Continuity of earthquake flow map transfers Teichmüller dynamics results.
problem Transfer results from Teichmüller dynamics to earthquake flow.
method Analyze continuity of earthquake flow map and its inverse.
result Transfer results from Teichmüller dynamics to earthquake flow.
Extends earthquake and horocycle flows to new measures.
problem Ergodic theory of earthquake flow on measured laminations.
method Generalizes shear coordinates to arbitrary measured laminations.
result Classifies ergodic measures for P action on bundle of quadratic differentials.
Financial losses follow earthquake-like patterns, study finds.
problem Analyzing the timing between financial market losses.
method Fitting empirical interevent times with a Hawkes process.
result Financial market losses exhibit long-term memory similar to earthquakes.
This paper adapts Thurston's earthquake metric to Riemann surfaces with marked points.
problem Defining a norm and metric on Teichmüller spaces for surfaces of arbitrary genus.
method Adapting Thurston's earthquake norm to Riemann surfaces with marked points and using complex Legendre transforms.
result Establishes a complete analogue of Thurston's earthquake norm in the conformal setting.
The paper generalizes Thurston's earthquake map to cluster algebras of finite type.
problem Tackling Thurston's earthquake map in the context of cluster algebras of finite type.
method Introducing a cluster algebraic generalization of Thurston's earthquake map, defined by gluing exponential maps.
result Proves an analogue of the earthquake theorem for cluster algebras of finite type, showing the cluster earthquake map is a homeomorphism.
Study earthquake deformations on a once-punctured torus.
problem Understanding earthquake deformations on Teichmüller space.
method Two methods: linear recurrence relations and hyperbolic geometry.
result Algebraic and geometric interpretations of earthquake deformations.
Proof of Thurston's earthquake theorem using Anti-de Sitter geometry.
problem Proving Thurston's earthquake theorem for orientation-preserving homeomorphisms.
method Using the bi-invariant geometry of Anti-de Sitter three-space.
result Provided a proof of Thurston's earthquake theorem.
Deep neural networks predict earthquake locations with high accuracy.
problem Predicting the location of earthquakes with high precision.
method Recurrent Convolutional Neural Networks (R-CNN) model that accounts for spatio-temporal dependencies.
result Neural networks model outperforms baseline models in predicting earthquakes with ROC AUC 0.975 and PR AUC 0.0890.
Study shows house buyers in Christchurch value earthquake risk differently based on time since 2011 quake.
problem Understanding how house buyers' perception of earthquake risk changes over time.
method Used a hedonic price model to analyze house prices in Christchurch over three periods.
result Buyers value earthquake risk differently based on the time since the 2011 Christchurch earthquake.
In this paper we study the typical speed of a generic earthquake trajectory leaving compact sets in the moduli space of the once-punctured torus. Mirzakhani showed that the earthquake flow is measurably equivalent to the horocyclic flow, which has been studied extensively. Our main result shows that the earthquake flow…
Deviance Voronoi residuals improve earthquake insurance risk assessment.
problem Assessing earthquake insurance risk using spatio-temporal point process models.
method Extended Voronoi residuals and created simulation-based approach.
result Proposed formula for country-wide minimum capital test.
We prove that the bijective correspondence between the space of bounded measured laminations MLb(H) and the universal Teichmüller space T(H) given by λ↦Eλ∣S1 is a homeomorphism for the Fréchet topology on MLb(H) and the Teichmüller topology on T(H), where $E^λ…
EQShapelets detect earthquakes with high accuracy and interpretability.
problem Automated detection and cataloging of earthquakes.
method Time-series shape-based approach embedded in machine learning.
result EQShapelets detected all cataloged and 281 uncataloged events with lower false detection rate.
We give a short proof of the fact that bounded earthquakes of the unit disk induce quasisymmetric maps of the unit circle. By a similar method, we show that symmetric maps are induced by bounded earthquakes with asymptotically trivial measures.
