arXiv research

New methods control false discoveries near the boundary in conformal novelty detection.

New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.

Study on controllability and groups of manifolds with boundaries.

In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…

A new method solves American put options with high accuracy and speed.

This paper controls a boundary term in Huisken's formula for entropy.

In this paper we consider the Ricci flow on manifolds with boundary with appropriate control on its mean curvature and conformal class. We obtain higher order estimates for the curvature and second fundamental form near the boundary, similar to Shi's local derivative estimates. As an application, we prove a version of …

Develops control and observer methods for complex systems.

New boundary and point constraints for controlling conformal surfaces.

The study bounds the topology of free boundary minimal surfaces in 3D manifolds.

Quantifies fractional isoperimetric inequality with strong control over boundary oscillation.

Improved numerical solution for BSDEs with reduced boundary errors.

This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.

A famous open problem asks whether the asymptotic dimension of a CAT(0) group is necessarily finite. For hyperbolic groups, it is known that asymptotic dimension of the group is bounded above by the dimension of the boundary plus one, which is known to be finite. For CAT(0) groups, the latter quantity is also known to …

LGAC enhances heat transfer in turbulent boundary layers using slot jets.

We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale. The scale allows us to apply a blow-up argument to obtain c…

Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non co…

Proves ε-regularity for capillary surfaces in Riemannian manifolds.

We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determi…

We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal inve…

We study the short-time existence and regularity of solutions to a boundary value problem for the Ricci-DeTurck equation on a manifold with boundary. Using this, we prove the short-time existence and uniqueness of the Ricci flow prescribing the mean curvature and conformal class of the boundary, with arbitrary initial …

Study controllability of diffeomorphisms of simple polytopes.

Smoothly attaches manifolds with controlled curvature.

Constructs minimal surfaces in balls, maximizing eigenvalues.

The paper proves stability for scalar-flat metrics on manifolds with boundary.

In high-dimensional classification settings, we wish to seek a balance between high power and ensuring control over a desired loss function. In many settings, the points most likely to be misclassified are those who lie near the decision boundary of the given classification method. Often, these uninformative points sho…

This article presents some methods to control the bottom of the spectrum of the Laplacian $λ_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $λ_0$ of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built …

Researchers recover Riemannian manifolds and lower order terms from travel time data.

We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …

In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated Quasi-Variational-Inequalities include an essential game comp…

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general…

New theory extends LQ control to non-exponential discount scenarios.

Consider a compact Riemannian manifold with boundary. In this short note we prove that under certain positive curvature assumptions on the manifold and its boundary the Steklov eigenvalues of the manifold are controlled by the Laplace eigenvalues of the boundary. Additionally, in two dimensions we obtain an upper bound…

Solves inventory control with unknown demand trend using singular control.

New BdryMatérn GP model for reliable boundary integration on irregular domains.

Optimizes maps with controlled distortion for geometric tasks.

Paper examines stability of minimizing metrics on manifolds with boundary.

The paper tackles dynamic collateral control for spot-perpetual basis trading in decentralized finance.

We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems (OCPs). It covers the standard PMP, as well as gives necessary optimality condi…

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and deri…

Groups' boundary actions are stable under small perturbations.

A model optimizes carbon emission reduction and allowance purchasing for companies.

For a sequence of coupled fields $\{(φ_n,ψ_n)\}$ from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up pr…

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditio…

Study optimal consumption with relaxed benchmarks and drawdown constraints.

We improve Riemannian metrics for constrained systems control.

Framework calculates positional influence in causal residual Transformers.

Inspired by work of Ejiri-Micallef on closed minimal surfaces, we compare the energy index and the area index of a free-boundary minimal surface of a Riemannian manifold with boundary, and show that the area index is controlled from above by the area and the topology of the surface. Combining these results with work of…