A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified fiber channel model.
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48 results for “fiber nonlinearities”
Extends Higgs fields theory to complex fiber bundles.
problem Characterize nonlinear flat connections on complex fiber bundles.
method Representation of extension class by curvature, nonlinear Higgs bundles, and nonabelian Hodge structure.
result Established a faithful functor from nonlinear flat bundles to nonlinear Higgs bundles.
LSTM neural networks improve fiber nonlinearities in coherent systems.
problem Compensating fiber nonlinearities in digital coherent systems.
method Utilization of Long short-term memory (LSTM) neural networks.
result LSTM neural networks provide superior performance compared to digital back propagation, especially in multi-channel scenarios.
Machine learning techniques have recently received significant attention as promising approaches to deal with the optical channel impairments, and in particular, the nonlinear effects. In this work, a machine learning-based classification technique, known as the Parzen window (PW) classifier, is applied to mitigate the…
Study Higgs sections and flat sections for nonlinear harmonic bundles.
problem Equivalence of Higgs and flat sections for nonlinear harmonic bundles.
method Analyze harmonic vector bundles, generalize to sub-fibrations and morphisms.
result Vanishing of a degree obstruction for general nonlinear harmonic bundles.
Study compares bundles with connections to prehomogeneous geometries.
problem Comparing bundle structures to prehomogeneous geometries.
method Analyzes fibered manifolds, jet bundles, and nonlinear PDEs.
result Identifies similarities and differences between bundle structures and prehomogeneous geometries.
Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learningcs.IT
Machine learning is used to compute achievable information rates (AIRs) for a simplified fiber channel. The approach jointly optimizes the input distribution (constellation shaping) and the auxiliary channel distribution to compute AIRs without explicit channel knowledge in an end-to-end fashion.
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.
Physics-based deep learning improves fiber-optic communication efficiency.
problem Improving signal propagation in fiber-optic communication systems.
method Parameterizing the split-step method of solving the nonlinear Schrödinger equation as a deep neural network.
result Filters can be pruned to as few as 3 taps/step without sacrificing performance.
We present a simulation framework for spunbond processes and use a design of experiments to investigate the cause-and-effect-relations of process and material parameters onto the fiber laydown on a conveyor belt. The virtual experiments are analyzed by a blocked neural network. This forms the basis for the prediction o…
A neural-network-based approach is presented to efficiently implement digital backpropagation (DBP). For a 32x100 km fiber-optic link, the resulting "learned" DBP significantly reduces the complexity compared to conventional DBP implementations.
Nonlinear soft-tissue elasticity, remodeling, and degradation described by an extended Finsler geometrycond-mat.soft
Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.
problem Understanding and predicting the behavior of nonlinear soft tissues, especially in biologic contexts.
method Formulated a continuum mechanical theory incorporating extended Finsler geometry to describe the complex behaviors of fibrous soft solids.
result The model quantifies residual strains from growth, remodeling, and degradation, and predicts equilibrium configurations.
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEsmath.AP
In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimens…
New method learns nonlinear projections for reduced-order modeling of complex dynamical systems.
problem Modeling transient dynamics near a manifold in nonlinear systems.
method Constrained autoencoder neural networks with invertible activation functions and biorthogonal weight matrices.
result Demonstrated effectiveness on a vortex shedding model, learning oblique fibers for fast dynamics.
In this paper we investigate for further symmetry properties of the nonlinear fin equations of the general form rather than recent works on these equations. At first, we study the projective (fiber-preserving) symmetry to show that equations of the above class can not be reduced to linear equa…
Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representatio…
In this paper, an unsupervised machine learning method for geometric constellation shaping is investigated. By embedding a differentiable fiber channel model within two neural networks, the learning algorithm is optimizing for a geometric constellation shape. The learned constellations yield improved performance to sta…
Fiber nonlinear interference (NLI) modeling and monitoring are the key building blocks to support elastic optical networks (EONs). In the past, they were normally developed and investigated separately. Moreover, the accuracy of the previously proposed methods still needs to be improved for heterogenous dynamic optical …
The study proves properties of spectral selectors for contact manifolds and applies them to contact big fibers and geodesics.
problem Properties of spectral selectors for contact manifolds.
method Algebraic properties of spectral selectors for strongly orderable contact manifolds.
result Established contact big fiber theorem and constructed norms on contactomorphism group universal cover.
Continuum mechanics theory describes skin's complex anisotropic behavior.
problem Modeling the anisotropic tearing of skin.
method Finsler geometry fiber bundle approach, variational method, phase-field mechanics.
result Analytical solutions capture experimental data on skin tearing.
An important problem in fiber-optic communications is to invert the nonlinear Schrödinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a computation graph that is reminiscent of a deep neural network. This observation all…
The mixed scalar curvature of a foliated Riemannian manifold, i.e., an averaged mixed sectional curvature, has been considered by several geometers. We explore the Yamabe type problem: to prescribe the constant mixed scalar curvature for a foliation by a conformal change of the metric in normal directions only. For a h…
The work proposes a geometric background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagra…
Fibered Correspondencemath.DG
Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …
Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.
problem Characterize essential surfaces in Seifert fiber spaces with singular surfaces.
method Extends Frohman and Rannard's approach to handle surfaces with singular fibers.
result Characterizes essential surfaces in Seifert fiber spaces with singular surfaces.
