Mathematical formulas for elliptic curve integrals solve anomaly equations.
problem Mathematical formulation of contact term singularities on elliptic curves.
method Residue formulas and holomorphic anomaly equations.
result Regularized integrals on elliptic curves satisfy holomorphic anomaly equations.
Anomaly flow solves Fu-Yau equation on toric fibrations.
problem Existence and uniqueness of solutions for Fu-Yau equation.
method Anomaly flow approach, convergence on toric fibrations.
result First case where Anomaly flow exists for all time.
New geometric flow preserves balanced metrics and solves anomaly equations.
problem Balanced metrics and anomaly equations in Strominger systems.
method Introduced a geometric flow on (2,2)-forms preserving balanced metrics, using Nash-Moser implicit function theorem. result Existence of solutions for a short time established.
Study on new flow equation on Riemann surfaces, with existence and singularity results.
problem Understanding the Anomaly flow on Riemann surfaces.
method Reduction of the Anomaly flow, criterion for long-time existence, singularity formation analysis.
result Criterion for long-time existence and singularity formation ranges for initial data.
Paper tackles anomaly detection and RCA in dynamical systems using ICODE Networks.
problem Anomalies in dynamical systems impact performance and reliability.
method Proposes ICODE Networks for anomaly detection, RCA, and type classification.
result Demonstrates the ability to accurately detect anomalies, classify types, and pinpoint origins.
The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.
We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of …
The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…
Cohomotopy theory predicts M-theory anomaly cancellation on 8-manifolds.
problem Anomaly cancellation in M-theory on 8-manifolds.
method Using J-twisted Cohomotopy theory, we prove anomaly cancellation conditions.
result Cohomotopy theory implies specific anomaly cancellation conditions in M-theory.
Anomaly flow studied on flat and non-flat nilmanifolds.
problem Analyzing the Anomaly flow on nilmanifolds.
method Examined with respect to Hermitian connections, focusing on flat and non-flat cases.
result General solutions and qualitative behavior of the Anomaly flow on nilmanifolds.
Study Hull-Strominger system and Anomaly flow on specific solvmanifolds.
problem Characterize invariant solutions to Hull-Strominger system and investigate flow of invariant metrics.
method Characterization of invariant solutions using Gauduchon connections, investigation of Anomaly flow, and proof of flow immortality under certain conditions.
result Anomaly flow reduces to a special form and always converges to a Kähler metric when slope parameter is zero.
Geometric framework for higher derivative corrections in N=2 vector multiplets.
problem Higher derivative corrections in N=2 vector multiplets.
method Enlarged scalar manifold with complex deformation parameter, Hesse potential.
result Holomorphic anomaly equation from integrability condition.
The main new result here is the cancellation of global anomalies in the Type I superstring, with and without D-branes. Our argument here depends on a precise interpretation of the 2-form abelian gauge field using KO-theory; then the anomaly cancellation follows from a geometric form of the full Atiyah-Singer index theo…
Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.
problem Integrating quantum flag manifold σ-models with fermions.
method Gauging bosonic Thirring/Gross-Neveu-type systems, adding fermions to cancel anomalies, and checking Ricci flow equations.
result Trigonometrically deformed geometries of flag manifold σ-models satisfy generalized Ricci flow equations.
Higher-order geometry modifies Newtonian dynamics and predicts anomalies in spacecraft motion.
problem Observing and understanding higher-order effects in general relativity.
method Generalizing the Einstein-Hilbert action to include higher-order infinitesimals and studying field equations and cosmologies.
result Higher-order corrections predict anomalies like the Pioneer and flyby effects.
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
Holomorphic supergravity theory simplifies anomaly cancellation in heterotic moduli.
problem Anomaly cancellation in heterotic moduli space.
method Formulated a ten-dimensional version of Kodaira-Spencer gravity, quantized fluctuations, and showed partition function simplification.
result Holomorphic supergravity theory simplifies anomaly cancellation and relates to type I Kodaira-Spencer theory.
Study the connection between supersymmetry and geometric flows in supergravity.
problem Relate supersymmetry to geometric flows in supergravity.
method Derive flow equations from a functional of squares of supersymmetry operators, match with mathematics anomaly flow, generalize to higher dimensions.
result Flow equations match known mathematics anomaly flow and simplify to scalar equations on torus fibrations.
We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimensions seven and eight. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to i…
We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation t…
Massive fermions help understand index theorems without chiral symmetry.
problem Understanding index theorems in massive fermion systems.
method Reformulate chiral anomaly and index theorems with massive Dirac operators.
result Nontrivial mathematical relations between massless and massive fermions.
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special Kähler geometry and the ring of almost-holomorphic modular forms defined on modular curves.
A new method detects and ranks anomalies in cloud computing platforms using multi-view learning.
problem High false-alarm rate in traditional anomaly detection methods.
method Online model using machine learning theory, ELM for efficiency, and multi-view feature fusion.
result Improved accuracy and efficiency in anomaly detection and ranking.
We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with re…
Improves anomaly detection with contaminated unlabeled data.
problem Weakness in existing semi-supervised anomaly detection methods when unlabeled data contain anomalies.
method Integrates positive-unlabeled learning with deep anomaly detection models.
result Achieves better detection performance on various datasets.
End-to-end anomaly detection framework using labeled anomalies.
problem Limited deep learning for anomaly detection and inefficiency of existing methods.
method Deviation learning neural network with labeled anomalies and prior probability.
result Significantly better anomaly scoring than state-of-the-art methods.
PReNet detects seen and unseen anomalies using pairwise relations.
problem Detecting unseen anomalies in semi-supervised learning.
method Pairwise Relation prediction Network (PReNet) learns anomaly and normal patterns.
result PReNet significantly outperforms nine competing methods in anomaly detection.
