Search

We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the $H^1$-norm of the error and the dual norm of the residual. We then derive reliable and efficient estimators for a broad class of stabilized first-order finite element methods. We also show that in the case of affine-preserving stabilizations, the estimator can be further simplified to the standard residual estimator. Numerical experiments illustrate the computational gains in efficiency and accuracy from the estimators in the context of adaptive methods.

This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $\mathbb{Z}$ that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) $n\geq 2$. Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.

TOI-2015 is a known exoplanetary system around an M4 dwarf star, consisting of a transiting sub-Neptune planet in a 3.35-day orbital period, TOI-2015b, accompanied by a non-transiting companion, TOI-2015c. High-precision RV measurements were taken with the MAROON-X spectrograph, and high-precision photometric data were collected several networks. We re-characterize the target star by combining optical spectr, Bayesian Model Averaging (BMA) and Spectral Energy Distribution (SED) analysis. The TOI-2015 host star is a K=10.3mag M4-type dwarf with a sub-solar metallicity of [Fe/H]=-0.31+/-0.16, and a Teff=3200K. Our photodynamical analysis of the system strongly favors the 5:3 mean motion resonance and in this scenario the planet b has an orbital period of 3.34days, a mass of Mp=9.02+/-0.34Me, a radius of Rp=3.309+/-0.012Re, resulting in a density of rhop= 1.40+/-0.06g/cm3, indicative of a Neptune like composition. Its transits exhibit large (>1hr) timing variations indicative of an outer perturber in the system. We performed a global analysis of the high-resolution RV measurements, the photometric data, and the TTVs, and inferred that TOI-2015 hosts a second planet, TOI-2015c, in a non-transiting configuration. TOI-2015c has an orbital period of Pc=5.583days and a mass of Mp=8.91+0.38-0.40Me. The dynamical configuration of TOI-2015b and TOI-2015c can be used to constrain the system's planetary formation and migration history. Based on the mass-radius composition models, TOI-2015b is a water-rich or rocky planet with a hydrogen-helium envelope. Moreover, TOI-2015b has a high transmission spectroscopic metric (TSM=149), making it a favorable target for future transmission spectroscopic observations with JWST to constrain the atmospheric composition of the planet. Such observations would also help to break the degeneracies in theoretical models of the planet's interior structure., Comment: The paper has been accepted for publication in Astronomy and Astrophysics

The allostatic load index (ALI) is a composite measure of whole-person health. Data from electronic health records (EHR) present a huge opportunity to operationalize the ALI in the learning health system, except they are prone to missingness and errors. Validation of EHR data (e.g., through chart reviews) can provide better-quality data, but realistically, only a subset of patients' data can be validated, and most protocols do not recover missing data. Using a representative sample of 1000 patients from the EHR at an extensive learning health system (100 of whom could be validated), we propose methods to design, conduct, and analyze statistically efficient and robust studies of the ALI and healthcare utilization. With semiparametric maximum likelihood estimation, we robustly incorporate all available data into statistical models. Using targeted design strategies, we examine ways to select the most informative patients for validation. Incorporating clinical expertise, we devise a novel validation protocol to promote the quality and completeness of EHR data. Validating the EHR data uncovered relatively low error rates and recovered some missing data. Through simulation studies based on preliminary data, residual sampling was identified as the most informative strategy for completing our validation study. Statistical models of partially validated data indicated higher odds of engaging in the healthcare system were associated with worse whole-person health (i.e., higher ALI), adjusting for age. Targeted validation with an enriched protocol allowed us to ensure the quality and promote the completeness of the EHR. Findings from our validation study were incorporated into analyses as we operationalize the ALI as a whole-person health measure intended to predict healthcare utilization in the academic learning health system., Comment: 16 pages, 2 tables, 6 figures, supplementary materials and code on GitHub

