Related papers: Rough flows
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible…
This is a survey article on Morse theory based on lectures to graduate students and advanced undergraduates. After a brief review of standard material, mostly without proofs, the Morse theory of complex Grassmannian manifolds is worked out…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
Whenever an It\^o-Wentsel type of formula holds for composition of flows of a certain differential dynamics, there exists locally a decomposition of the corresponding flow according to complementary distributions (or foliations, in the case…
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine…
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full…
We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of…
We introduce one-way flows in near algebras and two-way flows in double near algebras with two interrelated multiplications. We establish parametric representations of the one-way and two-way flows in terms of a single element of the…
We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study flows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory.
The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with application in IT and neurogeometry (see Citti-Franceschiello-Sanguinetti-Sarti, 2016). Unfortunately this equation…
The two phase model for vehicular traffic flows recently appeared in \cite{goatin2006aw} and \cite{BenyahiaRosini01} is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths…
In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Here we carry out computations that help clarify the Lagrangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the theory outlined in Holm, Marsden, and Ratiu…
This paper introduces the path derivatives, in the spirit of Dupire's functional It\^o calculus, for the controlled paths in the rough path theory with possibly non-geometric rough paths. The theory allows us to deal with rough integration…
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…
This paper proposes a theoretical framework for modeling and optimizing the bounded functions based on the Fourier series approximation and Ricci flow. Specifically, the initial manifold, $\mathcal{M}_0$ is approximated using Fourier series…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…