An \emph{-admissible almost complex structure} on a -dimensional symplectic manifold is a -calibrated almost complex structure admitting a nowhere vanishing -closed -form . After giving some examples we consider the moduli space of admissible almost complex structures a…
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48 results for “Almost calibrated”
In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the…
Ancient solutions in Lagrangian flow are classified based on their blow-down.
problem Understanding ancient solutions in Lagrangian mean curvature flow.
method Structural and classification results for ancient solutions, focusing on the almost calibrated case.
result Classification of Type II blow-ups in terms of their blow-down.
In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean space. As a consequence, we show a non-existence result for eternal solutions of almost-calibrated Lagrangian mean curvature flow.
Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, …
We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents
Variational characterization of calibrated submanifolds in different contexts.
problem Characterize calibrated submanifolds using variational principles.
method Variational approach with special variations of ambient metrics and calibrations.
result Critical points of volume functional correspond to calibrated submanifolds.
Study of geometric properties of almost calibrated forms on Kähler manifolds.
problem Understanding the geometry of almost calibrated forms on compact Kähler manifolds.
method Investigates the infinite dimensional Riemannian manifold structure, CAT(0) geodesic metric space, and geodesics of the space of almost calibrated forms.
result The space of almost calibrated forms is an infinite dimensional Riemannian manifold with non-positive sectional curvature and CAT(0) geodesic metric space.
This paper improves Reifenberg's theorem for almost calibrated sets, ensuring rectifiability with volume bounds.
problem Improving the rectifiability of sets that are close to subspaces under certain calibrations.
method Using ε-calibrations and positivity conditions, the paper shows that almost calibrated sets are rectifiable with volume bounds.
result Almost calibrated sets are rectifiable with uniform volume bounds.
We prove that tangent cones to 2-dimensional calibrated cycles are unique. Using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle towards the limiting density. With the same techniques, we can also prove such a rate for J-holomorphic maps between almost complex man…
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
Ancient solutions and translators identified for Lagrangian flow.
problem Characterizing ancient solutions and translators of Lagrangian mean curvature flow.
method Analyzing almost calibrated, exact, ancient solutions with specific geometric properties.
result All ancient solutions with entropy less than 3 are special Lagrangian, planes, or translators in \(\mathbb{C}^2\).
New tan-concavity property for Lagrangian phase operators helps in studying dHYM metrics.
problem Lack of concavity in Lagrangian phase operator for dHYM metrics.
method Introduce tangent Lagrangian phase flow (TLPF) on almost calibrated (1,1)-forms.
result TLPF exists for all positive time and converges to dHYM metrics under certain conditions.
Boosting trees can test necessary conditions for regression model calibration.
problem Testing calibration and auto-calibration in regression models.
method Using boosting trees to test calibration and auto-calibration.
result Boosting trees prove to be very powerful in testing calibration and auto-calibration in large insurance datasets.
New metric creates a surface with infinite topology.
problem Constructing a surface with infinite topology.
method Constructing a Riemannian metric and a curve, then finding an area-minimizing surface.
result The area-minimizing surface has infinite topology.
The shear constructionmath.DG
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed …
Exact distribution of split conformal prediction coverage found.
problem Determining the reliability of prediction sets in batch mode.
method Analysis of exchangeable data to find universal distribution of empirical coverage.
result Exact distribution of empirical coverage is universal and determined by nominal miscoverage level and calibration sample size.
Validation of ML-UQ calibration statistics using simulated reference values: a sensitivity analysisstat.ML
Study validates ML-UQ calibration statistics using simulated reference values.
problem Validation of ML-UQ calibration statistics is lacking due to lack of predefined reference values.
method Proposed validation workflow using simulated reference values derived from synthetic datasets.
result Some statistics, like CC and ENCE, are overly sensitive to generative distribution choice.
Focal loss improves deep neural networks' accuracy and calibration.
problem Miscalibration in deep neural networks.
method Using focal loss and temperature scaling to improve model calibration.
result Focal loss leads to state-of-the-art calibrated models without sacrificing accuracy.
The paper extends Liouville's theorem to calibrated geometries in various dimensions.
problem Extending Liouville's theorem to calibrated geometries in different dimensions.
method Analyzing Sobolev mappings and calibrations in calibrated geometries.
result Calibrations in certain dimensions have the Liouville property.
The paper connects hyperbolicity in calibrated geometry to properties of Smith immersions.
problem Hyperbolicity in calibrated manifolds and its relation to Smith immersions.
method Establishes a theorem relating hyperbolicity to the equicontinuity of Smith immersions, proving a new Schwarz lemma.
result Calibrated hyperbolicity of compact -replete manifolds is equivalent to the equicontinuity of Smith immersions.
Improved segmentation model adaptation for new domains.
problem Reduced performance of pre-trained models on new domains.
method Calculated soft-label prototypes and predicted closest to class probabilities.
result Significant performance improvements on synthetic-to-real segmentation.
