The study examines the stability of Einstein metrics on Sasaki Einstein and nearly parallel G2 manifolds.
problem Linear instability of Einstein metrics on Sasaki Einstein and nearly parallel G2 manifolds.
method Analysis of the second and third Betti numbers for Sasaki Einstein and nearly parallel G2 manifolds.
result Positive second and third Betti numbers lead to linear instability for the respective manifolds.
Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solu…
Generative adversarial nets (GANs) are a promising technique for modeling a distribution from samples. It is however well known that GAN training suffers from instability due to the nature of its maximin formulation. In this paper, we explore ways to tackle the instability problem by dualizing the discriminator. We sta…
Study shows instability of Kähler Ricci solitons and stability of orbifold singularities.
problem Linear stability and instability of Kähler Ricci solitons.
method Extending the approach of \cite{chi04} and \cite{hm11}, via recent work \cite{cm21} on gradient shrinking Ricci solitons.
result Linear instability of the BCCD shrinking soliton and stability of orbifold singularities of Kähler solitons.
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian product structures on the base. As an application, we estimate the coindex of the E…
The paper shows instability in Minkowski spacetime for a quantum system.
problem Linear instability of the semiclassical Einstein-Klein-Gordon system in Minkowski spacetime.
method Formulated a forcing problem for metric and state perturbations, used tensor decomposition and quantum Møller operator.
result Metric perturbations grow exponentially, bounded by a universal scale H, indicating quantum backreaction.
This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial da…
We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface …
Study on instability of extreme Reissner-Nordström spacetime perturbations.
problem Linear stability of gravitational and electromagnetic perturbations in extreme Reissner-Nordström spacetime.
method Extends Giorgi's framework to prove instability results for a set of gauge invariant quantities along the event horizon.
result Proves decay, non-decay, and polynomial blow-up estimates for certain quantities along the event horizon, depending on the number of derivatives.
We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distribut…
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with correctio…
NGRC shows numerical instabilities with short lags and high-degree polynomials.
problem Numerical instabilities in NGRC feature matrix.
method Combining numerical linear algebra and dynamical systems theory, we study feature matrix conditioning. We evaluate different numerical algorithms for solving the regularized least-squares problem.
result SVD-based training achieves accurate forecasts without regularization, preferable for short lags and high-degree polynomials.
Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets fro…
We improve current instability-based methods for the selection of the number of clusters k in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…
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…
New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.
problem Comparative analysis of regularization norms in ill-posed problems.
method Small noise analysis framework for Tikhonov and RKHS regularizations.
result Optimal convergence rates achieved with adaptive fractional RKHS, but hyper-parameters decay too fast.
Modeling HFT interactions reveals market instability.
problem Market instability caused by HFT dynamic coupling.
method Developed a recurrence relations framework to model HFT interactions.
result Unexpected latency and feedback can trigger market instability.
The paper explores how AI trading agents' similar information representation can cause financial market instability.
problem Systemic instability in AI-dominated financial markets due to similar information representation.
method Structural multi-agent market model with two-layer decision architecture for AI agents.
result Representation homogeneity can lead to systemic instability in financial markets.
New proof of instability for certain Einstein metrics.
problem Einstein metrics on specific 4-manifolds.
method Proving instability of conformally Kähler, Einstein metrics.
result Proven instability of certain Einstein metrics.
The study explains delayed spikes in batch-normalized models.
problem Delayed spikes in batch-normalized models.
method Analyzing batch-normalized linear models, deriving conditions for delayed onset and waiting time.
result Explicit conditions for delayed-onset and waiting time in whitened square-loss linear regression.
Study examines USD exchange rate dynamics using Kramers-Moyal expansion.
problem Understanding and predicting exchange rate instability.
method Kramers-Moyal expansion and Fokker-Planck formalism applied to log-return data.
result Identifies a stabilizing linear drift and nonlinear diffusion term in exchange rate fluctuations.
Study stability and instability of Ricci-flat metrics under generalized Ricci flow.
problem Stability and instability of Ricci-flat metrics under Ricci flow.
method Analysis of generalized Ricci flow for Ricci-flat metrics and vanishing 3-forms.
result Dynamical stability and instability results for Ricci-flat metrics and vanishing 3-forms.
Introduces TDRC to balance TD's ease and soundness.
problem TD learning's instability and divergence issues.
method Gradient Temporal-Difference Learning with Regularized Corrections (TDRC).
result TDRC performs as well as TD when TD works, but is sound in divergent cases.
Interval Neural Networks detect instabilities in image reconstructions.
problem Detecting instabilities in deep learning image reconstructions.
method Employed uncertainty quantification methods with Interval Neural Networks.
result Interval Neural Networks effectively reveal image reconstruction instabilities.
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
Momentum affects optimization differently at small vs large batch sizes near instability.
problem Understanding how momentum impacts optimization near the edge of stability.
method Demonstrated through batch-size dependent behavior of SGD with momentum.
result Momentum operates in two distinct regimes: amplifying stochastic fluctuations at small batch sizes and stabilizing at large batch sizes.
