gates. This has prompted an experimental push to study such states using confined geometries where the statistics can be tested. We study the transport properties of quantum point contacts (QPCs) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits well-developed fractional quantum Hall effect, including at bulk filling fraction 5/2. We find that a plateau at effective QPC filling factor 5/2 is identifiable in point contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5 microns. We study the temperature and dc-current-bias dependence of the 5/2 plateau in the QPC, as well as neighboring fractional and integer plateaus in the QPC while keeping the bulk at filling factor 3. Transport near QPC filling factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms in this confined geometry

A New Era in Extragalactic Background Light Measurements: The Cosmic History of Accretion, Nucleosynthesis and Reionization

(Brief Summary) What is the total radiative content of the Universe since the epoch of recombination? The extragalactic background light (EBL) spectrum captures the redshifted energy released from the first stellar objects, protogalaxies, and galaxies throughout cosmic history. Yet, we have not determined the brightness of the extragalactic sky from UV/optical to far-infrared wavelengths with sufficient accuracy to establish the radiative content of the Universe to better than an order of magnitude. Among many science topics, an accurate measurement of the EBL spectrum from optical to far-IR wavelengths, will address: What is the total energy released by stellar nucleosynthesis over cosmic history? Was significant energy released by non-stellar processes? Is there a diffuse component to the EBL anywhere from optical to sub-millimeter? When did first stars appear and how luminous was the reionization epoch? Absolute optical to mid-IR EBL spectrum to an astrophysically interesting accuracy can be established by wide field imagingat a distance of 5 AU or above the ecliptic plane where the zodiacal foreground is reduced by more than two orders of magnitude.Comment: 7 pages; Science White Paper for the US Astro 2010-2020 Decadal Survey. If interested in further community-wide efforts on this topic please contact the first autho

Electromagnetic Window into the Dawn of Black Holes

The origin of massive black holes in the early universe is one of the major puzzles in astrophysics. Future X-ray surveys can detect BHs with mass M &lt; 105 M☉ at z &gt; 10, and OIR observations can characterize their immediate environment. These observations will open a window into the "Dawn of Black Holes" and distinguish models of their origin. <p/