arXiv research

Study of fastest paths in anisotropic media via Finsler geometry.

The paper finds inequalities in Grassmannian geometry.

By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…

In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection law.

Generalizes Fermat's principle for wave propagation in cone structures.

Study proves uniqueness for ray transform on surfaces with obstacles.

Reflective Hamiltonian Monte Carlo struggles with high-dimensional sampling.

On a time-oriented Lorentzian manifold $(M,g)$ with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets $S\subset M$ of sources is uniquely determined by measurements of the intersection of future light cones from points in $S$ …

A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…

We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…

Study of billiards in sub-Finsler geometry, including unusual orbits.

Study shows cliff-learning in transfer learning from foundation models.

This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz' law and investment opportunities are constant. Healthcare slows the natural growth of mortality, indirectly increasing utility from c…

Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of …

We show that power-law analyses of financial commentaries from newspaper web-sites can be used to identify stock market bubbles, supplementing traditional volatility analyses. Using a four-year corpus of 17,713 online, finance-related articles (10M+ words) from the Financial Times, the New York Times, and the BBC, we s…

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. Thi…

The {\em drawdown} process $Y$ of a completely asymmetric Lévy process $X$ is equal to $X$ reflected at its running supremum $\bar{X}$: $Y = \bar{X} - X$. In this paper we explicitly express in terms of the scale function and the Lévy measure of $X$ the law of the sextuple of the first-passage time of $Y$ over the leve…

The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenom…

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simpl…

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

Optimal trading strategy derived for nonlinear price impact models.

The energy in a square membrane $Ω$ subject to constant viscous damping on a subset $ω\subset Ω$ decays exponentially in time as soon as $ω$ satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch" condition. The rate $τ(ω)$ of this decay satisfies $τ(ω)= 2 \min(-μ(ω), g(ω))$ (see Lebeau [Math. Phys. Stud. …

Two-sample tests improve on existing methods for microtubule data.

Smart contracts are a digital technology with potential but also flaws.

Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws similar to, for example, turbulent fluids. They are believed to reflect the comp…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should seek alternatives. Fortunately, many of the laws of behaviour of the physical wor…

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensitie…

Accumulated stock returns exhibit tempered skew t-distribution.

New method uses scalars to approximate physics functions.

We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…

Paper develops an attention mechanism for long-term scientific impact prediction.

Is the present economic and financial crisis similar to some previous one? It would be so nice to prove that universality laws exist for predicting such rare events under a minimum set of realistic hypotheses. First, I briefly recall whether patterns, like business cycles, are indeed found, and can be modeled within a …

Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor $λ\approx 2$, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place w…

Bayesian method learns from aggregated quantile data.

Reflective of income and wealth distributions, philanthropic gifting appears to follow an approximate power-law size distribution as measured by the size of gifts received by individual institutions. We explore the ecology of gifting by analysing data sets of individual gifts for a diverse group of institutions dedicat…

This work generalizes Hamiltonian mechanics using closed differential forms.

We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in t…

Paper investigates separating times for general diffusions, providing new insights.

A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.

New method produces reflections with nonseparating fixed points.

Survey explores interactions between four conformal dynamics branches.

Based on the tick-by-tick price changes of the companies from the U.S. and from the German stock markets over the period 1998-99 we reanalyse several characteristics established by the Boston Group for the U.S. market in the period 1994-95, which serves to verify their space and time-translational invariance. By increa…

One reflection suffices for orthogonal weights, reducing GPU usage.

This paper uses LLMs and cycle consistency for better machine translation evaluation.

A framework detects where constitutive models fail in elastography, improving clinical interpretation.

Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.

Study thin hyperbolic reflection groups and their properties.

Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.