arXiv research

Study stability and instability of Ricci-flat metrics under generalized Ricci flow.

Modeling HFT interactions reveals market instability.

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.

The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.

We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the Laplace spectrum. In particular, we prove dynamical stability of some classes of E…

Study uses DNM theory to detect early warning signals of market instability.

The paper analyzes numerical instability in variational flows and proposes a diagnostic method.

Proposes a continuous flow model to understand and control instability in gradient descent for deep learning.

Binary perceptron's instability linked to replica symmetry breaking.

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 …

We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affe…

This paper improves forecast stability without sacrificing accuracy using dynamic loss weighting.

Study examines USD exchange rate dynamics using Kramers-Moyal expansion.

Bayesian neural network predicts planetary instability.

The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.

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…

Novel approach analyzes ReLU networks' training dynamics and proposes GmP for improved optimization.

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…

Noncompact Ricci-flat solutions have infinite unstable dimensions.

Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.

NGRC shows numerical instabilities with short lags and high-degree polynomials.

New method stabilizes GAN training by solving ODEs.

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…

Gradient flossing stabilizes RNN training by controlling Lyapunov exponents.

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, cross-correlation matrices are calculated with a rolling win…

We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and percolation phase transitions pr…

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is…

Crowded trades cluster investors, affecting stock price stability.

Investment diversification affects financial stability, depending on network connectivity.

Ankle sprains and instability are major public health concerns. Up to 70% of individuals do not fully recover from a single ankle sprain and eventually develop chronic ankle instability (CAI). The diagnosis of CAI has been mainly based on self-report rather than objective biomechanical measures. The goal of this study …

Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that adapt to information. Surprising connections are found between two apparently unr…

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 describe the innovations in finances, introduced over the recent decades, and analyze most of the business and regulatory challenges, faced by the financial industry, because of the present disruptive changes in the global capital markets. We use the integrative thinking approach to formulate the new central bank st…

Network geometry measures predict market instability.

Momentum affects optimization differently at small vs large batch sizes near instability.

New proof of instability for certain Einstein metrics.

Survey discusses recent advances on Brakke flows and their properties.

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…

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high frequency cojumps. We show that the dynamics of these jumps is described neither …

Interval Neural Networks detect instabilities in image reconstructions.

Note on instabilities in super-time-stepping methods for Heston model.

The paper explores how word embeddings affect the stability of downstream NLP models.

In speculative markets, risk-free profit opportunities are eliminated by traders exploiting them. Markets are therefore often described as "informationally efficient", rapidly removing predictable price changes, and leaving only residual unpredictable fluctuations. This classical view of markets absorbing information a…

Static spacetimes are stable attractors in a flow equation.

Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.

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…

This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.

New method selects data points for better model performance.