A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
Gaussian Process Hydrodynamics approximates fluid flow equations using probabilistic kernels.
We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent flui…
The paper studies geometric properties of hydrodynamical density manifolds.
Smooth solutions found for hydrodynamic equations.
Derives a fluid model for fish swarming in arbitrary dimensions.
We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to t…
Hydrodynamics principles applied to finance, solving complex market models.
Hydrodynamic hierarchy deformed using conservation laws.
Quantum systems learn like machine learning models, influenced by dissipation.
Combines geometric hydrodynamics with magnetic systems to derive new equations and prove well-posedness.
Survey and new results link hydrodynamics, molecular physics, and financial engineering.
The paper connects PSO and CBO methods using stochastic modeling and mean-field limits.
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet manifold D is equipped with a Riemannian metric g^{D} and an affine connection \nabla^{D} which are infinite dimensional analogues of the Fisher…
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform be…
Supervised learning with a deep convolutional neural network is used to identify the QCD equation of state (EoS) employed in relativistic hydrodynamic simulations of heavy-ion collisions from the simulated final-state particle spectra . High-level correlations of learned by the neural network act a…
Tensor measures chirality for curves, even those with rough edges.
Survey on matrix hydrodynamics, a 2D fluid model.
This paper presents the theory of non-smooth Lie group actions on chains of Banach manifolds. The rigorous functional analytic spaces are given to deal with quotients of such actions. A hydrodynamical example is studied in detail.
Hydrodynamic structures linked to F-manifolds.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
HyperCR Einstein--Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydrodynamic reductions …
Proves helicity is the only regular Casimir for 3D hydrodynamics.
Geometric approach links hydrodynamic integrability to compatible nets.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
In this article a homotopy co-momentum map (à la Callies-Frégier-Rogers-Zambon) trangressing to the standard hydrodynamical co-momentum map of Arnol'd, Marsden and Weinstein and others is constructed and then generalized to a special class of Riemannian manifolds. Also, a covariant phase space interpretation of the coa…
We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless Lax pairs and an infinity of hydrodynamic reductions.
We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…
In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solv…
We classify in this paper infinitesimal quasitrivial deformations of semisimple bihamiltonian structures of hydrodynamic type.
A new method for generating samples without training, using smoothed score matching.
Develops Poisson structures on weak Sobolev loop spaces for integrable systems.
We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run fo…
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamiltonian pencils of hydrodynamic type with one independent and \( N\) dependent variables. In particular, we rederive the result of Dubrovin-Liu…
We prove in this paper the quasitriviality of a class of deformations of the one component bihamiltonian structures of hydrodynamic type.
We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic type, there ex…
Geometric Hydrodynamics tackles open problems in fluid dynamics.
Machine learning predicts ship performance changes over time.
We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.
We present a brief spray theory necessary for the geometric method in hydrodynamics. We make use of the convenient calculus to complete a unitary approach started by P. Michor and A. Kriegl.
Extends method for solving certain hydrodynamic systems.
Simplified Ricci curvature for spherical fluid dynamics models.
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according t…
New methods for solving hydrodynamic-type equations using quasi-rectifiable Lie algebras.
Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance sampling---to impute the missing events in an incomplete sequence. We develop a trainable fa…
The Madelung transform connects quantum mechanics and hydrodynamics.