Improved spectral-based GCN for directed graphs.
problem Cannot directly work on directed graphs.
method Redefined Laplacians to improve propagation model.
result Outperforms state-of-the-art methods on directed graph datasets.
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48 results for “redefined Laplacians”
Uniform spectral gap for convex cocompact hyperbolic surfaces and expanders.
problem Spectral gap for convex cocompact hyperbolic surfaces and their covers.
method Using thermodynamic formalism for twisted Selberg zeta functions.
result Uniform resonance-free regions for convex cocompact hyperbolic surfaces and expanders.
We redefine the cord algebra, which was introduced by Lenhard Ng as a topological knot invariant, in terms of Morse Theory. The determination of the cord algebra of the unknot and of the righthanded trefoil are given. We proove that the cord algebra in our definition is a knot invariant.
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a…
The famous Švarc-Milnor Lemma says that a group acting properly and cocompactly via isometries on a length space is finitely generated and induces a quasi-isometry equivalence for any . We redefine the concept of coarseness so that the proof of the Lemma is automatic.
Graph machine learning and Super-App data improve credit risk prediction for financial inclusion.
problem Improving credit risk prediction for financial inclusion.
method Two graph-based experiments using centrality, behavior, and transactionality features.
result Graph features enhance credit risk models, leading to more inclusive financial systems.
Researchers redefine spinor field derivatives in generalized geometry.
problem Defining a natural Lie derivative for spinor fields.
method Revisit Kosmann and Bourguignon-Gauduchon constructions in generalized geometry.
result Developed a theory of generalized Lie derivative for spinor fields.
In this paper we will prove that for a compact, symplectic manifold and for -compatible almost-complex structure J any properly perturbed J-holomorphic curve has a non-negative symplectic area. This non-negative property provides us with a new obstruction to the bubbling off phenomenon and thus allows us to…
Chi-Square Test Neural Network: A New Binary Classifier based on Backpropagation Neural Networkcs.LG
We introduce the chi-square test neural network: a single hidden layer backpropagation neural network using chi-square test theorem to redefine the cost function and the error function. The weights and thresholds are modified using standard backpropagation algorithm. The proposed approach has the advantage of making co…
Copulas and time series with long-ranged dependencesphysics.data-an
We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework…
Defines vector Laplacian on statistical manifolds.
problem No specific problem stated; focuses on mathematical definition.
method Defines and derives vector Laplacian formula.
result Derives formula for vector Laplacian.
BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.
problem Comparing combinatorial and Hodge Laplacians for discrete data.
method Introducing Boundary-Induced Graph (BIG) Laplacians using DEC.
result BIG Laplacian eigenvalues converge to Hodge Laplacian for simple shapes.
Paper introduces magnetic Hodge Laplacian for differential forms.
problem No specific problem stated; general spectral analysis of differential forms.
method Introduced magnetic Hodge Laplacian, discussed spectral results.
result Similarities and differences with magnetic Laplacian on functions.
The paper extends Laplacian spectra approximations to vector bundles.
problem Approximating the spectrum of the connection Laplacian.
method Extending the graph connection Laplacian to vector bundles and proving spectrum approximation.
result The spectrum of the extended operator approximates the spectrum of the connection Laplacian.
Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.
problem Analyzing sectoriality of Laplacian and Lichnerowicz Laplacian on asymptotically hyperbolic spaces.
method Proves sectoriality in weighted Hölder spaces using asymptotically hyperbolic metrics.
result Analytic semigroups apply, yielding well-posedness results for parabolic evolution equations.
We introduce a general method of performing Residual Network inference and learning in the JPEG transform domain that allows the network to consume compressed images as input. Our formulation leverages the linearity of the JPEG transform to redefine convolution and batch normalization with a tune-able numerical approxi…
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving important features and structures.
method Laplacian-based methods including spectral clustering, Laplacian eigenmap, locality preserving projection, graph embedding, and diffusion map.
result Comprehensive overview of various optimization variants and applications of Laplacian-based techniques.
