This research tackles ocean remote sensing data enhancement using locally-adapted convolutional models.
problem Super-resolution of irregularly-sampled ocean remote sensing images.
method Optimal interpolation as low-resolution reconstruction, locally-adapted multimodal convolutional models, and dictionary-based decompositions (PCA, sparse priors, non-negativity constraints).
result Locally-adapted parametrizations with non-negativity constraints outperform optimally-interpolated reconstructions.
New model combines physics and machine learning for ocean dynamics.
problem Discovering hidden laws governing ocean dynamics.
method Develops Deep Neural Numerical Models (DNNMs) to learn hidden variables of physical laws.
result Illustrates DNNMs applied to Sea Surface Height dynamics, connecting to QG model.
Study uses ANFIS to assess wind power under climate change.
problem Tackles climate change impact on wind power potential.
method Employed ANFIS to match climate model data with reference data.
result Real wind power potential lower than projected.
Study analyzes wind data from Greek islands to predict sea conditions.
problem Predicting sea conditions for refugee influx in Greece.
method Statistical analysis, ARMA models, cross-site correlation.
result ARMA(7,5) models predict average wind speed with RMSE < 1.9 km/h.
New algorithms compute Koopman operators on RKHSs efficiently and accurately.
problem Data-driven spectral analysis of Koopman operators on RKHSs.
method General, provably convergent algorithms for RKHSs.
result Optimal algorithms with error control and spectral measures.
Study equiangular surfaces in 3D, extending plane spirals.
problem Understanding 3D surfaces with constant normal-vector angles.
method Investigates three-dimensional extensions of equiangular spirals.
result Identifies self-similar structures in sea shell geometry.
Deep learning model predicts wind-wave relationship.
problem Characterize ocean wave climate for engineering applications.
method Two-stage deep learning model: CNN for spatial features, LSTM for temporal dependencies.
result Predicts spatio-temporal relationship between wind and significant wave height.
New model uses heteroscedastic Gaussian process for alkenone SST proxy.
problem Restoring historical sea surface temperatures using proxies.
method Heteroscedastic Gaussian process regression method.
result Nonparametric approach handles variable noise patterns and outliers.
Fibre surfaces in 3-sphere can have unbounded stabilisation height.
problem Understanding the stabilisation height of fibre surfaces in 3-sphere.
method Using Hopf plumbing operations and Stallings twists.
result Families of fibre surfaces can have unbounded stabilisation height.
Estimates heights of special surfaces in warped products.
problem Estimating heights of special surfaces in warped products.
method Provided a vertical height estimate.
result Vertical height estimates for special Weingarten surfaces of elliptic type in warped products.
Study introduces a probabilistic framework for air-sea fluxes using neural networks.
problem Accurately quantifying air-sea fluxes for understanding interactions and improving weather/climate models.
method Gaussian distributions conditioned on input variables, artificial neural networks, eddy-covariance data, minimizing negative log-likelihood loss.
result Trained neural networks provide alternative mean flux estimates and quantify uncertainty.
Constructs currents and heights on K3 surfaces.
problem Understanding the geometry and arithmetic of K3 surfaces.
method Constructs canonical positive currents and heights on K3 surfaces, equivariant for automorphism group.
result Continuous family of currents and heights defined over an enlarged boundary of the ample cone.
Paper proves unbounded stabilization heights of fiber surfaces using Hopf invariant.
problem Unbounded stabilization heights of fiber surfaces.
method Alternative proof using Hopf invariant.
result Proves unbounded stabilization heights of fiber surfaces.
Combines ocean surface and interior data to study ocean dynamics.
problem Modeling local ocean currents and global climate patterns.
method Observation-driven framework using Latent-class regression.
result Improved prediction of vertical ocean temperature.
SIMPGEN improves SWOT SSH data interpretation by removing noise and preserving fine-scale features.
problem Noisy data and limited fine-scale observations in oceanic processes.
method Simulation-Informed Metric and Prior for Generative Ensemble Networks (SIMPGEN) combining real SWOT observations with simulated reference data.
result SIMPGEN effectively removes noise, preserving fine-scale features better than existing neural methods.