Robot-led physical therapy (PT) offers a promising avenue to enhance the care provided by clinical exercise specialists (ES) and physical and occupational therapists to improve patients' adherence to prescribed exercises outside of a clinic, such as at home. Collaborative efforts among roboticists, ES, physical and occupational therapists, and patients are essential for developing interactive, personalized exercise systems that meet each stakeholder's needs. We conducted a user study in which 11 ES evaluated a novel robot-led PT system for people with Parkinson's disease (PD), introduced in [1], focusing on the system's perceived efficacy and acceptance. Utilizing a mixed-methods approach, including technology acceptance questionnaires, task load questionnaires, and semi-structured interviews, we gathered comprehensive insights into ES perspectives and experiences after interacting with the system. Findings reveal a broadly positive reception, which highlights the system's capacity to augment traditional PT for PD, enhance patient engagement, and ensure consistent exercise support. We also identified two key areas for improvement: incorporating more human-like feedback systems and increasing the robot's ease of use. This research emphasizes the value of incorporating robotic aids into PT for PD, offering insights that can guide the development of more effective and user-friendly rehabilitation technologies., Comment: 11 pages, 4 figures

We investigate the application of quantum cognition machine learning (QCML), a novel paradigm for both supervised and unsupervised learning tasks rooted in the mathematical formalism of quantum theory, to distance metric learning in corporate bond markets. Compared to equities, corporate bonds are relatively illiquid and both trade and quote data in these securities are relatively sparse. Thus, a measure of distance/similarity among corporate bonds is particularly useful for a variety of practical applications in the trading of illiquid bonds, including the identification of similar tradable alternatives, pricing securities with relatively few recent quotes or trades, and explaining the predictions and performance of ML models based on their training data. Previous research has explored supervised similarity learning based on classical tree-based models in this context; here, we explore the application of the QCML paradigm for supervised distance metric learning in the same context, showing that it outperforms classical tree-based models in high-yield (HY) markets, while giving comparable or better performance (depending on the evaluation metric) in investment grade (IG) markets.

Misclassified binary outcome or mediator variables can cause unpredictable bias in resulting parameter estimates. As more datasets that were not originally collected for research purposes are being used for studies in the social and health sciences, the need for methods that address data quality concerns is growing. In this paper, we describe two R packages, COMBO and COMMA, that implement bias-correction methods for misclassified binary outcome and mediator variables, respectively. These likelihood-based approaches do not require gold standard measures and allow for estimation of sensitivity and specificity rates for the misclassified variable(s). In addition, these R packages automatically apply crucial label switching corrections, allowing researchers to circumvent the inherent permutation invariance of the misclassification model likelihood. We demonstrate COMBO for single-outcome cases using a study of bar exam passage. We develop and evaluate a risk prediction model based on noisy indicators in a pretrial risk assessment study to demonstrate COMBO for multi-outcome cases. In addition, we use COMMA to evaluate the mediating effect of potentially misdiagnosed gestational hypertension on the maternal ethnicity-birthweight relationship., Comment: 99 pages, 7 figures

Given a metric space (X, d), we continue our study of the distance function x\mapsto d(x,-) and its relation to bi-Lipschitz embeddings of (X, d) into R^N. As application, given a compact metric-measure space (X, d,\mu), we give three sufficient conditions for the existence of such a bi-Lipschitz embedding.

This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the pullback of the affine-invariant metric. In the case of a truly separable covariance, we demonstrate a joint approximation in the multiway space outperforms a mean-field approximation in optimization efficiency and provides a superior approximation to an unstructured Inverse-Wishart posterior under the average Mahalanobis distance of the data while maintaining a multiway interpretation. We moreover establish efficient expressions for the Euclidean and Riemannian gradients in both cases of the joint and mean-field approximation. We end with an analysis of commodity trade data., Comment: 40 pages, 4 figures, 1 table

