arXiv research

The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.

Stability of singularity formation in Yang-Mills fields in higher dimensions.

Global stability bounds for matrix frames in phase retrieval problems.

Extends Minkowski stability proof to minimal decay assumptions.

Extends global stability of Minkowski spacetime to minimal decay assumptions.

This paper deals with global asymptotic stability of prolongations of flows induced by specific vector fields and their prolongations. The method used is based on various estimates of the flows.

Stability proved for open Milne spacetime, showing gravity's long-term behavior.

Proves stability of Minkowski space for specific initial data.

New method creates vacuum data at minimal and borderline decay thresholds.

New method for private density estimation of high-dimensional Gaussian mixtures.

The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the…

New study on replicability and stability in machine learning algorithms.

Paper analyzes SHB method for neural networks, proving stability, connectivity, and global convergence.

Solves Tian's stabilization problem for toric Fano manifolds.

Study global solutions for Boussinesq systems on curved manifolds.

Study stability of surfaces in spacetimes, proving new estimates and theorems.

Study on discrete Okounkov bodies and their applications.

Smooth actions on manifolds can be globally defined under certain conditions.

New stability thresholds detect K-stability in Fano manifolds.

Paper presents neural network controllers for offset-free setpoint tracking.

Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.

Private classification and online prediction are shown to be equivalent.

Study on stability and continuity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds.

Stable blowup profile identified for wave maps in all dimensions.

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $λ$, we study Hyers-Ulam stability of the global differential equation $Vy=λy+f$.

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems for compact foliations in Kaehler manifolds of Edwards-Millett-Sullivan and Hollma…

The stability analysis of socioeconomic systems has been centered on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. …

New stabilization found in planar elasticae with degenerate diffusion.

Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving a small data semi-global existence result for the characteristic initial value p…

Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.

Global stability proved for Navier-Stokes equations on hyperbolic space.

Study on stability of geodesic maps in non-isotropic manifolds.

A new proof of Friedrich's theorem on the existence and stability of asymptotically de Sitter spaces in 3+1 dimensions is given, which extends to all even dimensions. In addition, we characterize the possible limits of spaces which are globally asymptotically de Sitter, to the past and future.

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …

Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes rational decisions that would absolutely minimize the risk. Here we show that, for…

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global market…

We study the stability and convergence of training deep ResNets with gradient descent. Specifically, we show that the parametric branch in the residual block should be scaled down by a factor $τ=O(1/\sqrt{L})$ to guarantee stable forward/backward process, where $L$ is the number of residual blocks. Moreover, we establi…

We establish novel generalization bounds for learning algorithms that converge to global minima. We do so by deriving black-box stability results that only depend on the convergence of a learning algorithm and the geometry around the minimizers of the loss function. The results are shown for nonconvex loss functions sa…

We introduce a holomorphic sheaf E on a Sasaki manifold and study two new notions of stability for E along the Sasaki-Ricci flow related to the `jumping up' of the number of global holomorphic sections of E at infinity. First, we show that if the Mabuchi K-energy is bounded below, the transverse Riemann tensor is bound…

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy problem. This solution is linearly unstable, and we show that this …

We consider an evolving plane curve with two endpoints that can move freely on the $x$-axis with generating constant contact angles. We discuss the asymptotic behavior of global-in-time solutions when the evolution of this plane curve is governed by area-preserving curvature flow equation. The main result shows that an…

Study on stability of cylindrical singularities in MCF of finite codimensions.

We give a topological stability result for the action of the fundamental group of a compact manifold of negative curvature on its boundary at infinity: any nearby action of this group by homeomorphisms of the sphere is semi-conjugate to the standard boundary action. Using similar techniques we prove a global rigidity r…

The article analyzes the stability of a curve shortening flow for planar networks.

Groups' boundary actions are stable under small perturbations.

Paper proves stability for recovering connections from holonomy traces.

The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international …

The paper explores maximal destabilizers for both K-stability and Chow-stability in unstable situations.