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👩‍💻 Paige Bailey

Chronological feed of everything captured from 👩‍💻 Paige Bailey.

paper / dynamicwebpaige / Jun 11

Bridging Exceptional Orthogonal Polynomials and Quasi-Orthogonality via Degree-Skipping Constructions

Bailey and Gavrilov construct monic orthogonal polynomial sequences that omit exactly one degree using linear combinations of classical polynomial families (e.g., Hermite, Laguerre, Jacobi), extending the conceptual framework of Exceptional Orthogonal Polynomials (XOPs). The core result establishes a formal connection between these degree-skipping sequences and quasi-orthogonal polynomials of order 2, providing a new structural lens on both families. This work sits at the intersection of classical analysis and spectral theory (MSC 33C45, 42C05), with potential implications for Sturm-Liouville problems and approximation theory.

orthogonal-polynomialsclassical-analysisexceptional-sequencesspecial-functionspure-mathematicsarxiv-preprint
“It is possible to construct monic orthogonal polynomial sequences that omit a single degree using linear combinations of classical polynomial families.”
paper / dynamicwebpaige / Jun 11

Human Conformity Heuristics Are Mismatched to Social Media: A Deep MARL Analysis of Opinion Dynamics

This paper applies GPU-accelerated multi-agent reinforcement learning (MARL) to model opinion dynamics at population scales up to 1,000 agents, replacing hand-crafted interaction rules with learned behaviors optimized via simple rewards. The model is validated against real Bluesky network data, recovering agent importance structures from graph topology via a learned attention layer. A key finding is that high conformity — which best matches observed human behavior — is adaptive in small, dynamic hunter-gatherer-scale networks but becomes collectively harmful in large social media networks, degrading accuracy and incentivizing dishonest agents. This suggests that evolved human conformity instincts are structurally mismatched to modern large-scale social media, potentially driving misinformation dynamics.

multi-agent-reinforcement-learningopinion-dynamicssocial-networksmisinformationagent-based-modelinggame-theorysocial-media
“Highly conforming agent populations most closely match real human behavior observed in the Bluesky social network.”
paper / dynamicwebpaige / Jun 11

A Choked-Jet Shock Breakout Bridges the Gap Between X-Ray Transients and Low-Luminosity GRBs

EP260321a is the faintest shock breakout X-ray transient yet associated with a broad-lined Type Ic supernova (SN 2026gzf) at z=0.0344, detected by the Einstein Probe. Its thermal X-ray emission (kT=160 eV, peak luminosity 2.2×10⁴⁴ erg/s) is consistent with shock breakout, yet deep Chandra observations rule out any canonical GRB afterglow. The most parsimonious explanation is a mildly relativistic, weak outflow choked by the progenitor star — a scenario that accounts for both the low X-ray luminosity and the absence of prompt gamma-ray emission. This event occupies a previously sparse region of parameter space between SN 2008D-like shock breakouts and low-luminosity GRBs, pointing to broader diversity in the terminal collapse of stripped-envelope stars.

supernovashock-breakoutx-ray-transientsgamma-ray-burstshigh-energy-astrophysicsstellar-explosioneinstein-probe
“EP260321a exhibits thermal X-ray emission with kT=160 eV and a peak luminosity of 2.2×10⁴⁴ erg/s, consistent with a shock breakout origin.”
paper / dynamicwebpaige / Jun 11

SN 2026gzf: First Direct Evidence Linking Pre-Explosion Eruptive Mass Loss to Circumstellar Interaction in a Stripped-Envelope Supernova

SN 2026gzf, a broad-lined Type Ic supernova, was observed just 1.25 hours post-detection by Einstein Probe, revealing a luminous blue first-day excess inconsistent with standard radioactive decay models. This excess is explained by ejecta interaction with ~0.02 M☉ of circumstellar material (CSM), likely shed during late-stage nuclear burning. Archival Pan-STARRS imaging spanning ~12 years prior to explosion shows a ~1.5× brightening in the final ~3 years, providing the first direct observational link between long-term precursor variability, eruptive mass loss, and CSM interaction in a stripped-envelope progenitor. The X-ray shock-breakout signal is attributed to a distinct, compact CSM shell likely produced during a silicon-burning episode shortly before core collapse.

supernovacircumstellar-interactionstellar-evolutionhigh-energy-astrophysicstransient-astronomypre-explosion-activitycore-collapse
“A luminous blue first-day optical excess in SN 2026gzf cannot be explained by standard radioactive decay models and requires ~0.02 M☉ of circumstellar material interaction.”
paper / dynamicwebpaige / Jun 11

A Sporadic srg(120,56,28,24) Finally Explained via Ovoids, Spreads, and Overlarge Steiner Systems

Of the three non-isomorphic strongly regular graphs with parameters (120,56,28,24) whose automorphism groups act primitively on vertices, two belong to well-known classical families, but the third has remained poorly understood. Adriaensen et al. resolve this gap by constructing the sporadic graph from ovoids and spreads of the hyperbolic quadric Q⁺(7,2), establishing an equivalence with overlarge sets of Steiner systems S(3,4,8). This combinatorial characterization ties a previously opaque graph to well-studied geometric and design-theoretic structures, grounding it in the rich theory surrounding the symmetric group on 7 elements.

graph-theorycombinatoricsstrongly-regular-graphsgroup-theoryfinite-geometrysteiner-systemsalgebraic-combinatorics
“There are exactly three non-isomorphic strongly regular graphs with parameters (120,56,28,24) whose automorphism group acts primitively on the vertices.”