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the vector normal, also known as separable covariance matrices. Separable covariance matrices have been studied extensively in the context of multiway data, but little work has been done within the scope of MCMC beyond Gibbs sampling. This paper aims to fill this gap by considering the pullback geometry induced from the Kronecker structure of the parameter space to develop a geodesic Hamiltonian Monte Carlo sampler., Comment: 67 pages, 24 figures, 1 table

Handling incomplete data in real-world applications is a critical challenge due to two key limitations of existing methods: (i) they are primarily designed for numeric data and struggle with categorical or heterogeneous/mixed datasets; (ii) they assume that data is missing completely at random, which is often not the case in practice -- in reality, data is missing in patterns, leading to biased results if these patterns are not accounted for. To address these two limitations, this paper presents a novel approach to handling missing values using the Probability Mass Similarity Kernel (PMK), a data-dependent kernel, which does not make any assumptions about data types and missing mechanisms. It eliminates the need for prior knowledge or extensive pre-processing steps and instead leverages the distribution of observed data. Our method unifies the representation of diverse data types by capturing more meaningful pairwise similarities and enhancing downstream performance. We evaluated our approach across over 10 datasets with numerical-only, categorical-only, and mixed features under different missing mechanisms and rates. Across both classification and clustering tasks, our approach consistently outperformed existing techniques, demonstrating its robustness and effectiveness in managing incomplete heterogeneous data.

As chatbots become increasingly integrated into everyday tasks, designing systems that accommodate diverse user populations is crucial for fostering trust, engagement, and inclusivity. This study investigates the ability of contemporary Large Language Models (LLMs) to generate African American Vernacular English (AAVE) and evaluates the impact of AAVE usage on user experiences in chatbot applications. We analyze the performance of three LLM families (Llama, GPT, and Claude) in producing AAVE-like utterances at varying dialect intensities and assess user preferences across multiple domains, including healthcare and education. Despite LLMs' proficiency in generating AAVE-like language, findings indicate that AAVE-speaking users prefer Standard American English (SAE) chatbots, with higher levels of AAVE correlating with lower ratings for a variety of characteristics, including chatbot trustworthiness and role appropriateness. These results highlight the complexities of creating inclusive AI systems and underscore the need for further exploration of diversity to enhance human-computer interactions.

To review the lessons learnt from recent deep geothermal case studies and plan strategically the research, development, regulation, and communication work required for the implementation of an Enhanced Geothermal System (EGS) at Cornell University, a group of engineers and scholars convened a two-day workshop on the Ithaca campus, on October 23-24, 2024. The event was funded by Cornell Atkinson Center for Sustainability. This report is a summary of the content of the presentations and discussions that took place during the workshop. The first section focuses on philosophical, sociological, economic, and regulatory questions posed by EGS deployment as a means to mitigate climate change. The second section tackles the scientific and technological research areas associated with EGS. The third section aims to assess the feasibility of developing EGS for heat direct use at Cornell University, based on results and information available to date. The report concludes with a summary of the most salient technological and scientific breakthroughs, and a plan for future technological and academic engagement in EGS projects at Cornell.

Human-AI cooperative classification (HAI-CC) approaches aim to develop hybrid intelligent systems that enhance decision-making in various high-stakes real-world scenarios by leveraging both human expertise and AI capabilities. Current HAI-CC methods primarily focus on learning-to-defer (L2D), where decisions are deferred to human experts, and learning-to-complement (L2C), where AI and human experts make predictions cooperatively. However, a notable research gap remains in effectively exploring both L2D and L2C under diverse expert knowledge to improve decision-making, particularly when constrained by the cooperation cost required to achieve a target probability for AI-only selection (i.e., coverage). In this paper, we address this research gap by proposing the Coverage-constrained Learning to Defer and Complement with Specific Experts (CL2DC) method. CL2DC makes final decisions through either AI prediction alone or by deferring to or complementing a specific expert, depending on the input data. Furthermore, we propose a coverage-constrained optimisation to control the cooperation cost, ensuring it approximates a target probability for AI-only selection. This approach enables an effective assessment of system performance within a specified budget. Also, CL2DC is designed to address scenarios where training sets contain multiple noisy-label annotations without any clean-label references. Comprehensive evaluations on both synthetic and real-world datasets demonstrate that CL2DC achieves superior performance compared to state-of-the-art HAI-CC methods.