Binary perceptron's instability linked to replica symmetry breaking.
problem Understanding the relationship between algorithmic instability and replica symmetry breaking in binary perceptron learning.
method Established the connection between algorithmic instability and replica symmetry breaking by comparing the instability condition around the fixed point to the instability for breaking the replica symmetric solution of the free energy function.
result The instability condition around the algorithmic fixed point is identical to the instability for breaking the replica symmetric saddle point solution of the free energy function.
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …
Batch normalization prevents rank collapse in deep networks, improving training stability.
problem Rank collapse in randomly initialized deep networks with increasing depth.
method Investigates spectral instabilities in random matrices and uses batch normalization to avoid rank collapse.
result Batch normalization prevents rank collapse in both linear and ReLU networks, improving training stability.
We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a uniq…
Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, …
The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.
problem Stability and instability of Poincaré-Einstein metrics.
method Variant of expander entropy for asymptotically hyperbolic manifolds, local positive mass theorem, volume comparison.
result Characterization of stability and instability in terms of local positive mass theorem and volume comparison.
Many industrial machine learning (ML) systems require frequent retraining to keep up-to-date with constantly changing data. This retraining exacerbates a large challenge facing ML systems today: model training is unstable, i.e., small changes in training data can cause significant changes in the model's predictions. In…
Study shows instability of naked singularities in perfect fluid models.
problem Instability of naked singularities in Einstein equations coupled with isothermal perfect fluid.
method Investigated spherically symmetric self-similar naked singularities under C1,α perturbations of an external massless scalar field. result Spherically symmetric self-similar naked singularities are unstable to trapped surface formation.
Study on spectral stability of Riemannian coverings.
problem Stability of eigenvalues in Riemannian coverings.
method Analysis of Laplacian eigenvalues under finite coverings.
result Necessary conditions for spectral stability or instability.
Investigates stability of piecewise flat Ricci flow using analysis and simulations.
problem Stability of piecewise flat Ricci flow.
method Linear stability analysis and numerical simulations.
result Adaptations avoided numerical instability and led to convergence to smooth solutions.
Clinical models can be unstable, leading to unreliable predictions.
problem Stability of clinical prediction models developed using statistical or machine learning methods.
method Simulation and case studies of statistical and machine learning approaches to show instability in model predictions.
result Model instability often leads to miscalibration of predictions in new data.
The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of classifiers to adversarial perturbations, and show fundamental upper bound…
A data-driven approach predicts morphological development under structural instability.
problem Understanding and predicting spatiotemporal complexities of morphogenesis under structural instability.
method Machine-learning framework based on physical modeling of morphogenesis.
result Identification of key bifurcation characteristics and prediction of history-dependent development.
Study shows instability of naked singularities in scalar field models.
problem Stability of naked singularities in spherically symmetric Einstein-Scalar field systems.
method Analysis of a family of incoming null cones becoming increasingly singular.
result Naked singularities are unstable to black hole formation under certain perturbations.
Study shows instability of certain MOTSs with continuous symmetry.
problem Stability of MOTSs with continuous symmetry.
method Analysis of initial data sets with continuous symmetry and non-preserved MOTSs.
result Exotic MOTSs are unstable except in exceptional cases.
The paper studies stability and instability of minimal submanifolds in complex Einstein spaces.
problem Stability and instability of minimal submanifolds in complex Einstein spaces.
method Computation of index and nullity, investigation of stability, and algorithm for higher eigenvalues.
result Criterion for instability of minimal submanifolds in some cases.
Paper extends Simons theorem to F-Yang-Mills connections for instability.
problem Tackles instability of F-Yang-Mills connections. method Extends Simons theorem to F-Yang-Mills connections using Kobayashi-Ohnita-Takeuchi's method. result Derives a sufficient condition for instability of non-flat F-Yang-Mills connections. In this short article, we improve the dynamical stability and instability results for Ricci-flat metrics under Ricci flow proved by Sesum and Haslhofer, getting rid of the integrability assumption.
Proposes a new measure to evaluate stability of statistical parameters under distributional shifts.
problem Difficulty in transferring knowledge across data sets due to distributional changes.
method Introduces a measure of instability quantifying sensitivity of statistical parameters to Kullback-Leibler divergence and directional shifts.
result The proposed measure can elucidate the type of shifts a parameter is sensitive to and improve estimation accuracy under shifted distributions.
The paper analyzes numerical instability in variational flows and proposes a diagnostic method.
problem Numerical instability in variational flows affects sampling, density evaluation, and ELBO estimation.
method Treated variational flows as dynamical systems, used shadowing theory for theoretical guarantees, and developed a diagnostic procedure.
result Despite numerical instability, results from variational flows can be accurate enough for practical applications.
Proposes a continuous flow model to understand and control instability in gradient descent for deep learning.
problem Understanding and controlling the instability of gradient descent in deep learning.
method Introduces the Principal Flow (PF), a continuous time flow that approximates gradient descent dynamics.
result The PF captures divergent and oscillatory behaviors of gradient descent, including escaping local minima and saddle points.
In this paper, we study stability for harmonic foliations on locally conformal Kähler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces.