New method shapes constellation to reduce fiber nonlinearities.
problem Nonlinear fiber effects in deep learning.
method Unsupervised machine learning for constellation optimization.
result Gains up to 0.13 bit/4D in fiber nonlinearities.
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48 results for “Geometric constellation shaping”
Paper optimizes fiber optic communication constellations using machine learning.
problem Improving fiber optic communication performance through better constellation shaping.
method An unsupervised learning approach embedding a fiber channel model into neural networks.
result Improved performance up to 0.13 bit/4D in simulation and experimentally up to 0.12 bit/4D.
Autoencoders improve communication system performance by optimizing constellation geometry and probability.
problem Optimizing constellation geometry and probability for better communication system performance.
method Leveraging autoencoders to learn capacity-achieving symbol distributions and constellations.
result Learned constellations achieve information rates very close to capacity on AWGN channels and outperform existing methods on fading channels.
Gradient descent finds better constellations for GMI-based learning.
problem Nonconvexity in end-to-end GMI learning.
method Gradient descent initialized with Gray-labeled APSK constellations.
result State-of-the-art constellations in 2D and 4D provide up to 26% reach increase.
New scheme optimizes BMI through probabilistic and geometric shaping.
problem Optimizing bit-wise mutual information (BMI) for coded modulation.
method Joint optimization of BMI through probabilistic and geometric shaping.
result Joint optimization enables a continuum of constellation geometries and probability distributions.
Autoencoder shapes QAM symbols for improved GMI performance.
problem Improving Geometric Mean Information (GMI) in QAM constellation shapes.
method End-to-end learning of bit mappings using autoencoders.
result Achieved up to 0.2 bits/QAM symbol gain in GMI.
New MIMO constellation design for noncoherent communications reduces hardware complexity.
problem Designing efficient MIMO constellations for noncoherent communications over fading channels.
method Geodesic curves of the Grassmann manifold for structured constellation design.
result Achieves comparable error performance to unstructured designs with reduced hardware complexity.
Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learningcs.IT
Machine learning optimizes fiber communication rates without channel knowledge.
problem Achieving information rates in nonlinear fiber communication.
method Jointly optimizes input and auxiliary channel distributions using end-to-end autoencoder learning.
result Computes achievable information rates without explicit channel knowledge.
Deep Learning-Based Constellation Optimization for Physical Network Coding in Two-Way Relay Networkscs.IT
Deep learning optimizes constellation for two-way relaying networks, boosting sum rate.
problem Optimizing constellation for better performance in two-way relaying networks.
method Deep neural networks (DNNs) trained to minimize cross entropy loss for direct constellation optimization.
result Significant performance gain in achievable sum rate compared to conventional relaying schemes.
Starfield optimizes satellite links for LEO mega-constellations by aligning ISLs with regional traffic patterns.
problem Forming a stable satellite topology in LEO mega-constellations with limited ISLs and unstable acquisition.
method Starfield uses a demand-aware heuristic algorithm based on traffic flows and Riemannian geometry to assign satellite links.
result Starfield reduces hop count and improves stretch factor by up to 30% compared to existing methods.
Constellation learns group-level visual relationships for abstract reasoning.
problem Learning configurational properties of entire groups of objects.
method Introduces Constellation, a network that learns relational abstractions over static visual scenes.
result Offers a basis for abstract relational reasoning and sensory imagination.
Workshop on shape analysis discusses new research directions.
problem No specific problem stated; focus on new directions in shape analysis.
method Discussion and collaboration among researchers.
result Promising new directions in shape analysis were discussed.
We analyze and correct bias in template shape estimation using geometric statistics.
problem Asymptotic bias in template shape estimation.
method Tools from geometric statistics, stratified geometry of shape space, Taylor expansion, bootstrap procedures.
result Proposed methods to quantify and correct bias in template shape estimation.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
problem Machine learning methods struggle with geometric data
method Shape space analysis provides a mathematical and computational framework
result Characterizes shape variability, compares geometric objects, and analyzes structural trajectories
A Python implementation of some geometric tools on Kendall 3D shape space for practical applicationsstat.CO
Python tools for 3D shape analysis on Kendall's space.
problem Lack of practical utilities for advanced 3D shape analysis.
method Developed Python tools for 3D shape analysis on Kendall's 3D Shape Space.
result Efficient, accessible software solutions for researchers.
Minimal surfaces help compare geometric shapes.
problem Comparing different geometric shapes.
method Applications of minimal surfaces.
result New insights into geometric comparisons.
Study fourth-order geometric flow of shape operator for co-dimension one immersions.
problem Analyzing the geometry of isometric immersions in Riemannian manifolds.
method Introduce a moduli flow to decrease curvature variation energy.
result The flow decreases a natural energy measuring curvature variation.
New technique shows any group can be a map's automorphism.
problem Finding maps with any given automorphism group.
method Universal technique for showing any finite automorphism group is possible.
result Any finite automorphism group can be realized by many non-isomorphic maps.
SVarM uses varifold representations for shape classification and regression.
problem Challenges in analyzing geometric data due to non-Euclidean shape spaces.
method Develops a neural network-based framework for varifold representations of shapes.
result Demonstrates strong performance and robustness in shape classification and regression.
Machine learning shapes bodies via inverse scattering.
problem Generating 3D human bodies with customizable characteristics.
method Combining inverse scattering with machine learning.
result Generates geometric bodies from characteristic parameters.
The paper presents a method for analyzing shape graphs using specific features.
problem Analyzing geometric and topological variations in shape graphs.
method Curated set of topological, geometric, and directional features for shape graph analysis.
result The feature representation is effective for tasks like group comparison and classification.