Deep learning has achieved remarkable success in image classification and segmentation tasks. However, fairness concerns persist, as models often exhibit biases that disproportionately affect demographic groups defined by sensitive attributes such as race, gender, or age. Existing bias-mitigation techniques, including Subgroup Re-balancing, Adversarial Training, and Domain Generalization, aim to balance accuracy across demographic groups, but often fail to simultaneously improve overall accuracy, group-specific accuracy, and fairness due to conflicts among these interdependent objectives. We propose the Fair Distillation (FairDi) method, a novel fairness approach that decomposes these objectives by leveraging biased ``teacher'' models, each optimized for a specific demographic group. These teacher models then guide the training of a unified ``student'' model, which distills their knowledge to maximize overall and group-specific accuracies, while minimizing inter-group disparities. Experiments on medical imaging datasets show that FairDi achieves significant gains in both overall and group-specific accuracy, along with improved fairness, compared to existing methods. FairDi is adaptable to various medical tasks, such as classification and segmentation, and provides an effective solution for equitable model performance.

We propose to measure the beam normal single spin asymmetry in elastic scattering of transversely polarized electron from target nuclei with 12 $\leq Z \leq$ 90 at Q$^2$ = 0.0092 GeV$^2$ to study its nuclear dependence. While the theoretical calculations based on two-photon exchange suggest no nuclear dependence at this kinematics, the results of 208Pb from Jefferson Lab show a striking disagreement from both theoretical predictions and light nuclei measurements. The proposed measurements will provide new data for intermediate to heavy nuclei where no data exists for $Z \geq$ 20 in the kinematics of previous high-energy experiments. It will allow one to investigate the missing contributions that are not accounted in the current theoretical models., Comment: Submitted to Jefferson Lab PAC52

AstroSage-Llama-3.1-8B is a domain-specialized natural-language AI assistant tailored for research in astronomy, astrophysics, and cosmology. Trained on the complete collection of astronomy-related arXiv papers from 2007-2024 along with millions of synthetically-generated question-answer pairs and other astronomical literature, AstroSage-Llama-3.1-8B demonstrates remarkable proficiency on a wide range of questions. AstroSage-Llama-3.1-8B scores 80.9% on the AstroMLab-1 benchmark, greatly outperforming all models -- proprietary and open-weight -- in the 8-billion parameter class, and performing on par with GPT-4o. This achievement demonstrates the potential of domain specialization in AI, suggesting that focused training can yield capabilities exceeding those of much larger, general-purpose models. AstroSage-Llama-3.1-8B is freely available, enabling widespread access to advanced AI capabilities for astronomical education and research.

We carry out a quantitative Bayesian analysis of the evolution of credences in low energy supersymmetry (SUSY) in light of the most relevant empirical data. The analysis is based on the assumption that observers apply principles of optimism or pessimism about theory building in a coherent way. On this basis, we provide a rough assessment of the current range of plausible credences in low energy SUSY and determine in which way LHC data changes those credences. For observers who had been optimistic about low energy SUSY before the LHC, the method reports that LHC data does lead to decreased credences in accordance with intuition. The decrease is moderate, however, and keeps posteriors at very substantial levels. The analysis further establishes that a very high but not yet indefensible degree of pessimism regarding the success chances of theory building still results in quite significant credences in GUT and low energy SUSY for the time right before the start of the LHC. The pessimist's credence in low energy SUSY remains nearly unchanged once LHC data is taken into account., Comment: 30 pages

