arXiv research

Example found of non-conical Hermitian Yang-Mills connection.

Paper proves Łojasiewicz inequalities near simple bubble trees on surfaces.

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.

The paper models cryptocurrency market bubbles using agent-based models.

In this paper, we study the weak compactness of the set of conformal metrics in any Riemann surface without boundary whose Calabi energy and area are uniformly bounded. We prove that for any sequence of such metrics, there alwasy exists a subsequence which converges in H\sp{2,2}_\sb{loc} everywhere except a finite numb…

Degenerations of rank-two bundles on threefolds lead to isolated point singularities, with rigidity and bubbling properties.

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of the hypotheses offered to …

We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls C1 boundary regularity. We examin…

Methodology that recently lead us to predict to an amazing accuracy the date (July 11, 2008) of reverse of the oil price up trend is briefly summarized and some further aspects of the related oil price dynamics elaborated. This methodology is based on the concept of discrete scale invariance whose finance-prediction-or…

The principal aim of this work is the evidence on empirical way that catastrophic bifurcation breakdowns or transitions, proceeded by flickering phenomenon, are present on notoriously significant and unpredictable financial markets. Overall, in this work we developed various metrics associated with catastrophic bifurca…

Local examples of singular connections with bounded energy.

Machine learning is used extensively in recommender systems deployed in products. The decisions made by these systems can influence user beliefs and preferences which in turn affect the feedback the learning system receives - thus creating a feedback loop. This phenomenon can give rise to the so-called "echo chambers" …

A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, whi…

Study shows how tangle geometry maps onto pillowcase surfaces.

Analog to the classical result of Kazdan-Warner for the existence of solutions to the prescribed Gaussian curvature equation on compact 2-manifolds without boundary, it is widely known that if $(M,g_0)$ is a closed 4-manifold with zero $Q$-curvature and if $f$ is any non-constant, smooth, sign-changing function with $\…

The paper revisits classical competition theory to explain speculative asset price dynamics.

In this paper we will prove that for a compact, symplectic manifold $(M, ω)$ and for $ω$-compatible almost-complex structure J any properly perturbed J-holomorphic curve has a non-negative symplectic area. This non-negative property provides us with a new obstruction to the bubbling off phenomenon and thus allows us to…

We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a…

We investigated the temporally evolving network structures of the Japanese and Korean stock markets through the minimum spanning trees composed of listed stocks. We tested the validity of conventional grouping by industrial categories, and found a common trend of decrease for Japan and Korea. This phenomenon supports t…

Characterizes critical points in convex double and triple bubbles.

The paper studies associative Smith maps and proves their properties, including regularity and energy gap.

Survey on soap bubble partitions and their stability.

Bubbles are essential in certain economic models with high growth and low interest rates.

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Rational bubbles form in nonstationary models of real assets.

Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.

CR Yamabe flow fails to converge on small deformations of the standard CR three-sphere.

It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This holds true in market models where no equivalent local martingale measure exists but only a square-integrable market price of…

Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.

Degenerate solutions found in 2D H-system bubbles with higher degrees.

Study detects Chinese stock market bubbles using LPPLS confidence indicator.

This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that docum…

On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experime…

Continuous time analysis of bubble formation in harmonic maps.

Trading bubbles form when traders adapt to price mismatches.

Solves the quintuple bubble problem on spheres and Euclidean spaces.

This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that documen…

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The …

Paper evaluates whether AI is a bubble or a productivity revolution.

Study detects Bitcoin bubbles and predicts crashes using adaptive multilevel time series detection.

Study on metric bubbles in complex dimensions 1 and 2.

Modeling stochastic arbitrage bubbles in Black-Scholes framework.

Study predicts NFT bubbles using LPPL model.

Study asset price bubbles in markets with short sales prohibitions and model uncertainty.

Study reveals investor behavior in NFT bubbles.

Study of immersions with Willmore energy leading to spherical and catenoid bubbles.

The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detec…