This study redefines probability for finite outcomes using axioms and examples.
problem Defining probability for finite outcomes and preserving information.
method Developed three axioms for relative probability functions and provided examples and a system for their composition.
result Proved the topological closure of the relative probability space, preserving information under limits.
New approach predicts microfinance borrower risk to manage portfolios.
problem Non-repayment problem in microfinance due to asymmetric information.
method Modeling and simulation of ordinary differential systems.
result Prediction of solvent and insolvent borrowers over time.
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph -Laplacian. Unlike the …
The paper sets up eigenvalue comparison theorems for specific Laplacians on manifolds.
problem Eigenvalue comparison theorems for Witten-Laplacian and weighted -Laplacian on manifolds with modified Ricci curvature.
method Established Cheng-type eigenvalue comparison theorems for the first Dirichlet eigenvalues of the Witten-Laplacian and weighted -Laplacian on geodesic balls.
result Successfully set up eigenvalue comparison theorems for the Witten-Laplacian and weighted -Laplacian.
Extended bounds on small eigenvalues for pseudo-Laplacians on hyperbolic surfaces.
problem Bounding small eigenvalues of pseudo-Laplacians on hyperbolic surfaces.
method Extended Otal-Rosas bound and Colin de Verdière's spectral theory to hyperbolic surfaces with multiple cusps.
result Extended bounds on small eigenvalues for pseudo-Laplacians.
Rigidity phenomena on lower -weighted Ricci curvature bounds with -range for non-symmetric Laplacianmath.DG
Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.
problem Investigating rigidity phenomena for weighted Ricci curvature bounds.
method Derived comparison geometric estimates and generalized for non-symmetric Laplacian.
result Obtained rigidity results for Laplacian comparison theorem, diameter comparisons, and volume comparisons.
Study Hodge Laplacians for manifold data, improving error bounds.
problem Approximating Laplace-Beltrami operator on differential forms.
method Higher-order graph Laplacians (Hodge Laplacians) as approximations.
result High-probability error bound for Dirichlet forms.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
New perspective on G2-structures flow from DeTurck Laplacian.
problem Understanding G2-structures and their flows.
method Introducing a new flow (DeTurck Laplacian flow) for G2-structures.
result DeTurck Laplacian flow is a flow of G2-structures.
A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.
problem Ambiguity in viscous operator choice for Navier-Stokes equations on Riemannian manifolds.
method Kinematic construction of strain rate from Lie-dragged vectors, excluding Hodge Laplacian due to antisymmetric part.
result Kinematic selection uniquely identifies the deformation Laplacian, resolving analytical obstructions.
Study solves sub-Laplacian equivalence on a specific Heisenberg group.
problem Contact equivalence problem for sub-Laplacians on the second Heisenberg group.
method Solves the contact equivalence problem for generalised sub-Laplacians on $\He^2$.
result Parameterises sub-Laplacians on $\He^2$ by .
Explains BV Laplacian on half-densities in simple terms.
problem None explicitly stated; focuses on explanation.
method Didactical review of BV Laplacian on half-densities.
result Explains BV Laplacian concept in plain language.
Study shows rates for Laplacian-eigenmap methods in nonparametric regression.
problem Minimizing error in nonparametric regression using Laplacian-eigenmap.
method Adaptive and non-adaptive minimax rates using Sobolev space constraints.
result Extends minimax rates to various weighted Laplacian matrices.
Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.
problem Finding lower bounds for eigenvalues of p-Laplacian on quaternionic Kähler manifolds.
method Analytical proofs for both Neumann and Dirichlet boundary conditions.
result Established lower bounds for eigenvalues on compact quaternionic Kähler manifolds.
The paper finds new inequalities for Laplacian and biharmonic eigenvalues on manifolds.
problem Eigenvalue inequalities for Laplacian and biharmonic operators on submanifolds.
method Using Sobolev inequalities to establish new eigenvalue inequalities.
result Established new inequalities for Laplacian and biharmonic eigenvalues.