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by Morse Theory, we algorithmically produce a PL approximation of the original shape …
Study examines heart and football-shaped metrics, verifying geometric structure.
problem Analyzing reducible spherical conical metrics and their geometric properties.
method Examined 1-parameter heart shape and 3-parameter football shape families, verified structure theorem, used explicit metric and geodesic calculations.
result Naturally arise from Abelian differentials of the third kind, offer new evidence for spherical geometry and complex analytic structure interaction.
A framework for generating 3D shapes by sequentially assembling primitives.
problem Combinatorial complexity in generating 3D shapes.
method Bayesian optimization for efficient exploration and exploitation of feasible combinations.
result Successfully generates realistic combinatorial 3D shapes.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
Geometric theory on the elasticity of bio-membranescond-mat.soft
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed…
Reduces 3-body problem to shape and spherical geometry.
problem Investigates the motion of three bodies in a plane.
method Geometric reduction using equivariant Riemannian geometry.
result Time parametrization of moduli curve determined by shape curve and potential function.
Surveying tools for estimating geometric properties of hyperbolic knots.
problem Determining geometric properties of hyperbolic knots.
method Analyzing link diagrams to estimate geometric invariants.
result Estimating volume, cusp shape, and cusp area of hyperbolic knots.
Optimizing shapes for a specific eigenvalue problem involving two balls.
problem Optimizing shapes for the first mixed Steklov-Dirichlet eigenvalue.
method Geometric proof based on Newton's shell theorem.
result Geometric insight into eigenvalue optimization.
Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flowmath.OC
Optimizes shapes in uncertain Navier-Stokes flow problems.
problem Optimizing shapes with geometric constraints and physical uncertainty.
method Multi-shape calculus and stochastic augmented Lagrangian method.
result Successfully optimized shapes in uncertain Navier-Stokes flow.
LIMP learns latent shapes with metric preservation, improving generative models.
problem Insufficient training data for high-fidelity latent representations.
method Metric preservation as a prior, geometric distortion criterion, geodesic loss.
result Synthetic samples of higher quality achieved through metric preservation.
The paper introduces a new method to measure the shape relations between biological objects using r-parallel sets.
problem The influence of neighboring objects on the shape and function of biological objects.
method The authors develop a theory based on spatial point processes to measure the geometrical interaction between objects.
result The proposed measures provide detailed information about the shape of individual objects and their interactions.
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…
Deep learning models complex multivariate extremes using geometric shapes.
problem Modeling complex extremal dependencies in high-dimensional data.
method Geometric representation and deep learning for flexible semi-parametric models.
result First approach to modeling limit sets using deep learning for high-dimensional data.
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
problem Identifying sundial design adjustments based on installation location.
method Shape analysis in a high-dimensional space, regression in shape space.
result Sundial design adjustments were latitude-dependent.
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surfa…
This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order QAM constellations. Four new iterative batch BSS algorithms are p…
We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model…
Transforms curves and surfaces for efficient geometric analysis.
problem Efficiently analyzing and comparing curves and surfaces.
method Square root velocity transformation for curves and intrinsic comparison for surfaces.
result Fundamental geometric properties of curves under the transformation.
Enhanced 3D shape analysis using information geometry.
problem Challenges in comparing 3D point clouds due to their unstructured nature and complex geometry.
method Information geometric framework for 3D point cloud shape analysis using Gaussian Mixture Models (GMMs) on a statistical manifold. Proposed MSKL divergence with upper and lower bounds.
result MSKL provides stable and monotonically varying values that directly reflect geometric variation, outperforming traditional distances and existing KL approximations.
New approach reduces shape optimization anomalies and improves design quality.
problem Improving global optimization efficiency and avoiding geometrical anomalies in shape optimization.
method Reducing design variables, modeling generative process via probabilistic models, penalizing anomalous designs.
result Abnormal designs are penalized, leading to high-quality designs and improved convergence.
Foliation of star-shaped polygons with fixed perimeter and area.
problem Characterizing star-shaped polygons with fixed perimeter and area.
method Analyzing families of star-shaped n-polygons in the Euclidean plane.
result Existence and properties of foliations on the space of star-shaped n-polygons.
In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.
A new geometric perceptron model improves 3D shape classification.
problem Challenges in geometric tasks involving point clouds using machine learning.
method Introduces multilayer geometric perceptron (MLGP) with geometric neurons.
result MLGP outperforms vanilla MLP in 3D shape classification and noise resistance.
GNPs learn operators on non-Euclidean geometries using neural networks.
problem Learning operators on complex geometries like manifolds.
method Geometric Neural Operators (GNPs) that incorporate geometric properties.
result GNPs can estimate metrics, solve PDEs, and learn LB operators on manifolds.
Anisotropic weighted isoperimetric inequalities for star-shaped and -mean convex hypersurfacemath.DG
The paper proves inequalities for star-shaped and -mean convex hypersurfaces in .
problem Proving geometric inequalities for specific types of hypersurfaces.
method Using anisotropic -momentum, perimeter, and volume, the paper derives inequalities for star-shaped and -mean convex hypersurfaces.
result The Wulff shape of is the unique minimizer of the corresponding functionals among all star-shaped and -mean convex sets.
New method learns shape correspondences robustly from raw geometry.
problem Inaccurate and poor generalization of shape correspondences.
method Learning-based approach with feature-extraction network and functional map representation.
result Robust and accurate shape correspondence learning with less training data.