Study of hyperbolic surface laminations and their Teichmüller spaces.
problem Understanding the Teichmüller spaces of non-compact surfaces.
method Deformations of hyperbolic surfaces, grafting formula derivation.
result Infinite-dimensional Teichmüller space of non-trivial hyperbolic surface laminations.
Study on earthquake metric on Teichmüller space, proving properties and new completions.
problem Understanding the earthquake metric on Teichmüller space.
method Proofs of properties, new completions, and interpretation of the metric.
result Coincidence of various completions for the earthquake metric.
Let $\cT$ be Teichmüller space of a closed surface of genus at least 2. For any point $c\in \cT$, we describe an action of the circle on $\cT\times \cT$, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of $\cT$. This circle action shares some of the …
A measured laminations on the universal hyperbolic solenoid § is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on theuniversal hyperbolic solenoid § is uniquely determined by a measured lamination on §; it is a leafwise earthquake with…
The earthquake flow is asymmetric and cannot be extended to an SL(2,R) action.
problem The asymmetry of Thurston's earthquake flow and its implications.
method Analysis of orbifold automorphisms and measured geodesic laminations.
result The earthquake flow does not extend to an SL(2,R) action and lacks continuous self-symmetries.
A machine learning surrogate model predicts earthquake-induced building responses.
problem Expensive FE model simulations for earthquake damage estimation.
method SVD-based earthquake characterization and machine learning model training.
result Deep neural network provides most accurate predictions of building responses.
New benchmark for earthquake forecasting models shows current neural point processes are not yet suitable.
problem Lack of a modern benchmark for evaluating neural point process models in earthquake forecasting.
method Curated and standardized earthquake catalog, evaluation protocols, and datasets.
result None of the tested NPPs outperformed the classical ETAS model.
Paper defines and studies measures related to earthquakes and best Lipschitz maps.
problem Understanding Thurston's conjecture about maps and measures on hyperbolic surfaces.
method Examining Lie algebra valued transverse measures and their relation to earthquakes.
result Defines and shows correspondence between best Lipschitz maps and earthquakes.
Mirzakhani connects earthquake and Teichmuller flows on surfaces.
problem Understanding the relationship between earthquake and Teichmuller flows.
method Geometric account of connections between flows, avoiding technical prerequisites.
result Mirzakhani's theorem relating earthquake and Teichmuller flows.
The paper proves a theorem about earthquake extensions of vector fields on circles.
problem Proving a theorem about earthquake extensions of vector fields on circles.
method Using the geometry of the dual of Minkowski three-space and Half-pipe three-geometry.
result A generalization of Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader setting.
Deep learning applied to coastal LULC classification post-earthquake.
problem Automatic land cover classification on coastal areas post-disaster.
method Manual tracing, simple image segmentation, image transformation using deep learning.
result Deep learning method showed over 69% accuracy for vegetation classification.
We prove an "Earthquake Theorem" for hyperbolic metrics with geodesic boundary on a compact surfaces S with boundary: given two hyperbolic metrics with geodesic boundary on a surface with k boundary components, there are 2k right earthquakes transforming the first in the second. An alternative formulation arises…
CRED detects microearthquakes efficiently and reliably.
problem Detecting small and weak earthquake signals in noisy data.
method Deep neural network combining convolutional and recurrent units.
result 99.95 F-score on validation data, detects microearthquakes far from training region.
The paper models earthquake frequency-magnitude distribution using asymmetric Laplace mixture models.
problem Describing the complete earthquake frequency-magnitude distribution above a completeness magnitude.
method Proposes an asymmetric Laplace mixture model (GFMD-ALMM) to estimate parameters and retrieve mc distribution.
result GFMD-ALMM can accurately model different FMD shapes in various catalogues and sequences.
Bayesian neural networks improve earthquake rupture prediction and uncertainty estimation.
problem Insufficient data for earthquake rupture studies.
method Used Bayesian neural networks to model earthquake rupture simulations.
result Improved F1-score of 0.8334 compared to plain NN, indicating better performance.
The Hilbert metric on Teichmüller space is studied for punctured surfaces.
problem Understanding the geometry of Teichmüller space.
method Parametrization of Teichmüller space and study of Hilbert metric.
result Every earthquake ray is an almost geodesic under the Hilbert metric.
