We assume a vector bundle with a general linear connection and a classical linear connection $\Lam$ on . We prove that all classical linear connections on the total space naturally given by $(\Lam, K)$ form a 15-parameter family. Further we prove that all connections on naturally given by…
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48 results for “Lamé coefficients”
The paper expands cluster algebra formulae to non-orientable surfaces and proves positivity.
problem Proving positivity for quasi-cluster algebras from non-orientable surfaces.
method Generalizing Musiker, Schiffler, and Williams' expansion formulae to principal laminations and quasi-triangulations.
result Positivity for quasi-cluster algebras is proven with respect to any choice of coefficients.
Let be a closed orientable surface with genus . For a sequence $\s_i$ in the Teichmüller space of , which converges to a projective measured lamination $[\lam]$ in the Thurston boundary, we obtain a relation between $\lam$ and the geometric limit of pants decompositions whose lengths are uniformly bound…
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACV…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an important task is to choose the regularization parameter $\lam$ appropriately, i.e.…
It was shown by Fomin, Shapiro and Thurston that some cluster algebras arise from orientable surfaces. Subsequently, Dupont and Palesi extended this construction to non-orientable surfaces. We link this framework to Lam and Pylyavskyy's Laurent phenomenon algebras, showing that both orientable and non-orientable unpunc…
This paper contains some vanishing theorems for harmonic forms on complete Riemannian manifolds with a weighted Poincaré inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but without assumptions of sign and growth rate of the weight function, so they can be a…
It was shown by Fock, Goncharov and Fomin, Shapiro, Thurston that some cluster algebras arise from triangulated orientable suraces. Subsequently Dupont and Palesi generalised this construction to include unpunctured non-orientable surfaces, giving birth to quasi-cluster algebras. Previously we linked this framework to …
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of …
The amplituhedra arise as images of the totally nonnegative Grassmannians by projections that are induced by linear maps. They were introduced in Physics by Arkani-Hamed \& Trnka (Journal of High Energy Physics, 2014) as model spaces that should provide a better understanding of the scattering amplitudes of quantum fie…
We prove the equality case of the Penrose inequality in all dimensions for asymptotically flat hypersurfaces. It was recently proven by G. Lam that the Penrose inequality holds for asymptotically flat graphical hypersurfaces in Euclidean space with non-negative scalar curvature and with a minimal boundary. Our main the…
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets of $\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the int…
The paper studies totally nonnegative parts of flag varieties and their topologies.
problem Understanding the topology of totally nonnegative flag varieties.
method Algebraic, geometric, and dynamical perspectives; orbit context; gradient flows; Riemannian metrics.
result Positivity is preserved in certain metrics on the totally nonnegative part of flag varieties.
The elliptic Hall algebra governs torus link homology.
problem Proving the elliptic Hall algebra's role in torus link homology.
method Developed a rational Shareshian-Wachs involution to prove the symmetry of generating functions.
result Resolved a conjecture by establishing the elliptic Hall algebra's role in torus link homology.
Financial markets are systems with the complex behavior, that can be hardly analyzed by means of linear methods. Recurrence Quantification Analysis (RQA) is a nonlinear methodology, which is able to work with the nonstationary and short data series. Thus, we apply RQA for the studying of the critical events on financia…
Classifies finite orbits of mapping class group action on character varieties.
problem Classifying finite orbits of mapping class group action on character varieties of punctured spheres.
method Inductive proof using Lisovyy--Tykhyy's classification for 4-punctured spheres as base case.
result Proves no finite orbits for 7-punctured spheres and unique 1-parameter family for 6-punctured spheres.
The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.
problem Understanding the relationship between Legendrian links and cluster theory.
method Using exact Lagrangian fillings and cluster theory, the paper establishes connections between Legendrian links and cluster varieties.
result The augmentation variety of certain Legendrian 2-bridge links is isomorphic to a product of cluster varieties.
In this paper we survey a number of recent results concerning the existence and moduli spaces of solutions of various geometric problems on noncompact manifolds. The three problems which we discuss in detail are: I. Complete properly immersed minimal surfaces in $\RR^3$ with finite total curvature. II. Complete embedde…
Study on braid monodromy of Lefschetz fibrations, proving infinite index subgroup.
problem Understanding the structure of braid monodromy in Lefschetz fibrations.
method Developed methods to show infinite index of subgroup, relating to character varieties.
result Proved infinite index subgroup for various cases of Lefschetz fibrations.
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.
Efficiently optimizes constrained problems with two-step lookahead BO.
problem Optimizing constrained problems with limited computational resources.
method Two-step lookahead Bayesian optimization with inequality constraints, using a novel unbiased gradient estimator.
result Significantly improves query efficiency over previous methods.
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.
ePF improves PF for ITS by balancing exploration and exploitation, outperforming baselines.
problem Premature exploitation in PF leads to suboptimal solutions under constrained budgets.
method Integrates Entropic Annealing and Look-ahead Modulation to preserve diversity and evaluate potential.
result Significant improvement in task reward (up to 50% relative) on math benchmarks.
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.
Privacy amplification improved through contraction coefficients and -divergence.
problem Improving privacy guarantees in iterative algorithms.
method Using contraction coefficients derived from -divergence to determine differential privacy parameters.
result Tighter bounds on differential privacy parameters of iterative algorithms.