arXiv research

The JLS model explains market crashes as critical phenomena.

In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.

Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis p…

A new sampler tackles critical phenomena by leveraging scale invariance.

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that obser…

Empirical study on trends reversion in financial markets.

This paper studies the critical dynamics of random surfaces, focusing on area and genus evolution.

We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.

An agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied. The model considered, while manageable, is significantly complex, however. It is alrea…

Optimistic Actor-Critic improves exploration efficiency in reinforcement learning.

Paper studies fractional CR Yamabe equation on sphere, proving multiplicity of solutions.

Grokking occurs in simple binary logistic classification near linear separability and noise.

Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believe…

Learning the distribution of natural images is one of the hardest and most important problems in machine learning. The problem remains open, because the enormous complexity of the structures in natural images spans all length scales. We break down the complexity of the problem and show that the hierarchy of structures …

We introduce a scalable measure of curvature for analyzing training dynamics of large language models.

The article uses complex system methods to predict cryptocurrency crises.

We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u=f .u^{\frac{n+2}{n-2}}$ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this purpose, we use a concept of "critical function" that was original…

We analyze the financial crash in 2008 for different financial markets from the point of view of log-periodic function model. In particular, we consider Dow Jones index, DAX index and Hang Seng index. We shortly discuss the possible relation of the theory of critical phenomena in physics to financial markets.

The self-similar analysis of time series, suggested earlier by the authors, is applied to the description of market crises. The main attention is payed to the October 1929, 1987 and 1997 stock market crises, which can be successfully treated by the suggested approach. The analogy between market crashes and critical phe…

We investigated the critical dynamics on the daily Taiwan stock exchange index (TSE) from 1971 to 2005, and the 5-min intraday data from 1996 to 2005. A global persistence exponent $θ_{p}$ was defined for non-equilibrium critical phenomena \cite{Janssen,Majumdar}, and describing dynamic behavior in an economic index \c…

Study critical exponents for L^p-cohomology of higher rank Lie groups and manifolds.

Study shows how close functions are to optimal in Riemannian manifolds.

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financia…

We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u = f.u^{\frac{n+2}{n-2}}$ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this purpose, we use a concept of "critical function" that was original…

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local…

Minimal model reveals power laws in financial markets.

In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Unfortunately, this model is unable to generate realistic market dynamics. The second model discards the requirement of centralized trading. Under vari…

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifest…

Survey of rigidity and gap phenomena in sphere-ball submanifolds.

Study predicts crypto-currency price collapses using standard deviation.

Predicts language model performance from public models without training.

Forecast future volatilities and correlations based on current trends.

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

Geometric study of linear neural networks identifies pure and spurious critical points.

Research examines coamenable subgroups in higher rank groups.

Machine learning integrates diverse biological data to understand complex phenomena.

The paper argues against the inefficiency of explaining deep learning phenomena.

Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the …

A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes, and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective p…

Modeling rainfall with a flexible Hawkes process.

The paper studies concentration of measure on manifolds with boundary, focusing on $1$-Lipschitz functions.

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…

Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.

The paper explores higher property T in lattices and its connections to geometric phenomena.

This research connects topological changes to cosmic phenomena like black hole formation.

Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.

In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…

Method detects critical events in complex systems by learning latent causal structure.