We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we use the property of the associated calibration form to be parallel with respect to a metric connection which may have no…
We prove an optimal control on the time-dependent measure of a measurable set under a reparametrized Lagrangian mean curvature flow of almost calibrated submanifolds in a Calabi-Yau manifold. Moreover we give a classification of those Lagrangian translating solitons in that evolve by this reparametrized …
We enhance short-rate models to control implied volatility analytically.
problem Controlling implied volatility in short-rate models.
method Randomized Affine Diffusion (RAnD) method applied to Heath-Jarrow-Morton framework.
result Randomized short-rate models improve calibration and control implied volatility shapes.
We study the analogue of the Goldberg conjecture on non-compact solvmanifolds. In contrast to the almost-Kähler case we prove that a 7-dimensional solvmanifold cannot admit any left-invariant calibrated -structure such that the induced metric is Einstein, unless is flat.…
In this paper we mainly study the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K ähler-Einstein surface. We show the relation between the maximum of the Kähler angle and the maximum of on the limit flow.
Improved pricing of vanilla options using modified Adams method and sinh-acceleration.
problem Calibration of rough Heston model leads to incorrect implied volatility surfaces.
method Modified Adams method and sinh-acceleration for Fourier inversion.
result Corrected implied volatility surface is significantly flatter and fits data poorly.
New examples show flat singular sets can be arbitrarily complex.
problem Understanding the structure of singular sets in almost-minimizing currents.
method Construction of specific examples of area almost-minimizing currents.
result Flat singular sets can contain any closed empty interior subset of a plane.
We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee,…
This paper improves neural network predictions with early stopping using conformal calibration.
problem Lack of precise statistical guarantees for neural networks trained with early stopping.
method Conformalized early stopping that combines early stopping with conformal calibration.
result Models provide both accuracy and precise inferences without additional data splits.
New research shows calibration error is flawed when dealing with model uncertainty.
problem Current model evaluation techniques conflate model uncertainty with aleatoric uncertainty.
method Posterior predictive checks to evaluate deep learning models.
result Calibration error and variants are incorrect when model uncertainty is present.
Framework improves classifier calibration under differential privacy for domain shift.
problem Improving classifier calibration under domain shift with privacy constraints.
method Differential privacy framework for adapting recalibration algorithms.
result Novel accuracy temperature scaling algorithm outperforms existing methods on private datasets.
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we…
New findings show that not all area-minimizing surfaces are calibrated, even on complex manifolds.
problem Understanding when area-minimizing surfaces cannot be calibrated.
method Analyzing homology classes and metrics on manifolds to determine if area-minimizers are calibrated.
result Calibrated area-minimizers are non-generic, challenging the common assumption that they are typical.
Deep Radar Detectorcs.CV
Paper introduces deep learning for radar processing.
problem Lack of labeled radar data and need for expensive calibration.
method Uses deep learning on radar complex data, trains on calibration data, introduces radar augmentation.
result Superior performance on radar 4D detection task compared to classical methods.
Noise titration benchmarks time series forecasting models rigorously.
problem Evaluation of time series forecasting models is often flawed due to lack of interventionist methods.
method Interventionist benchmarking using Gaussian noise titration of dynamical systems.
result Fern model outperforms state-of-the-art models in non-stationary conditions.
Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.
problem Existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation.
method Introduce coerciveness and properness of the J-functional on almost calibrated (1,1)-forms.
result Equivalence of coerciveness and properness to the existence of solutions.
We study the out-of-sample properties of robust empirical optimization problems with smooth -divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness parameter" that controls the size of the deviations from the nominal model. Bu…
The paper proves rigidity theorems for Type II singularities in Lagrangian flows.
problem Understanding Type II singularities in Lagrangian flows with zero Maslov class.
method Rigidity theorems for blow-up limits of Type II singularities.
result Generalized previous results from 2D to arbitrary dimensions.
New method gives provable error bounds for neural nets under distribution shift.
problem Proving reliable error bounds for neural networks under distribution shift.
method Optimizing a classifier to disagree with another, using a new 'disagreement loss'.
result Valid error bounds with comparable accuracy to competitive methods.
Self-poisoning in adaptive OOD detectors is explained with a sharp threshold theory and certified calibration.
problem Self-poisoning in adaptive OOD detectors.
method Modeling bank impurity as a generalized Pólya urn, proving almost-sure convergence to a mean-field equilibrium.
result A certified admission gate removes the transition at every contamination rate, controlling false positives label-free.
DNLL loss improves deep LDA accuracy and consistency.
problem Pathological solutions in unconstrained Deep LDA.
method Introducing Discriminative Negative Log-Likelihood (DNLL) loss.
result Deep LDA trained with DNLL produces clean latent spaces and better calibrated probabilities.
This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. The stochastic recovery specification only models the first two moments of the spot recovery rate as its higher moments have almost no contribution to the loss distributio…
Extends K-energy to complexified Kähler classes for scalar curvature study.
problem Scalar curvature equation with B-field on complexified Kähler classes.
method Extended K-energy functional, convex along geodesics.
result Uniqueness of solutions in some cases.
This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. It is aimed at graduate students i…
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold is Lagrangian and almost calibrated by ReΩin a Calabi-Yau n-fold (M,Ω), and T>0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature f…
LASSO-PCA combines LASSO and PCA for automated forecast averaging.
problem Automating the selection of forecast averaging methods and tuning parameters.
method LASSO estimation combined with PCA, using information criteria for parameter selection.
result LASSO-PCA outperforms other methods in forecast error reduction.