economics & mathematics

Institution: the Department of Economics, UMNTC

Duration: May 2026 - Sept 2026. 

Links: [Code] [Paper]

Keywords: Science of Science, Network Geometry, Science Economics, Network Science, Graph Learning. 

Abstract

Scientific breakthroughs can change the value of a research field much faster than research institutions can change what they know how to do. In this paper, I identify whether path dependence exists when a research institution expands its research directions. To identify such dependencies, I define an institution’s “capability neighborhood” as the region of scientific knowledge space that lies close to its existing research portfolio. I develop a scientific capability geometry (SciGeometry) that uses capability distance to measure how far a potential field lies from what an institution already knows how to do. I conduct two empirical analyses—measuring capability distance across 1,000 institutions and examining the first direct detection of gravitational waves—and a computational benchmark of field-entry prediction. I find that institutions are substantially more likely to enter fields close to their existing capabilities, with a one-standard- deviation increase in portfolio distance lowering entry probability by 0.210 from a baseline mean of 56.9%, and that the gravitational-wave discovery increased external citation attention to as-trophysics and astronomy by 0.849 percentage points relative to its synthetic counterfactual; only 4.3 percent of 3,828 placebo pairs showed a larger post-event attention gap. In institution-held-out prediction, SciGeometry-GCN achieves an AUC of 0.8047, compared with 0.7737 for a vanilla GCN, while also improving PR-AUC and log loss. Across two different outcomes—institutional entry and field-level attention—research activity is concentrated close to existing knowledge.

Outcomes

Y. Lu (2026). SciGeometry: The Geometry of Scientific Opportunity Allocation. University of Minnesota. 

Other

This paper got the highest score(103/100) for Economic Capstone Project, recognized as the best project in 2026 academic year.

A Spatial and Temporal Analysis from 2013 to 2023

Advisor: Prof. Halil Akil(Instructor), Jessie Dickens(Writing Assistant)

Institution: the Department of Economics, UMNTC

Duration: June 2025 - April 2025

Links: [Code] [Paper]

Keywords: Urban/Regional Economics, Economic Development, Convergence Analysis, Spatial Statistics

Abstract

This study investigates the convergence of digital infrastructure across U.S. counties and states from 2013 to 2023, with a focus on whether regional disparities in digital access have narrowed over time. Using microdata from the Integrated Public Use Microdata Series (IPUMS USA), we construct a household-level digital access index based on device and internet connectivity variables. We apply both standard sigma- and beta-convergence models as well as a spatial lag beta-convergence model to evaluate two key hypotheses: (1) initially disadvantaged regions have experienced faster digital growth, and (2) geographically proximate regions converge together through spatial spillovers. Our results provide strong evidence of both sigma- and beta-convergence at the county and state levels, indicating a general reduction in the digital divide. However, we find no robust support for spatial spillovers—regions do not appear to converge faster as a result of their neighbors’ growth. This suggests that while local catch-up dynamics are at play, geographic diffusion of digital development may be limited by policy fragmentation, administrative boundaries, or infrastructure barriers. The findings highlight the need for regional coordination to enhance digital equity.

Outcomes

Y. Lu (2025). Digital Infrastructure Convergence in the United States: Digital Infrastructure Convergence in the United States. University of Minnesota. 

Y. Lu (2025). Digital Infrastructure Convergence in the United States: Digital Infrastructure Convergence in the United States[Computer Software]. Github Repository. https://github.com/HarryLuUMN/Digital-Drifting 

Other

The paper presented at the Undergraduate Economic Workshop, Heller Hurwicz Economic Institute, University of Minnesota, Twin Cities. Apr 2026. 

The paper got the 1st Place at the Undergraduate Economic Writing Competition ($750), University of Minnesota, Twin Cities. Jan 2026. 

This paper got the highest score(1/30) in ECON4331W: Economic Development, Summer 2025, a research writing course in economics major.

Measuring Temporal Linguistic Emergence in Diffusion Language Models

Institution: the School of Mathematics, UMNTC

Duration: March 2026 - Present

Links: [Paper] [Code]

Keywords: diffusion language models, interpretability, linguistic analysis. 

Abstract

Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of \texttt{GSAI-ML/LLaDA-8B-Base} on masked WikiText-103 text, each with 1{,}000 probe-training sequences and 200 held-out evaluation sequences. From saved trajectories, we derive four temporal measurements: token commitment; linear recoverability of part-of-speech (POS), coarse semantic category, and token identity; confidence and entropy dynamics; and sensitivity under mid-trajectory re-masking. Across seeds in this specific LLaDA+WikiText setting, the same ordering recurs: content categories stabilize earlier than function-heavy categories, POS and coarse semantic labels remain substantially more linearly recoverable than exact lexical identity under our compact probe setup, uncertainty remains higher for tokens that ultimately resolve incorrectly even though late confidence becomes less calibrated, and re-masking sensitivity peaks in the middle of the trajectory. A direct/collateral decomposition shows that this peak is overwhelmingly local to the perturbed positions themselves. We therefore present denoising time as a useful analysis axis for this configuration, not as a universal emergence law: under our measurements, coarse labels are recovered earlier and more robustly than lexical identity, trajectory-level uncertainty tracks eventual correctness, and mid-trajectory states are the most re-masking-sensitive.

Outcomes

Lu, Yilin. "Measuring Temporal Linguistic Emergence in a Diffusion Language Model." In Submission to IJCAI-ECAI 2026, Explainable AI Workshop arXiv:2604.23235 (2026).

Extending Partial Orders: From Binary Relations to Linear Orderings

Advisor: Prof. Karel Prikry

Institution: the School of Mathematics, UMNTC

Duration: September 2025 - December 2025

Links: [Paper]

Keywords: Set Theory, Combinatorics, Ordering Theory

Abstract

In this paper, we will explore the relationship between the two kinds of orderings, namely partial orderings and linear orderings. 

The two key theorems that we will discuss are the Hausdorff maximality theorem, that every partial ordering contains a maximal linearly ordered subset, and the linear extension theorem, discussed first by Polish mathematicians in 1920's, that every partial ordering can be extended to a linear ordering. Our main source is Linear Operators Part 1 by N. Dunford and J. T. Schwartz, which we will refer to as LO. 

Outcomes

Y. Lu (2025). Extending Partial Orders: From Binary Relations to Linear Orderings. University of Minnesota.