arXiv research

Selective relevance method improves motion explainability in 3D activity recognition models.

We propose a method to classify cardiac pathology based on a novel approach to extract image derived features to characterize the shape and motion of the heart. An original semi-supervised learning procedure, which makes efficient use of a large amount of non-segmented images and a small amount of images segmented manu…

Explains planetary motion in a sub-Riemannian setting.

Modeling stock price fluctuations using Brownian motion and stochastic differential equations.

We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …

Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.

We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that o…

Current techniques for explainable AI have been applied with some success to image processing. The recent rise of research in video processing has called for similar work n deconstructing and explaining spatio-temporal models. While many techniques are designed for 2D convolutional models, others are inherently applica…

GCRL learns causal factors for motion forecasting, improving out-of-distribution prediction.

This paper explains how predictable order flow can lead to Brownian motion in financial prices.

In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…

The study tackles rough noise in high-frequency financial data using fractional Brownian motion.

We prove conjectures of Rene Thom and Vladimir Arnold for C^2 solutions to the degenerate elliptic equation that is the level set equation for motion by mean curvature. We believe these results are the first instances of a general principle: Solutions of many degenerate equations behave as if they are analytic, even wh…

Study examines how body segments respond to random vibrations.

NYSE stock prices show persistent correlations over years, exploitable through arbitrage strategies.

Study of a generalized geometric Brownian motion with varying entry and exit rates.

We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …

The Lie group Sol(p,q) is the semidirect product induced by the action of the real numbers R on the plane R^2 which is given by (x,y) --> (exp{p z} x, exp{-q z} y), where z is in R. Viewing Sol(p,q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift …

The paper uses the variance-gamma model to price options and explain excess kurtosis.

I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric mechanics and Mathematical Physics. After a short discussion of the Lagrangian and Hamiltonian formalisms, including the use of symmetry groups, and a presentation of the Tulczyjew's isomorphisms (which expl…

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evide…

The paper teaches robots to navigate by learning costs from expert demonstrations.

For autonomous agents to successfully operate in real world, the ability to anticipate future motions of surrounding entities in the scene can greatly enhance their safety levels since potentially dangerous situations could be avoided in advance. While impressive results have been shown on predicting each agent's behav…

Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6, 7]. This widespread observed regularity has been explained in many ways: genera…

Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model j…

Introduces Motion Programs for better video analysis of human motion.

We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Per…

We develop a second-order model for limit order books in a single scaling regime.

Study motion planning for points avoiding obstacles in a plane.

Programmatic Motion Concepts learn human actions from paired videos.

Unified framework for human motion generation on Riemannian manifolds.

Study on determinants of unitary Brownian motion and their asymptotic laws.

Treebolic space is an analog of the Sol geometry, namely, it is the horocylic product of the hyperbolic upper half plane H and the homogeneous tree T with degree p+1 > 2, the latter seen as a one-complex. Let h be the Busemann function of T with respect to a fixed boundary point. Then for real q > 1 and integer p > 1, …

New framework predicts diverse, contextually plausible 3D human motions.

We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion. We construct a large set of scaling solutions of Fokker-Planck partial differential equations where H is not 1/2. Thus Markov processes, …

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This result has been established using high frequency volatility estimations from histor…

Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex d…

Study refracted skew Brownian motion, find densities and asymptotics.

Neural network predicts vessel motions with high accuracy.

Study fractal dimension for motion without crossing a subset.

Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We consider a holomorphic motion $φ$ of $E$ over a complex manifold $M$, that is, a holomorphic family of injections on $E$ parametrized by $M$. It is known that if $M$ is the unit disk $Δ$ in the complex plane, then any holomorphic motion of $E$ ove…

Study cohomological equation for robotic screw motions on SE(3).

New approach for obstacle avoidance in robotics using learned representations.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

The paper presents a method to reduce arm motion complexity for prosthetics and robotics.

The paper develops a method to learn navigation costs from expert demonstrations in partially observable environments.

Researchers calculate the Laplace transform of a geometric Brownian motion integral.

Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…