The paper shows translating solitons in have symmetry.
problem Understanding the symmetry of translating solitons in .
method Analyzing the blow-up limits of embedded, mean convex mean curvature flow.
result Translating solitons in have symmetry.
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48 results for “Translational Symmetry”
The study examines translating solitons of mean curvature flow and finds upper bounds and symmetries.
problem Understanding translating solitons in mean curvature flow.
method Non-existence results, upper bounds, graphical perturbations, and symmetry analysis.
result Compact translators between parallel planes inherit symmetries of their boundaries.
New proof shows symmetry for certain curved surfaces in higher dimensions.
problem Understanding symmetries in curved surfaces evolving over time.
method Generalized previous result to higher dimensions, proving symmetry condition.
result Uniformly 3-convex translating solitons must have symmetry.
Study classifies special surfaces in space with translational and rotational symmetries.
problem Classifying surfaces with specific symmetries and densities.
method Analyzes -translating solitons with invariant properties under translations and rotations.
result Classifies all -translating solitons with invariant surfaces.
Researchers prove existence of convex translators in slab regions in all dimensions.
problem Existence of translating solutions in slab regions.
method Proof in all dimensions ; slab width ; convexity and regularity results for symmetrical translators.
result Existence of convex translators in specific slab regions.
Symmetries of Analytic Pathsmath-ph
The symmetries of paths in a manifold are classified with respect to a given pointwise proper action of a Lie group on . Here, paths are embeddings of a compact interval into . There are at least two types of symmetries: Firstly, paths that are parts of an integral curve of a fundamental vector field on $…
Constructing solutions to geometric flows with rotational symmetry.
problem Finding solutions to extrinsic geometric flows with specific properties.
method Rotationally symmetric translating solutions constructed for -homogeneous speeds.
result These solutions are necessarily convex and have specific asymptotic behaviors.
Classification of groups as symmetries of infinite translation surfaces.
problem Classifying groups as isometry groups of translation surfaces.
method Adapting ideas from hyperbolic surfaces to translation surfaces.
result Every countable subgroup of GL+(2,ℝ) can be realized as the Veech group of a translation surface.
The paper classifies and describes translators in under specific symmetry conditions.
problem Classifying translators in under invariant symmetry groups.
method Analyzing translators invariant by one-parameter groups of isometries, using Iwasawa decomposition and Killing vector fields.
result Explicit parametrizations of translators are obtained for some cases.
Book explores infinite translation surfaces, challenging traditional geometry.
problem Understanding infinite-type translation surfaces.
method Detailed classification, construction, and analysis of symmetries.
result Complex dynamics in infinite-type translation flows.
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
problem Learning from raw time-series data efficiently and effectively.
method Constructing scale-translation equivariant neural networks based on wavelet symmetries.
result Wavelet Networks outperform conventional CNNs on raw waveforms and spectrograms.
New methods prove existence of rotating shapes moving in space.
problem Existence of rotating shapes moving in space.
method Different methods to prove existence based on singular ordinary differential equation.
result Existence of rotationally symmetric translating solutions proven without partial differential equations.
New Lagrangian and special Lagrangian examples found in complex space.
problem Constructing exact Lagrangian and special Lagrangian submanifolds with symmetries.
method Using an Ansatz generalizing Castro-Lerma's construction, with admissible compact and non-compact subgroups.
result Explicit examples of Lagrangian translators and special Lagrangians with various symmetries.
We prove the existence of a complete, embedded, singly periodic minimal surface, whose quotient by vertical translations has genus one and two ends. The existence of this surface was announced in our paper in {\it Bulletin of the AMS}, 29(1):77--84, 1993. Its ends in the quotient are asymptotic to one full turn of the …
The height functions of K^(1/4)-flow translators in Euclidean space R^3 solve the unimodular Hessian equation. We explicitly and geometrically determine the moduli space of all helicoidal K^(1/4)-flow translators, which are generated from planar curves by the action of helicoidal groups.
New translation equivariant neural processes improve spatio-temporal data modeling.
problem Improving posterior prediction maps for spatio-temporal data.
method Introduced translation equivariant transformers within neural processes.
result TE-TNPs outperform non-equivariant TNPs and other baselines.
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered. We establish when there exist generalized symmetries from these subspaces, which …
Maximal hypersurfaces in spacetimes with translational symmetry are characterized and their properties studied.
problem Characterizing maximal hypersurfaces in spacetimes with translational symmetry.
method Analyzing quotient spacetimes and using properties of maximal hypersurfaces.
result Complete noncompact maximal hypersurfaces in quotient spacetimes are either cylinders or conformal to the Euclidean plane.
Classifies and constructs translators for curvature flows.
problem Understanding translating solitons in curvature flows.
method Developed rotational theory, introduced signed-neck framework.
result Classified and constructed catenoidal-type translators.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
problem Improving graph neural network performance on asymmetric graphs.
method Formalizing approximate symmetries via graph coarsening, introducing a bias-variance formula.
result Best generalization performance achieved by choosing a larger symmetry group than automorphisms but smaller than permutations.
Symmetry augmentation speeds up learning in robotics tasks.
problem Learning efficiency in robotics tasks with limited data.
method Data augmentation using symmetry in the quadruped domain of DeepMind control suite.
result Agent learns faster with augmented symmetry experiences.
We consider conformally flat hypersurfaces in four dimensional space forms with their associated Guichard nets and Lamé's system of equations. We show that the symmetry group of the Lamé's system, satisfying Guichard condition, is given by translations and dilations in the independent variables and dilations in the dep…
The decomposition of the space of continuous and translation invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger type theorem for continuous translation invariant and SO(n)-equivariant tensor valuations is also given. As an application, symme…
Study shows instability of certain MOTSs with continuous symmetry.
problem Stability of MOTSs with continuous symmetry.
method Analysis of initial data sets with continuous symmetry and non-preserved MOTSs.
result Exotic MOTSs are unstable except in exceptional cases.