G-FuNK learns solutions for nonlinear PDEs on multiple domains and parameters.
problem Predicting time-dependent dynamics of complex systems governed by nonlinear PDEs with varying parameters and domains.
method Graph Fourier Neural Kernels combining domain-adapted and transferable components for non-diffusive and diffusive terms.
result G-FuNK achieves low relative errors on unseen domains and fiber fields, significantly accelerating predictions.
Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
problem Conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
method Analysis of GKM graphs and fiber bundles, counterexamples, and classification of twist automorphisms.
result Realizability of fiber bundles of GKM graphs depends on the twist automorphism and can be decided in terms of the classification.
Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
problem Characterize fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
method Construct a class of involutions, extend product involutions, and use double covering.
result Any fiber-preserving, orientation-reversing involution factors as a product of an orientation-preserving and a specific class of involutions.
Fibered ribbon disksmath.GT
We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…
Darboux-Lie derivativesmath.DG
Introduces Darboux-Lie derivative for fiber bundles.
problem None explicitly stated; focuses on introducing a new derivative.
method Study of Darboux-Lie derivative for fiber-bundle maps.
result Properties of Darboux-Lie derivative for fiber bundles.
The paper proves non-existence of positive scalar curvature on certain fiber bundles.
problem The existence of positive scalar curvature metrics on fiber bundles.
method Analyzing fiber bundles over specific manifolds with incompressible or homotopically nontrivial fibers.
result Non-existence of PSC metrics on certain fiber bundles under specific conditions.
New examples show not all homology fiber bundles are topological.
problem Disprove conjecture about homology fiber bundles.
method Construct flat, projective morphisms that are -homology fiber bundles.
result Disprove conjecture about homology fiber bundles.
New exotic 4-manifolds found with fiber bundles.
problem Finding non-diffeomorphic exotic 4-manifolds.
method Smooth fiber bundles over the circle.
result Exotic 4-manifolds with non-simply-connected fiber.
Study shows simplicial volume of certain fiber bundles is zero.
problem Understanding simplicial volume in fiber bundles with nonpositive curvature.
method Proved simplicial volume is zero for specific fiber bundles.
result Simplicial volume of certain fiber bundles is zero.
Smooth, globally PŁ functions are essentially nonlinear least-squares.
problem Understanding the structure of functions satisfying the Polyak-Łojasiewicz condition.
method Analyzing smooth functions on Riemannian manifolds with the PŁ condition.
result Smooth, globally PŁ functions are of the form .
We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel…
We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a characterisation of fibered surfaces with zero signature.
Constructs a family to handle unstable fibers on complex surfaces.
problem Handling unstable fibers on complex surfaces.
method Uses Teichmüller theory to construct a degenerating family over the moduli space.
result Any fibered complex surface with unstable fibers can be pulled back from the constructed family.
Fibered F-Algebramath.DG
The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.
Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
On fiber linear convexitymath.GT
Boundary of fiber convex domains is a cohomological sphere.
problem Understanding the boundary properties of fiber convex domains.
method Analyzing smooth fiber convex domains with smooth boundaries.
result The boundary is a cohomological sphere.
Veech fibrationsmath.GT
Study complex surfaces fibered over Teichmüller curves with Veech fibers.
problem Understanding the geometric and topological properties of complex surfaces.
method Compute invariants via monodromy action on fiber's mod- homology.
result Exact values of invariants for all known algebraically primitive Teichmüller curves.
In this paper, we define the primitive/Seifert-fibered property for a knot in S^3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2 and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of exa…
Describes 3-manifolds by families of singularly fibered surfaces.
problem Understanding the structure of 3-manifolds through fibered surfaces.
method Explicitly describes a fibration of the complement of a homogeneous braid.
result Each fiber intersects every cross-section of .
Virtual Covers of Links IImath.GT
A fibered concordance of knots, introduced by Harer, is a concordance between fibered knots that is well-behaved with respect to the fibrations. We consider semi-fibered concordance of two component ordered links with fibered. These are concordances that restrict to fibered concordances on the first …
Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.
problem Characterizing Veech groups in fibered 3-manifolds.
method Analyzing pseudo-Anosov monodromies and foliations, proving properties of Veech groups.
result Veech groups in fibers typically contain no parabolic elements.
Paper connects homologically fibered links to solutions of equations.
problem Existence of homologically fibered links in 3-manifolds.
method Interprets existence in terms of first homology group and torsion linking form, or surgery diagrams.
result Computes hc for specific 3-manifolds.
Defines products for fibered corners manifolds, generalizing resolutions.
problem Resolving fibered corners manifolds.
method Introduces a category of fibered corners manifolds with products and transverse fiber products, defining the 'ordered product' for wedge metrics.
result The 'ordered product' is a natural product for wedge metrics.