Due to the isotropy -dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the -radius hyperboloid model of -dimensional hyperbolic geometry with and , we compute azimuthal Fourier expansions for a fundamental so…
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48 results for “Gegenbauer coefficients”
For a fundamental solution of Laplace's equation on the -radius -dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion for a fundamental solution of Laplace's equation in hyperspherical geometry in geo…
Sharp uniqueness result for Q-curvature type equation on S^6.
problem Proving uniqueness of axially symmetric solutions to a Q-curvature type equation on S^6.
method New estimates on semi-norm and Gegenbauer coefficients.
result Axially symmetric solutions are constants for a specific range of α.
Sharp inequality proven for symmetric functions on a 4D sphere.
problem Proving a sharp Beckner's inequality for axially symmetric functions on .
method Utilized pointwise properties of Gegenbauer polynomials.
result Sharp Beckner's inequality established for axially symmetric functions on .
We perform global and local analysis of oscillatory and damped spherically symmetric fundamental solutions for Helmholtz operators in -dimensional, -radius hyperbolic and hyperspherical geometry, which represent Riemannian manifolds with positive constant…
Study degenerate solutions on product of spheres using bifurcation theory.
problem Existence of degenerate solutions on product of spheres.
method Bifurcation theory, isoparametric functions, Gegenbauer polynomials.
result Existence of degenerate solutions that depend on both factors.
We analyze kernel matrices in polynomial high-dimensional settings and explain double descent in KRR.
problem Understanding the spectrum of kernel matrices in polynomial high-dimensional settings and its implications for KRR risk.
method Generalized decomposition of kernel matrices into low-rank spike matrix, identity, and Gegenbauer matrix.
result The test error in KRR can exhibit double descent behavior, depending on effective regularization and signal-to-noise ratio.
Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor performance of the traditional iterative gradient-based learning algorithms. Although the famous extreme learning machine (ELM) has successfully addre…
Dual model predicts electricity spot prices using neural networks and wavelets.
problem Forecasting hourly electricity spot prices.
method Dual generalized long memory modelling with k-factor GARMA and G-GARCH models, using LLWNN and PSO for variance prediction.
result The hybrid k-factor GARMA-LLWNN model outperforms other methods in forecasting accuracy.
Green functions for GJMS operators on spheres derived, linking geometry and rigidity.
problem Deriving Green functions for GJMS operators on spheres.
method Explicit representation formulae derived using Gegenbauer polynomials.
result Spheres uniquely characterized by their Green functions, with strong rigidity theorems for .
Study improves electricity price forecasting accuracy using a hybrid model.
problem Accurate short-term electricity price forecasting is challenging due to social and natural factors.
method Hybrid model combining GARMA, G-GARCH, Wavelet, LLWNN, and optimization algorithms.
result The hybrid model outperforms other models in Nord Pool Electricity markets.
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
Formula connects linking coefficients to Kontsevich integral coefficients.
problem Linking coefficients from Kontsevich integral.
method Purely combinatorial approach.
result Expresses linking coefficients as combinations of Kontsevich integral coefficients.
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Machine learning predicts Kronecker coefficients with high accuracy.
problem Predicting Kronecker coefficients from tensor products of symmetric group representations.
method Training machine learning models (NN, CNN, GBDT) to classify Kronecker coefficients as zero or non-zero.
result Trained models achieve high accuracy () in classifying Kronecker coefficients.
Abstract: Determines thermoelastic coefficients from boundary data.
problem Determining coefficients of thermoelastic system from boundary information.
method Explicit expression for thermoelastic Dirichlet-to-Neumann map with variable coefficients.
result Thermoelastic Dirichlet-to-Neumann map uniquely determines coefficients on the manifold.
New filling functions for groups with coefficients show different asymptotic behavior.
problem Difficulty in filling loops with surfaces in Cayley graphs.
method Defining homological filling functions with coefficients and proving their differences.
result Filling functions for -cycles with coefficients in different groups have distinct asymptotic behavior.
Abstract: Determines Lamé coefficients from boundary measurements.
problem Determining Lamé coefficients from elastic boundary measurements.
method Explicit symbol of elastic Dirichlet-to-Neumann map, partial derivatives determination.
result Elastic Dirichlet-to-Neumann map uniquely determines Lamé coefficients.
Defines and proves properties of weighted renormalized volume coefficients.
problem None explicitly stated; focuses on mathematical definitions and proofs.
method Defines weighted renormalized volume coefficients and proves their variational nature and polynomial representation.
result Weighted renormalized volume coefficients are variational and can be expressed as polynomials of specific tensors.
Improved 3D LiDAR data classification using product coefficients.
problem Enhancing accuracy in 3D LiDAR data classification.
method Introducing product coefficients derived from measure theory as additional features in the classification process, alongside PCA.
result Significant improvement in classification accuracy with product coefficients.
