Tropical cyclone wind-intensity prediction is a challenging task considering drastic changes climate patterns over the last few decades. In order to develop robust prediction models, one needs to consider different characteristics of cyclones in terms of spatial and temporal characteristics. Transfer learning incorpora…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “tropical cyclones”
AI helps forecasters understand TC convective evolution before intensification.
problem Challenges in extracting scientific insights from complex TC data.
method Combining AI prediction algorithms and classical statistical inference.
result Identifies patterns in TC convective structure leading to intensification.
Nonparametric Conditional Density Estimation In A Deep Learning Framework For Short-Term Forecastingstat.ML
Paper proposes a method for estimating tropical cyclone intensity distribution using deep learning.
problem Lack of full accounting of prediction variability in single-point forecasts.
method Smooth model over target and covariates, logistic transformation for conditional density, case-control sampling approximation.
result Method provides insights into predicted response behavior, improving decision-making and policy.
Tropical Cyclone Track Forecasting using Fused Deep Learning from Aligned Reanalysis Dataphysics.ao-ph
The forecast of tropical cyclone trajectories is crucial for the protection of people and property. Although forecast dynamical models can provide high-precision short-term forecasts, they are computationally demanding, and current statistical forecasting models have much room for improvement given that the database of…
New method predicts spatial events like hurricanes and earthquakes with uncertainty.
problem Quantifying uncertainty in natural hazard predictions.
method Representing spatial point clouds as empirical measures, constraining prediction sets to spatial data manifold, using Wasserstein distance.
result Achieves near-nominal coverage and lower energy/manifold distances compared to baselines.
New method detects TC imagery patterns for rapid intensity change.
problem Detecting upcoming rapid intensity changes in TC satellite imagery.
method Nonparametric test of association between images and event labels using neural networks and bootstrap.
result Identifies archetypes of infrared imagery associated with elevated rapid intensification risk.
Paper examines adversarial attacks on weather forecasting models, focusing on TC trajectory prediction.
problem Adversarial attacks can mislead downstream TC trajectory predictions in DLWF models.
method Proposes Cyc-Attack, a method using a surrogate model and skewness-aware loss function to generate adversarial TC paths.
result Cyc-Attack achieves higher true positive rates and lower false alarm rates compared to conventional methods.
Rapid intensification (RI) of tropical cyclones often causes major destruction to human civilization due to short response time. It is an important yet challenging task to accurately predict this kind of extreme weather event in advance. Traditionally, meteorologists tackle the task with human-driven feature extraction…
Trustworthy Predictive Distributions for Tail Events with Semiparametric Diagnostic Transport Mapsstat.ML
Paper improves predictive distributions for rare events using a simple framework.
problem Local miscalibration of predictive distributions for rare events.
method Semiparametric diagnostic transport maps to correct tail probabilities.
result Semiparametric maps improve predictions for severe weather hazards.
The paper introduces diagnostic transport maps to improve the reliability of rare event predictions.
problem Improper calibration of predictive distributions, especially for rare events.
method Diagnostic transport maps to adjust base model's probabilities for better calibration.
result Diagnostic transport maps improve predictive performance for rare events, including 24-hour rapid intensity change.
A new method selects robust features for ML models using causal discovery.
problem Challenges in feature selection for ML models with limited domain knowledge.
method Multidata causal feature selection using PC1 or PCMCI algorithms.
result The method improves model performance and provides interpretable drivers.
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribu…
Paper uses deep learning to detect cyclone rapid intensification.
problem Detecting rare cyclone rapid intensification events.
method Deep learning, ensemble learning, and data augmentation frameworks.
result Data augmentation improves rapid intensification detection.
Hurricanes are cyclones circulating about a defined center whose closed wind speeds exceed 75 mph originating over tropical and subtropical waters. At landfall, hurricanes can result in severe disasters. The accuracy of predicting their trajectory paths is critical to reduce economic loss and save human lives. Given th…
Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology classmath.AG
Proves a tropical version of Clemens-Schmid sequence for tropical varieties.
problem Existence of tropical cycles with specific cohomology classes.
method Tropical Hodge theory and Clemens-Schmid sequence analogy.
result Proves tropical Hodge conjecture for rationally triangulable varieties.
TML package uses tropical geometry for machine learning tasks.
problem Statistical learning problems.
method Tropical convexity computations, Hit and Run sampler, tropical metrics.
result First R package for tropical geometric machine learning.
Hodge theory applied to tropical curves.
problem Developing Hodge theory for tropical curves.
method Analytical approach using tropical differential forms and cohomologies.
result Construction of Hodge theory analog on tropical curves.
Homology of tropical fansmath.AG
The paper studies homology of tropical fans and introduces smoothness.
problem Homological properties of tropical fans and smoothness.
method Proposes a notion of smoothness in tropical geometry, proving the Hodge isomorphism theorem.
result Chow rings of smooth unimodular tropical fans are isomorphic to tropical cohomology rings.
Proves tropical Hodge theory for smooth projective varieties, conditional on Laplacian regularity.
problem Proving log-concavity of characteristic polynomials of matroids.
method Combinatorial approach, conditional proof of Kähler package.
result Conditional proof of Kähler package for tropical cohomology.
We introduce in this paper the concept of tropical mirror hypersurfaces and we prove a complex tropical localization Theorem which is a version of Kapranov's Theorem \cite{K-00} in tropical geometry. We give a geometric and a topological equivalence between coamoebas of complex algebraic hypersurfaces defined by a maxi…
Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we can not directly apply statistical learning models in data science to a set of phylogenetic trees since the space of phylogenetic trees is …
Proves cohomology theorems for tropical varieties.
problem Cohomology of smooth projective tropical varieties.
method Introduces and proves new results in tropical geometry.
result Establishes tropical analogs of three fundamental theorems.