Hamiltonian properties of earthquakes on surfaces with boundary lengths are proven.
problem Hamiltonian properties of earthquakes on surfaces with boundary lengths.
method Provided a Hamiltonian function extending the classical length map, proving Hamiltonian sum of infinitesimal earthquakes.
result Any sum of infinitesimal earthquakes on a surface with boundary lengths is Hamiltonian.
Let X0 be a complete hyperbolic surface of infinite type that has a geodesic pants decomposition with cuff lengths bounded above. The length spectrum Teichmüller space Tls(X0) consists of homotopy classes of hyperbolic metrics on X0 such that the ratios of the corresponding simple closed geodesic for the hy…
Unsupervised method detects earthquakes from raw waveforms, generalizing across datasets.
problem Lack of labeled data for earthquake detection.
method Uses deep autoencoders with cross-covariance triggering at bottleneck.
result Performance comparable to supervised methods, with strong cross-dataset generalization.
We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.
Neural model outperforms ETAS in forecasting Central Apennines earthquakes.
problem Short-term seismicity forecasting with incomplete data.
method Extended a neural network model to the magnitude domain, using it to forecast earthquakes above a target magnitude threshold.
result Neural model outperforms ETAS at lower magnitude thresholds, due to its robustness to missing data.
We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichmüller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into th…
We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result is that the space of ``globally hyperbolic'' AdS manifolds with ``parti…
The landslide flow, introduced in [5], is a smoother analog of the earthquake flow on Teichmüller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide flow is the Hamiltonian flow of a convex function. The smooth grafting map sgr taking …
Let S be a closed surface of genus at least 2, and consider two measured geodesic laminations that fill S. Right earthquakes along these laminations are diffeomorphisms of the Teichmüller space of S. We prove that the composition of these earthquakes has a fixed point in the Teichmüller space. Another way to state this…
Generative model synthesizes earthquake acceleration data.
problem Robust estimation of ground motions for engineering applications.
method Wasserstein GAN formulation for conditioning on physical variables.
result Trained model synthesizes realistic 3-component accelerograms.
Estimates Schwarzian derivative on long complex projective tubes.
problem Behaviour of Schwarzian derivative on complex projective structures.
method Analyzes Schwarzian derivative on long complex projective tubes, estimating its pairing with infinitesimal earthquakes and graftings.
result Obtains bounds for the variation of renormalized volume under complex earthquake paths and its asymptotic behavior under pinching.
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite type case of the canonicla Wick rotation-rescaling theory, previously developed b…
The dynamics of earthquake flow equidistributes geodesics on hyperbolic surfaces.
problem Equidistribution of geodesics on hyperbolic surfaces.
method Dynamics of the earthquake flow.
result The dynamics of the earthquake flow equidistributes geodesics on hyperbolic surfaces.
We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observation…
New geometric definition of Lie bracket for undirected curves.
problem Understanding the Lie bracket of undirected curves on a surface.
method Local geometric definition and proof of three results.
result The TWG bracket counts intersection and suggests disjoint representatives.
Spatially-aware model improves earthquake hazard assessment accuracy.
problem Misrepresentation of seismic effects across diverse landscapes.
method Causal Bayesian network with Gaussian Processes and normalizing flows.
result Achieves up to 35.2% AUC improvement over existing methods.
Bayesian approach models earthquake clustering with spatial mainshocks and aftershocks.
problem Estimating uncertainty in earthquake clustering models due to complex likelihood functions.
method Nonparametric Dirichlet process mixture prior for spatial mainshocks and an auxiliary latent variable routine for efficient inference.
result Efficient Bayesian forecasting of spatial earthquake occurrences with uncertainty quantification.
Shapelet transform improves time series classification for earthquake, wind, and wave events.
problem Autonomous detection of specific events from large time series datasets in civil engineering.
method Shapelet transform for local similarity in time series subsequences, combined with machine learning.
result Shapelet transform yields a new feature representation for time series signals in civil engineering.