相关论文: Stochastics of shapes and Kunita flows

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…

We identify most probable flows for Kunita Brownian motions, i.e. stochastic flows with Eulerian noise and deterministic drifts. Such stochastic processes appear for example in fluid dynamics and shape analysis modelling coarse scale…

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape model based on a description of shapes as functions in a…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making…

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…

We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…

This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…

Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…

Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes…

We extend the It\^o-Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to $k$-form-valued stochastic processes. The result is the Kunita-It\^o-Wentzell (KIW) formula for $k$-forms. We also…

Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between…