A bit of tropical geometrymath.AG
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking. Each definition is explained with concrete examples and illustrations. To a …
We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden laye…
This note is devoted to the definition of moduli spaces of rational tropical curves with n marked points. We show that this space has a structure of a smooth tropical variety of dimension n-3. We define the Deligne-Mumford compactification of this space and tropical -class divisors.
Study of algebraic dynamics on Markov cubics in tropical geometry.
problem Understanding the dynamics of Markov cubics over non-archimedean fields.
method Tropicalization and -triangle reflection group on hyperbolic plane.
result Existence of Fatou domain and finitude of orbits with rational points over prime power denominators.
Then detection and identification of extreme weather events in large-scale climate simulations is an important problem for risk management, informing governmental policy decisions and advancing our basic understanding of the climate system. Recent work has shown that fully supervised convolutional neural networks (CNNs…
The paper provides a combinatorial criterion for realizing tropical pluri-canonical divisors.
problem Determining when a tropical pair corresponds to a smooth algebraic curve with a pluri-canonical divisor.
method Introducing tropical normalized covers and reducing the problem to their realizability.
result Generalizes previous work on tropical canonical divisors and incorporates recent progress on -differentials.
Knots and tropical curvesmath.GT
Using elementary ideas from Tropical Geometry, we assign a a tropical curve to every -holonomic sequence of rational functions. In particular, we assign a tropical curve to every knot which is determined by the Jones polynomial of the knot and its parallels. The topical curve explains the relation between the AJ Con…
Tropical curves match to special Lagrangian shapes.
problem Connecting tropical geometry to special Lagrangian shapes.
method Gluing construction that matches tropical local models to Lagrangian shapes.
result Locally planar tropical curves can be realized as special Lagrangian limits.
Paper constructs braid invariants using tropical Ptolemy equation.
problem Constructing invariants of braids.
method Tropical version of the Ptolemy equation.
result Invariants of braids constructed.
To a tropical -cycle in , we naturally associate a normal closed and -dimensional current on denoted by . Such a "tropical current" will not be an integration current along any analytic set, si…
Develops tropical geometry for weighted Hurwitz numbers, generalizing previous results.
problem Understanding weighted Hurwitz numbers across various cases.
method Tropical geometry framework for weighted Hurwitz numbers.
result Generalized structural results for weighted Hurwitz numbers.
We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic zero. Given a pair consisting of a stable tropical curve …
We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. We apply this construction to the tropical curves obtained from the 2875 lines on the quintic Calabi-Yau threefold. Each admissible tropical curve gives a Lagrang…
New theorem links tropical phased matroids to higher-dimensional spheres.
problem Understanding topological properties of tropical phased matroids.
method Proving homeomorphism between topological order complex and a sphere.
result Topological order complex of tropical phased matroids is a -sphere.
This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of algebraic geometry, to characterize the decision boundaries of a simple network of the form (Affine, Re…
This survey consists of two parts. Part 1 is devoted to amoebas. These are images of algebraic subvarieties in the complex torus under the logarithmic moment map. The amoebas have essentially piecewise-linear shape if viewed at large. Furthermore, they degenerate to certain piecewise-linear objects called tropical vari…
Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curvesmath.GT
Let be the outer automorphism group of the free group . It acts properly on the outer space of marked metric graphs, which is a finite-dimensional infinite simplicial complex with some simplicial faces missing. In this paper, we construct complete geodesic metrics and complete piecewise s…
A tropical curve in contributes to Gromov-Witten invariants in all genus. Nevertheless, we present a simple formula for how a given tropical curve contributes to Gromov-Witten invariants when we encode these invariants in a generating function with exponents of recording Euler characteristic. Our ma…
New method initializes sigmoidal MLPs for interpretable shapes.
problem Creating interpretable decision boundaries in neural networks.
method Introducing a geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs) using tropical geometry.
result Sigmoidal MLPs can have decision boundaries aligned with prescribed shapes at initialization.
In this paper, we study the reconstruction problem of the holomorphic tangent bundle of the complex projective plane . We introduce the notion of tropical Lagrangian multi-section and cook up one by tropicalizing the Chern connection associated the Fubini-Study metric. Then we …
We construct from a real affine manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical order-by-order description of the degeneration via f…
Characterizes local tropicalizations of splice type surface singularities.
problem Understanding splice type surface singularities from a tropical geometry perspective.
method Characterization of local tropicalizations as cones over splice diagrams, using tropical methods.
result Characterizes local tropicalizations of splice type surface singularities as cones over associated splice diagrams.
In this paper, we present a unified study of the moduli space of tropical curves and Outer space which we link via period maps to the moduli space of tropical abelian varieties and the space of positive definite quadratic forms. Our work is a first step towards exhibiting Outer space and the space of positive definite …
New model for rational tropical points using -webs and measures.
problem Understanding rational tropical points of Fock-Goncharov moduli space.
method Introducing rational bounded -laminations and defining tropical coordinate systems.
result Established a bijection between rational tropical points and -webs.
New invariant links graph structure to tropical curve properties.
problem Understanding graph and curve minor structures.
method Defined Ceresa-Zharkov class for graphs, related to tropical curves.
result Ceresa-Zharkov class is zero for hyperelliptic graphs.
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, …