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.
Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal conv…
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.
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.
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.
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.
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.
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.
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.
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.
The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height.
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 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 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.
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.
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.
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.
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.
In this study, the wind data series from five locations in Aegean Sea islands, the most active `hotspots' in terms of refugee influx during the Oct/2015 - Jan/2016 period, are investigated. The analysis of the three-per-site data series includes standard statistical analysis and parametric distributions, auto-correlati…
We investigate three-dimensional surfaces where the normal vector forms a constant angle with the radius vector. These surfaces naturally extend equiangular (logarithmic) spirals in the plane.
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.
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).
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.
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…
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.
In this paper, we investigate three geometrical invariants of knots, the height, the trunk and the representativity. First, we give a conterexample for the conjecture which states that the height is additive under connected sum of knots. We also define the minimal height of a knot and give a potential example which has…
The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in M2(κ)×R whose mean curvature is given as a C1 function depending on their angle function. We cover topics such as the existence of a priori curvature e…
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.
The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and more appealing to benefit from available large-scale observation and simulation dat…
Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal resolution while in situ autonomous probes supply high vertical resolution, but horiz…
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."
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.
In this article, we consider compact surfaces Σ having constant mean curvature H (H-surfaces) whose boundary Γ=∂Σ⊂M0=M×f{0} is transversal to the slice M0 of the warped product M×fR, here M denotes a Hadamard surface…
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.
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 …
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.
Let a contact 3-manifold (Y,ξ0) be the link of a normal surface singularity equipped with its canonical contact structure ξ0. We prove a special property of such contact 3-manifolds of "algebraic" origin: the Heegaard Floer invariant c+(ξ0)∈HF+(−Y) cannot lie in the image of the U-action on HF+(−Y).…
The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribe…
Signed heights of knotoids are defined and studied.
problem Understanding the signed height of knotoids.
method Defined positive and negative parts of height, proved they determine unsigned height, provided lower bounds with polynomials, studied associated sequences.
result Positive and negative parts of height determine unsigned height.
We will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reache…
Given H∈[0,∞), some sufficient conditions for existence of CMC H graphs with boundary in two parallel planes of H2×R are presented. Height estimates for outwards-oriented CMC surfaces (horo)cyllindrically bounded are also exhibited.
Decision tool helps manage biofouling risks for ships in the Baltic Sea.
problem Biofouling of ships causes environmental and economic issues.
method Bayesian networks to identify biofouling management strategies.
result Optimal biofouling management includes biocidal-free coating and in-water cleaning.