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we explicitly determine the dependance of coefficients of generalized symmetries fro…
Paper defines new topological invariants for DP tangles.
problem Classifying and understanding doubly periodic tangles.
method Organized components into interlinked compounds; introduced axis-motif.
result Directional type is an invariant of DP tangles.
Study invariant -translators in Lorentz-Minkowski space.
problem Characterize -translators invariant under translations and rotations.
method Analyze 1-parameter group of translations and rotations, find explicit parametrizations, and solve non-linear autonomous systems.
result Explicit parametrizations and qualitative properties of invariant -translators.
The paper proves nonexistence results for translating solitons in r-mean curvature flow.
problem Proving nonexistence of translating solitons in r-mean curvature flow.
method Establishing nonexistence results under suitable growth conditions on curvature and second fundamental form.
result Properly immersed translating solitons cannot be confined to certain half-spaces.
We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. This is done by const…
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the intera…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over the model's parameters, which can pose challenges both for performing inference a…
Study geodesic diameter on surfaces with special symmetry.
problem Geodesic diameter on surfaces with involutive isometry.
method Analyzes surfaces with specific symmetry properties.
result Determines geodesic diameter for these surfaces.
We prove that any holomorphic locally homogeneous geometric structure on a complex torus, modelled on a complex homogeneous surface, is translation invariant. We conjecture that this result is true is any dimension. In higher dimension we prove it here for nilpotent models. We also prove that in any dimension the trans…
The paper studies counting problems on square-tiled surfaces.
problem Understanding the frequency of properties in square-tiled surfaces.
method Examining properties of the square torus and their implications in translation surfaces.
result Implications between properties and their frequency in translation surfaces.
Paper analyzes CycleGAN solutions and symmetries.
problem CycleGAN image translation without paired data.
method Theoretical analysis of exact and approximate solutions.
result Exact solution space is invariant to automorphisms.
The study of compact -translating solitons with boundary conditions.
problem Understanding the shape and existence of compact -translating solitons with boundary constraints.
method Analyzing the mean curvature equation and boundary conditions to deduce the existence and shape of -translating solitons.
result Conditions for the existence of compact -translating solitons with boundary and estimates of surface area.
The paper proves unique ancient solutions to mean curvature flow in higher dimensions are symmetric.
problem Proving uniqueness of ancient solutions to mean curvature flow in higher dimensions.
method Analyzing strictly convex, uniformly two-convex, and noncollapsed ancient solutions.
result Ancient solutions are rotationally symmetric translating solitons.
Generates valid Euclidean distance matrices for molecular structures.
problem Generating point clouds in arbitrary rotations and translations is challenging.
method Developed a neural network architecture that produces valid Euclidean distance matrices invariant to rotations and translations.
result The architecture can generate molecular structures in a one-shot fashion by producing Euclidean distance matrices with a three-dimensional embedding.
MDS benefits from symmetry, revealing key frequencies.
problem Understanding MDS in symmetrical data.
method Analyzed MDS on groups, focusing on symmetry properties.
result Only a few frequencies contribute to MDS output.
Learning molecular energies using localized graph kernelsphysics.comp-ph
GRAPE uses graph kernels to predict molecular energies efficiently.
problem Efficiently predicting molecular energies with physical constraints.
method GRAPE approach based on graph theory incorporating symmetries.
result GRAPE predicts atomization energies accurately on organic molecules.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
problem Applying convolutional neural networks to non-Abelian lattice gauge theories while preserving gauge symmetry.
method Developed a geometric formulation of L-CNNs that are equivariant under global symmetries and gauge transformations.
result Convolutional operations in L-CNNs are a specific case of gauge-equivariant neural networks on SU() principal bundles.
We extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, w…
This paper aims to incorporate passive symmetries in machine learning for better generalization.
problem Machine learning's reliance on arbitrary choices leads to passive symmetries that can limit generalization.
method Translation among physics, mathematics, and machine learning to understand and implement passive symmetries.
result Respecting passive symmetries can improve machine learning's ability to generalize.
Proposes learning invariances in neural networks using a weight-space approach.
problem Learning invariances from data in neural networks remains an open problem.
method Minimizes a lower bound on the marginal likelihood in weight space.
result Results in higher performing models with naturally learned invariances.
Stability of the Catenoid for the Hyperbolic Vanishing Mean Curvature Equation Outside Symmetrymath.AP
Stability of catenoid in hyperbolic space proven without symmetry assumptions.
problem Stability of catenoid in hyperbolic space.
method Profile construction, modulation analysis, integrated local energy decay, vectorfield method.
result Nonlinear asymptotic stability of catenoid for without symmetry assumptions.
G-CNNs reduce sample complexity by exploiting symmetries.
problem Reducing sample complexity in neural networks.
method Group equivariant convolutions that exploit symmetries.
result Achieve state-of-the-art results on CIFAR10 and rotated MNIST.
The study constructs minimal surfaces in a product space with specific properties.
problem Constructing minimal surfaces with specific topological and geometric properties in a product space.
method 1-parameter families of complete properly Alexandrov-embedded minimal surfaces with dihedral symmetry and finite total curvature.
result Examples of minimal surfaces with genus 1 and 2k ends in quotient spaces.
New mesh network preserves symmetries in deep learning.
problem No existing mesh processing architecture is equivariant to all symmetries.
method Equivariant attention-based mesh network using relative tangential features.
result The network achieves improved performance and is equivariant to various transformations.