Estimates derivatives of max-stable fields for risk analysis.
problem Estimating derivatives of max-stable random fields.
method Two unbiased stochastic derivative estimation approaches: Likelihood Ratio Method (LRM) and Infinitesimal Perturbation Analysis (IPA).
result Proposes conditions for the validity of LRM and IPA in Brown--Resnick and Smith fields.
An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having …
A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extrem…
Deep learning used for parameter estimation in hard-to-infer models.
problem Parameter estimation in intractable models like max-stable processes.
method Train deep neural networks on simulated data to estimate parameters.
result Deep learning provides accurate and faster parameter estimation.
This paper develops DRO estimators for EVT statistics using point processes.
problem Scarcity of extreme data leads to model misspecification error in EVT.
method Developed DRO estimators informed by semi-parametric max-stable constraints in the space of point processes.
result Proposed DRO estimators improve out-of-sample performance and are validated on synthetic and real data.
Divide-and-conquer framework speeds up black-box inference for large data.
problem Computational intractability of uncertainty quantification for expensive data simulation.
method Divide data into partitions, train on a subset, bootstrap on partitions, combine results.
result Feasibility of estimating max-stable process parameters with tens of thousands of locations.
New method models precipitation extremes and spatial dependence.
problem Estimating dependencies of precipitation maxima in space and time.
method Generative neural networks for max-stable processes.
result Explicit nonparametric estimate of spatial dependence.
Proposes flexible spatial models for better understanding spatial heterogeneity.
problem Poor characterisation of spatial heterogeneity in conventional models.
method Spatial Bayesian Neural Networks (SBNNs) incorporating a spatial embedding layer and possibly spatially-varying parameters.
result SBNNs better match the finite-dimensional distribution of target spatial processes.
Efficient neural Bayes estimators for censored peaks-over-threshold models improve inference speed and accuracy.
problem Computational burden in inference with spatial extremal dependence models due to intractable or censored likelihoods.
method Developed neural Bayes estimators using data augmentation techniques to encode censoring information.
result Significant gains in computational and statistical efficiency compared to traditional methods.
Graph neural networks extend neural Bayes estimators to irregular spatial data.
problem Estimating parameters from irregular spatial data with computational efficiency.
method Employing graph neural networks to approximate Bayes estimators for irregular spatial data.
result Extending neural Bayes estimation to irregular spatial data with computational benefits.
Characterizes winding of braided vector fields in tubular domains.
problem Understanding the topology of braided vector fields in complex domains.
method Defines field line winding as a measure of entanglement, proving its uniqueness in classifying vector field topology.
result Field line winding uniquely classifies the topology of braided vector fields.
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
The paper explores how fields in higher dimensions are quantized.
problem Understanding non-perturbative completions of higher gauge fields.
method Generalizes the Chern-Dold character map to higher-dimensional supergravity theories.
result Flux and charge quantization laws for higher gauge fields are understood via non-linear Bianchi identities.
Paper transforms torse-forming vector fields into simpler forms.
problem Generalizing vector fields and their transformations.
method Present techniques to transform torse-forming vector fields into simpler cases.
result Concrete examples of transformations are provided.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
problem Characterizing Killing tensor fields on projective spaces.
method Analyzing Killing tensor fields on quaternionic and complex projective spaces, proving algebraic properties.
result Generated algebras of Killing tensor fields on quaternionic and complex projective spaces.
Every smooth vector field is a combination of gradient fields.
problem Expressing arbitrary smooth vector fields as combinations of gradient fields.
method Proving every smooth vector field can be written as a finite linear combination of iterated Lie brackets of gradient vector fields.
result Every smooth vector field is a combination of gradient fields.
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
Paper describes holomorphic polyvector fields on toric varieties.
problem No specific problem stated; general description of fields.
method Explicit description of holomorphic polyvector fields on smooth compact toric varieties.
result Generalizes Demazure's result of holomorphic vector fields on toric varieties.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.
problem Proving triviality of modified conformal vector fields on Riemannian manifolds.
method Analyzing properties of homothetic, conformal, and gradient vector fields on compact and non-compact manifolds.
result Established conditions under which m-modified conformal vector fields are trivial. We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes…
The paper establishes a connection between force-free fields and conformally geodesic fields.
problem Understanding the relationship between force-free fields and conformally geodesic fields.
method Developed an equivalence between force-free fields and conformally geodesic fields, generalized to arbitrary dimensions.
result Established that stationary points of hierarchies of L2 and L1-optimization problems are related by a conformal change of metric. Unified physics field theories through a general conservation law.
problem Unified physics field theories.
method Introduced general field as a formal sum of differential forms, defined conservation law using action principle.
result Physics field theories become instances of the general conservation law.
