arXiv subjects

Katherine Moore

Publications and source records attributed to Katherine Moore.

4 recordsLinked to original sources

arXiv2026

Preparing Students for AI-Powered Materials Discovery: A Workflow-Aligned Framework for AI Literacy, Equity, and Scientific Judgment

Artificial intelligence (AI) is reshaping education, scientific training, and materials discovery. In materials science, AI models increasingly support property prediction, experiment prioritization, and hypothesis generation; however, the limiting factor is no longer only algorithmic capability but also whether students and educators can use AI with domain-specific scientific judgment. This workshop-informed white paper and curriculum-oriented position article argues that AI education for AI-powered materials discovery must move beyond tool access and surface-level interaction with generative AI systems toward a workflow-aligned model of AI literacy. We connect AI literacy to materials-informatics competencies: data provenance, domain-specific featurization, model validation, uncertainty quantification, physics informed reasoning, reproducibility, and experimental feedback. We also emphasize outcome-oriented equity: institutions should evaluate not only access, participation, and engagement, but also whether AI-enabled instruction produces comparable learning gains, transfer of learning, confidence calibration, defined as the alignment with students confidence and the quality or correctness of their work, persistence, and research readiness across student subgroups. The paper synthesizes relevant evidence, identifies risks for learners such as cognitive off-loading and cognitive surrender, and provides a dual-track curriculum model and implementation recommendations such as curriculum guides and an assessment plan for courses, bootcamps, workshops, and program-level reform. The central goal is to prepare students to become better scientists, not merely more efficient users of AI tools.

physics.ed-ph↗

arXiv2017

Characterizations and Enumerations of Patterns of Signed Shifts

Signed shifts are generalizations of the shift map in which, interpreted as a map from the unit interval to itself sending x to the fractional part of Nx, some slopes are allowed to be negative. Permutations realized by the relative order of the elements in the orbits of these maps have been studied recently by Amigo, Archer and Elizalde. In this paper, we give a complete characterization of the permutations (also called patterns) realized by signed shifts. In the case of the negative shift, which is the signed shift having only negative slopes, we use the characterization to give an exact enumeration of these patterns. Finally, we improve the best known bounds for the number of patterns realized by the tent map, and calculate the topological entropy of signed shifts using these combinatorial methods.

math.CO↗

arXiv2017

Random Walk Null Models for Time Series Data

Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying uniform distribution of patterns. In this paper, we analyze random walk null models for time series and determine the corresponding permutation distributions. These new techniques allow us to explicitly describe the behavior of real world data in terms of more complex generative processes. Additionally, building on recent results of Martinez, we define a validation measure that allows us to determine when a random walk is an appropriate model for a time series. We demonstrate the usefulness of our methods using empirical data drawn from a variety of fields.

stat.ME↗

arXiv2016

Patterns of Negative Shifts and Beta-Shifts

The $β$-shift is the transformation from the unit interval to itself that maps $x$ to the fractional part of $βx$. Permutations realized by the relative order of the elements in the orbits of these maps have been studied for positive integer values of $β$ and for real values $β>1$. In both cases, a combinatorial description of the smallest positive value of $β$ needed to realize a permutation is provided. In this paper we extend these results to the case of negative $β$, both in the integer and in the real case. Negative $β$-shifts are related to digital expansions with negative real bases, studied by Ito and Sadahiro, and Liao and Steiner.

math.CO↗