We extend prior work comparing linear multilevel models (MLM) and fixed effect (FE) models to the generalized linear model (GLM) setting, where the coefficient on a treatment variable is of primary interest. This leads to three key insights. (i) First, as in the linear setting, MLM can be thought of as a regularized form of FE. This explains why MLM can show large biases in its treatment coefficient estimates when group-level confounding is present. However, unlike the linear setting, there is not an exact equivalence between MLM and regularized FE coefficient estimates in GLMs. (ii) Second, we study a generalization of "bias-corrected MLM" (bcMLM) to the GLM setting. Neither FE nor bcMLM entirely solves MLM's bias problem in GLMs, but bcMLM tends to show less bias than does FE. (iii) Third, and finally, just like in the linear setting, MLM's default standard errors can misspecify the true intragroup dependence structure in the GLM setting, which can lead to downwardly biased standard errors. A cluster bootstrap is a more agnostic alternative. Ultimately, for non-linear GLMs, we recommend bcMLM for estimating the treatment coefficient, and a cluster bootstrap for standard errors and confidence intervals. If a bootstrap is not computationally feasible, then we recommend FE with cluster-robust standard errors.

Among many-body instabilities in correlated quantum systems, electronic nematicity, defined by the spontaneous breaking of rotational symmetry, has emerged as a critical phenomenon, particularly within high-temperature superconductors. Recently, this behavior has been identified in CsTi$_3$Bi$_5$, a member of the AV$_3$Sb$_5$ (A = K, Rb, Cs) kagome family, recognized for its intricate and unconventional quantum phases. Despite accumulating indirect evidence, the fundamental mechanisms driving nematicity in CsTi$_3$Bi$_5$ remain inadequately understood, sparking ongoing debates. In this study, we employ polarization-dependent angle-resolved photoemission spectroscopy to reveal definitive signatures of an orbital-selective nematic deformation in the electronic structure of CsTi$_3$Bi$_5$. This direct experimental evidence underscores the pivotal role of orbital degrees of freedom in symmetry breaking, providing new insights into the complex electronic environment. By applying the functional renormalization group technique to a fully interacting ab initio model, we demonstrate the emergence of a finite angular momentum ($d$-wave) Pomeranchuk instability in CsTi$_3$Bi$_5$, driven by the concomitant action of electronic correlations within specific orbital channels and chemical potential detuning away from Van Hove singularities. By elucidating the connection between orbital correlations and symmetry-breaking instabilities, this work lays a crucial foundation for future investigations into the broader role of orbital selectivity in quantum materials, with far-reaching implications for the design and manipulation of novel electronic phases.

We propose a deep mixture of multimodal hierarchical variational auto-encoders called MMHVAE that synthesizes missing images from observed images in different modalities. MMHVAE's design focuses on tackling four challenges: (i) creating a complex latent representation of multimodal data to generate high-resolution images; (ii) encouraging the variational distributions to estimate the missing information needed for cross-modal image synthesis; (iii) learning to fuse multimodal information in the context of missing data; (iv) leveraging dataset-level information to handle incomplete data sets at training time. Extensive experiments are performed on the challenging problem of pre-operative brain multi-parametric magnetic resonance and intra-operative ultrasound imaging., Comment: Manuscript under review

We investigate the electronic structure of high-density layers of Sb dopants in a silicon host, so-called Si:Sb $\delta$-layers. We show that, in spite of the known challenges in producing highly confined Sb $\delta$-layers, sufficient confinement is created such that the lowest conduction band states ($\Gamma$ states, studied in depth in other silicon $\delta$-layers), become occupied and can be observed using angle-resolved photoemission spectroscopy. The electronic structure of the Si:Sb $\delta$-layers closely resembles that of Si:P systems, where the observed conduction band is near-parabolic and slightly anisotropic in the $\mathbf{k}_\parallel$ plane. The observed $\Gamma$ state extends ~ 1 nm in the out-of-plane direction, which is slightly wider than the 1/3 monolayer thick dopant distribution. This is caused by a small segregation of the dopant layer, which is nevertheless minimal when comparing with earlier published attempts. Our results serve to demonstrate that Sb is still a feasible dopant alternative for use in the semiconductor $\delta$-layer platform, providing similar electronic functionality to Si:P systems. Additionally, it has the advantages of being less expensive, more controllable, safer to handle, and more compatible with industrial patterning techniques. Si:Sb is therefore a viable platform for emerging quantum device applications.