Study proves density of harmonic fields in continuous quaternion fields.
problem Characterizing harmonic quaternion fields and their density in continuous fields.
method Analyzes harmonic quaternion fields on smooth compact Riemannian manifolds, proving density via Stone-Weierstrass theorem.
result Subalgebra generated by harmonic fields is dense in continuous quaternion fields.
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…
Vector fields invariant under Lie group action are finitely generated by polynomial fields.
problem Understanding invariant vector fields under Lie group actions.
method Analyzing the module of smooth vector fields invariant under a linear action of a compact Lie group.
result The module of invariant vector fields is finitely generated by polynomial fields.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
problem Describing the time evolution of quantum field theories.
method Defines a functorial field theory on Lorentzian bordism pseudo-category.
result Lorentzian bordisms naturally arise in algebraic quantum field theory.
The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …
This work discovers latent field effects governing interacting dynamical systems.
problem Discovering field effects governing interacting dynamical systems.
method Proposes neural fields to learn latent force fields from observed dynamics, disentangling local object interactions and global field effects.
result Accurately discovers latent field effects in various dynamical systems.
Study on vector fields on Lie groups reveals surprising algebraic coincidences.
problem Characterizing vector fields on Lie groups with Riemannian metrics.
method Algebraic and geometric analysis of left-invariant vector fields on nilpotent Lie groups.
result Spaces of Killing, one-harmonic, and conformal vector fields coincide with the center of the Lie algebra on nilpotent Lie groups.
Study proves conformal vector fields on certain Finsler manifolds are Killing fields.
problem Characterizing conformal vector fields on compact homogeneous Finsler manifolds.
method Analyzes properties of conformal vector fields and homogeneous Finsler metrics.
result Conformal vector fields on compact homogeneous Finsler manifolds are Killing fields.
For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.
problem Separate Earth's magnetic field from vehicle's magnetic field for accurate magnetic navigation.
method Use machine learning (ML) and integrate physics of magnetic navigation (SciML) to remove aircraft magnetic field from total magnetic field.
result A model can be constructed to effectively remove aircraft magnetic field from the dataset.
A Ricci soliton (M,g,v,λ) on a Riemannian manifold (M,g) is said to have concurrent potential field if its potential field v is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is …
New field invariant refines real spectrum and relates to absolute Galois group.
problem Understanding field invariants related to absolute Galois groups.
method Introducing Artin-Schreier quandles and computing their properties for different types of fields.
result Artin-Schreier quandles provide relations between fields and their absolute Galois groups.
Study biharmonic vector fields and unit vector fields on Riemannian manifolds.
problem Determine the equivalence of biharmonicity and harmonicity for vector fields and unit vector fields on Riemannian manifolds.
method Analyze biharmonic vector fields and unit vector fields on (M,g) with pseudo-Riemannian g-natural metrics on TM and T1M. result Contrary to Sasaki metric, biharmonicity and harmonicity are not equivalent for large classes of g-natural metrics on TM. Classifies vector fields in the kernel of a 1-form, up to equivalence.
problem Classifying vector fields in the kernel of a 1-form.
method Equivalence relation, local models, transversal unfoldings.
result Provides a list of local models and transversal unfoldings for vector fields.
Semisimple 4D field theories can't distinguish smooth 4-manifolds.
problem Detecting exotic smooth structures in 4-manifolds.
method Proving field theories lead to stable invariants, distinguishing only homeomorphic and homotopy equivalent manifolds.
result Semisimple 4D field theories can't distinguish homotopy equivalent 4-manifolds.
Stable knots and links can exist in electromagnetic fields.
problem Stability of knots and links in electromagnetic fields.
method Proving the existence of electromagnetic fields preserving link topology.
result Every link can be realized as stable field lines in electromagnetic fields.
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth famil…
Defines quaternionic k-vector fields on quaternionic Kähler manifolds.
problem No specific problem stated; focuses on definition and properties.
method Introduced a modified Dirac operator to define quaternionic k-vector fields.
result Calculated the dimension of quaternionic k-vector fields on HPn. Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field mode…
The paper classifies Killing tensor fields on Riemannian symmetric spaces.
problem Understanding Killing tensor fields on Riemannian symmetric spaces.
method Reduced study to compact irreducible spaces, introduced top slot Killing tensor fields, and classified quadratic fields.
result Quadratic Killing tensor fields on Riemannian symmetric spaces of rank one are spanned by top-slot and decomposable fields.
A spiking neural network model for probabilistic inference of binary Markov random fields.
problem Implementing probabilistic inference in spiking neural networks.
method Designing a spiking recurrent neural network and proving its equivalence to mean-field inference of binary Markov random fields.
result The spiking neural network model can implement inference of arbitrary binary Markov random fields.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…
Enhances Hamiltonian systems stability through generalized double bracket vector fields.
problem Stabilizing already stable points in Hamiltonian systems.
method Generalized double bracket vector fields on Poisson manifolds with pseudo-Riemannian metrics.
result Enhanced equilibria stability through dissipation terms.