Distance Correlation Methods for Discovering Associations in Large Astrophysical Databasesastro-ph.CO
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between…
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose ele…
On the third coefficient in the TYCZ-expansion of the epsilon function of Kaehler-Einstein manifoldsmath.DG
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
problem Local elliptic regularity for operators with low regularity coefficients in Sobolev-type spaces.
method Rescaling estimates and multiplication results for function spaces.
result Unified set of interior estimates and regularity inference for operators with Sobolev-type coefficients.
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
problem Behavior of twist coefficients after capping off a boundary component.
method Heegaard Floer homology to constrain twist coefficients.
result Results about fractional Dehn twists and Floer homology of cyclic branched covers.
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
problem Tackles the B-type skein relation and introduces new coefficient polynomials.
method Introduces coefficient polynomials associated with the B-type skein relation and proves their invariance under Reidemeister moves.
result Shows that the generating series of these coefficient polynomials recovers the Kauffman polynomial.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
Bounding twist number of surface links using polynomial coefficients.
problem Bounding the twist number of alternating surface links.
method Introducing a generalized homological Kauffman bracket and applying it to surface link diagrams.
result A bound for the twist number of alternating surface links in terms of polynomial coefficients.
Characterizes differential forms and vector fields with constant coefficients on manifolds.
problem Understanding constant coefficient differential forms and vector fields on manifolds.
method Analyzes differential forms and vector fields of specific degrees, proving obstructions and characterizing solutions to partial differential systems.
result Characterizes differential forms and vector fields with constant coefficients of various degrees on smooth manifolds.
Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with - and -Mixingstat.ML
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
problem Analyzing convergence of gradient descent in Hilbert spaces with stationary Markov chains.
method Examined strictly stationary Markov chains with - and -mixing coefficients, derived probabilistic upper bounds.
result Probabilistic upper bounds on convergence behavior of gradient descent algorithm based on mixing coefficients.
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two va…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family of self-adjoint elliptic differential operators. is a non-Laplace-type perturbation …
Guts determine the leading coefficients of -Alexander torsions for 3-manifolds.
problem Determining the leading coefficient of -Alexander torsions for 3-manifolds.
method Using a new criterion for the convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.
result The leading coefficient equals the relative -torsion of the guts associated to the cohomology class.
Survey of recent measures of association, including a new coefficient.
problem Exploring new measures of association in statistics.
method Survey and introduction of a new correlation coefficient.
result Proposed a new extension of the correlation coefficient to standard Borel spaces.
Diffusion models adapt to low-dimensional data regardless of coefficient choices.
problem Understanding how diffusion models adapt to low-dimensional data structures.
method Analysis of diffusion models with flexible coefficient choices.
result Proven that iterations suffice for accurate sampling in total variation distance.
Paper finds coefficients of Catalan states using Θ_A-state expansion.
problem Finding coefficients of Catalan states of lattice crossings.
method Uses Θ_A-state expansion to express coefficients as a linear combination of other states.
result Shows that coefficients can be found using Θ_A-state expansion.
GenMod: A generative modeling approach for spectral representation of PDEs with random inputsstat.ML
GenMod uses generative models to approximate high-dimensional PDE solutions with limited evaluations.
problem Quantifying uncertainty in high-dimensional PDE systems with random parameters.
method Develops a method using generative models to approximate polynomial chaos coefficients in underdetermined systems.
result The method outperforms sparsity-promoting methods in approximating PDE solutions with limited evaluations.
We prove the -manifold $\RP^3 \# \RP^3$ is of -coefficient homology -systolic freedom. Given a Riemannian metric on $\RP^{3}\# \RP^{3}$, we define -coefficient homology -systole as the infimum of lengths of all nonseparating geodesic loops representing nontrivial classes in $H_{1}(\RP^3\#\…
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucia…
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
We construct explicitly the Khovanov homology theory for virtual links with arbitrary coefficients by using the twisted coefficients method. This method also works for constructing Khovanov homology for ``non-oriented virtual knots'' in the sense of Viro, in particular, for knots in .
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and give its applications to intersection forms with local coefficients of 4-manifolds. The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients. The second is a local …
A new tree-based model for varying coefficients using CGBM.
problem Modeling varying coefficients with high dimensionality and complex interactions.
method Tree-based varying coefficient model with CGBM for varying coefficients, dimension-wise early stopping, and feature importance scores.
result The model produces comparable out-of-sample loss to neural networks, demonstrating effectiveness.
Paper tests if beta coefficients in AMF model are consistent over time.
problem Testing time-invariance of beta coefficients in AMF model.
method Used AMF model with GIBS algorithm to identify relevant factors, compared to FF5 model.
result AMF model shows time-invariant beta coefficients for most periods, FF5 does not.
Extends Kyle model to multiple traders with different time-preference coefficients.
problem Existence and convergence of discrete-time Kyle models with multiple insiders.
method Extends Basak and Cuoco's model to include traders with different time-preference coefficients.
result Parameter restrictions ensure the existence of a Radner equilibrium and long-term survival of traders.
Let be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various -related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…