Study compares machine learning algorithms for predicting SST in the Great Barrier Reef.
problem Predicting sea surface temperature in the Great Barrier Reef region.
method Ridge regression, LASSO, Random Forest, and Extreme Gradient Boosting (XGBoost) algorithms were evaluated.
result XGBoost significantly outperforms other algorithms in terms of predictive accuracy and Kullback-Leibler Divergence.
Study describes singularities of height functions on specific singular surfaces.
problem Analyzing singularities of height functions on singular surfaces.
method Using geometric language and blowing-ups, investigate singularities of height functions and dual surfaces.
result Characterized singularities of height functions and dual surfaces on specific singular surfaces.
Study predicts wind energy potential in Gulf of Oman using climate models.
problem Predicting future wind energy potential in the Gulf of Oman.
method Used ERA5 and MENA simulations to project historical and future wind energy variability.
result Selected locations have suitable potential for wind power turbine construction.
The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.
problem Decomposing the height function of different types of surfaces into simpler components.
method Using Euler-Ramanujan identities and Weierstrass-Enneper representation to decompose height functions of minimal, maximal, timelike minimal, and Born-Infeld surfaces.
result The height function of various surfaces can be expressed as a finite sum of scaled and translated versions of itself.
Forecast dam inflow using sea surface feature weights.
problem Accurate dam inflow forecasting for flood mitigation.
method Extracted sea surface features, applied L2-norm ensemble weighting, used PCA and t-SNE for dimensionality reduction, and calibrated regression models.
result The proposed method improves predictor stability and accuracy in dam inflow forecasting.
Defines height pairing for differential forms on Riemann surface degenerations.
problem Calculating heights for differential forms on degenerating Riemann surfaces.
method Defines Archimedean height pairing, uses Dai-Yoshikawa asymptotics, extends Filip-Tosatti construction.
result Relates new pairing to current-valued pairing, extends geometric settings.
The paper extends CMC surface theory to product spaces, proving height estimates and classifying surfaces.
problem Extending CMC surface theory to product spaces with specific curvature conditions.
method Analyzing graphs and using angle function to derive curvature estimates and classify surfaces.
result Classification of all simply connected, properly embedded surfaces with finite topology.
Neural networks improve ocean temperature forecasting and data interpolation.
problem Forecasting and reconstructing sea surface temperature from satellite data.
method Patch-level neural network representations that mimic numerical integration schemes.
result Neural networks outperform other data-driven models in forecasting and missing data interpolation.
We describe spaces of essential finite height (measured) laminations in a surface S using a parameter space we call S, an ordered semi-ring. We show that for every finite height essential lamination L in S, there is an action of π1(S) on an S-tree dual to the lift of L to the universal co…
The paper derives height estimates for surfaces with constant curvature in warped product spaces.
problem Estimating heights of surfaces with constant curvature in warped product spaces.
method Use of conformal parameters and geometric applications to derive height estimates.
result Derives height estimates for surfaces with positive extrinsic or mean curvature in RimesfR2. The paper modifies a warped product space to find conditions for constant height functions.
problem Finding sufficient conditions for the height function to be constant in a modified warped product space.
method The paper modifies the warped product space by adding a warping function and discusses the sufficient condition for the height of immersed surfaces.
result The paper establishes a sufficient condition for the height function to be constant in the modified warped product space.
The paper estimates heights of H-surfaces in warped products with conditions.
problem Estimating heights of constant mean curvature surfaces in warped products.
method Analyzing surfaces with transversal boundaries in warped product spaces.
result Height estimates involving area and bounded volume for H-surfaces.
Develops probabilistic forecasting for Sea Level Anomalies using Conformal Prediction on functional time series.
problem Forecasting and uncertainty quantification for Sea Level Anomalies.
method Functional data analysis, Conformal Prediction, Functional Autoregressive Processes.
result Proposed method provides accurate probabilistic predictions and uncertainty quantification for Sea Level Anomalies.
Computes canonical heights for arithmetic log surfaces using Hurwitz zeta function.
problem Computing canonical heights for arithmetic log surfaces.
method Introduces a canonical height and uses limits of periods to compute it.
result Explicit formulas for canonical heights of arithmetic log surfaces, including (P_1,D).
Deep learning models informed by physics improve sea surface temperature prediction.
problem Improving accuracy in predicting sea surface temperatures using machine learning.
method Incorporating prior scientific knowledge into deep learning models for better performance.
result Deep learning models informed by physics outperform traditional numerical methods in sea surface temperature prediction.
