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1. Bulk reconstruction of metrics with a compact space asymptotically

   https://doi.org/10.1007/JHEP08(2020)108  

   Hernández-Cuenca, Sergio; Horowitz, Gary T. (August 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is the case for any asymptotically locally AdS n × $$ \mathbbm{S} $$ S k spacetime. Almost all previous work on metric reconstruction ignores these dimensions and would thus at most apply to dimensionally-reduced metrics. In this work, we generalize the approach to bulk reconstruction using light-cone cuts and propose a prescription to obtain the full higher-dimensional metric of generic spacetimes up to an overall conformal factor. We first extend the definition of light-cone cuts to include information about the asymptotic compact dimensions, and show that the full conformal metric can be recovered from these extended cuts. We then give a prescription for obtaining these extended cuts from the dual field theory. The location of the usual cuts can still be obtained from bulk-point singularities of correlators, and the new information in the extended cut can be extracted by using appropriate combinations of operators dual to Kaluza-Klein modes of the higher-dimensional bulk fields. 

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2. Some aspects of Ricci flow on the 4-sphere

   https://doi.org/10.53733/152  

   Chang, Sun-Yung Alice; Chen, Eric (September 2021, New Zealand Journal of Mathematics)

   In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with L^2 norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the L^p norm for certain p>2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere. 

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3. Stability and statistical inversion of travel time tomography

   https://doi.org/10.1088/1361-6420/ad4911  

   Tarikere, Ashwin; Zhou, Hanming (May 2024, Inverse Problems)

   Abstract In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under somea prioriconditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements. 

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4. Discrete conformal equivalence of polyhedral surfaces

   https://doi.org/10.1145/3450626.3459763  

   Gillespie, Mark; Springborn, Boris; Crane, Keenan (July 2021, ACM Transactions on Graphics)

   This paper describes a numerical method for surface parameterization, yielding maps that are locally injective and discretely conformal in an exact sense. Unlike previous methods for discrete conformal parameterization, the method is guaranteed to work for any manifold triangle mesh, with no restrictions on triangulatiothat each task can be formulated as a convex problem where the triangulation is allowed to change---we complete the picture by introducing the machinery needed to actually construct a discrete conformal map. In particular, we introduce a new scheme for tracking correspondence between triangulations based onnormal coordinates, and a new interpolation procedure based on layout in thelight cone.Stress tests involving difficult cone configurations and near-degenerate triangulations indicate that the method is extremely robust in practice, and provides high-quality interpolation even on meshes with poor elements. 

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5. Assessing Classification Models of Pharmaceuticals With Conformal Prediction

   https://doi.org/10.1002/cem.70017  

   Booksh, Karl S.; Celani, Caelin P.; Ralbovsky, Nicole M.; Smith, Joseph P. (March 2025, Journal of Chemometrics)

   ABSTRACT Conformal predictions transform a measurable, heuristic notion of uncertainty into statistically valid confidence intervals such that, for a future sample, the true class prediction will be included in the conformal prediction set at a predetermined confidence. In a Bayesian perspective, common estimates of uncertainty in multivariate classification, namelyp‐values, only provide the probability that the data fits the presumed class model,P(D|M). Conformal predictions, on the other hand, address the more meaningful probability that a model fits the data,P(M|D). Herein, two methods to perform inductive conformal predictions are investigated—the traditional Split Conformal Prediction that uses an external calibration set and a novel Bagged Conformal Prediction, closely related to Cross Conformal Predictions, that utilizes bagging to calibrate the heuristic notions of uncertainty. Methods for preprocessing the conformal prediction scores to improve performance are discussed and investigated. These conformal prediction strategies are applied to identifying four non‐steroidal anti‐inflammatory drugs (NSAIDs) from hyperspectral Raman imaging data. In addition to assigning meaningful confidence intervals on the model results, we herein demonstrate how conformal predictions can add additional diagnostics for model quality and method stability. 

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