Tootfinder

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
Xin He, Ya-Ping Fang
https://arxiv.org/abs/2509.08258

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $μ_F$- and $μ_G$-strongly convex functions, respectively. By incorporating Nesterov acceleration for strongly convex optimization, we first propose an optimal first-order discrete primal-dual gradient algorithm. We show that it achieves the optimal convergence rate $\mathcal{O}\left(\left(1 - \min\left\{\sqrt{\frac{μ_F}{L_F}}, \sqrt{\frac{μ_G}{L_G…

Running: approx 6min/km - feels good! I' back in the saddle and soon I'll do a km on 5 min average again

Replaced article(s) found for physics.chem-ph. https://arxiv.org/list/physics.chem-ph/new
[1/1]:
- Efficient Implementation of Gaussian Process Regression Accelerated Saddle Point Searches with Ap...
Rohit Goswami, Maxim Masterov, Satish Kamath, Alejandro Pe\~na…

Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity
Jos\'e Valero
https://arxiv.org/abs/2507.22452 https://

Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac delta distribution, we analyze the stability of the stationary solutions and demonstrate that they exhibit a saddle-point structure. As a result, we establish the hyperbolicity of the fixed points.

Superlinear gradient growth for 2D Euler equation without boundary
In-Jee Jeong, Yao Yao, Tao Zhou
https://arxiv.org/abs/2507.15739 https://

Superlinear gradient growth for 2D Euler equation without boundary
We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus $\mathbb{T}^{2}$ and the whole plane $\mathbb{R}^{2}$. In the torus, whenever we have a steady state $ω^*$ that is orbitally stable up to a translation and has a saddle point, we construct ${\tildeω}_0 \in C^\infty(\mathbb{T}^2)$ that is arbitrarily close to $ω^*$ in $L^2$, such that superlinear growth of the vorticity gradient occurs for an open set …

Disorder-aided Early Warning Signals: Predicting Catastrophic Shifts in Athermal Systems
Tapas Bar, Anurag Banerjee, Blai Casals, Gustau Catalan, Javier Rodr\'iguez-Viejo
https://arxiv.org/abs/2509.01601

Disorder-aided Early Warning Signals: Predicting Catastrophic Shifts in Athermal Systems
The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat becomes particularly acute in low-fluctuation environments, where tipping occurs through saddle-node bifurcation without prior warning in noise dynamics. In this study, we investigate the tipping point dynamics of avalanche catastrophes in low-fluctuation domain,…

Space-Time Coded RIS-Assisted Wireless Systems with Practical Reflection Models: Error Rate Analysis and Negative Moment-Based Optimization with Saddle Point Approximation
Tayfun Yilmaz, Haci Ilhan, Ibrahim Hokelek
https://arxiv.org/abs/2508.19129

Space-Time Coded RIS-Assisted Wireless Systems with Practical Reflection Models: Error Rate Analysis and Negative Moment-Based Optimization with Saddle Point Approximation
RIS-assisted communication has recently attracted significant attention for enhancing wireless performance in challenging environments, making accurate error analysis under practical hardware constraints crucial for future multi-antenna systems. This paper presents a theoretical framework for SER analysis of RIS-assisted multiple antenna systems employing OSTBC under practical reflection models with amplitude-dependent and quantized phase responses. By exploiting the Gramian structure of the ca…

Coupling Anisotropic Curvature and Nematic Order: Mechanisms of Membrane Shape Remodeling
Yoav Ravid, Samo Peni\v{c}, Luka Mesarec, Nir S. Gov, Veronika Kralj-Igli\v{c}, Ale\v{s} Igli\v{c}, Mitja Drab
https://arxiv.org/abs/2506.14347

Coupling Anisotropic Curvature and Nematic Order: Mechanisms of Membrane Shape Remodeling
This study theoretically investigates how anisotropic curved membrane components (CMCs) control vesicle morphology through curvature sensing, nematic alignment, topological defects, and volume constraints. By comparing arc-shaped and saddle-shaped CMCs, we identify a rich spectrum of steady-state phases. For fully CMC-covered vesicles, arc-shaped components drive a pearling-to-cylinder transition as nematic interactions strengthen, while on partially CMC-covered vesicles, the saddle-shaped CMCs…

Testing the effective action approach to bubble nucleation in holography
Oscar Henriksson, Niko Jokela, Xin Li
https://arxiv.org/abs/2507.11622 https://

Testing the effective action approach to bubble nucleation in holography
The nucleation of bubbles during a first-order phase transition has recently been explored using holographic duality, which can provide an important complement to standard perturbative methods. These computations typically require finding static and spatially inhomogeneous saddle points, known as critical bubbles, which correspond in the gravitational dual to solutions of nonlinear partial differential equations. A computationally simpler alternative is to use the gravitational dual to derive t…

Higher-Oder Splitting Schemes for Fluids with Variable Viscosity
Richard Schussnig, Niklas Fehn, Douglas Ramalho Queiroz Pacheco, Martin Kronbichler
https://arxiv.org/abs/2506.14424

Higher-Oder Splitting Schemes for Fluids with Variable Viscosity
This article investigates matrix-free higher-order discontinuous Galerkin (DG) discretizations of the Navier-Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a rheological law, as often found in biomedical or industrial applications. We compare several linearized variants of saddle point block systems and projection-based splitting time integration schemes in terms of their computational performance. Compared to…

$C^1$ invariant and inertial manifolds for non-autonomous dynamical systems
Rados{\l}aw Czaja, Piotr Kalita
https://arxiv.org/abs/2508.00165 https://arxiv.…

$C^1$ invariant and inertial manifolds for non-autonomous dynamical systems
Recent article by Carvalho et al. [J. Differential Equations 416 (2025)] presents in a~unified framework the Lyapunov--Perron construction of invariant and inertial manifolds together with the saddle point property. We extend their results on the existence of non-autonomous inertial manifolds by considering the gap condition which is known to be sharp. Moreover, we show that the constructed inertial manifolds have $C^1$ regularity.

Gradient descent avoids strict saddles with a simple line-search method too
Andreea-Alexandra Mu\c{s}at, Nicolas Boumal
https://arxiv.org/abs/2507.13804 ht…

Gradient descent avoids strict saddles with a simple line-search method too
It is known that gradient descent (GD) on a $C^2$ cost function generically avoids strict saddle points when using a small, constant step size. However, no such guarantee existed for GD with a line-search method. We provide one for a modified version of the standard Armijo backtracking method with generic, arbitrarily large initial step size. In contrast to previous works, our analysis does not require a globally Lipschitz gradient. We extend this to the Riemannian setting (RGD), assuming the…

Complexity of Coexistence Regions in the GRHT Map
Sishu Shankar Muni
https://arxiv.org/abs/2506.13515 https://arxiv.org/pdf/2506.1351…

Complexity of Coexistence Regions in the GRHT Map
GRHT map refers to a planar map which showcases the coexistence of infinitely many stable periodic orbits via the phenomenon of Globally Resonant Homoclinic Tangencies. This paper investigates the geometric properties of coexistence regions in the case of codimension-three scenario. We introduce parameters into the non-invertible GRHT map to understand the unfolding behavior of the GRHT. Near the infinite coexistence regions, there exists series of codimension-one saddle-node and period-doublin…