The Heights Theorem is extended to all Riemann surfaces with a first kind fundamental group.
problem Establishing the Heights Theorem for all Riemann surfaces.
method Extending the theorem to all surfaces with a first kind fundamental group, using measured laminations and straightening horizontal trajectories.
result The horizontal map is injective for arbitrary Riemann surfaces with a conformal hyperbolic metric.
We define the notions of St1×Ss1-valued lightcone Gauss maps, lightcone pedal surface and Lorentzian lightcone height function of Lorentzian surface in semi-Euclidean 4-space and established the relationships between singularities of these objects and geometric invariants of the surface as applications of s…
The paper explores knots' height, trunk, and representativity, finding gaps and bounds.
problem Investigating the properties of knots and their invariants.
method Analyzing conjectures, defining new invariants, and comparing knot positions.
result Found gaps between height and minimal height, and bounds on representativity.
Generative AI predicts Arctic sea ice dynamics over decades.
problem Reproducing realistic sea ice dynamics from days to decades is computationally challenging.
method Introduced GenSIM, a generative AI model trained on 20 years of sea-ice-ocean simulation data.
result Generative AI predicts realistic sea ice evolution for 30 years, capturing long-term trends and physical consistency.
Study proves no minimal surfaces can be contained in certain half-spaces or cones.
problem Prohibiting minimal surfaces from certain geometric configurations.
method Analyzes weighted minimal surfaces in R3 with height-dependent weights. result No proper surfaces can be contained in specific half-spaces or cones.
The study finds conditions for CMC surfaces in a specific space with boundary in parallel planes.
problem Existence and boundary conditions for constant mean curvature surfaces in a hyperbolic space.
method Presented sufficient conditions and height estimates for CMC surfaces with boundary in parallel planes.
result Sufficient conditions and height estimates for CMC surfaces in H2imesR with boundary in parallel planes. Neural-network emulators predict sea-level changes due to Antarctic ice melt.
problem High computational cost and time in projecting sea-level changes.
method Built neural-network emulators of sea-level change using GRD effects from future Antarctic Ice Sheet mass change.
result Neural-network emulators are as accurate as baseline machine learning emulators and offer substantial computational efficiency.
Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces.
We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."
Deep CNN models improve spatio-temporal forecasting efficiency.
problem Efficiently forecasting spatio-temporal dynamics with realistic models.
method Hierarchical statistical IDE framework with CNN for dynamic extraction.
result CNN provides accurate, interpretable, and computationally efficient forecasts.
We show that Scherk's first surface, a one-parameter family of solutions to the minimal surface equation, may be written as a linear superposition of other solutions with specific parametric values.
Sharp bounds on Fano varieties' heights proven for specific cases.
problem Determining the maximal height of arithmetic Fano varieties.
method Logarithmic extension of a conjecture, applied to specific Fano varieties.
result The conjecture settled for specific cases, including hypersurfaces and toric varieties.
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on surface meshes is important and challenging, and some existing methods often produce …
New method corrects seasonal Arctic sea ice predictions with probabilistic models.
problem Systematic biases and errors in climate model forecasts of Arctic sea ice.
method Conditional Variational Autoencoder model to map observation distribution given biased model predictions.
result Probabilistic adjusted forecasts are better calibrated and have smaller errors.
DYffusion improves diffusion models for spatiotemporal forecasting.
problem Challenges in generating stable and accurate forecasts for dynamic data.
method Leverages temporal dynamics in data, directly coupling it with diffusion steps.
result Improves computational efficiency and performs competitively on complex dynamics.
Study on contact structures of surface singularity links using Heegaard Floer homology.
problem Understanding contact structures on singularity links using Heegaard Floer homology.
method Interplay between Heegaard Floer homology and Némethi's lattice cohomology.
result Heegaard Floer invariant cannot lie in the image of the U-action for canonical contact structures on singularity links.
New method discovers El Niño states from ocean data.
problem Discovering El Niño states from micro-level climate data.
method Causal feature learning framework applied to ZW and SST.
result Method identifies El Niño states without past occurrences.
Study examines forces between partially immersed plates and singular configurations.
problem Forces between partially immersed parallel plates and singular configurations.
method Analyzes forces and singular configurations of partially immersed parallel plates in an infinite liquid bath.
result New estimates on meniscus height details presented.