arXiv research

Ricci flow simulations show unstable Fubini-Study metrics develop singularities.

Noncompact Ricci-flat solutions have infinite unstable dimensions.

Study shows instability of naked singularities in scalar field models.

The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstei…

Study shows instability of naked singularities in perfect fluid models.

The paper proves stability of certain singularities in integrable systems.

The intent of this short note is to provide context for and an independent proof of the discovery of Klaus Kroencke that complex projective space with its canonical Fubini--Study metric is dynamically unstable under Ricci flow in all complex dimensions N>1. The unstable perturbation is not Kaehler. This provides a coun…

Study on stability of network flow shrinkers with findings on instability of specific shapes.

The paper assesses machine learning robustness with covariate perturbations.

Some of the most effective influential spreader detection algorithms are unstable to small perturbations of the network structure. Inspired by bagging in Machine Learning, we propose the first Perturb and Combine (P&C) procedure for networks. It (1) creates many perturbed versions of a given graph, (2) applies a node s…

We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This resu…

We show that, for odd $d$, the $L^{\frac{d+2}2}$ bounds of Sogge and Xi for the Nikodym maximal function over manifolds of constant sectional curvature, are unstable with respect to metric perturbation, in the spirit of the work of Sogge and Minicozzi. A direct consequence is the instability of the bounds for the corre…

There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments,lacking a microscopic underpinning in M-brane charge quantizatio…

Study on instability of extreme Reissner-Nordström spacetime perturbations.

Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…

Fateev's sausage sigma models in two and three dimensions are known to be integrable. We study their stability under RG flow in the target space by using results from the mathematics of Ricci flow. We show that the three dimensional sausage is unstable, whereas the two dimensional sausage appears to be stable at least …

In this announcement, we exhibit the second variation of Perelman's $λ$ and $ν$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central density" of a shrinking Ricci soliton and compute its values for certain examples in dimension 4. Using these tools, one can somet…

This note is devoted to Keller-Lieb-Thirring spectral estimates for Schrödinger operators on infinite cylinders: the absolute value of the ground state level is bounded by a function of a norm of the potential. Optimal potentials with small norms are shown to depend on a single variable. The proof is a perturbation arg…

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly using the weak form of master equation for probability evolution. In the small ste…

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated R…

Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…

On the one hand, we prove that the Clifford torus in $\mathbb{C}^2$ is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian $F$-stable and locally area minimising under Hamiltonian variations. On the other hand, we show that the Clifford torus is r…

Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.

Proposes a stable classifier using inflated argmax for multiclass classification.

MAS scores cluster size consistency from points, robust to label changes.

An elementary family of local Hamiltonians $H_{\c ,\ell}, \ell = 1,2,3, ldots$, is described for a $2-$dimensional quantum mechanical system of spin $={1/2}$ particles. On the torus, the ground state space $G_{\circ,\ell}$ is $(\log)$ extensively degenerate but should collapse under $ł$perturbation" to an anyonic syste…

This paper analyzes GANs using Fourier modes to stabilize training.

Generalised Degrees of Freedom (GDF), as defined by Ye (1998 JASA 93:120-131), represent the sensitivity of model fits to perturbations of the data. As such they can be computed for any statistical model, making it possible, in principle, to derive the number of parameters in machine-learning approaches. Defined origin…

New loss function helps learn unstable dynamical systems.

Unstable minimal surfaces in n-space link to hyperbolic products.

Segre varieties' hyperplane sections are unstable under certain conditions.

The paper improves confidence ellipsoids for ridge regression with PAC bounds.

Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…

Proves transitivity of real Anosov diffeomorphisms with specific properties.

Study shows instability of specific cone solutions in high-dimensional spaces.

In this note we show that the bi-invariant Einstein metric on the compact Lie group $G_{2}$ is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, $G_{2}$ is the only unstable exceptional…

Algorithm identifies and transfers unstable features to create robust classifiers.

Survey of computations for Riemann surface moduli spaces, focusing on unstable homology.

Constructs a family to handle unstable fibers on complex surfaces.

SFB uses stable features to adapt unstable ones for better performance.

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.

Researchers develop a numerical method to compute the index of self-shrinkers, finding it to be 5 for the Angenent torus.

In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like $g_{ij}=(1+\frac{1}{l})^{2}δ_{ij}+O(l^{-2})$. The existence of uns…

New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.

We show that the pair $(X, -K_X)$ is K-unstable for a del Pezzo manifold $X$ of degree five with dimension four or five. This disprove a conjecture of Odaka and Okada.

Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic n…

A crypto coin designed to provide a stabilization instrument backed up by minded like financial investments instruments to maintain the purchase value of savings across time, in order to construct new tools for unstable economies.