Algorithm extracts wavefront sets from images using deep learning.
problem Extracting wavefront sets from images for imaging sciences.
method Combines shearlet transform and deep neural networks.
result Algorithm outperforms other methods in edge and ramp orientation detection.
Conflict sets are loci of intersecting wavefronts emanating from l different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in Rn occur when 0≤n−l≤4. Other related sets, such as kite curves a…
Paper finds local normal forms for wavefronts in flat coordinates.
problem Understanding local diffeomorphic types of wavefronts.
method Using connections and the metric, criteria for wavefront types are derived in affine flat coordinates.
result Local normal forms of e/m-wavefronts in affine flat coordinates are derived. Abstract: Characterizes frontals and wavefronts with formulas.
problem Characterizing frontals and wavefronts.
method Representation formulas for frontals and wavefronts.
result Representation formulas for various types of frontals and wavefronts.
We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.
A systematic geometric theory for the ultradifferentiable (non-quasianalytic and quasianalytic) wavefront set similar to the well-known theory in the classic smooth and analytic setting is developed. In particular an analogue of Bony's Theorem and the invariance of the ultradifferentiable wavefront set under diffeomorp…
Study on curvature invariants near singularities of wavefronts.
problem Conditions for extendibility and boundedness of curvature invariants.
method Investigation of Gaussian curvature, Mean curvature, and principal curvatures near singularities.
result Relationship between convergence to infinity and uniform approximation of fronts.
Paper approximates backward heat equation using wave equations and Ricci flow.
problem Solving backward heat equation on manifolds using wave equations.
method Approximates solutions of a wave equation on a larger manifold with Ricci flow to solve the backward heat equation.
result The approximation provides solutions to the backward heat equation on manifolds.
We introduce the notion of reticular Legendrian unfoldings in order to investigate stabilities of bifurcations of wavefronts generated by a hypersurface germ with a boundary, a corner, or an r-corner in a smooth n dimensional manifold. We define several stabilities of reticular Legendrian unfoldings and prove that they…
We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold.
We extend the notion of reticular Legendrian unfoldings in order to investigate multi-time bifurcations of wavefronts generated by an r-corner. We give a classification list of generic and stable bifurcations with two time parameter and give all generic figures in the plane and the space.
Study of fastest paths in anisotropic media via Finsler geometry.
problem Optimal paths in media with varying speeds and interfaces.
method Finsler geodesics refracted at interfaces, satisfying specific conditions.
result Establishes generalized Snell's and reflection laws.
Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct time…
Recent advances in twistor theory are applied to geometric optics in R3. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming w…
Paper presents a neural network for estimating wavefronts in direction of arrival scenarios.
problem Estimating the number of wavefronts in direction of arrival scenarios.
method Cross-entropy trained multilayer neural network for online adaptation of antenna array imperfections.
result The method outperforms classical model order selection schemes in accuracy, especially at low signal-to-noise-ratios.
We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destablization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of …
Study finds rigid submanifolds in spacelike waves under specific conditions.
problem Understanding rigidity of submanifolds in spacelike waves.
method Proves submanifolds are contained in characteristic lightlike hypersurfaces under certain conditions.
result Complete codimension two submanifolds are wavefronts under specific conditions.
A new model predicts wildfire spread with wind and slope effects.
problem Predicting wildfire spread with wind and slope effects.
method Geometric model based on Lorentz-Finsler framework, considering wind and slope.
result Infinitesimal wavefronts are no longer restricted to be elliptical, allowing for more accurate predictions.
We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.
problem Constructing smooth multiplication of distributions on locally convex spaces.
method Using diffeological colimits and wavefront-set criterion.
result Proving smooth multiplication of microlocally multipliable distributions.
Study extends Huygens' principle to Finsler spaces, with applications in gravity.
problem Validating Huygens' principle in Finsler spaces for wavefronts.
method Extending a theorem to n-dimensional Finsler spaces and applying to analogue gravity.
result Finsler geometry reveals directional spacetime structures like horizons and ergospheres.
Study null surfaces of pseudo-spherical curves in anti-de Sitter space.
problem Characterize null surfaces of pseudo-spherical spacelike framed curves in anti-de Sitter 3-space.
method Introduced nullcone fronts, classified singularities, defined Anti-de Sitter distance-squared functions.
result Relate singularities of nullcone fronts to those of framed curves.
Transforms uniquely determine Higgs fields on real-analytic manifolds.
problem Determining Higgs fields from transforms on manifolds.
method Matrix-weighted real-analytic double fibration transforms.
result Higgs fields can be uniquely determined from transforms.
We consider the four-dimensional nonholonomic distribution defined by the 4-potential of the electromagnetic field on the manifold. This distribution has a metric tensor with the Lorentzian signature (+,−,−,−), therefore, the causal structure appears as in the general relativity theory. By means of the Pontryagin's m…
Let X be a compact manifold with boundary. Suppose that the boundary is fibred, $φ:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of those vector fields V on X satisfying Vx=O(x2) and which are tangent to the f…
Study of billiards in sub-Finsler geometry, including unusual orbits.
problem Exploring billiard dynamics in sub-Finsler spaces.
method Symplectic and variational approaches, control theory.
result Unusual orbits like gliding and creeping orbits exist.