Researchers find second-order estimates for -Laplacian in RCD spaces.
problem Estimating functions with -Laplacian in RCD spaces.
method Establishing quantitative second-order Sobolev regularity.
result Second-order estimates for -Laplacian functions in RCD spaces.
Study on -structures using Laplacian coflow and solitons.
problem Characterizing and understanding -structures and their solitons.
method Using the irreducible -decomposition of the Hodge Laplacian and Lie derivative, characterizing infinitesimal symmetries and soliton conditions.
result Proof of the absence of compact shrinking solitons for the Laplacian coflow.
Study of Yang-Mills fields on 4-manifolds using modified Lévy Laplacians.
problem Connection between Yang-Mills fields and modified Lévy Laplacians on 4-manifolds.
method Analysis of modified Lévy Laplacians and their relation to Yang-Mills equations under nontrivial holonomy groups.
result Existence of a modified Lévy Laplacian related to Yang-Mills self-duality equations.
For a bounded domain with a piecewise smooth boundary in an -dimensional Euclidean space , we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Lap…
Fractional Laplacian inverse problem solved for connection Laplacians.
problem Determining structures from metric, bundle, and map knowledge.
method Local knowledge of metric, bundle, and map determines global structures.
result Global structures determined from local knowledge of metric, bundle, and map.
New upper bound for Neumann Laplacian eigenvalues on convex domains.
problem Bounding Neumann eigenvalues on convex domains.
method Deriving a new upper bound for eigenvalues.
result Universal inequalities for Neumann eigenvalues derived from the upper bound.
Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domainmath.SP
Universal inequalities found for Laplacian eigenvalues on convex domains.
problem Finding bounds for Laplacian eigenvalues on convex domains.
method Established two universal inequalities.
result Found new bounds for Laplacian eigenvalues.
A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domainmath.SP
Universal inequalities for Laplacian eigenvalues on convex domains.
problem Eigenvalue distribution of the Laplacian on convex domains.
method Established two universal inequalities.
result Two new inequalities for Laplacian eigenvalues.
Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domainmath.SP
New inequalities for planar convex domains' Laplacian eigenvalues.
problem Neumann eigenvalues of the Laplacian on planar convex domains.
method Established two new universal inequalities.
result New inequalities for Laplacian eigenvalues on convex domains.
This paper shows how we can build a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we are able to redefine concepts like account balance, yield curve and the law of diminishing returns. The model provides us with a …
We investigate the existence of closed -structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed -structure do admit a Laplacian soliton. Moreover, one of them admits a continuous family of Laplacian solitons which are pai…
New examples found for a type of geometric solitons.
problem Finding new shrinking Laplacian solitons.
method One-parameter family of examples and study of torsion forms.
result No closed eigenform for the Laplacian on the family.
New theorems compare Laplacian on Kähler manifolds.
problem Comparing Laplacian on Kähler manifolds.
method New curvature notions between Ricci and holomorphic bisectional curvatures.
result Established Laplacian comparison theorems and rigidity theorems.
The paper studies eigenfunctions and nodal sets of the Witten-Laplacian.
problem Characterizing nodal lines and eigenfunctions of the Witten-Laplacian.
method Courant-type nodal domain theorem for Dirichlet and closed eigenvalue problems.
result Upper bound for the multiplicity of closed eigenvalues of the Witten-Laplacian.
Maps commuting with sub-Laplacians on Carnot groups are conformal.
problem Characterizing maps preserving sub-Laplacians on sub-Riemannian Lie groups.
method Analyzing smooth maps between sub-Riemannian Lie groups that commute with sub-Laplacians.
result Sub-Laplacian determines the sub-Riemannian structure in Carnot groups.
In this paper, we obtain "universal" inequalities for eigenvalues of the weighted Hodge Laplacian on a compact self-shrinker of Euclidean space. These inequalities generalize the Yang-type and Levitin-Parnovski inequalities for eigenvalues of the Laplacian and Laplacian. From the recursion formula of Cheng and Yang \ci…