相关论文: The Excursion set approach: Stratonovich approxima…

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…

We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…

The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here…

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

We discuss in the framework of the excursion set formalism a recent discovery from N-body simulations that the clustering of haloes of given mass depends on their formation history. We review why the standard implementation of this…

Among various analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation and its extensions in Lagrangian scheme are known to be accurate even in mildly non-linear regime. The aim of…

Surveys of the cosmic large-scale structure carry opportunities for building and testing cosmological theories about the origin and evolution of the Universe. This endeavor requires appropriate data assimilation tools, for establishing the…

Cosmic shear estimation is an essential scientific goal for large galaxy surveys. It refers to the coherent distortion of distant galaxy images due to weak gravitational lensing along the line of sight. It can be used as a tracer of the…

Aims. We aim to study the stochastic evolution of the smoothed overdensity $\delta$ at scale $S$ of the form $\delta(S) = \int_{0}^S K(S,u)\mathrm{d}W(u)$, where $K$ is a kernel and $\mathrm{d}W$ is the usual Wiener process. Methods. For a…

Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the…

We present high--spatial resolution studies of the density field as predicted by Lagrangian perturbation approximations up to the third order. The first--order approximation is equivalent to the ``Zel'dovich approximation'' for the type of…

This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its…

We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and…

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation…

We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions.…

We propose a stochastic reachability computation framework for occupancy prediction in automated driving by directly solving the underlying transport partial differential equation governing the advection of the closed-loop joint density…

We investigate the extreme first-passage statistics of $N$ non-interacting random walkers on discrete, hierarchical networks. {By distinguishing between transport limited by escape from localized initial states (injection-limited) and…

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate…

Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of…