Study on evolutes and focal surfaces of pseudo-spherical framed immersions in anti-de Sitter space.
problem Investigating singularities of evolutes and focal surfaces of pseudo-spherical framed immersions.
method Introduced pseudo-spherical non-null framed curves, defined moving frames, and analyzed evolutes and focal surfaces.
result Evolutes of pseudo-spherical framed immersions are the sets of singular points of their focal surfaces.
Machine learning models predict DM performance for AO systems.
problem Designing high-performance AO systems with large-scale DMs.
method Simulated FE model, neural network estimation, VARX input models, steady-state control.
result Estimated models reproduce DM input-output behavior and predict steady-state performance.
Determining Finsler manifold structure from boundary distance map and elastic wave measurements.
problem Determine the structure of a compact Finsler manifold from its boundary distance map.
method Construct optimal fiberwise open subset of tangent bundle, use inverse problem in elasticity to measure travel times of waves.
result Finsler function can be uniquely determined from boundary distance map and travel times of waves.
Wave propagation framework using cone structures and observers' vector fields.
problem Describing classic wave propagation in anisotropic media.
method Introduces a cone structure C and an observers' vector field ∂t to describe wave propagation. result Reduces the PDE for wavefronts to ODE for cone geodesics of C. Study of evolutoids and involutoids of convex curves in 2D space forms.
problem Characterizing evolutoids and involutoids of convex curves in various 2D space forms.
method Explicit parametrization and analysis of geodesics, singularity theory, and wavefronts.
result Existence and properties of involutoids for convex curves in M−1,0. Study Legendrian surfaces using N-graphs and flag moduli.
problem Characterize and apply Legendrian surfaces in contact geometry.
method Develop diagrammatic calculus and algebraic-geometric characterization.
result Show applications in Lagrangian concordance, exact fillings, and rational point counts.
Study shows Julia sets and gasket limit sets are quasiconformally different.
problem Quasiconformal non-equivalence of Julia sets and gasket limit sets.
method Proved quasiconformal non-equivalence of Julia sets and gasket limit sets.
result Julia sets and gasket limit sets are quasiconformally different.
New deep learning model for matching sets of items, preserving exchangeability.
problem Matching two different sets of items while preserving exchangeability.
method Exchangeable deep neural networks architecture and efficient training framework.
result Significant improvements in fashion set recommendation and group re-identification.
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
The paper analyzes set-to-set matching with neural networks, focusing on theoretical generalization.
problem Theoretical analysis of set-to-set matching with neural networks.
method Generalization error analysis of set-to-set matching with neural networks.
result Theoretical insights into the behavior of set-to-set matching models.
Generative model learns to autoencode and generate sets of images.
problem Learning to represent and generate sets of images with unknown number of sets.
method Set Distribution Networks (SDNs) learn set encoder, discriminator, generator, and prior.
result SDNs can reconstruct and generate sets of images with preserved attributes.
Study on cold and freezing sets in digital images.
problem Properties of cold sets in digital images.
method Analysis of properties and relationships between cold and freezing sets.
result Examined relationships between cold and freezing sets.
Paper solves whether zero sets are mapping degree sets.
problem Whether finite sets containing zero are mapping degree sets.
method Examined oriented closed connected manifolds of the same dimension.
result Affirmative answer given for both integer and rational settings.
Maps sets to probability distributions to minimize information loss.
problem Learning to map sets to probability distributions to preserve information.
method Relates set operations to probability distribution interpolations and demonstrates a preliminary solution.
result Experimental results show the effectiveness of the set embedding approach.
Unified framework for generating set-valued outputs.
problem Handling unordered set outputs with varying sizes.
method Sequential Set Generation (SSG) framework.
result SSG outperforms baseline methods in experiments.
New model predicts sets from feature vectors without discontinuity issues.
problem Discontinuity issues in predicting sets from feature vectors.
method General model that respects set structure, auto-encodes point sets, predicts bounding boxes, and attributes.
result Model successfully predicts sets from a single feature vector without discontinuity.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give an exa…
Study dynamics and topology of flows near non-saddle sets or W-sets.
problem Understanding the dynamics and topology of flows near specific invariant sets.
method Cohomological relations and global properties analysis.
result Dynamical classification of surfaces and robustness of non-saddle-sets.
Bayesian optimization for set inputs using approximate set kernels.
problem Permutation-invariant optimization over sets with black-box functions.
method Developed a Bayesian optimization method with set kernel, efficient approximate set kernel, and constrained acquisition function.
result Our method outperforms other methods in numerical experiments.
The study explores mapping degree sets and their properties for manifolds.
problem Understanding the structure and properties of mapping degree sets for manifolds.
method Analyzes the properties of mapping degree sets and their relationships with self-mapping degree sets.
result Not every multiplicative set containing 0,1 is a self-mapping degree set.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Model learns set representations through optimized permutations.
problem Challenges in learning set representations due to permutation-invariance.
method Proposes a Permutation-Optimisation module to learn set permutations.
result Achieves state-of-the-art results on various set learning tasks.