arXiv subjects

Jane Wang

Publications and source records attributed to Jane Wang.

At least 19 recordsLinked to original sources

arXiv2026

Complexity of Billiards in Polygons Associated to Hyperbolic $(p,q)$-Tilings

The complexity of the billiard language of regular polygons in the hyperbolic plane with $p$ sides and $2\pi/q$ internal angles is known to grow exponentially and the exponential growth rate is known to equal the topological entropy of the billiard system. In this paper we compute these exponential growth rates explicitly when $q$ is even and give bounds when $q$ is odd. Additionally, for the $q$ even case, we give complete grammar rules that establish when a word (finite, infinite or bi-infinite) in $p$ letters is realized by a billiard path. This latter result is roughly stated and not rigorously proved in a paper of Giannoni and Ullmo (1995). In this paper, we provide a precise statement and a complete proof using new methods relating to minimal tiling paths.

math.DS↗

arXiv2026

Deployment and Evaluation of an EHR-integrated, Large Language Model-Powered Tool to Triage Surgical Patients

Surgical co-management (SCM) is an evidence-based model in which hospitalists jointly manage medically complex perioperative patients alongside surgical teams. Despite its clinical and financial value, SCM is limited by the need to manually identify eligible patients. To determine whether SCM triage can be automated, we conducted a prospective, unblinded study at Stanford Health Care in which an LLM-based, electronic health record (EHR)-integrated triage tool (SCM Navigator) provided SCM recommendations followed by physician review. Using pre-operative documentation, structured data, and clinical criteria for perioperative morbidity, SCM Navigator categorized patients as appropriate, not appropriate, or possibly appropriate for SCM. Faculty indicated their clinical judgment and provided free-text feedback when they disagreed. Sensitivity, specificity, positive predictive value, and negative predictive value were measured using physician determinations as a reference. Free-text reasons were thematically categorized, and manual chart review was conducted on all false-negative cases and 30 randomly selected cases from the largest false-positive category. Since deployment, 6,193 cases have been triaged, of which 1,582 (23%) were recommended for hospitalist consultation. SCM Navigator displayed high sensitivity (0.94, 95% CI 0.91-0.96) and moderate specificity (0.74, 95% CI 0.71-0.77). Post-hoc chart review suggested most discrepancies reflect modifiable gaps in clinical criteria, institutional workflow, or physician practice variability rather than LLM misclassification, which accounted for 2 of 19 (11%) false-negative cases. These findings demonstrate that an LLM-powered, EHR-integrated, human-in-the-loop AI system can accurately and safely triage surgical patients for SCM, and that AI-enabled screening tools can augment and potentially automate time-intensive clinical workflows.

cs.CY↗

arXiv2025

Measuring AI Diffusion: A Population-Normalized Metric for Tracking Global AI Usage

Measuring global AI diffusion remains challenging due to a lack of population-normalized, cross-country usage data. We introduce AI User Share, a novel indicator that estimates the share of each country's working-age population actively using AI tools. Built from anonymized Microsoft telemetry and adjusted for device access and mobile scaling, this metric spans 147 economies and provides consistent, real-time insight into global AI diffusion. We find wide variation in adoption, with a strong correlation between AI User Share and GDP. High uptake is concentrated in developed economies, though usage among internet-connected populations in lower-income countries reveals substantial latent demand. We also detect sharp increases in usage following major product launches, such as DeepSeek in early 2025. While the metric's reliance solely on Microsoft telemetry introduces potential biases related to this user base, it offers an important new lens into how AI is spreading globally. AI User Share enables timely benchmarking that can inform data-driven AI policy.

cs.CY↗

arXiv2025

Holonomy of affine surfaces

We identify the moduli space of complex affine surfaces with the moduli space of regular meromorphic connections on Riemann surfaces and show that it satisfies a corresponding universal property. As a consequence, we identify the tangent space of the moduli space of affine surfaces, at an affine surface X, with the first hypercohomology of a two-term sequences of sheaves on X. In terms of this identification, we calculate the derivative and coderivative of the holonomy map, sending an affine surface to its holonomy character. Using these formulas, we show that the holonomy map is a submersion at every affine surface that is not a finite-area translation surface, extending work of Veech. Finally, we introduce a holomorphic foliation of some strata of meromorphic affine surfaces, which we call the isoresidual foliation, along whose leave holonomy characters and certain residues are constant. We equip this foliation with a leafwise indefinite Hermitian metric, again extending work of Veech.

math.AG↗

arXiv2024

An Effective Slope Gap Distribution for Lattice Surfaces

We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an effective gap distribution result for the Farey fractions. As an intermediate step, we prove an effective equidistribution result for the intersection points of long horocycles with a particular transversal of the horocycle flow in $\mathrm{SL}_2 (\mathbb R)/\Gamma$ where $\Gamma$ is a lattice.

math.DS↗

arXiv2023

Gait Event Detection and Travel Distance Using Waist-Worn Accelerometers across a Range of Speeds: Automated Approach

Estimation of temporospatial clinical features of gait (CFs), such as step count and length, step duration, step frequency, gait speed, and distance traveled, is an important component of community-based mobility evaluation using wearable accelerometers. However, accurate unsupervised computerized measurement of CFs of individuals with Duchenne muscular dystrophy (DMD) who have progressive loss of ambulatory mobility is difficult due to differences in patterns and magnitudes of acceleration across their range of attainable gait velocities. This paper proposes a novel calibration method. It aims to detect steps, estimate stride lengths, and determine travel distance. The approach involves a combination of clinical observation, machine-learning-based step detection, and regression-based stride length prediction. The method demonstrates high accuracy in children with DMD and typically developing controls (TDs) regardless of the participant's level of ability. Fifteen children with DMD and fifteen TDs underwent supervised clinical testing across a range of gait speeds using 10 m or 25 m run/walk (10 MRW, 25 MRW), 100 m run/walk (100 MRW), 6-min walk (6 MWT), and free-walk (FW) evaluations while wearing a mobile-phone-based accelerometer at the waist near the body's center of mass. Following calibration by a trained clinical evaluator, CFs were extracted from the accelerometer data using a multi-step machine-learning-based process and the results were compared to ground-truth observation data. Model predictions vs. observed values for step counts, distance traveled, and step length showed a strong correlation. Our study findings indicate that a single waist-worn accelerometer calibrated to an individual's stride characteristics using our methods accurately measures CFs and estimates travel distances across a common range of gait speeds in both DMD and TD peers.

eess.SP↗

arXiv2023

DiscoGen: Learning to Discover Gene Regulatory Networks

Accurately inferring Gene Regulatory Networks (GRNs) is a critical and challenging task in biology. GRNs model the activatory and inhibitory interactions between genes and are inherently causal in nature. To accurately identify GRNs, perturbational data is required. However, most GRN discovery methods only operate on observational data. Recent advances in neural network-based causal discovery methods have significantly improved causal discovery, including handling interventional data, improvements in performance and scalability. However, applying state-of-the-art (SOTA) causal discovery methods in biology poses challenges, such as noisy data and a large number of samples. Thus, adapting the causal discovery methods is necessary to handle these challenges. In this paper, we introduce DiscoGen, a neural network-based GRN discovery method that can denoise gene expression measurements and handle interventional data. We demonstrate that our model outperforms SOTA neural network-based causal discovery methods.

q-bio.MN↗

arXiv2022

Beyond Bayes-optimality: meta-learning what you know you don't know

Meta-training agents with memory has been shown to culminate in Bayes-optimal agents, which casts Bayes-optimality as the implicit solution to a numerical optimization problem rather than an explicit modeling assumption. Bayes-optimal agents are risk-neutral, since they solely attune to the expected return, and ambiguity-neutral, since they act in new situations as if the uncertainty were known. This is in contrast to risk-sensitive agents, which additionally exploit the higher-order moments of the return, and ambiguity-sensitive agents, which act differently when recognizing situations in which they lack knowledge. Humans are also known to be averse to ambiguity and sensitive to risk in ways that aren't Bayes-optimal, indicating that such sensitivity can confer advantages, especially in safety-critical situations. How can we extend the meta-learning protocol to generate risk- and ambiguity-sensitive agents? The goal of this work is to fill this gap in the literature by showing that risk- and ambiguity-sensitivity also emerge as the result of an optimization problem using modified meta-training algorithms, which manipulate the experience-generation process of the learner. We empirically test our proposed meta-training algorithms on agents exposed to foundational classes of decision-making experiments and demonstrate that they become sensitive to risk and ambiguity.

cs.AI↗

arXiv2022

Learning to Induce Causal Structure

The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them using either score-based methods (including continuous optimization) or independence tests. In our work, we instead treat the inference process as a black box and design a neural network architecture that learns the mapping from both observational and interventional data to graph structures via supervised training on synthetic graphs. The learned model generalizes to new synthetic graphs, is robust to train-test distribution shifts, and achieves state-of-the-art performance on naturalistic graphs for low sample complexity.

stat.ML↗

arXiv2022

An Artificial Intelligence Dataset for Solar Energy Locations in India

Rapid development of renewable energy sources, particularly solar photovoltaics (PV), is critical to mitigate climate change. As a result, India has set ambitious goals to install 500 gigawatts of solar energy capacity by 2030. Given the large footprint projected to meet renewables energy targets, the potential for land use conflicts over environmental values is high. To expedite development of solar energy, land use planners will need access to up-to-date and accurate geo-spatial information of PV infrastructure. In this work, we developed a spatially explicit machine learning model to map utility-scale solar projects across India using freely available satellite imagery with a mean accuracy of 92%. Our model predictions were validated by human experts to obtain a dataset of 1363 solar PV farms. Using this dataset, we measure the solar footprint across India and quantified the degree of landcover modification associated with the development of PV infrastructure. Our analysis indicates that over 74% of solar development In India was built on landcover types that have natural ecosystem preservation, or agricultural value.

cs.LG↗

arXiv2022

Moduli spaces of complex affine and dilation surfaces

We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points of fixed complex order is a holomorphic affine bundle over the moduli space of Riemann surfaces. Similarly, the moduli space of dilation surfaces is a covering space of the moduli space of Riemann surfaces. We classify the connected components of the moduli space of dilation surfaces and show that any component is an orbifold K(G,1) where G is the framed mapping class group of Calderon-Salter.

math.GT↗

arXiv2021

Gait Characterization in Duchenne Muscular Dystrophy (DMD) Using a Single-Sensor Accelerometer: Classical Machine Learning and Deep Learning Approaches

Differences in gait patterns of children with Duchenne muscular dystrophy (DMD) and typically-developing (TD) peers are visible to the eye, but quantifications of those differences outside of the gait laboratory have been elusive. In this work, we measured vertical, mediolateral, and anteroposterior acceleration using a waist-worn iPhone accelerometer during ambulation across a typical range of velocities. Fifteen TD and fifteen DMD children from 3-16 years of age underwent eight walking/running activities, including five 25 meters walk/run speed-calibration tests at a slow walk to running speeds (SC-L1 to SC-L5), a 6-minute walk test (6MWT), a 100 meters fast-walk/jog/run (100MRW), and a free walk (FW). For clinical anchoring purposes, participants completed a Northstar Ambulatory Assessment (NSAA). We extracted temporospatial gait clinical features (CFs) and applied multiple machine learning (ML) approaches to differentiate between DMD and TD children using extracted temporospatial gait CFs and raw data. Extracted temporospatial gait CFs showed reduced step length and a greater mediolateral component of total power (TP) consistent with shorter strides and Trendelenberg-like gait commonly observed in DMD. ML approaches using temporospatial gait CFs and raw data varied in effectiveness at differentiating between DMD and TD controls at different speeds, with an accuracy of up to 100%. We demonstrate that by using ML with accelerometer data from a consumer-grade smartphone, we can capture DMD-associated gait characteristics in toddlers to teens.

eess.SP↗

arXiv2021

The Realization Problem for Dilation Surfaces

Dilation surfaces, or twisted quadratic differentials, are variants of translation surfaces. In this paper, we study the question of what elements or subgroups of the mapping class group can be realized as affine automorphisms of dilation surfaces. We show that dilation surfaces can have exotic Dehn twists in their affine automorphism groups and will establish that only certain types of mapping class group elements can arise as affine automorphisms of dilation surfaces. We also generalize a construction of Thurston that constructs a translation surface from a pair of filling multicurves to dilation surfaces. This construction will give us dilation surfaces that realize a pair of Dehn multitwists in their affine automorphism groups.

math.GT↗

arXiv2021

Slope Gap Distributions of Veech Surfaces

The slope gap distribution of a translation surface is a measure of how random the directions of the saddle connections on the surface are. It is known that Veech surfaces, a highly symmetric type of translation surface, have gap distributions that are piecewise real analytic. Beyond that, however, very little is currently known about the general behavior of the slope gap distribution, including the number of points of non-analyticity or the tail. We show that the limiting gap distribution of slopes of saddle connections on a Veech translation surface is always piecewise real-analytic with \emph{finitely} many points of non-analyticity. We do so by taking an explicit parameterization of a Poincar\'{e} section to the horocycle flow on $\text{SL}(2,\mathbb{R})/\text{SL}(X,\omega)$ associated to an arbitrary Veech surface $\text{SL}(X,\omega)$ and establishing a key finiteness result for the first return map under this flow. We use the finiteness result to show that the tail of the slope gap distribution of Veech surfaces always has quadratic decay.

math.DS↗

arXiv2020

A Full Study of the Dynamics on One-Holed Dilation Tori

An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of directions, the directional flow has an attracting periodic orbit, is minimal, or is completely periodic. We further show that for directions in this Cantor set, the directional flow is attracted to either a saddle connection or a lamination on the surface that is locally the product of a measure zero Cantor set and an interval.

math.DS↗

arXiv2020

W-measurable sensitivity of semigroup actions

This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a classification result of conservative ergodic dynamical systems that states all are either W-measurably sensitive or act by isometries with respect to some metric and have refined structure. We generalize this result to a class of semigroup actions. Furthermore, a counterexample is provided that shows W-measurable sensitivity is not preserved under factors. We also consider the restriction of W-measurably sensitive semigroup actions to sub-semigroups and show that the restriction remains W-measurably sensitive when the sub-semigroup is large enough (e.g. when the sub-semigroups are syndetic or thick).

math.DS↗

arXiv2020

Causally Correct Partial Models for Reinforcement Learning

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have considered partial models, which model only part of the observation. In this paper, we show that partial models can be causally incorrect: they are confounded by the observations they don't model, and can therefore lead to incorrect planning. To address this, we introduce a general family of partial models that are provably causally correct, yet remain fast because they do not need to fully model future observations.

cs.LG↗

arXiv2019

Statistics of Square-tiled Surfaces: Symmetry and Short Loops

Square-tiled surfaces are a class of translation surfaces that are of particular interest in geometry and dynamics because, as covers of the square torus, they share some of its simplicity and structure. In this paper, we study counting problems that result from focusing on properties of the square torus one by one. After drawing insights from experimental evidence, we consider the implications between these properties and their frequency in each stratum of translation surfaces.

math.GT↗