arXiv research

Study attached submanifolds in solvmanifolds, generalizing symmetric space results.

This paper improves linear system solving by optimizing matrix diagonal scaling.

Defines compatibility between Jacobi structures and pseudo-Riemannian metrics on Jacobi algebroids.

This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.

Unified Jacobi coupling construction for various geometric settings.

We use the supergeometric formalism, more precisely, the so-called "big bracket" (for which brackets and anchors are encoded by functions on some graded symplectic manifold) to address the theory of Jacobi algebroids and bialgebroids (following mainly Iglesias-Marrero and Grabowski-Marmo as a guideline). This formalism…

We etablish a necessary and sufficient condition under which there exists a tangential and well graded star product, differential or not, on the dual g^* of a nilpotent Lie algebra g. We also give enlightening examples with explicit computations.

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

In this paper we prove some classification theorems of real hypersur- faces in Mn(c) satisfying certain conditions on the covariant derivative of the structure Jacobi operator. We also prove the non-existence of real hypersurfaces with Codazzi type structure Jacobi operator in Mn(c).

Defines Jacobi fields in nonholonomic mechanics.

The paper studies Jacobi fields and conjugate points in projective sprays.

The paper establishes conditions for harmonic forms on noncompact manifolds.

We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd vector field is deformed in a very specific way. This leads to the notion of a quasi…

Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.

This paper extends Jacobi field theory to Jacobi curves and their curvatures.

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for lo…

If $W_+$ denotes the self dual part of the Weyl tensor of any Kähler 4-manifold and $S$ its scalar curvature, then the relation $|W_+|^2 = S^2/6$ is well-known. For any almost Kähler 4-manifold with $S \ge 0$, this condition forces the Kähler property. A compact almost Kähler 4-manifold is already Kähler if it satisfie…

We study Jacobi structures on the dual bundle $A^\ast$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on $A$ and a 1-cocycle $φ\in Γ(A^\ast)$ indu…

The paper explores transformations between power law problems and geodesics on cones.

Paper proves non-existence of certain hypersurfaces in complex quadric.

Study on stability of 3D sessile drops, identifying degenerate kernel.

A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jac…

Reformulates elasticity complex with new differential and Hodge star operators.

Machine learning helps create accurate models of neutron star postmerger signals.

Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models

The study shows infinitely many Reeb orbits on star-shaped hypersurfaces with growth rate like prime numbers.

Introduces Star-Shaped deviation measures for risk analysis.

Algorithm learns weight matrix from single trajectory of nonlinear dynamical system.

In this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent a generalization of Jacobi fields from the classical calculus of variations, but…

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on the existence of Kähler metrics of constant scalar curvature. In the third part…

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

The paper generalizes offset Rademacher complexities to convex and non-convex problems.

The paper explores risk measures and arbitrage in financial markets.

New algorithm improves heteroskedastic PCA performance.

Let (M,g) be a Riemannian manifold and G a nondegenerate g-natural metric on its tangent bundle T M . In this paper we establish a relation between the Jacobi operators of (M,g) and that of (T M,G). In the case of a Riemannian surface (M,g), we compute explicitly the spectrum of some Jacobi operators of (TM,G) and give…

A unified framework for Poisson and Jacobi structures from 2-covariant tensors

The paper bounds eigenvalues of the Jacobi operator and derives rigidity results for CMC hypersurfaces.

Gradient descent with preconditioning finds global optima in overparameterized nonconvex factorization.

Study magnetic Hamiltonian systems with constraints, deriving Hamilton-Jacobi equations.

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low rank matrix $Θ^\star$ with a second matrix $Γ^\star$ endowed with a complementary …

In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field $T$, that is, $R_ξφT=TR_ξφ$, where $T=A$ or $T=S$ for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. By using simultaneous diagonalzation for commuting symmetric operators…

New algorithm for robust density estimation in corrupted data.

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.

Improved guarantees for nonconvex matrix factorization with rank overparameterization.

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

In this paper, we have considered a new commuting condition, that is, $(R_ξφ) S = S (R_ξφ)$ \big(resp. $(\Bar{R}_Nφ) S = S (\Bar{R}_Nφ$)\big) between the restricted Jacobi operator~$R_ξφ$ (resp. $\Bar{R}_Nφ$), and the Ricci tensor $S$ for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$. In terms of this condition we…

This paper provides guarantees for DFM models using KL divergence.