Review of sigma models on flag manifolds, linking to spin chains and integrable theories.
problem Understanding phase transitions and anomalies in spin chains and sigma models.
method Analyzing topological angles, discrete 't Hooft anomalies, and integrable models.
result Gapless phases in certain spin chains can be explained by discrete anomalies in continuum theories.
CANARI detects near-anomalies to predict future anomalies proactively.
problem Uncertainty in anomaly detection near distribution boundaries.
method Christoffel-based ANomaly Anticipation for eaRly dIscovery (CANARI) method.
result CANARI outperforms baseline methods in detecting near-anomalies and predicting future anomalies.
Proposes a method for anomaly detection with inexact labels.
problem Handling anomaly detection with inexact labels.
method Trains an anomaly score function using a neural network-based unsupervised method, maximizing the inexact AUC.
result Improves anomaly detection performance with inexact labels and outperforms existing methods.
Survey of recent geometric flows in complex geometry.
problem Preserving conformally balanced property of Hermitian metrics.
method Anomaly flow, a flow of (2,2)-forms on a 3-fold. result Anomaly flow is a higher order extension of the Ricci flow.
Detects anomalies relative to typical observations.
problem Common anomaly detection methods fail for frequent anomalies.
method Relative anomaly detection, considering location relative to typical observations.
result Effective for frequent anomalies, computationally feasible, real-time detection.
Deep RL detects anomalies from few labeled examples and large unlabeled data.
problem Anomaly detection with limited labeled data and large unlabeled data.
method Deep reinforcement learning to optimize detection of labeled and unlabeled anomalies.
result Significantly outperforms state-of-the-art methods on 48 real-world datasets.
A new method assigns anomaly scores to features for better interpretation.
problem Interpreting anomaly scores from feature attributions.
method Proposes a characteristic function to attribute anomaly scores using Shapley value.
result Demonstrates the potential utility of the proposed attribution methods.
Efficient method detects point and collective anomalies in data sequences.
problem Efficiently identifying anomalies in data sequences, especially collective anomalies.
method CAPA: a computationally efficient approach for detecting collective and point anomalies.
result CAPA is consistent at detecting collective anomalies and has close to linear computational cost.
Ensemble learning improves anomaly detection for milder symptoms.
problem Difficulty in detecting incipient anomalies due to similarity to normal conditions.
method Utilize uncertainty information from ensemble learning to identify misclassified incipient anomalies.
result Ensemble learning methods show improved performance on incipient anomaly detection.
New anomaly estimator reduces bias in MLE for normally distributed data.
problem Bias in Maximum Likelihood Estimation of structured anomalies.
method Derive a new anomaly estimator using a mixture model.
result New estimator is asymptotically unbiased regardless of anomaly family size.
The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface Z over CP1. We show that for the ∂ˉ-operator along the fiber the logarithm of the regularized determinant −1/2logdet′(∂ˉ∗∂ˉ) satisfies the anomaly equation of the …
TPA-AD detects axle-box bearing anomalies using pseudo anomalies near normal boundaries.
problem Detecting axle-box bearing anomalies with only normal training data.
method Two-stage approach: pseudo anomalies, contrastive learning, KNN.
result Improves anomaly detection separability and sensitivity to degradation.
Paper proposes RAN for better anomaly detection in time series data.
problem Anomaly detection algorithms often fail to accurately detect anomalies due to incomplete reconstruction of anomaly data.
method RAN uses adversarial learning and latent vector-constrained Autoencoder to ensure consistent reconstruction of anomaly data.
result RAN outperforms other algorithms in detecting meaningful anomalies with higher AUC-ROC scores.
We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and …
A new method combines generative and feature-based approaches for unsupervised anomaly detection.
problem Identifying subtle anomalies in test samples compared to a normative distribution.
method A generative cold-diffusion pipeline trained to restore synthetically-corrupted images, combined with a novel synthetic anomaly generation procedure and ensembling restorations.
result Surpasses prior state-of-the-art for unsupervised anomaly detection in three Brain MRI datasets.
Study identifies high-density anomalies in normal data regions.
problem Detecting anomalies in normal data regions.
method Introduces non-parametric algorithmic frameworks for unsupervised detection.
result IPP framework yields the best detection results.
Develops efficient method to detect multiple collective anomalies in multivariate data streams.
problem Detecting anomalies in multivariate data streams, especially collective anomalies.
method MVCAPA: A method that efficiently detects multiple collective anomalies without approximations.
result MVCAPA consistently estimates the number and location of collective anomalies.
Algorithm detects anomalies in large, complex data sets.
problem Detecting shifts in data distribution, especially in high-dimensional, non-uniform data.
method Adversarial autoencoder for gaussianization of data.
result Effective detection of soft anomalies in various domains.
Improves relevancy of black-box anomaly detectors with user feedback.
problem Users often ignore many detected anomalies, requiring a method to identify and prioritize relevant ones.
method Uses user feedback to adjust anomaly selection process based on identified anomaly types.
result Significant improvements in precision and recall over various anomaly detectors.
Paper studies dual Anomaly flow under T-duality.
problem Understanding dual Anomaly flow under T-duality.
method Introduced a family of monotone functionals to estimate the dilaton function.
result Detailed examples and reductions of the dual Anomaly flow.
Paper introduces an unsupervised tensor-based anomaly detection method for spatiotemporal data.
problem Challenges in detecting anomalies in spatiotemporal data, especially in urban traffic monitoring and medical imaging.
method Formulates anomaly detection as a regularized robust low-rank + sparse tensor decomposition, incorporating spatiotemporal smoothness and local dependencies.
result Demonstrates improved anomaly detection performance on both synthetic and real data.