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.
We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our model allows for contagious simultaneous jumps in credit ratings and provides flexib…
Graph auto-encoders predict stock market instability by measuring graph structure changes.
problem Forecasting stock market instability and volatility.
method Use graph auto-encoders to reconstruct graph structure and measure changes.
result Higher GAE reconstruction error correlates with higher volatility.
Researchers compute cohomology of mapping class groups with Prym representations, showing instability for large genus.
problem Computing the cohomology of mapping class groups with level structures and Prym representations.
method Using twisted cohomology and Prym representations for any positive integer r.
result Cohomology exhibits instability for large genus, but remains stable for r=0 or r=1.
Following the financial crisis of 2007-2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the…
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.
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.
Topic models can provide us with an insight into the underlying latent structure of a large corpus of documents. A range of methods have been proposed in the literature, including probabilistic topic models and techniques based on matrix factorization. However, in both cases, standard implementations rely on stochastic…
Study uses DNM theory to detect early warning signals of market instability.
problem Detecting early warning signals of financial market instability.
method Applying Dynamical Network Marker (DNM) theory to trading data from the Tokyo Stock Exchange.
result Early warning signals of large price movements can be detected on a daily time scale.
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 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…
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.
New model addresses instability in hierarchical clustering of social networks.
problem Instability in existing hierarchical clustering algorithms for social networks.
method Introduce T-Stochastic Graphs, a probabilistic model that relaxes ultrametric assumptions. result Prove spectral approach combining Neighbor-Joining is statistically consistent.
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.
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…
This paper examines how investors mislearn factor risk premia under structural breaks in a misspecified Bayesian framework.
problem Investors' mislearning of factor risk premia under structural breaks in asset pricing models.
method Proposes a minimal Bayesian framework to study how investors learn under a misspecified model that underestimates structural breaks.
result Elevated mislearning is associated with stronger long-horizon returns and Sharpe ratios, consistent with an equilibrium premium for acute model uncertainty.
Bayesian neural network predicts planetary instability.
problem Predicting planetary instability in compact systems.
method Novel Bayesian neural network trained on raw orbital elements.
result Model predicts planetary instability times with high accuracy and robust generalization.
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.
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…
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.
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 …
AEN-SAEs address feature starvation in sparse autoencoders by stabilizing the geometric alignment of sparse coding.
problem Feature starvation in sparse autoencoders, leading to unstable and misaligned representations.
method Adaptive Elastic Net SAEs (AEN-SAEs) combine ℓ2 and ℓ1 terms to stabilize the sparse coding map and control feature interactions. result AEN-SAEs mitigate feature starvation without heuristic resampling, maintaining competitive reconstruction abilities.
Neural networks allow Q-learning reinforcement learning agents such as deep Q-networks (DQN) to approximate complex mappings from state spaces to value functions. However, this also brings drawbacks when compared to other function approximators such as tile coding or their generalisations, radial basis functions (RBF) …
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.
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.
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is regarded as a convex combination of a small number of vectors corresponding to `topic…
Network geometry measures predict market instability.
problem Predicting financial market instability using network geometry.
method Discrete Ricci curvatures to capture network fragility.
result Different geometric measures distinguish normal and crash periods.
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.
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.
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.
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.
The Euler-Lagrange equations for the variational approach to the Seiberg-Witten equations always admit reducible solutions. In this context, the existence of unstable reducible solutions is achieved by assuming the existence of a parallel spinor or the negativeness of a Perelman-Yamabe type of invariant defined for a $…
Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.
problem Traditional risk measures fail to capture market dynamics' geometric structure.
method Applied Takens' Delay Embedding Theorem to generate point cloud, computed persistent homology groups, defined Topological Persistence Norm.
result Proposed leverage calibration heuristic based on persistence of 1-dimensional cycles.
Dual-objective GANs reduce training instabilities with tunable α-loss parameters.
problem Training instabilities in Generative Adversarial Networks (GANs).
method Introduce (αD,αG)-GANs with dual objectives modeled using α-loss. result Upper bounds on estimation error show improved performance under certain conditions.
We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal sur…
We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces Nk,l=SU(3)/ik,l(S1) (which are all nearly G2 except N1,0), and Sasaki Einstein circle bundles over certain ir…