Despite strong advisory against it, large generative models (LMs) are already being used for decision making tasks that were previously done by predictive models or humans. We put popular LMs to the test in a high-stakes decision making task: recidivism prediction. Studying three closed-access and open-source LMs, we analyze the LMs not exclusively in terms of accuracy, but also in terms of agreement with (imperfect, noisy, and sometimes biased) human predictions or existing predictive models. We conduct experiments that assess how providing different types of information, including distractor information such as photos, can influence LM decisions. We also stress test techniques designed to either increase accuracy or mitigate bias in LMs, and find that some to have unintended consequences on LM decisions. Our results provide additional quantitative evidence to the wisdom that current LMs are not the right tools for these types of tasks.

In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication units, thus providing theoretical guidance for designing reduced- and mixed-precision FE algorithms on CPUs and GPUs. Guided by this analysis, we introduce hardware-accelerated mixed-precision implementation strategies which are provably robust to low-precision computations. Indeed, these algorithms are accurate to the lower-precision unit roundoff with an error constant that is independent from: the conditioning of FE basis function evaluations, the ill-posedness of the cell, the polynomial degree, and the number of quadrature nodes. Consequently, we present the first AMX-accelerated FE kernel implementations on Intel Sapphire Rapids CPUs. Numerical experiments demonstrate that the proposed mixed- (single/half-) precision algorithms are up to 60 times faster than their double precision equivalent while being orders of magnitude more accurate than their fully half-precision counterparts., Comment: Keywords: Mixed precision, finite element method, finite element kernel and assembly, rounding error analysis, hardware acceleration, matrix units, Intel AMX

How is identity constructed and performed in the digital via face-based artificial intelligence technologies? While questions of identity on the textual Internet have been thoroughly explored, the Internet has progressed to a multimedia form that not only centers the visual, but specifically the face. At the same time, a wealth of scholarship has and continues to center the topics of surveillance and control through facial recognition technologies (FRTs), which have extended the logics of the racist pseudoscience of physiognomy. Much less work has been devoted to understanding how such face-based artificial intelligence technologies have influenced the formation and performance of identity. This literature review considers how such technologies interact with faciality, which entails the construction of what a face may represent or signify, along axes of identity such as race, gender, and sexuality. In grappling with recent advances in AI such as image generation and deepfakes, I propose that we are now in an era of "post-facial" technologies that build off our existing culture of facility while eschewing the analog face, complicating our relationship with identity vis-a-vis the face. Drawing from previous frameworks of identity play in the digital, as well as trans practices that have historically played with or transgressed the boundaries of identity classification, we can develop concepts adequate for analyzing digital faciality and identity given the current landscape of post-facial artificial intelligence technologies that allow users to interface with the digital in an entirely novel manner. To ground this framework of transgression, I conclude by proposing an interview study with VTubers -- online streamers who perform using motion-captured avatars instead of their real-life faces -- to gain qualitative insight on how these sociotechnical experiences.

We present a novel approach to calibrating linguistic expressions of certainty, e.g., "Maybe" and "Likely". Unlike prior work that assigns a single score to each certainty phrase, we model uncertainty as distributions over the simplex to capture their semantics more accurately. To accommodate this new representation of certainty, we generalize existing measures of miscalibration and introduce a novel post-hoc calibration method. Leveraging these tools, we analyze the calibration of both humans (e.g., radiologists) and computational models (e.g., language models) and provide interpretable suggestions to improve their calibration.