arXiv subjects

Madeline Brown

Publications and source records attributed to Madeline Brown.

4 recordsLinked to original sources

arXiv2026

Social Network Structure, Wealth, and Wealth Inequality Across Cultures

Despite theory tying wealth inequality to social structure, empirical evidence has been limited to a few studies based on online social media data. This study uses a very different type of data, expands the global coverage to very different types of societies, and investigates new questions. In particular, we collect data from ~3500 sharing units (households) in 46 communities across the globe, representing considerable human social and cultural diversity. In each, we analyze the relationship between people's material wealth and the structure of social networks: borrowing money, sharing food, working together, socializing, etc. In almost all communities, a sharing unit's material wealth is positively associated with the number of other sharing units it both helps and is helped by. A sharing unit's wealth is also associated with the relative wealth of the sharing units to which it is linked---a form of economic homophily. Notably, communities with greater wealth inequality are also characterized by a network structure in which poorer sharing units are less well connected to wealthier ones. We augment our unique cross-cultural data with other community-level environmental, institutional, and economic attributes, opening new avenues for future research into the co-determination of wealth and social networks.

cs.SI↗

arXiv2026

Enhanced Interband Optical Nonlinearities from Coupled Quantum Wells

The recent, rapid advances in nonlinear chipscale nanophotonics in the visible and near-infrared have been largely driven by manipulating the local dielectric environment proximate to decades-old workhorse bulk nonlinear optical materials, rather than increasing the inherent strength of their nonlinear response. While proposed decades ago, we demonstrate the first experimental realization of a new class of designer nonlinear materials that leverage the interband optical transition in asymmetric structures to provide strong second order susceptibility, $\chi^{(2)}$. Using simple AlGaAs/GaAs coupled quantum wells operating in the near-infrared as a prototype, we observed strong second harmonic generation enhancement of 1550 nm to 775 nm over bulk controls. Extracted $\chi^{(2)}$ values were as high as 2750 pm/V, which is $>$7x that of bulk GaAs. Furthermore, measured susceptibilities agreed well with quantum mechanical calculations of $\chi^{(2)}$ using layer profiles extracted from electron microscopy. Growth interruptions were employed to improve interfacial abruptness in response to electron microscopy characterization, resulting in increased $\chi^{(2)}$ toward the simulation predictions for ideal heterointerfaces. More complex layer designs showed predicted $\chi^{(2)}$ up to 7 nm/V. Such materials are anticipated to find myriad applications, including entangled photon generation at telecommunications wavelengths for chipscale quantum information processing.

physics.optics↗

arXiv2024

Activated Random Walks on $\mathbb{Z}$ with Critical Particle Density

The Activated Random Walk (ARW) model is a promising candidate for demonstrating self-organized criticality due to its potential for universality. Recent studies have shown that the ARW model exhibits a well-defined critical density in one dimension, supporting its universality. In this paper, we extend these results by demonstrating that the ARW model on $\mathbb{Z}$, with a single initially active particle and all other particles sleeping, maintains the same critical density. Our findings relax the previous assumption that required all particles to be initially active. This provides further evidence of the ARW model's robustness and universality in depicting self-organized criticality.

math.PR↗

arXiv2021

G-Family Polynomials

We introduce two notions of quandle polynomials for G-families of quandles: the quandle polynomial of the associated quandle and a G-family polynomial with coefficients in the group ring of G. As an application we define image subquandle polynomial enhancements of the G-family counting invariant for trivalent spatial graphs and handlebody-links. We provide examples to show that the new enhancements are proper.

math.GT↗